JP4767809B2 - Continuously variable transmission belt, continuously variable transmission belt design method and design program - Google Patents

Description

  The present invention relates to a continuously variable transmission belt wound around a drive pulley and a driven pulley, a design method and a design program for a continuously variable transmission belt.

  In a belt-type continuously variable transmission, a belt is wound around a drive pulley and a driven pulley, and the gear ratio is changed steplessly by changing the belt diameter of the drive pulley and the driven pulley steplessly. be able to. The belt here is generally configured by arranging a large number of plate-like elements in the circumferential direction and fastening them with a hoop.

  In such a belt-type continuously variable transmission, when each element of the belt enters (engages in) the pulley or separates from the pulley, an excitation force acts on the belt (element) to generate vibration and noise. . Patent Document 1 listed below discloses a continuously variable transmission belt in which a plurality of types of elements having different thicknesses are randomly arranged in order to reduce the peak value of vibration and noise generated in a belt type continuously variable transmission. ing.

  Further, even in a chain type continuously variable transmission in which a chain is wound around a driving pulley and a driven pulley, vibration and noise are generated when each link of the chain enters or leaves the pulley. Patent Document 2 listed below includes a plurality of links and pins that connect these to each other and contact a pulley in order to reduce the peak value of vibration and noise generated in a chain-type continuously variable transmission. A continuously variable transmission chain is disclosed in which the distance between the contact positions of the pin and the pulley is set at random.

Japanese Patent No. 2532253 JP 2004-301257 A JP 2006-170393 A

  When a plurality of types of elements having different thicknesses are arranged at random, the peak value of vibration / noise generated in the continuously variable transmission varies depending on the arrangement (arrangement) of the elements. However, in a continuously variable transmission, for example, about 400 elements are arranged, so there are innumerable combinations of element arrangements. For this reason, simply arranging a plurality of types of elements at random does not necessarily provide an element array in which the peak values of vibration and noise are sufficiently low. For example, when the arrangement of elements is determined using random numbers, it is difficult to find an element arrangement in which the peak values of vibration and noise are sufficiently low from among innumerable combinations of element arrangements.

  Similarly, in chain type continuously variable transmissions, the peak values of vibration and noise are not always sufficiently reduced by simply connecting a plurality of types of links at random. For example, when using a random number to determine how to link links (arrangement), it is not possible to find a link sequence where the peak value of vibration and noise is sufficiently low from among the numerous combinations of link alignment methods. Have difficulty.

  An object of the present invention is to sufficiently reduce the peak value of vibration and noise generated in a continuously variable transmission. Another object of the present invention is to easily perform a design for sufficiently reducing the peak value of vibration and noise generated in a continuously variable transmission.

  A method for designing a continuously variable transmission belt according to the present invention is a method for designing a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and in which two types of elements having different thicknesses are arranged in the circumferential direction. When the number of elements arranged is an even number m, each element has an array of m elements in which the condition that the thicknesses of elements separated by m / 2 are different for all elements is satisfied. Based on an index representing the frequency component of the belt vibration generated when the excitation force is input, the computer executes a replacement procedure that repeats replacement of elements separated by m / 2 pieces, so that two types of different thicknesses are obtained. The gist is to determine the arrangement of elements.

  In a continuously variable transmission belt in which two types of elements with different thicknesses are arranged in the circumferential direction, the frequency component of the belt vibration that occurs when an excitation force is input to each element depends on how the elements are arranged. Therefore, it is possible to evaluate the influence on the frequency component of the belt vibration caused by exchanging elements having different thicknesses. However, if the elements having a short circumferential distance are replaced, the influence on the belt vibration due to the replacement becomes local, and there is a case where the frequency component of the belt vibration is hardly influenced as a whole. In that case, the amount of calculation (number of element replacements) required to obtain an element array that sufficiently reduces the peak value of the frequency component of the belt vibration increases. In the present invention, m / 2 based on an index representing the frequency component of the belt vibration with respect to an arrangement of m elements in which the conditions in which the thicknesses of elements separated by m / 2 are different for all elements are satisfied. Replace elements that are separated from each other (approximately the belt half circumference). For example, elements that are m / 2 apart are exchanged based on the maximum value of the index that represents the frequency component of the belt vibration. As a result, when elements with different thicknesses are exchanged, the influence on the belt vibration due to the change in the element thickness at each exchange location can be prevented from canceling each other, and the peak value of the frequency component of the belt vibration Can be obtained with a small amount of calculation (a small number of element replacements). Therefore, according to the present invention, it is possible to easily design a belt for sufficiently reducing the peak value of vibration and noise generated in the continuously variable transmission.

で表されることが好適である。 In one aspect of the present invention, when the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m, i is a natural number, and n is an integer greater than or equal to 0, the replacement procedure includes m / For an array of m elements in which the condition that the thicknesses of two separated elements are different for all elements is satisfied, an element corresponding to corresponding values i to i + n and an element m / 2 away from the element And a procedure for determining whether or not to replace the element based on a comparison result between the index before the element replacement and the index after the element replacement. It is preferable that the procedure be executed by a computer with respect to all combinations of i and n that satisfy ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. In this aspect, an element arrangement that further reduces the peak value of the frequency component of the belt vibration can be obtained by causing the computer to execute the replacement procedure a plurality of times. In one aspect of the present invention, the corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the arrangement order, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the belt vibration. Where j is the number of vibration cycles per belt revolution,

It is preferred that

の最大値で表されることが好適である。ここでの所定範囲については、少なくともｍ及びその近傍を含む範囲であることや、少なくとも２×ｍ及びその近傍を含む範囲であることが好適である。 In one aspect of the present invention, as the replacement procedure, the maximum value of the index is set for an array of m elements in which a condition that the thicknesses of elements separated by m / 2 are different is established for all elements. By causing the computer to repeat the replacement of elements separated by m / 2 so as to decrease, the peak value of the frequency component of the belt vibration can be efficiently reduced with a small number of element replacements. In this aspect, when the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m, i is a natural number, and n is an integer greater than or equal to 0, the replacement procedure is separated by m / 2. For an array of m elements in which the condition that the thicknesses of the elements differ is the same for all elements, the element corresponding to the corresponding value i to i + n and the element m / 2 away from the element are respectively replaced. A procedure and a procedure for returning the replacement of the element when the maximum value of the index does not decrease before and after the replacement of the element, and 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. It is preferred that the procedure be executed by a computer for all i and n combinations that satisfy. Furthermore, until the condition that the maximum value of the index does not decrease before and after the replacement of elements is satisfied for all combinations of i and n satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2, By repeating the replacement procedure and causing the computer to execute it, it is possible to obtain an element array that converges the peak value of the frequency component of the belt vibration almost to the minimum. Further, in this aspect, the replacement procedure is a procedure in which replacement of elements separated by m / 2 is repeated until the maximum value of the index converges to a minimum, whereby the peak value of the frequency component of the belt vibration is obtained. An element arrangement that converges to a minimum can be obtained. Further, in this aspect, the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the arrangement order, the phase in the circumferential direction of the elements corresponding to the corresponding value i is α _i , and the belt 1 of the belt vibration. Assuming that the number of vibration cycles per circumference is j, the maximum value of the index is relative to the number of vibration cycles j within a predetermined range.

It is preferable that the maximum value is represented. The predetermined range here is preferably a range including at least m and the vicinity thereof, or a range including at least 2 × m and the vicinity thereof.

の最大値と最小値との差で表されることが好適である。ここでの所定範囲については、少なくともｍ及びその近傍を含む範囲であることや、少なくとも２×ｍ及びその近傍を含む範囲であることが好適である。 In one aspect of the present invention, as the replacement procedure, for the arrangement of m elements in which the condition that the thicknesses of m / 2 separated elements are different from each other is satisfied for all elements, By causing the computer to repeat the replacement of elements m / 2 apart so that the difference from the minimum value decreases, the difference between the maximum value and the minimum value of the frequency component of belt vibration can be reduced with a small number of element replacements. It can reduce efficiently and can make the frequency component of belt vibration uniform. In this aspect, when the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m, i is a natural number, and n is an integer greater than or equal to 0, the replacement procedure is separated by m / 2. For an array of m elements in which the condition that the thicknesses of the elements differ is the same for all elements, the element corresponding to the corresponding value i to i + n and the element m / 2 away from the element are respectively replaced. The procedure and the procedure for returning the replacement of the element when the difference between the maximum value and the minimum value of the index does not decrease before and after the replacement of the element, and 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ It is preferable that the procedure be executed by the computer for all combinations of i and n that satisfy m / 2-2. Further, the conditions under which the difference between the maximum value and the minimum value of the index does not decrease before and after the replacement of the elements are all i and n satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. By repeating the replacement procedure until the combination is established, the computer can execute the replacement sequence, thereby obtaining an element array that converges the difference between the maximum value and the minimum value of the frequency components of the belt vibration almost to the minimum. Further, in this aspect, the replacement procedure is a procedure of repeating replacement of elements separated by m / 2 until the difference between the maximum value and the minimum value of the index converges to approximately the minimum, whereby belt vibration It is possible to obtain an element array that converges the difference between the maximum value and the minimum value of the frequency components to a minimum. Further, in this aspect, the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the arrangement order, the phase in the circumferential direction of the elements corresponding to the corresponding value i is α _i , and the belt 1 of the belt vibration. When the number of vibration cycles per circumference is j, the difference between the maximum value and the minimum value of the index is the number of vibration cycles j within a predetermined range.

It is preferable to represent the difference between the maximum value and the minimum value. The predetermined range here is preferably a range including at least m and the vicinity thereof, or a range including at least 2 × m and the vicinity thereof.

の前記所定値に対する最大偏差で表されることが好適である。ここでの所定範囲については、少なくともｍ及びその近傍を含む範囲であることや、少なくとも２×ｍ及びその近傍を含む範囲であることが好適である。 In one aspect of the present invention, as the replacement procedure, for an array of m elements in which the condition that the thicknesses of elements separated by m / 2 are different for all elements is satisfied, By causing the computer to repeat the replacement of elements that are m / 2 apart so that the maximum deviation is reduced, the frequency component of the belt vibration can be brought close to the specified value efficiently with a small number of element replacements. Can be made uniform. In this aspect, when the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m, i is a natural number, and n is an integer greater than or equal to 0, the replacement procedure is separated by m / 2. For an array of m elements in which the condition that the thicknesses of the elements differ is the same for all elements, the element corresponding to the corresponding value i to i + n and the element m / 2 away from the element are respectively replaced. A procedure and a procedure for returning the replacement of the element when the maximum deviation of the index with respect to the predetermined value does not decrease before and after the replacement of the element, 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / It is preferable that the procedure be executed by the computer with respect to all combinations of i and n that satisfy 2-2. Furthermore, the conditions under which the maximum deviation of the index with respect to the predetermined value does not decrease before and after the element replacement are all i and n combinations satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. By repeating the above replacement procedure until the computer is executed, an element arrangement that converges the frequency component of the belt vibration to a predetermined value can be obtained. Further, in this aspect, the replacement procedure is a procedure of repeating replacement of elements separated by m / 2 until the maximum deviation of the index with respect to the predetermined value converges to a substantially minimum, whereby the frequency of the belt vibration is determined. It is possible to obtain an element array that converges components to a predetermined value. Further, in this aspect, the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the arrangement order, the phase in the circumferential direction of the elements corresponding to the corresponding value i is α _i , and the belt 1 of the belt vibration. Assuming that the number of vibration cycles per circumference is j, the maximum deviation of the indicator from the predetermined value is the number of vibration cycles j within a predetermined range.

It is preferable that the maximum deviation with respect to the predetermined value. The predetermined range here is preferably a range including at least m and the vicinity thereof, or a range including at least 2 × m and the vicinity thereof.

