JP5539178B2 - Oscillating grinding method for irregularly shaped workpieces and oscillating grinding machine - Google Patents

Description

The present invention makes it possible to grind a non-circular deformed workpiece with a cam as a representative example without using a master workpiece, or to allow each planar portion of a deformed workpiece having a polygonal cross section to be ground sequentially. The present invention relates to a rocking grinding method and a rocking grinding machine.
In this specification, the term “unshaped workpiece” means a workpiece having a non-circular cross section or an eccentric workpiece in which the eccentric portion of the perfect circle is eccentric with respect to the rotational axis, and is partially deformed with respect to the perfect circle. Of course, a workpiece having a polygonal cross section or a gourd cross section is also included.

In order to grind a deformed workpiece having a non-circular cross section, a similar master workpiece is used for the deformed workpiece. A grinding machine using this master work will be briefly described with reference to FIG. In FIG. 17, both the headstock 101 and the tailstock 102 are attached to the swing table 103, and the swing table 103 is supported by the base 104 so as to be swingable around the swing axis C ₀ . A master work W ₀ is attached to a spindle (not shown) on the spindle stock 101 concentrically with the axis C _{1 of the} spindle. On the other hand, the base 104, the master work W ₀ and opposed to the cam roller 105 is rotatably supported, the master work W ₀ has one end coupled to the arm portion 103a of the oscillating table 103, the other end Is pressed against the cam roller 105 by the restoring force of the tension spring 107 connected to the adjustment rod 106 a of the spring adjustment mechanism 106. Further, a grindstone base 108 is disposed so as to be able to advance and retreat in a horizontal direction perpendicular to the axis C ₁ of the main spindle, and each spindle 111 of the main spindle 101 and the tailstock 102 is provided by a grindstone 109 attached to the grindstone base 108. , 112 are supported by the grindstone 109 while the shape of the master work W ₀ is transferred as it is because the swing table 103 swings about the swing axis C _0. To be ground.

  However, the above-described method of grinding a deformed workpiece using the master workpiece requires that a master workpiece corresponding to the deformed workpiece be produced each time the deformed workpiece to be ground is different. However, since high accuracy is required, there is a problem that requires a lot of time and cost. In addition, when a product is ground using a master workpiece, if the accuracy of the outer shape of the product after grinding does not fall within the required range, that is, if the outer shape of the product is defective, It is necessary to correct or remanufacture the master work, and waste of the production of the master work may occur until a good product can be ground.

  On the other hand, Patent Document 1 discloses a method of grinding a deformed workpiece by moving the grindstone back and forth so as to correspond to the outer shape of the workpiece without using a master workpiece. Yes. However, the calculation (program) itself is considerably difficult to calculate the position of the longitudinal movement of the grindstone with respect to the rotation angle of the deformed workpiece. In addition, in order to move the grindstone table on which the grindstone is mounted back and forth, a linear servo motor is used to eliminate backlash that inevitably occurs when the rotational motion is changed to a linear motion. In order to eliminate the influence of thermal expansion and increase the grinding accuracy, it is inevitable to use a cooling device for cooling the linear servo motor and a hydrostatic sliding device for smoothly moving the grindstone table back and forth. Become.

  As described above, the method of grinding by moving the grindstone back and forth with respect to the deformed workpiece without using the master work is as described above. In addition to the high cost of the device itself and the difficulty in creating a grinding program, there are some that are black-boxed so that the user cannot easily change the program. Therefore, it was not easy to use for users.

JP 2005-18531 A

  It is an object of the present invention to make it possible to grind a non-circular cross-sectional workpiece having a cam as a representative example without using a master workpiece, or to sequentially grind each surface portion of a polymorphic workpiece having a polygonal cross-section. It is said.

The invention of claim 1 for solving the above-mentioned problem is that the deformed workpiece gripped by the chuck has a sectional shape so that the rotational axis of the deformed workpiece having a polygonal cross section is concentric with the axis of the main shaft. A method of grinding each outer peripheral surface by rotating within an angle corresponding to the central angle of each surface portion of the square and sequentially changing each surface portion to be ground, the spindle base and the tailstock on the table The entire grinding unit to which is attached is capable of swinging around a swinging shaft center disposed substantially parallel to the shaft center of the main shaft and immediately below the shaft center of the main shaft. An outer periphery shape specifying formula that specifies the relationship between the rotation angle from the reference position and the rocking angle of the grinding unit to determine the outer periphery grinding shape of each surface portion of the deformed workpiece is calculated in advance, and the outer periphery shape specification Based on the equation, the grinding unit is centered on the pivot axis. Each surface portion is rotated within an angle corresponding to the center angle while sequentially changing each surface portion of the deformed workpiece while swinging the workpiece, and each surface portion is specified by the outer peripheral shape specifying formula. It is characterized by grinding each shape.

When the deformed workpiece has a non-circular cross section, the relationship between the rotation