で表されることが好適である。 In one embodiment of the present invention, the number of elements having a smaller thickness is n ₁ , the number of elements having a larger thickness is n ₂ (n ₂ = m−n ₁ ), The thickness ratio with the element is 1 + Δ (Δ> 0), 0 when the element corresponding to the corresponding value k is the thinner element, and 1 when the element corresponding to the corresponding value k is the thicker element If the function to be T (k) is, the phase α _{i in} the circumferential direction of the element corresponding to the corresponding value _i is

It is preferred that

  In one aspect of the present invention, the computer further executes a procedure for inserting or removing a predetermined number of elements from the arrangement of elements after execution of the replacement procedure, thereby determining the arrangement of two types of elements having different thicknesses. You can also The predetermined number here is preferably sufficiently smaller than the number of elements arranged.

  Further, the gist of the continuously variable transmission belt according to the present invention is designed by the method for designing a continuously variable transmission belt according to the present invention.

  A continuously variable transmission belt according to the present invention is a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and in which two types of elements having different thicknesses are arranged in the circumferential direction. If the arrangement number of m is an even number m, m elements are arranged in the circumferential direction so that the condition that the thicknesses of elements separated by m / 2 are different for all elements is satisfied, and m / 2 Element so that the condition that the maximum value of the index indicating the frequency component of the belt vibration that occurs when the excitation force is input to each element does not decrease before and after replacing the separated elements holds for any replacement Is summarized in the circumferential direction.

  According to the present invention, two types of elements having different thicknesses are arranged in the circumferential direction so that the peak value of the frequency component of the belt vibration generated when an excitation force is input to each element is substantially minimized. Therefore, the peak value of vibration and noise generated in the continuously variable transmission can be sufficiently reduced.

  A continuously variable transmission belt according to the present invention is a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and has two types of elements having different thicknesses arranged in the circumferential direction. A predetermined number of elements are inserted or removed from the array of elements for which the condition is satisfied, and the array of elements for which the predetermined condition is satisfied is separated by m / 2, where m is an even number of elements. Of the belt vibration that occurs when the excitation force is input to each element before and after replacing the elements separated by m / 2. The gist is that the condition in which the maximum value of the index representing the frequency component does not decrease is an array that holds for any replacement.

  According to the present invention, a predetermined number of elements are inserted or removed from the element arrangement in which the peak value of the frequency component of the belt vibration generated when an excitation force is input to each element is substantially minimized. Thus, the peak values of vibration and noise generated in the continuously variable transmission can be sufficiently reduced. The predetermined number here is preferably sufficiently smaller than the number of elements arranged.

の最大値で表されることが好適である。ここでの所定範囲については、少なくともｍ及びその近傍を含む範囲であることや、少なくとも２×ｍ及びその近傍を含む範囲であることが好適である。 In one aspect of the present invention, the corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the arrangement order, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the belt of the belt vibration Assuming that the number of vibration cycles per round is j, the maximum value of the index is relative to the number of vibration cycles j within a predetermined range.

It is preferable that the maximum value is represented. The predetermined range here is preferably a range including at least m and the vicinity thereof, or a range including at least 2 × m and the vicinity thereof.

の最大値が、厚さの均一なｍ個のエレメントが周方向に配列された場合の０．３１倍以下となるように、エレメントが周方向に配列されていることを要旨とする。 A continuously variable transmission belt according to the present invention is a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and in which two types of elements having different thicknesses are arranged in the circumferential direction. M is an even number, the corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the order of arrangement, and the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i. / M elements are arranged in the circumferential direction so that the condition that the thicknesses of two separated elements are different is satisfied for all elements, and the value j is within a predetermined range.

The gist is that the elements are arranged in the circumferential direction so that the maximum value of m is 0.31 times or less that of m elements having a uniform thickness arranged in the circumferential direction.

  According to the present invention, the peak value of the frequency component of the belt vibration generated when the excitation force is input to each element is 0.31 times or less that when the elements having a uniform thickness are arranged in the circumferential direction. As described above, by arranging the two types of elements having different thicknesses in the circumferential direction, the peak value of vibration and noise generated in the continuously variable transmission can be sufficiently reduced. The predetermined range here is preferably a range including at least m and the vicinity thereof, or a range including at least 2 × m and the vicinity thereof.

の最大値が、厚さの均一なｍ個のエレメントが周方向に配列された場合の０．３１倍以下となる配列であることを要旨とする。 A continuously variable transmission belt according to the present invention is a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and has two types of elements having different thicknesses arranged in the circumferential direction. A predetermined number of elements are inserted or removed from the array of elements for which the condition is satisfied, and the array of elements for which the predetermined condition is satisfied is an element in which the number of elements is an even number m and arranged in the circumferential direction Assuming that the corresponding value corresponding to each of 1 to m is the order of arrangement and the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , all the conditions in which the thicknesses of m / 2 separated elements are different are all An array that holds for an element and for a value j within a predetermined range

The maximum value of is an arrangement that is 0.31 times or less of m elements having a uniform thickness arranged in the circumferential direction.

  According to the present invention, the peak value of the frequency component of the belt vibration generated when the excitation force is input to each element is 0.31 times or less that when the elements having a uniform thickness are arranged in the circumferential direction. Since a predetermined number of elements are inserted or removed from the element arrangement, the peak value of vibration and noise generated in the continuously variable transmission can be sufficiently reduced. The predetermined number here is preferably sufficiently smaller than the number of elements arranged. The predetermined range here is preferably a range including at least m and the vicinity thereof, or a range including at least 2 × m and the vicinity thereof.

  A continuously variable transmission belt according to the present invention is a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and in which two types of elements having different thicknesses are arranged in the circumferential direction. If the arrangement number of m is an even number m, m elements are arranged in the circumferential direction so that the condition that the thicknesses of elements separated by m / 2 are different for all elements is satisfied, and m / 2 The condition that the difference between the maximum value and the minimum value of the index indicating the frequency component of the belt vibration generated when the excitation force is input to each element is not reduced before and after replacing the separated elements. The gist is that the elements are arranged in the circumferential direction so as to be established.

  According to the present invention, two types of elements having different thicknesses are provided so that the difference between the maximum value and the minimum value of the frequency component of the belt vibration generated when an excitation force is input to each element is substantially minimized. By arranging in the circumferential direction, the peak values of vibration and noise generated in the continuously variable transmission can be sufficiently reduced.

  A continuously variable transmission belt according to the present invention is a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and has two types of elements having different thicknesses arranged in the circumferential direction. A predetermined number of elements are inserted or removed from the array of elements for which the condition is satisfied, and the array of elements for which the predetermined condition is satisfied is separated by m / 2, where m is an even number of elements. Of the belt vibration that occurs when the excitation force is input to each element before and after replacing the elements separated by m / 2. The gist is that the condition in which the difference between the maximum value and the minimum value of the index representing the frequency component does not decrease is an array that holds for any replacement.

  According to the present invention, a predetermined number of elements are inserted into an array of elements in which the difference between the maximum value and the minimum value of the frequency component of the belt vibration that occurs when an excitation force is input to each element is almost minimum. Alternatively, the peak value of vibration and noise generated in the continuously variable transmission can be sufficiently reduced by being removed. The predetermined number here is preferably sufficiently smaller than the number of elements arranged.

の最大値と最小値との差で表されることが好適である。ここでの所定範囲については、少なくともｍ及びその近傍を含む範囲であることや、少なくとも２×ｍ及びその近傍を含む範囲であることが好適である。 In one aspect of the present invention, the corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the arrangement order, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the belt of the belt vibration If the number of vibration cycles per round is j, the difference between the maximum value and the minimum value of the index is the number of vibration cycles j within a predetermined range.

It is preferable to represent the difference between the maximum value and the minimum value. The predetermined range here is preferably a range including at least m and the vicinity thereof, or a range including at least 2 × m and the vicinity thereof.

  A continuously variable transmission belt according to the present invention is a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and in which two types of elements having different thicknesses are arranged in the circumferential direction. If the arrangement number of m is an even number m, m elements are arranged in the circumferential direction so that the condition that the thicknesses of elements separated by m / 2 are different for all elements is satisfied, and m / 2 The condition that the maximum deviation with respect to the predetermined value of the index representing the frequency component of the belt vibration generated when the excitation force is input to each element is not reduced before and after replacing the separated elements so that any replacement can be established. Further, the gist is that the elements are arranged in the circumferential direction.

  According to the present invention, two types of elements having different thicknesses are arranged in the circumferential direction so that the maximum deviation of the frequency component of the belt vibration generated when an excitation force is input to each element is substantially minimized. By arranging, the peak value of vibration and noise generated in the continuously variable transmission can be sufficiently reduced.

  A continuously variable transmission belt according to the present invention is a continuously variable transmission belt that is wound around a drive pulley and a driven pulley and in which two types of elements having different thicknesses are arranged in the circumferential direction, and has a predetermined condition. A predetermined number of elements are inserted or removed from the array of elements for which the above is satisfied, and the array of elements for which the predetermined condition is satisfied is separated by m / 2 when the number of elements is an even number m The frequency of the belt vibration that occurs when an excitation force is input to each element before and after the elements that are separated by m / 2 are replaced with each other in an arrangement in which the conditions in which the thicknesses of the elements are different are satisfied for all the elements. The gist is that the condition in which the maximum deviation of the index representing the component with respect to the predetermined value does not decrease is an array that holds for any replacement.

  According to the present invention, a predetermined number of elements are inserted into or removed from the array of elements in which the maximum deviation from the predetermined value of the frequency component of the belt vibration generated when an excitation force is input to each element is almost minimized. Therefore, the peak value of vibration and noise generated in the continuously variable transmission can be sufficiently reduced. The predetermined number here is preferably sufficiently smaller than the number of elements arranged.

の前記所定値に対する最大偏差で表されることが好適である。ここでの所定範囲については、少なくともｍ及びその近傍を含む範囲であることや、少なくとも２×ｍ及びその近傍を含む範囲であることが好適である。 In one aspect of the present invention, the corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the arrangement order, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the belt of the belt vibration Assuming that the number of vibration cycles per revolution is j, the maximum deviation of the index from the predetermined value is the number of vibration cycles j within a predetermined range.

It is preferable that the maximum deviation with respect to the predetermined value. The predetermined range here is preferably a range including at least m and the vicinity thereof, or a range including at least 2 × m and the vicinity thereof.

  The continuously variable transmission according to the present invention is a continuously variable transmission capable of changing a gear ratio by changing a belt engagement diameter to a drive pulley and a driven pulley. The gist of the invention is a continuously variable transmission belt according to the invention.

  The design program for a continuously variable transmission belt according to the present invention is a belt for a continuously variable transmission that is wound around a drive pulley and a driven pulley and has two types of elements having different thicknesses arranged in the circumferential direction. Assuming that the number of elements arranged is an even number m, the computer determines that the condition that the thicknesses of the elements separated by m / 2 are different is satisfied for all elements. The gist of the present invention is to execute a replacement procedure that repeats replacement of elements separated by m / 2 on the basis of an index representing a frequency component of belt vibration generated when an excitation force is input to each element. As described above, the present invention can be grasped as an invention relating to a design program for a continuously variable transmission belt and a computer-readable recording medium on which the design program is recorded. Furthermore, this invention can also be grasped | ascertained as invention regarding the design apparatus of the belt for continuously variable transmissions.

  In addition, the design method for a continuously variable transmission chain according to the present invention is to design a chain for a continuously variable transmission that is wound around a drive pulley and a driven pulley and two types of links having different lengths are connected in the circumferential direction. When the number of links connected is an even number m, each of the links of m links in which the condition that the lengths of the links separated by m / 2 are different for all links is established. 2 having different lengths by causing the computer to execute a replacement procedure that repeats replacement of links separated by m / 2 based on an index representing a frequency component of chain vibration generated when an excitation force is input to the link. The gist is to determine the connection of the types of links. Thus, the present invention can also be grasped as an invention relating to a design method for a continuously variable transmission chain. Further, the present invention relates to an invention related to a continuously variable transmission chain, an invention related to a design program for a continuously variable transmission chain, an invention related to a computer-readable recording medium in which this design program is recorded, and a continuously variable transmission. It can also be grasped as an invention relating to a chain design device.

  According to the present invention, chain connection that sufficiently reduces the peak value of the frequency component of chain vibration generated when an excitation force is input to each link can be obtained with a small amount of calculation (small number of link replacements). Therefore, it is possible to easily design a chain for sufficiently reducing the peak value of vibration and noise generated in the continuously variable transmission.

  DESCRIPTION OF EMBODIMENTS Hereinafter, embodiments for carrying out the present invention (hereinafter referred to as embodiments) will be described with reference to the drawings.

  FIG. 1 is a diagram illustrating a schematic configuration of a continuously variable transmission including a continuously variable transmission belt according to an embodiment of the present invention, and FIG. 2 illustrates a continuously variable transmission belt according to an embodiment of the present invention. It is a figure which shows schematic structure. A belt type continuously variable transmission (CVT) 14 includes a primary pulley (drive pulley) 30 connected to an input shaft 26, a secondary pulley (driven pulley) 32 connected to an output shaft 36, and a primary pulley 30 and a secondary pulley 32. And an endless belt (belt for continuously variable transmission) 34 that is wound around the belt. The input shaft 26 (primary pulley 30) is connected to a power generation source (not shown) such as an engine, and the power generated by the power generation source is transmitted to the input shaft 26. The belt type continuously variable transmission 14 shifts the power transmitted to the input shaft 26 and transmits it to the output shaft 36 (secondary pulley 32). The power transmitted to the output shaft 36 is output to a load (not shown) connected to the output shaft 36, and used for driving a load such as driving a vehicle.

  The primary pulley 30 includes a primary movable sheave and a primary fixed sheave that can move in the direction of the input shaft 26, and the secondary pulley 32 includes a secondary movable sheave and a secondary fixed sheave that can move in the direction of the output shaft 36. It is comprised including. The endless belt 34 is sandwiched between the primary movable sheave and the primary fixed sheave and between the secondary movable sheave and the secondary fixed sheave. When the primary movable sheave and the secondary movable sheave move in the axial direction, the rotation radius (hanging diameter) of the portion where the endless belt 34 is wound around the primary pulley 30 and the secondary pulley 32 continuously changes. As a result, the gear ratio γ (= the rotational speed Nin of the primary pulley 30 / the rotational speed Nout of the secondary pulley 32) of the belt-type continuously variable transmission 14 continuously changes.

  As shown in FIGS. 1 and 2, the endless belt 34 includes a plurality of plate-like elements 18 and a pair of hoops 20. The plurality of elements 18 are arranged in the extending direction of the hoop 20 (the circumferential direction of the endless belt 34) and are locked to the hoop 20 while being sandwiched between the pair of hoops 20.

  In the belt-type continuously variable transmission 14, each element 18 of the endless belt 34 is added to the endless belt 34 (element 18) when entering (engaging) into the pulleys 30, 32 and when separating from the pulleys 30, 32. Vibration and noise are generated by vibration. The frequency characteristics of the vibration and noise generated here depend on the period in which the plurality of elements 18 are engaged with the pulleys 30 and 32 (or separated from the pulleys 30 and 32). As shown in FIG. 3A, when the plate thickness (thickness in the belt circumferential direction) t of the m elements 18 arranged in the belt circumferential direction is set uniformly, the endless belt 34 (each element 18). The excitation force (vibration force) input to () has a regular waveform depending on the plate thickness t of the element 18 as shown in FIGS. 3 (B) and 3 (C). Therefore, the frequency characteristic of vibration generated in the endless belt 34 by this excitation force is a frequency (belt rotation m) where the number of vibration cycles (belt rotation order) per belt rotation is m, as shown in FIG. Next, the peak value of the amplitude greatly increases at and around the corresponding frequency. As a result, the peak value of vibration / noise generated in the belt type continuously variable transmission 14 increases.

In this embodiment, in order to reduce the peak value of vibration and noise generated in the belt type continuously variable transmission 14, two types of elements having different plate thicknesses are arranged in the belt circumferential direction. Figure 4 element 18-1 and the plate thickness t ₁ of the sheet thickness t ₀ as shown in _{(A) (t 1> t} 0) element 18-2 are irregularly m pieces arranged in the circumferential direction of the belt e.g. In this case, the excitation force input to the endless belt 34 has an irregular waveform due to the irregular arrangement of the elements 18-1 and 18-2 as shown in FIGS. 4B and 4C. Therefore, as shown in FIG. 4D, the frequency characteristic of the vibration generated in the endless belt 34 by this excitation force greatly reduces the peak value of the amplitude at and around the frequency corresponding to the belt turn m. As a result, the peak value of vibration and noise generated in the belt type continuously variable transmission 14 can be reduced. Note that α ₁ , α ₂ , and α ₃ in FIGS. 3 (B), 3 (C), 4 (B), and 4 (C) are belts of the element 18 (18-1, 18-2). It represents the position (phase) in the circumferential direction.

“Embodiment 1”
Next, a method for designing a continuously variable transmission belt according to Embodiment 1 of the present invention, particularly a method for determining the arrangement (arrangement) of two types of elements 18-1 and 18-2 having different plate thicknesses will be described. . In the present embodiment, the computer is caused to execute a procedure for determining how the elements 18-1 and 18-2 are arranged.

  First, in order to express the arrangement (arrangement) of two types of elements 18-1 and 18-2 having different plate thicknesses as data digitized by a computer, as shown in FIG. 5, m elements arranged in the belt circumferential direction are used. Corresponding values (numbers) corresponding to the elements 18-1 and 18-2 are numbered 1 to m in the order of arrangement. Then, a function T (k) whose value changes according to the plate thickness of the element is set as data representing the plate thickness of the element corresponding to the corresponding value k (k is a natural number of 1 or more and m or less). More specifically, T (k) = 0 when the element corresponding to the corresponding value k is the thinner element 18-1, and the element corresponding to the corresponding value k is the thicker one. In the case of the element 18-2, T (k) = 1. In a computer, the arrangement of m elements 18-1 and 18-2 can be expressed by data in which values of a function T (k) (binary values of 0 or 1) for a natural number k of 1 or more and m or less are arranged. it can. For example, when the thinner element 18-1 and the thicker element 18-2 are alternately arranged, T (k) = 0 for odd k and k for even k It can be expressed as T (k) = 1.

  Next, in order to determine the element arrangement for reducing the peak value of vibration and noise generated in the belt type continuously variable transmission 14, an evaluation index representing the frequency component (amplitude at that frequency) of the belt vibration is set. The evaluation index here is an index representing the frequency component of the belt vibration (belt rotation order component) generated when the excitation force (vibration force) is input to each of the m elements 18-1 and 18-2. Set as Hereinafter, a method for deriving this index will be described.

The number of thickness of the thinner element 18-1 n _1, n ₂ the number of plate thickness thicker elements 18-2, t ₀ the thickness of the element 18-1, the thickness of the element 18-2 Where t ₁ = t ₀ × (1 + Δ) (Δ> 0) (the thickness ratio of the element 18-2 and the element 18-1 is 1 + Δ), the length of one circumference of the endless belt 34 is 2 × π. In this case, the position (phase) α _i (0 ≦ α _i <2 × π) in the belt circumferential direction of the element corresponding to the corresponding value i (i is a natural number greater than or equal to 1 and less than or equal to m) is expressed by the following equation (1). expressed.

  Further, when the position (phase) in the belt circumference is θ (0 ≦ θ <2 × π), as shown in FIG. 6, unit impulse input (element 1) is performed at the position (phase) α in the belt circumference. The belt vibration waveform f (θ, α) when the excitation force generated by the engagement of each pulley is simulated is expressed by the following equation (2) using the Fourier series expansion of the unit impulse function. expressed. In the formula (2), n (natural number) is the number of vibration cycles (belt rotation order) per belt rotation.

The total number of elements (arrangement number) is m, and as shown in FIG. 7, unit impulse input is performed at the phase α _{i of} each element (simulating the excitation force generated by the engagement of each element into the pulley) In this case, the belt vibration waveform F (θ) is obtained by superimposing the vibration waveforms f (θ, α _i ).

Therefore, if j (natural number) is the number of vibration cycles per belt rotation (belt rotation order), the belt rotation j-order component (amplitude at vibration cycle number j) of the belt vibration waveform F (θ) is (3 ) A _j / π using A _j represented by the formula (1).

In the present embodiment, A _j represented by the expression (3) is used as an index representing a frequency component (belt rotation j-order component) of belt vibration generated when an excitation force is input by each element.

  Next, details of the procedure for determining the arrangement of the elements 18-1 and 18-2 will be described with reference to the flowchart of FIG. In this embodiment, the computer executes the procedure according to the flowchart of FIG. The procedure shown in the flowchart of FIG. 8 can be realized in software by a program (design program) executed by a computer.

  First, in step S101, a procedure for setting an initial state (initial arrangement) of an array of m elements 18-1 and 18-2 (m is an even number) is executed by the computer. Here, for example, as shown in FIG. 5, m elements 18-1 and 18-2 are formed so that the condition that the thicknesses of the elements separated by m / 2 in the belt circumferential direction are different is established for all the elements. Are arranged in the belt circumferential direction. That is, the initial value of the function T (k) is set so that T (k) ≠ T (k + m / 2) holds for all natural numbers k satisfying 1 ≦ k ≦ m / 2. The initial value of the function T (k) (array data) set here is stored in a storage device (RAM) of the computer. FIG. 5 shows, as an example of the initial arrangement, all the elements corresponding to the corresponding values 1 to m / 2 are the thinner elements 18-1, and all the elements corresponding to the corresponding values m / 2 + 1 to m are the plates. The case of the thicker element 18-2 is shown. In that case, T (k) = 0 for 1 ≦ k ≦ m / 2, and T (k) = 1 for m / 2 + 1 ≦ k ≦ m. FIG. 5 also shows the value of T (k) corresponding to the plate thickness in the blocks representing the elements 18-1 and 18-2. However, the array of elements corresponding to the corresponding values 1 to m / 2 (the value of T (k) for 1 ≦ k ≦ m / 2) can be set at random using random numbers. In that case, the condition that the thicknesses of the elements separated by m / 2 in the belt circumferential direction are different holds for all elements (T (k) for all natural numbers k satisfying m / 2 + 1 ≦ k ≦ m). The array of elements corresponding to the corresponding values m / 2 + 1 to m (the value of T (k) with respect to m / 2 + 1 ≦ k ≦ m) is set so that (≠ T (k−m / 2) holds).

In step S102, the vibration period number j (natural number) is within a predetermined range with respect to the initial arrangement of elements 18-1 and 18-2 set in step S101 (initial value of the function T (k)). The above-described procedure for calculating the maximum value of the index A _j representing the belt circulation j-th order component of the belt vibration is executed by the computer. Here, it is possible to calculate the phase alpha _i of corresponding to the corresponding values i used in equation (1) based on the value of the function T (k) (i th) element, a phase alpha _i of the element The index A _j can be calculated using the formula (3) based on the vibration period number j. Since the belt vibration is generated when each element is engaged with (or detached from) the pulley, when the total number of elements is m, the frequency characteristic of the belt vibration is, for example, m-th order (or belt rotation) (or The amplitude reaches a peak (maximum) at a frequency corresponding to the vicinity thereof, a frequency corresponding to the belt circumference 2 × m order (or the vicinity thereof), and the like. Therefore, the predetermined range here is preferably a range including at least m and its vicinity. For example, m / 2 ≦ j ≦ 3 × m / 2 can be set. Further, the predetermined range here is preferably set to a range including at least 2 × m and the vicinity thereof, and can be set to 3 × m / 2 ≦ j ≦ 5 × m / 2, for example. Further, the predetermined range here is preferably set to a range including m and the vicinity thereof and 2 × m and the vicinity thereof. For example, m / 2 ≦ j ≦ 5 × m / 2 can also be set. .

  In step S103, a procedure for setting initial values of variables i (natural number) and n (integer of 0 or more) is executed by the computer. Here, i = 1 and n = 0 are set as initial values of the variables i and n.

  In step S104, a procedure is executed by the computer to replace the arrangement of the (i to i + n-th) elements corresponding to the corresponding values i to i + n and the elements separated m / 2 from the elements in the belt circumferential direction. That is, the values of T (i) to T (i + n) and the values of T (i + m / 2) to T (i + n + m / 2) are interchanged (however, for T (k) when k ≧ m / 2 + 1) By replacing the value with T (k−m / 2)), a procedure for rewriting the value (array data) of the function T (k) stored in the storage device (RAM) is executed by the computer.

In step S105, the belt rotation j-order component under the condition that the vibration period number j (natural number) is within a predetermined range with respect to the element arrangement (function T (k)) after the element replacement in step S104. A procedure for calculating the maximum value of the index A _j representing is executed by the computer. The predetermined range here can be set similarly to step S102.

In step S106, a procedure is executed by the computer to determine whether or not the maximum value of the index A _j has decreased before and after the element replacement in step S104. When the maximum value of the index A _j does not decrease (when the determination result of step S106 is NO), the process proceeds to step S107. In step S107, the procedure of returning the element replacement performed in step S104 to the original state, that is, returning the value of the function T (k) to the original state is executed by the computer. Then, the process proceeds to step S108. On the other hand, when the maximum value of the index A _j decreases in step S106 (when the determination result in step S106 is YES), the element replacement performed in step S104 (rewriting the value of the function T (k)) is maintained. Then, the process proceeds to step S108. In other words, based on a comparison result of an index A _j (maximum value) after the interchange indicative A _j (maximum value) of the element before replacement of the element, determining whether undo replacement of elements The procedure is executed. In the present embodiment, the total number m (even number) of elements is set to 6 or more in order to change the value of the index A _j when the elements are replaced.

  In step S108, a procedure for determining whether or not the value of the variable i is m / 2 is executed by the computer. When the value of the variable i is not m / 2 (less than m / 2) (when the determination result of step S108 is NO), the process proceeds to step S109. In step S109, a procedure for increasing the value of the variable i by 1 is executed by the computer. Then, the process returns to step S104. On the other hand, when the value of the variable i is m / 2 in step S108 (when the determination result in step S108 is YES), the process proceeds to step S110.

  In step S110, a procedure for determining whether or not the value of the variable n is m / 2-2 is executed by the computer. When the value of the variable n is not m / 2-2 (smaller than m / 2-2) (when the determination result of step S110 is NO), the process proceeds to step S111. In step S111, a procedure for incrementing the value of the variable n by 1 and setting the value of the variable i to 1 is executed by the computer. Then, the process returns to step S104. On the other hand, if the value of the variable n is m / 2-2 in step S110 (if the determination result in step S110 is YES), the process proceeds to step S112.

According to the procedure of steps S103 to S111 described above, first, for example, as shown in FIG. 9, the i-th element (1) and the i + m / 2-th element (1) are interchanged (the value of T (i) and T (i + m / 2) replacing the value of) the procedure, the procedure returns when the maximum value of the replacement index a _j before and after does not decrease based on this replacement is, i = 1 to m / 2 executing the order Is done. Here, FIG. 9 shows element replacement in the case of i = 1. Next, for example, as shown in FIG. 10, the i-th to i + 1-th elements (two) and the i + m / 2 to i + 1 + m / 2-th elements (two) are interchanged (T (i) to T (i + 1)). And a procedure for returning the replacement when the maximum value of the index A _j does not decrease before and after the replacement, and a procedure for replacing the value and a value of T (i + m / 2) to T (i + 1 + m / 2). The process is executed in the order of i = 1 to m / 2. Here, FIG. 10 also shows element replacement in the case of i = 1. Similarly, replacement of elements m / 2 apart (sequential n + 1 elements) is repeatedly performed until n = m / 2-2 is increased. That is, according to the procedure of steps S103 to S111, the procedure of exchanging the arrangement of the i to i + n-th element and the element that is m / 2 away from the element in the belt circumferential direction, and the index before and after the exchange of this element The procedure of reverting this element replacement when the maximum value of A _j does not decrease is executed for all combinations of i and n that satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. Is done. That is, replacement of elements separated by m / 2 in the belt circumferential direction is repeatedly performed a plurality of times so that the maximum value of the index A _j decreases. However, the order of exchanging elements separated by m / 2 elements is not limited to the order described above, and i satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. And various orders among the combinations of n.

In step S112, the computer executes a procedure for determining whether or not there is a combination of variables i and n in which the maximum value of the index A _j decreases before and after the element replacement in step S104. If there is a combination of variables i and n for which the maximum value of the index A _j decreases (if the determination result in step S112 is YES), the process returns to step S103. On the other hand, when there is no combination of the variables i and n in which the maximum value of the index A _j decreases (when the determination result in step S112 is NO), the execution of this procedure ends. According to the procedure of step S112, all the conditions that the maximum value of the index A _j does not decrease before and after the element replacement in step S104 satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. The process returns to step S103 until the combination of i and n is established (steps S103 to S111 are repeated a plurality of times). That is, until the maximum value of the index A _j converges to the minimum (or almost the minimum), the replacement of elements separated by m / 2 in the belt circumferential direction is repeatedly performed a plurality of times. However, step S112 may be omitted, and the execution of this procedure may be terminated when the determination result in step S110 is YES.

The endless belt 34 (the arrangement of the elements 18-1 and 18-2 is determined) designed according to the procedure (element replacement procedure) according to the flowchart of FIG. 8 described above is separated by m / 2 in the belt circumferential direction. The m elements 18-1 and 18-2 are arranged in the belt circumferential direction so that the condition that the thicknesses of the elements are different is satisfied for all the elements. Then, before and after replacing the elements with each other at a distance m / 2 pieces in the circumferential direction of the belt, as conditions the maximum value of the index A _j does not decrease, established with regard replacement of any (element between) element 18-1, 18-2 are arranged in the belt circumferential direction. More specifically, the maximum value of the index A _j with respect to the number of vibration periods j within a predetermined range is set before and after the i to i + n-th element and the element m / 2 apart from the element in the belt circumferential direction. The elements 18-1 and 18-2 are arranged in the belt circumferential direction so that the non-decreasing condition is satisfied with respect to all combinations of i and n satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. It is arranged. The predetermined range here is the same as the range described in the procedure of step S102.

Here, as an example, the number n ₁ = 223 of the plate thickness thinner elements 18-1, sequence number n ₂ = 223 (elements 18-1 and 18-2 of the thick direction of the element 18-2 The total number m = 446), Δ = 0.071428571, the initial value of the function T (k) is 1 ≦ k ≦ m / 2, T (k) = 0 and T / 2 for m / 2 + 1 ≦ k ≦ m In the case of (k) = 1, the value of the function T (k) (array of elements 18-1 and 18-2) was finally determined according to the procedure according to the flowchart of FIG. The frequency characteristics of the belt vibration in the final element arrangement are shown in FIGS. 11 and 12 in comparison with the case where two kinds of elements having different plate thicknesses are randomly arranged. FIG. 11 shows the characteristics of the belt vibration frequency component (index A _j ) with respect to the belt rotation order j in the present embodiment, and FIG. 12 shows the frequency component of the belt vibration in 1000 random arrays using random numbers. The characteristic when the peak value (the maximum value of the index A _j ) is minimum is shown. 11 and 12 show the peak value of the frequency component of the belt vibration (maximum value of the index A _j ) as 1 when m elements having a uniform thickness are arranged in the belt circumferential direction.

Further, the peak of the frequency component in the final arrangement obtained by executing the element replacement procedure according to the flowchart of FIG. 8 with respect to the 1000 initial arrangements in which the 1st to 2nd element arrangements are randomly set in step S101. value (maximum value of the index a _j in the belt rotation m order vicinity), compared to the maximum value of the index a _j in the random sequence (Street 1000) shown in FIGS. 13 and 14. FIG. 13 shows the peak value of the frequency component (maximum value of the index A _{j in} the vicinity of the belt rotation m-th order) for 1000 elements, and FIG. 14 shows the peak value of the frequency component (in the vicinity of the belt rotation m-th order). The frequency distribution of the maximum value of the index A _j is shown. 13 and 14 also show the peak value of the frequency component of the belt vibration when the m elements having a uniform thickness are arranged in the belt circumferential direction (the maximum value of the index A _{j in} the vicinity of the belt circumferential m-th order). Is shown as 1. As shown in FIGS. 13 and 14, when the element arrangement is set at random, the maximum value of the index A _j with respect to the vibration period number j within a predetermined range (for example, a range including m and the vicinity thereof) is uniform in thickness. When m elements are arranged in the circumferential direction, the maximum value of the index A _j is 0.346 times or more and 0.862 times or less. On the other hand, in the endless belt 34 in which the element arrangement is determined according to the element replacement procedure according to the flowchart of FIG. 8, the index A _j for the vibration period number j within a predetermined range (for example, a range including m and its vicinity) The maximum value is not less than 0.18 times and not more than 0.31 times (more precisely 0.309 times) the maximum value of the index A _j when m elements having a uniform thickness are arranged in the circumferential direction. It can be seen that the elements 18-1 and 18-2 are arranged in the belt circumferential direction.

When arranging the two different elements 18-1 and 18-2 of the plate thickness at random, the peak value of the frequency components of the belt vibration (maximum value of the index A _j) an array of elements 18-1 and 18-2 It changes according to the way (lineup). However, in the belt type continuously variable transmission 14, for example, a large number of elements 18-1 and 18-2, for example, are arranged, so that there are innumerable combinations of the arrangement of the elements 18-1 and 18-2. . Therefore, an element array in which the peak value of the frequency component of the belt vibration (the maximum value of the index A _j ) is sufficiently low by simply arranging the two types of elements 18-1 and 18-2 irregularly (randomly). It is not necessarily obtained. For example, when the arrangement of the elements 18-1 and 18-2 is determined using a random number, the maximum value of the index A _j is sufficient among the combinations of the arrangement of the elements 18-1 and 18-2 that exist innumerably. It is difficult to find a list of elements that are very low.

On the other hand, in the present embodiment, with respect to an array of m elements 18-1 and 18-2 in which the condition that the thicknesses of elements separated by m / 2 in the belt circumferential direction are different is established for all elements. By repeating the replacement of the elements separated by m / 2 in the belt circumferential direction, the replacement of the elements having different plate thicknesses is repeated. By calculating the maximum value of the index A _j before and after replacement of elements having different plate thicknesses, it is possible to evaluate the influence on the peak value of the frequency component of the belt vibration due to the change of the element arrangement. Therefore, by exchanging elements having different thicknesses so that the maximum value of the index A _j is reduced, an element array in which the peak value of the frequency component of the belt vibration is reduced can be obtained.

However, if elements with a short distance in the belt circumferential direction are exchanged, the influence on the belt vibration due to the exchange becomes local, and the maximum value of the index _Aj as a whole hardly changes. In this case, the amount of calculation (number of element replacements) required to obtain an element array in which the maximum value of the index A _j is sufficiently reduced increases.

On the other hand, in this embodiment, by replacing elements separated by m / 2 (substantially half the belt circumference) in the belt circumferential direction, the influence on the belt vibration due to the change in the element plate thickness at each replacement location cancels each other. Matching can be suppressed, and the influence of the element arrangement change on the maximum value of the index A _j can be efficiently evaluated. Then, by repeating the replacement of elements that are m / 2 (approximately half the belt circumference) apart so that the maximum value of the index A _j is reduced, the number of elements arranged to sufficiently reduce the peak value of the frequency component of the belt vibration is reduced. It can be found by the number of times (small number of element replacements). Therefore, according to the present embodiment, the peak value of vibration / noise generated in the belt-type continuously variable transmission 14 can be sufficiently reduced, and the endless belt for sufficiently reducing the peak value of vibration / noise. 34 (element array) can be easily designed. An element that converges the maximum value of the index A _j to the minimum is obtained by repeatedly exchanging elements separated by m / 2 (approximately half the belt circumference) until the maximum value of the index A _j does not decrease. An arrangement can be obtained, and the peak value of vibration and noise generated in the belt type continuously variable transmission 14 can be further reduced.

As shown in FIGS. 11 to 14, according to the endless belt 34 of the present embodiment, the peak value of the frequency component of the belt vibration (the maximum value of the index A _j ) can be significantly reduced as compared with the random arrangement. I understand that. More specifically, the value when the maximum value of the index A _j is the smallest among 1000 random arrays is 0.346, whereas the average value of the maximum values of the index A _j is 0.568. Thus, in the 1000 element arrangements obtained by the procedure of the flowchart of FIG. 8, the average value M ₁ = 0.218 (1.59 × M ₁ = 0.346) of the maximum value of the index A _j is obtained.

  In the present embodiment, a predetermined number of elements (array data of the function T (k)) (element T-1) after the element replacement procedure according to the flowchart of FIG. It is also possible to cause the computer to further execute a procedure for inserting data. The predetermined number is preferably sufficiently smaller than the total number m of the elements 18-1 and 18-2. For example, the predetermined number may be a natural number closest to 5% of the total number m of elements, or may be the minimum number. It can also be one. Further, the position where the element (data) is inserted and the plate thickness (data value) of the element to be inserted can be arbitrarily set.

  In this embodiment, a predetermined number of elements (array data of the function T (k)) (element T-1) after the element replacement procedure according to the flowchart of FIG. It is also possible to cause a computer to execute a procedure for removing data. The predetermined number here is preferably sufficiently smaller than the total number m of the elements 18-1 and 18-2. For example, the predetermined number may be a natural number closest to 5% of the total number m of elements, or may be the minimum. It can also be set to one. The location where the element (data) is removed and the plate thickness (data value) of the element to be removed can be arbitrarily set.

As described above, the element arrangement after the element replacement procedure according to the flowchart of FIG. 8 is an arrangement in which the conditions that the thicknesses of the elements separated by m / 2 in the belt circumferential direction are different are satisfied for all the elements. In addition, before and after replacing elements separated by m / 2 in the belt circumferential direction, the condition that the maximum value of the index A _j with respect to the vibration period number j within a predetermined range (for example, a range including m and its vicinity) does not decrease is as follows: An array that holds for any permutation. As shown in FIGS. 13 and 14, the element arrangement after the element replacement procedure according to the flowchart of FIG. 8 is an index A _j for the vibration period number j within a predetermined range (for example, a range including m and the vicinity thereof). Is an array in which the maximum value of _m is equal to or less than 0.31 times (more precisely 0.309 times) the maximum value of the index A _j when m elements having a uniform thickness are arrayed in the circumferential direction. . When a predetermined number of elements are inserted or removed as described above, a predetermined number of elements are inserted or removed from the element array that satisfies such a condition. Therefore, even in this case, an element arrangement that sufficiently reduces the maximum value of the index A _j can be obtained, and the peak values of vibration and noise generated in the belt type continuously variable transmission 14 can be sufficiently reduced. .

“Embodiment 2”
FIG. 15 is a flowchart for explaining the details of the procedure for determining the arrangement of the elements 18-1 and 18-2 in the continuously variable transmission belt designing method according to the second embodiment of the present invention. Also in this embodiment, the procedure according to the flowchart of FIG. 15 can be realized in software by a program for causing a computer to execute.

Step S201 is the same as step S101 in the flowchart of FIG. In step S202, the belt rotation j-order component of the belt vibration is expressed on the condition that the vibration period number j (natural number) is within a predetermined range with respect to the initial arrangement of the elements 18-1 and 18-2 set in step S201. A procedure for calculating the difference between the maximum value and the minimum value of the index A _j is executed by the computer. The predetermined range here can be set similarly to step S102. For example, when the characteristic of the index A _j with respect to the number of vibration periods j within a predetermined range is represented by the characteristic shown in FIG. 16, the difference between the maximum value and the minimum value of the index A _j is represented by δA1 in FIG. The

Steps S203 and S204 are the same as steps S103 and S104 in the flowchart of FIG. In step S205, the maximum value and the minimum value of the index A _j representing the belt rotation j-order component under the condition that the vibration period number j is within a predetermined range with respect to the element arrangement after the element replacement in step S204. The procedure for calculating the difference between is executed by the computer. The predetermined range here can be set similarly to step S202.

In step S206, a procedure is executed by the computer to determine whether or not the difference between the maximum value and the minimum value of the index A _j has decreased before and after the element replacement in step S204. If the difference between the maximum value and the minimum value of the index A _j does not decrease, the process proceeds to step S207, and the procedure for returning the element replacement performed in step S204 to the original is executed by the computer. On the other hand, if the difference between the maximum value and the minimum value of the index A _j decreases in step S206, the element replacement performed in step S204 is maintained and the process proceeds to step S208.

Steps S208 to S211 are the same as steps S108 to S111 in the flowchart of FIG. According to the procedure of steps S203 to S211, the procedure of exchanging the arrangement of the i to i + n-th element and the element that is m / 2 away from the element in the belt circumferential direction, and the index A _j before and after the element exchange If the difference between the maximum value and the minimum value of N does not decrease, the procedure for reversing this element replacement is all i and n satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. It is executed with respect to the combination. That is, replacement of elements separated by m / 2 in the belt circumferential direction is repeatedly performed a plurality of times so that the difference between the maximum value and the minimum value of the index A _j decreases.

In step S212, the computer executes a procedure for determining whether or not there is a combination of variables i and n that reduce the difference between the maximum value and the minimum value of the index A _j before and after the element replacement in step S204. If there is a combination of variables i and n in which the difference between the maximum value and the minimum value of the index A _j decreases, the process returns to step S203. On the other hand, when there is no combination of the variables i and n in which the difference between the maximum value and the minimum value of the index A _j decreases, the execution of this procedure ends. According to the procedure of step S212, the condition under which the difference between the maximum value and the minimum value of the index A _j does not decrease before and after the element replacement in step S204 is 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2. Steps S203 to S211 are repeated a plurality of times until all i and n combinations satisfying −2 are satisfied. In other words, until the difference between the maximum value and the minimum value of the index A _j converges to the minimum (or almost minimum), replacement of elements separated by m / 2 in the belt circumferential direction is repeatedly performed a plurality of times. However, it is also possible to omit step S212 and end the execution of this procedure when the determination result in step S210 is YES.

Even in the endless belt 34 in which the arrangement of the elements 18-1 and 18-2 is determined according to the procedure according to the flowchart of FIG. 15 described above, all the conditions in which the thicknesses of the elements separated by m / 2 in the belt circumferential direction are different are all. The m elements 18-1 and 18-2 are arranged in the belt circumferential direction so as to be established for the elements. The condition that the difference between the maximum value and the minimum value of the index A _j does not decrease before and after replacing elements separated by m / 2 in the belt circumferential direction is established with respect to arbitrary replacement (between elements). Elements 18-1 and 18-2 are arranged in the belt circumferential direction. More specifically, the maximum value of the index A _j with respect to the number of vibration periods j within a predetermined range before and after replacement of the i to i + n-th element and the element separated by m / 2 in the belt circumferential direction from this element, The elements 18-1 and 18- are such that the condition that the difference from the minimum value does not decrease holds for all combinations of i and n that satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2−2. 2 are arranged in the belt circumferential direction. The predetermined range here is also the same as the predetermined range in steps S202 and S205.

Here, as an example, the number n ₁ = 223 of the plate thickness thinner elements 18-1, sequence number n ₂ = 223 (elements 18-1 and 18-2 of the thick direction of the element 18-2 The total number m = 446), Δ = 0.071428571, the initial value of the function T (k) is 1 ≦ k ≦ m / 2, T (k) = 0 and T / 2 for m / 2 + 1 ≦ k ≦ m In the case of (k) = 1, the value of the function T (k) (array of elements 18-1 and 18-2) was finally determined according to the procedure according to the flowchart of FIG. FIG. 17 shows the frequency characteristics of the belt vibration in the finally determined element arrangement. FIG. 17 also shows the peak value of the frequency component of the belt vibration (the maximum value of the index A _j ) as 1 when m elements having a uniform thickness are arranged in the belt circumferential direction.

Further, the peak of the frequency component in the final arrangement obtained by executing the element replacement procedure according to the flowchart of FIG. 15 for 1000 initial arrangements in which the 1st to m / 2nd element arrangements are randomly set in step S201. A value (maximum value of the index A _{j in} the vicinity of the m th order of the belt circumference) is shown in FIGS. 18 and 19 in comparison with the maximum value of the index A _j in a random array (1000 types). FIG. 18 shows the maximum value of the index A _j for 1000 element arrangements, and FIG. 19 shows the frequency distribution of the maximum value of the index A _j . 18 and 19 also show the peak value of the frequency component of the belt vibration when the m elements having a uniform thickness are arranged in the belt circumferential direction (the maximum value of the index A _{j in} the vicinity of the belt circumferential m-th order). Is shown as 1. As shown in FIGS. 18 and 19, when the element arrangement is set at random, the maximum value of the index A _j with respect to the vibration period number j within a predetermined range (for example, a range including m and the vicinity thereof) is uniform in thickness. When m elements are arranged in the circumferential direction, the maximum value of the index A _j is 0.339 times or more and 0.843 times or less. On the other hand, in the endless belt 34 in which the element arrangement is determined according to the element replacement procedure according to the flowchart of FIG. 15, the index A _j for the vibration period number j within a predetermined range (for example, a range including m and the vicinity thereof) Elements 18-1 and 18-2 are set so that the maximum value is not less than 0.178 times and not more than 0.285 times the maximum value of the index A _j when m elements having a uniform thickness are arranged in the circumferential direction. It can be seen that 18-2 are arranged in the belt circumferential direction.

Also in the present embodiment described above, the influence on the belt vibration due to the change of the element plate thickness at each replacement position cancels each other by exchanging elements separated by m / 2 pieces (substantially half the belt circumference) in the belt circumferential direction. Can be suppressed, and the influence on the difference between the maximum value and the minimum value of the index A _j due to the element arrangement change can be efficiently evaluated. Then, by repeating the replacement of the elements separated by m / 2 so that the difference between the maximum value and the minimum value of the index A _j is reduced, the number of calculations for reducing the number of elements to equalize the frequency component of the belt vibration is reduced. (Small number of element replacements). Therefore, also in this embodiment, the peak value of vibration / noise generated in the belt type continuously variable transmission 14 can be sufficiently reduced, and the endless belt 34 (for reducing the vibration / noise peak value sufficiently) ( Element arrangement) can be easily designed. Further, the frequency components of the belt vibration can be made more uniform by repeatedly exchanging the elements separated by m / 2 until the difference between the maximum value and the minimum value of the index A _j does not decrease. The peak value of vibration and noise generated in the belt type continuously variable transmission 14 can be further reduced.

As shown in FIGS. 18 and 19, in the endless belt 34 of the present embodiment, the peak value of the frequency component of the belt vibration (the maximum value of the index _Aj ) can be significantly reduced as compared with the random arrangement. I understand. More specifically, the average value of the maximum value of the index A _j is 0.548 in the 1000 random arrays, whereas the index A is in the 1000 element arrays obtained by the procedure according to the flowchart of FIG. The average value of the maximum values of _j is 0.216.

  In this embodiment, the computer further executes a procedure for inserting or removing a predetermined number of elements from the arrangement of the elements 18-1 and 18-2 after the element replacement procedure according to the flowchart of FIG. It can also be made. The predetermined number here is also preferably sufficiently smaller than the total number m of the elements 18-1 and 18-2. For example, the predetermined number can be a natural number closest to 5% of the total number m of elements, or can be minimized. It can also be one. And the location where the element is inserted or removed and the plate thickness of the element to be inserted or removed can also be arbitrarily set.

As described above, the element arrangement after the element replacement procedure according to the flowchart of FIG. 15 is an arrangement in which the conditions that the thicknesses of the elements separated by m / 2 in the belt circumferential direction are different are satisfied for all the elements. The difference between the maximum value and the minimum value of the index A _j with respect to the number of vibration periods j within a predetermined range (for example, a range including m and the vicinity thereof) before and after replacing elements separated by m / 2 in the belt circumferential direction. An array in which the condition that does not decrease is satisfied for any replacement. As shown in FIGS. 18 and 19, the element arrangement after the element replacement procedure according to the flowchart of FIG. 15 is an index A _j for the number of vibration periods j within a predetermined range (for example, a range including m and the vicinity thereof). Is an array that is less than or equal to 0.285 times the maximum value of the index A _j when m elements having a uniform plate thickness are arrayed in the circumferential direction. When a predetermined number of elements are inserted or removed as described above, a predetermined number of elements are inserted or removed from the element array that satisfies such a condition. Therefore, even in this case, an element arrangement for making the frequency component of the belt vibration uniform can be obtained, and the peak value of vibration and noise generated in the belt type continuously variable transmission 14 can be sufficiently reduced. .

“Embodiment 3”
FIG. 20 is a flowchart for explaining the details of the procedure for determining the arrangement of the elements 18-1 and 18-2 in the continuously variable transmission belt designing method according to the third embodiment of the present invention. Also in this embodiment, the procedure according to the flowchart of FIG. 20 can be realized in software by a program that is executed by a computer.

Step S301 is the same as step S101 in the flowchart of FIG. In step S302, the belt rotation j-order component of the belt vibration is expressed under the condition that the vibration period number j (natural number) is within a predetermined range with respect to the initial arrangement of the elements 18-1 and 18-2 set in step S301. procedure for calculating the maximum deviation from the target value of the index a _j (maximum deviation (absolute value) between the index a _j and the target value) is performed by a computer. The predetermined range here can be set similarly to step S102. For example, when the characteristic of the index A _j with respect to the number of vibration periods j within a predetermined range is represented by the characteristic shown in FIG. 21, the maximum deviation of the index A _{j from} the target value is represented by δA2 in FIG. As the target value here, a value (constant) for sufficiently reducing the maximum value of the index A _j is set in advance.

Steps S303 and S304 are the same as steps S103 and S104 in the flowchart of FIG. In step S305, the maximum deviation from the target value of the index A _j representing the belt rotation j-order component with respect to the element arrangement after the element replacement in step S304 under the condition that the vibration period number j is within a predetermined range. The procedure for computing is executed by the computer. The predetermined range here can be set similarly to step S302.

In step S306, the computer executes a procedure for determining whether or not the maximum deviation of the target value of the index A _j has decreased before and after element replacement in step S304. When the maximum deviation of the index A _j with respect to the target value does not decrease, the process proceeds to step S307, and the procedure for returning the element replacement performed in step S304 is executed by the computer. On the other hand, if the maximum deviation from the target value of the index A _j decreases in step S306, the element replacement performed in step S304 is maintained, and the process proceeds to step S308.

Steps S308 to S311 are the same as steps S108 to S111 in the flowchart of FIG. According to the procedure of steps S303 to S311, the procedure of exchanging the arrangement of the i to i + n-th element and the element that is m / 2 away from the element in the belt circumferential direction, and the index A _j before and after the element exchange The procedure for reversing the replacement of this element when the maximum deviation from the target value does not decrease is for all i and n combinations satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. Executed. That is, replacement of elements separated by m / 2 in the belt circumferential direction is repeatedly performed a plurality of times so that the maximum deviation of the index A _{j from} the target value decreases.

In step S312, the computer executes a procedure for determining whether or not there is a combination of variables i and n that reduce the maximum deviation of the index A _{j from} the target value before and after element replacement in step S304. If there is a combination of variables i and n that reduces the maximum deviation of the index A _{j from} the target value, the process returns to step S303. On the other hand, if there is no combination of variables i and n that reduces the maximum deviation of the index A _{j from} the target value, the execution of this procedure is terminated. According to the procedure of step S312, the condition that the maximum deviation from the target value of the index A _j does not decrease before and after the element replacement in step S304 is 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. Until all the combinations of i and n that are satisfied are satisfied, the procedure of steps S303 to S311 is repeatedly executed a plurality of times. In other words, until the maximum deviation of the index A _j with respect to the target value converges to the minimum (or almost the minimum), replacement of elements separated by m / 2 in the belt circumferential direction is repeatedly performed a plurality of times. However, it is also possible to omit step S312 and terminate the execution of this procedure when the determination result in step S310 is YES.

Also in the endless belt 34 in which the arrangement of the elements 18-1 and 18-2 is determined according to the procedure according to the flowchart of FIG. 20 described above, all the conditions in which the thicknesses of the elements separated by m / 2 in the belt circumferential direction are different are all. The m elements 18-1 and 18-2 are arranged in the belt circumferential direction so as to be established for the elements. Then, before and after the elements separated by m / 2 in the belt circumferential direction are replaced, the condition that the maximum deviation with respect to the target value of the index A _j does not decrease is established with respect to any replacement (between elements). -1 and 18-2 are arranged in the belt circumferential direction. More specifically, the index A _j and the target value for the number of vibration periods j within a predetermined range before and after the i to i + n-th element and the element m / 2 away from the element in the belt circumferential direction are replaced. Elements 18-1, 18- so that the condition that the maximum value of the deviations of N is not reduced is satisfied with respect to all combinations of i and n that satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. 2 are arranged in the belt circumferential direction. The predetermined range here is also the same as the predetermined range in steps S302 and S305.

Here, as an example, the number n ₁ = 223 of the plate thickness thinner elements 18-1, sequence number n ₂ = 223 (elements 18-1 and 18-2 of the thick direction of the element 18-2 The total number m = 446), Δ = 0.071428571, the initial value of the function T (k) is 1 ≦ k ≦ m / 2, T (k) = 0 and T / 2 for m / 2 + 1 ≦ k ≦ m In the case of (k) = 1, the value of the function T (k) (array of elements 18-1 and 18-2) was finally determined according to the procedure according to the flowchart of FIG. FIG. 22 shows the frequency characteristics of the belt vibration in the finally determined element arrangement. FIG. 22 also shows the peak value of the frequency component of the belt vibration (maximum value of the index A _j ) as 1 when m elements having a uniform thickness are arranged in the belt circumferential direction. FIG. 22 shows frequency characteristics when the target value is set to 0.23.

Further, the peak of frequency components in the final arrangement obtained by executing the element replacement procedure according to the flowchart of FIG. 20 with respect to 1000 initial arrangements in which the 1st to m / 2nd element arrangements are randomly set in step S201. A value (maximum value of the index A _{j in} the vicinity of the mth order of the belt circumference) is shown in FIGS. 23 and 24 in comparison with the maximum value of the index A _j in a random array (1000 types). FIG. 23 shows the maximum value of the index A _j with respect to 1000 element arrangements, and FIG. 24 shows the frequency distribution of the maximum value of the index A _j . 23 and 24, the peak value of the frequency component of the belt vibration when the m elements having a uniform thickness are arranged in the belt circumferential direction (maximum value of the index A _{j in} the vicinity of the belt circumferential m-th order). Is shown as 1. 23 and 24, the target value is set to 0.23. As shown in FIGS. 23 and 24, when the element arrangement is set at random, the maximum value of the index A _j with respect to the vibration period number j within a predetermined range (for example, a range including m and the vicinity thereof) is uniform in thickness. When m elements are arranged in the circumferential direction, the maximum value of the index A _j is 0.359 times or more and 0.867 times or less. On the other hand, in the endless belt 34 in which the element arrangement is determined according to the element replacement procedure according to the flowchart of FIG. 20, the index A _j for the vibration period number j within a predetermined range (for example, a range including m and its vicinity) The elements 18-1 and 18-2 are set so that the maximum value is 0.210 times or more and 0.328 times or less of the maximum value of the index A _j when m elements having a uniform thickness are arranged in the circumferential direction. It can be seen that 18-2 are arranged in the belt circumferential direction.

Also in the present embodiment described above, the influence on the belt vibration due to the change of the element plate thickness at each replacement position cancels each other by exchanging elements separated by m / 2 pieces (substantially half the belt circumference) in the belt circumferential direction. Therefore, it is possible to efficiently evaluate the influence of the element arrangement change on the maximum deviation of the index A _j with respect to the target value. Then, by repeating the replacement of elements m / 2 apart so that the maximum deviation of the index A _{j from} the target value is reduced, the number of calculations to reduce the number of elements to bring the belt vibration frequency component closer to the target value (less) The frequency component of the belt vibration can be made uniform toward the target value. Therefore, also in this embodiment, the peak value of vibration / noise generated in the belt type continuously variable transmission 14 can be sufficiently reduced, and the endless belt 34 (for reducing the vibration / noise peak value sufficiently) ( Element arrangement) can be easily designed. Then, the frequency component of the belt vibration is made more uniform toward the target value by repeatedly exchanging elements separated by m / 2 until the maximum deviation from the target value of the index A _j does not decrease. The peak value of vibration and noise generated in the belt type continuously variable transmission 14 can be further reduced.

As shown in FIGS. 23 and 24, also in the endless belt 34 of the present embodiment, the peak value of the frequency component of the belt vibration (the maximum value of the index A _j ) can be significantly reduced as compared with the random arrangement. I understand. More specifically, the average value of the maximum value of the index A _j is 0.546 in the 1000 random arrays, whereas the index A is in the 1000 element arrays obtained by the procedure according to the flowchart of FIG. The average value of the maximum values of _j is 0.262.

  In this embodiment, the computer further executes a procedure for inserting or removing a predetermined number of elements from the arrangement of the elements 18-1 and 18-2 after the element replacement procedure according to the flowchart of FIG. It can also be made. The predetermined number here is also preferably sufficiently smaller than the total number m of the elements 18-1 and 18-2. For example, the predetermined number can be a natural number closest to 5% of the total number m of elements, or can be minimized. It can also be one. And the location where the element is inserted or removed and the plate thickness of the element to be inserted or removed can also be arbitrarily set.

As described above, the element arrangement after the element replacement procedure according to the flowchart of FIG. 20 is an arrangement in which the conditions in which the thicknesses of the elements separated by m / 2 in the belt circumferential direction are different are satisfied for all the elements. In addition, the maximum deviation of the target value of the index A _j with respect to the vibration period number j within a predetermined range (for example, a range including m and the vicinity thereof) does not decrease before and after the elements separated by m / 2 in the belt circumferential direction are exchanged. An array in which the condition is satisfied with respect to arbitrary replacement. When a predetermined number of elements are inserted or removed as described above, a predetermined number of elements are inserted or removed from the element array that satisfies such a condition. Therefore, even in this case, an element arrangement for making the frequency component of the belt vibration uniform toward the target value can be obtained, and the peak value of vibration and noise generated in the belt type continuously variable transmission 14 can be sufficiently obtained. Can be reduced.

In the first to third embodiments described above, as an index representing the belt vibration of belt rotation j th component generated when the excitation force is inputted to each element, in addition to A _j, for example, A _j ^2, etc. A _j It is also possible to use a power of A _j ^p (p> 0).

  In the above description, the case where the present invention is applied to a continuously variable transmission belt in which two types of elements 18-1, 18-2 having different plate thicknesses are arranged in the belt circumferential direction has been described. However, even in a chain-type continuously variable transmission in which a chain is wound around a drive pulley and a driven pulley, vibration and noise are generated when each link of the chain enters or leaves the pulley. Therefore, the present invention is applied to a continuously variable transmission chain in which two types of links having different link lengths (lengths) are connected in the chain circumferential direction by pins, that is, using the present invention, two types having different link lengths. It is also possible to determine the link connection (link arrangement). As a result, the peak value of vibration and noise generated in the chain type continuously variable transmission can be sufficiently reduced, and the chain can be easily designed to sufficiently reduce the peak value of vibration and noise. it can. In that case, in the description of the above embodiment, “belt” is “chain”, “element” is “link”, “element plate thickness” is “link length”, and “thick / thin plate thickness” is “link”. What has been replaced with “long (distance between pins) long / short” may be considered.

That is, in the first embodiment (procedure according to the flowchart of FIG. 8), for the connection of m links in which the condition that the link lengths of the links separated by m / 2 in the chain circumferential direction are different is established for all the links, The procedure of repeating replacement of links separated by m / 2 in the circumferential direction of the chain so that the maximum value of the index A _j indicating the frequency component of chain vibration generated when an excitation force is input to each link is reduced. It is executed by a computer to determine the connection (link arrangement) of two types of links having different link lengths. In a chain designed according to this procedure, m links are connected in the circumferential direction of the chain so that the condition that the link lengths of the links separated by m / 2 in the circumferential direction of the chain are different for all links. Yes. The condition that the maximum value of the index A _j with respect to the number of vibration periods j within a predetermined range does not decrease before and after the exchange of m / 2 links in the circumferential direction of the chain is established with respect to any exchange (between links). Thus, the links are connected in the chain circumferential direction. Furthermore, it is possible to cause the computer to execute a procedure for inserting or removing a predetermined number of links from the link list after executing this procedure.

Further, in the second embodiment (procedure according to the flowchart of FIG. 15), for the connection of m links in which the condition that the link lengths of the links separated by m / 2 in the chain circumferential direction are different is established for all the links, Links that are m / 2 apart in the circumferential direction of the chain so that the difference between the maximum value and the minimum value of the index A _j indicating the frequency component of the chain vibration that occurs when an excitation force is input to each link decreases. The computer is caused to execute the procedure of repeating the exchange of two, and the connection of two types of links having different link lengths is determined. Even in a chain designed according to this procedure, m links are connected in the circumferential direction of the chain so that the condition that the link lengths of the links separated by m / 2 in the circumferential direction of the chain are different is satisfied for all the links. Yes. The condition under which the difference between the maximum value and the minimum value of the index A _j with respect to the vibration period number j within a predetermined range does not decrease before and after the links separated by m / 2 in the chain circumferential direction is arbitrary (link) The links are connected in the circumferential direction of the chain so as to be established with respect to the exchange. Furthermore, it is possible to cause the computer to execute a procedure for inserting or removing a predetermined number of links from the link list after executing this procedure.

Further, in Embodiment 3 (procedure according to the flowchart of FIG. 20), for the connection of m links in which the condition that the link lengths of the links separated by m / 2 in the chain circumferential direction are different is established for all the links, Links separated by m / 2 in the circumferential direction of the chain so that the maximum deviation from the target value (predetermined value) of the index A _j representing the frequency component of the chain vibration generated when the excitation force is input to each link A procedure for repeating the interchange between them is executed by the computer, and the connection of two types of links having different link lengths is determined. Even in a chain designed according to this procedure, m links are connected in the circumferential direction of the chain so that the condition that the link lengths of the links separated by m / 2 in the circumferential direction of the chain are different is satisfied for all the links. Yes. The condition under which the maximum deviation from the target value of the index A _j at the vibration period number j within the predetermined range does not decrease before and after the links separated by m / 2 in the chain circumferential direction is arbitrary (between links). The links are connected in the chain circumferential direction so as to be established with respect to replacement. Furthermore, it is possible to cause the computer to execute a procedure for inserting or removing a predetermined number of links from the link list after executing this procedure.

For example, in the case where the number n ₁ = 50 of links having the shorter link length, the number n ₂ = 223 of links having the longer link length (total number of links m = 100), and Δ = 0.071428571 FIG. 25 and FIG. 26 show the frequency characteristics of the chain vibration in the link sequence finally determined according to the procedure of the flowchart of FIG. 8 in comparison with the case where two types of links having different link lengths are randomly connected. FIG. 25 shows the characteristics of the chain vibration frequency component (index A _j ) with respect to the chain circulation order j in the present embodiment, and FIG. 26 shows the frequency component of the chain vibration in 1000 random connections using random numbers. The characteristic when the peak value (the maximum value of the index A _j ) is minimum is shown. 25 and 26 show the peak value of the frequency component of the chain vibration (the maximum value of the index A _j ) as 1 when m links having a uniform link length are arranged in the chain circumferential direction.

As shown in FIGS. 25 and 26, according to the present embodiment, it can be seen that the peak value of the frequency component of the chain vibration (the maximum value of the index A _j ) can be greatly reduced as compared with the random connection. More specifically, in the 1000 random arrays, the value when the maximum value of the index A _j is minimum is 0.527, whereas the link sequence obtained by the procedure according to the flowchart of FIG. In this case, the maximum value of the index A _j is 0.323.

  Further, as an aspect of the present invention, an aspect of a program for causing a computer to execute the procedure according to the flowchart of FIG. 8, FIG. 15, or FIG. 20, or a computer-readable recording medium on which this program is recorded, for example, a CD A variety of recording media such as a ROM, a DVD-ROM, and a flexible disk are also suitable. By installing such a program on a computer and executing the program, the effects of the present invention can be achieved.

  As mentioned above, although the form for implementing this invention was demonstrated, this invention is not limited to such embodiment at all, and it can implement with a various form in the range which does not deviate from the summary of this invention. Of course.

It is a figure which shows schematic structure of a continuously variable transmission provided with the belt for continuously variable transmission which concerns on embodiment of this invention. It is a figure which shows schematic structure of the belt for continuously variable transmission which concerns on embodiment of this invention. It is a figure which shows the frequency characteristic of the vibration which arises in an endless belt when the plate | board thickness of an element is set uniformly. It is a figure which shows the frequency characteristic of the vibration which arises in an endless belt when two types of elements from which board thickness differs are irregularly arranged. It is a figure which shows an example of the initial stage arrangement | sequence of two types of elements from which board thickness differs. It is a figure which shows belt vibration waveform f ((theta), (alpha)) when a unit impulse input is performed in the position (phase) (alpha) in the belt 1 round. It is a figure which shows the belt vibration waveform F ((theta)) when unit impulse input is performed in the phase (alpha) _{i of} each element. It is a flowchart explaining the detail of the procedure which determines how to arrange two types of elements from which plate | board thickness differs. It is a figure explaining the procedure which replaces the elements which m / 2 pieces apart. It is a figure explaining the procedure which replaces the elements which m / 2 pieces apart. It is a figure which shows the frequency characteristic of the belt vibration in this embodiment. It is a figure which shows the frequency characteristic of a belt vibration when two types of elements from which board thickness differs are arranged at random. It is a figure which shows the peak value of the frequency component of the belt vibration with respect to 1000 kinds of element arrangements. It is a figure which shows frequency distribution of the peak value of the frequency component of belt vibration. It is a flowchart explaining the detail of the other procedure which determines how to arrange two types of elements from which plate | board thickness differs. It is a figure explaining an example of the difference of the maximum value and the minimum value of parameter _| index _Aj . It is a figure which shows the frequency characteristic of the belt vibration in this embodiment. It is a figure which shows the peak value of the frequency component of the belt vibration with respect to 1000 kinds of element arrangements. It is a figure which shows frequency distribution of the peak value of the frequency component of belt vibration. It is a flowchart explaining the detail of the other procedure which determines how to arrange two types of elements from which plate | board thickness differs. It is a figure explaining an example of the maximum deviation with respect to the target value of parameter _| index _Aj . It is a figure which shows the frequency characteristic of the belt vibration in this embodiment. It is a figure which shows the peak value of the frequency component of the belt vibration with respect to 1000 kinds of element arrangements. It is a figure which shows frequency distribution of the peak value of the frequency component of belt vibration. It is a figure which shows the frequency characteristic of the chain vibration in this embodiment. It is a figure which shows the frequency characteristic of the chain vibration at the time of connecting two types of links from which link length differs at random.

Explanation of symbols

  14 belt type continuously variable transmission, 18 (18-1, 18-2) element, 20 hoop, 30 primary pulley, 32 secondary pulley, 34 endless belt.

Claims (38)

A method for designing a belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
If the number of elements arranged is an even number m,
The frequency component of the belt vibration that occurs when the excitation force is input by each element for an array of m elements where the condition that the thicknesses of elements separated by m / 2 are different for all elements is satisfied. For a continuously variable transmission characterized by having a computer execute a replacement procedure that repeats replacement of elements separated by m / 2 based on an index to be represented, and determining an arrangement of two types of elements having different thicknesses Belt design method. A design method for a continuously variable transmission belt according to claim 1,
When the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the arrangement order, i is a natural number, and n is an integer of 0 or more,
The replacement procedure is as follows:
For an array of m elements in which the condition that the thicknesses of elements separated by m / 2 are different for all elements,
A procedure for exchanging elements corresponding to corresponding values i to i + n and elements separated by m / 2 from the elements;
A procedure for determining whether or not to replace the element based on a comparison result between the index before replacement of the element and the index after replacement of the element;
A design method of a belt for a continuously variable transmission, characterized in that the procedure is executed by a computer for all combinations of i and n that satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. A method for designing a continuously variable transmission belt according to claim 2,
A method for designing a belt for a continuously variable transmission, comprising causing a computer to execute the replacement procedure a plurality of times. A design method for a continuously variable transmission belt according to any one of claims 1 to 3,
Corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the order of arrangement, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the number of vibration cycles per belt circumference of the belt vibration Is j,
The indicator is

A method for designing a belt for a continuously variable transmission, characterized by: A design method for a continuously variable transmission belt according to claim 1,
As the replacement procedure, m / 2 elements so that the maximum value of the index decreases with respect to an array of m elements in which the condition that the thicknesses of elements separated by m / 2 elements are different for all elements. A design method for a belt for a continuously variable transmission, characterized by causing a computer to execute a procedure for repeating replacement of separated elements. A method for designing a belt for a continuously variable transmission according to claim 5,
When the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the arrangement order, i is a natural number, and n is an integer of 0 or more,
The replacement procedure is as follows:
For an array of m elements in which the condition that the thicknesses of elements separated by m / 2 are different for all elements,
A procedure for exchanging elements corresponding to corresponding values i to i + n and elements separated by m / 2 from the elements;
A procedure for returning the replacement of the element when the maximum value of the index does not decrease before and after the replacement of the element;
A design method of a belt for a continuously variable transmission, characterized in that the procedure is executed by a computer for all combinations of i and n that satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. A design method for a continuously variable transmission belt according to claim 6,
Until the condition that the maximum value of the index does not decrease before and after the element replacement is satisfied for all combinations of i and n satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2, A design method of a belt for a continuously variable transmission, characterized in that a computer is executed by repeating a replacement procedure. A design method for a continuously variable transmission belt according to any one of claims 5 to 7,
The method for designing a continuously variable transmission belt, wherein the replacement procedure is a procedure of repeating replacement of elements separated by m / 2 until the maximum value of the index converges to a minimum. A design method for a continuously variable transmission belt according to any one of claims 5 to 8,
Corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the order of arrangement, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the number of vibration cycles per belt circumference of the belt vibration Is j,
The maximum value of the index is relative to the number of vibration periods j within a predetermined range.

A method for designing a belt for a continuously variable transmission, characterized by being expressed by a maximum value of A design method for a continuously variable transmission belt according to claim 1,
As the replacement procedure, the difference between the maximum value and the minimum value of the index is reduced with respect to the arrangement of m elements in which the condition that the thicknesses of m / 2 elements are different from each other is satisfied for all elements. A method for designing a belt for a continuously variable transmission, characterized by causing a computer to execute a procedure of repeatedly exchanging elements separated by m / 2. A method for designing a belt for a continuously variable transmission according to claim 10,
When the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the arrangement order, i is a natural number, and n is an integer of 0 or more,
The replacement procedure is as follows:
For an array of m elements in which the condition that the thicknesses of elements separated by m / 2 are different for all elements,
A procedure for exchanging elements corresponding to corresponding values i to i + n and elements separated by m / 2 from the elements;
When the difference between the maximum value and the minimum value of the index before and after the replacement of the element does not decrease, a procedure for returning the replacement of the element,
A design method of a belt for a continuously variable transmission, characterized in that the procedure is executed by a computer for all combinations of i and n that satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. A design method for a continuously variable transmission belt according to claim 11,
The conditions under which the difference between the maximum value and the minimum value of the index does not decrease before and after the replacement of the elements are all i and n combinations satisfying 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. A design method for a continuously variable transmission belt, wherein the computer repeats the replacement procedure until it is established. A method for designing a belt for a continuously variable transmission according to any one of claims 10 to 12,
The belt for a continuously variable transmission is characterized in that the replacement procedure is a procedure of repeating replacement of elements separated by m / 2 until the difference between the maximum value and the minimum value of the index converges to a minimum. Design method. A method for designing a belt for a continuously variable transmission according to any one of claims 10 to 13,
Corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the order of arrangement, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the number of vibration cycles per belt circumference of the belt vibration Is j,
The difference between the maximum value and the minimum value of the index is the number of vibration periods j within a predetermined range.

A method for designing a belt for a continuously variable transmission, characterized by being expressed by a difference between a maximum value and a minimum value. A design method for a continuously variable transmission belt according to claim 1,
As the replacement procedure, m is arranged so that the maximum deviation with respect to a predetermined value of the index decreases with respect to an array of m elements in which the condition that the thicknesses of elements separated by m / 2 are different for all elements is satisfied. A method for designing a belt for a continuously variable transmission, comprising causing a computer to execute a procedure of repeatedly exchanging two elements apart from each other. A method for designing a belt for a continuously variable transmission according to claim 15,
When the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the arrangement order, i is a natural number, and n is an integer of 0 or more,
The replacement procedure is as follows:
For an array of m elements in which the condition that the thicknesses of elements separated by m / 2 are different for all elements,
A procedure for exchanging elements corresponding to corresponding values i to i + n and elements separated by m / 2 from the elements;
A procedure for returning the replacement of the element when the maximum deviation of the index with respect to the predetermined value does not decrease before and after the replacement of the element;
A design method of a belt for a continuously variable transmission, characterized in that the procedure is executed by a computer for all combinations of i and n that satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. It is a design method of the belt for continuously variable transmission according to claim 16,
The condition that the maximum deviation of the index with respect to the predetermined value does not decrease before and after the element replacement is satisfied with respect to all combinations of i and n that satisfy 1 ≦ i ≦ m / 2 and 0 ≦ n ≦ m / 2-2. The design method of the belt for continuously variable transmission, characterized in that the replacement procedure is repeatedly executed by a computer. A design method for a continuously variable transmission belt according to any one of claims 15 to 17,
The design of the continuously variable transmission belt, wherein the replacement procedure is a procedure of repeating replacement of elements separated by m / 2 until the maximum deviation of the index with respect to the predetermined value converges to a minimum. Method. A method for designing a belt for a continuously variable transmission according to any one of claims 15 to 18, comprising:
Corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the order of arrangement, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the number of vibration cycles per belt circumference of the belt vibration Is j,
The maximum deviation of the index with respect to the predetermined value is a vibration period number j within a predetermined range.

The design method of the belt for continuously variable transmission, characterized in that it is expressed by the maximum deviation with respect to the predetermined value. A method for designing a continuously variable transmission belt according to any one of claims 9, 14, and 19, comprising:
The method for designing a belt for a continuously variable transmission, wherein the predetermined range is a range including at least m and the vicinity thereof. A method for designing a belt for a continuously variable transmission according to any one of claims 9, 14, 19, and 20, comprising:
The method for designing a belt for a continuously variable transmission, wherein the predetermined range is a range including at least 2 × m and the vicinity thereof. A method for designing a continuously variable transmission belt according to any one of claims 4, 9, 14, 19, 20, and 21,
The number of the thinner elements is n ₁ , the number of the thicker elements is n ₂ (n ₂ = m−n ₁ ), and the thickness ratio between the thicker and thinner elements is 1 + Δ (Δ> 0), a function that becomes 0 when the element corresponding to the corresponding value k is the thinner element, and 1 when the element corresponding to the corresponding value k is the thicker element is T (k )
The phase α _{i in} the circumferential direction of the element corresponding to the corresponding value i is

A method for designing a belt for a continuously variable transmission, characterized by: A method for designing a belt for a continuously variable transmission according to any one of claims 1 to 22,
The computer further executes a procedure for inserting or removing a predetermined number of elements from the element arrangement after execution of the replacement procedure, and determines the arrangement of two types of elements having different thicknesses. A method for designing a belt for a step transmission.   24. A continuously variable transmission belt designed by the design method according to claim 1. A belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
If the number of elements arranged is an even number m,
m elements are arranged in the circumferential direction so that the condition that the thicknesses of m / 2 separated elements are different for all elements is satisfied,
The condition that the maximum value of the index representing the frequency component of the belt vibration generated when the excitation force is input to each element does not decrease before and after the elements separated by m / 2 is to be satisfied for any replacement. And a continuously variable transmission belt, wherein the elements are arranged in a circumferential direction. A belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
A predetermined number of elements have been inserted or removed from the array of elements that satisfy the predetermined condition,
The array of elements that satisfy the predetermined condition is:
If the number of elements arranged is an even number m,
An array in which the condition that the thicknesses of elements separated by m / 2 are different is established for all elements,
In addition, a condition that the maximum value of the index representing the frequency component of the belt vibration generated when the excitation force is input to each element is not reduced before and after the elements separated by m / 2 is exchanged. A belt for continuously variable transmission, characterized by being an array. A continuously variable transmission belt according to claim 25 or 26,
Corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the order of arrangement, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the number of vibration cycles per belt circumference of the belt vibration Is j,
The maximum value of the index is relative to the number of vibration periods j within a predetermined range.

A belt for a continuously variable transmission, characterized by the maximum value of A belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
If the number of elements arranged is an even number m, the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the order of arrangement, and the phase in the circumferential direction of the elements corresponding to the corresponding value i is α _i .
m elements are arranged in the circumferential direction so that the condition that the thicknesses of m / 2 separated elements are different for all elements is satisfied,
For a value j within a given range

Continuously variable transmission characterized in that the elements are arranged in the circumferential direction so that the maximum value of is less than 0.31 times that of m elements having a uniform thickness arranged in the circumferential direction Belt for machine. A belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
A predetermined number of elements have been inserted or removed from the array of elements that satisfy the predetermined condition,
The array of elements that satisfy the predetermined condition is:
If the number of elements arranged is an even number m, the corresponding values corresponding to the elements arranged in the circumferential direction are 1 to m in the order of arrangement, and the phase in the circumferential direction of the elements corresponding to the corresponding value i is α _i .
An array in which the condition that the thicknesses of elements separated by m / 2 are different is established for all elements,
And for a value j within a predetermined range

The continuously variable transmission belt is characterized in that the maximum value of is an arrangement that is 0.31 times or less of m elements having a uniform thickness arranged in the circumferential direction. A belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
If the number of elements arranged is an even number m,
m elements are arranged in the circumferential direction so that the condition that the thicknesses of m / 2 separated elements are different for all elements is satisfied,
The condition that the difference between the maximum value and the minimum value of the index indicating the frequency component of the belt vibration generated when the excitation force is input to each element is not reduced before and after the elements separated by m / 2. A belt for continuously variable transmission, characterized in that the elements are arranged in the circumferential direction so as to be established with respect to the replacement. A belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
A predetermined number of elements have been inserted or removed from the array of elements that satisfy the predetermined condition,
The array of elements that satisfy the predetermined condition is:
If the number of elements arranged is an even number m,
An array in which the condition that the thicknesses of elements separated by m / 2 are different is established for all elements,
In addition, before and after exchanging elements separated by m / 2, the condition that the difference between the maximum value and the minimum value of the index representing the frequency component of the belt vibration generated when the excitation force is input to each element is not reduced. A belt for continuously variable transmission, characterized in that the arrangement is established with respect to arbitrary replacement. A continuously variable transmission belt according to claim 30 or 31,
Corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the order of arrangement, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the number of vibration cycles per belt circumference of the belt vibration Is j,
The difference between the maximum value and the minimum value of the index is the number of vibration periods j within a predetermined range.

A belt for a continuously variable transmission, characterized by being represented by a difference between a maximum value and a minimum value. A belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
If the number of elements arranged is an even number m,
m elements are arranged in the circumferential direction so that the condition that the thicknesses of m / 2 separated elements are different for all elements is satisfied,
The condition that the maximum deviation with respect to the predetermined value of the index representing the frequency component of the belt vibration generated when the excitation force is input to each element is not reduced before and after replacing the elements separated by m / 2. A belt for continuously variable transmission, wherein the elements are arranged in a circumferential direction so as to be established. A belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two types of elements having different thicknesses arranged in the circumferential direction,
A predetermined number of elements have been inserted or removed from the array of elements that satisfy the predetermined condition,
The array of elements that satisfy the predetermined condition is:
If the number of elements arranged is an even number m,
An array in which the condition that the thicknesses of elements separated by m / 2 are different is established for all elements,
In addition, before and after replacing elements separated by m / 2 pieces, the condition that the maximum deviation from the predetermined value of the index representing the frequency component of the belt vibration generated when the excitation force is input to each element is not changed arbitrarily. A belt for continuously variable transmission, characterized in that A belt for continuously variable transmission according to claim 33 or 34,
Corresponding values corresponding to each of the elements arranged in the circumferential direction are 1 to m in the order of arrangement, the phase in the circumferential direction of the element corresponding to the corresponding value i is α _i , and the number of vibration cycles per belt circumference of the belt vibration Is j,
The maximum deviation of the index with respect to the predetermined value is a vibration period number j within a predetermined range.

A belt for a continuously variable transmission, which is expressed by a maximum deviation from the predetermined value. A continuously variable transmission capable of changing a gear ratio by changing a belt diameter of a drive pulley and a driven pulley;
A continuously variable transmission, wherein the belt is a continuously variable transmission belt according to any one of claims 24 to 35. A program for designing a belt for a continuously variable transmission wound around a driving pulley and a driven pulley and having two kinds of elements having different thicknesses arranged in the circumferential direction,
If the number of elements arranged is an even number m,
On the computer,
The frequency component of the belt vibration that occurs when an excitation force is input to each element for an array of m elements in which the condition that the thicknesses of elements separated by m / 2 are different for all elements is satisfied. A design program for a continuously variable transmission belt for executing a replacement procedure that repeats replacement of elements separated by m / 2 based on an index to be expressed. A method of designing a chain for a continuously variable transmission that is wound around a driving pulley and a driven pulley and in which two types of links having different lengths are connected in the circumferential direction,
If the number of links connected is an even number m,
The frequency component of the chain vibration generated when the excitation force is input to each link for the connection of m links where the condition that the lengths of the links separated by m / 2 are different is established for all links. For a continuously variable transmission characterized in that a computer executes a replacement procedure that repeats replacement of links separated by m / 2 based on an index to be represented, and determines the connection of two types of links having different lengths. Chain design method.

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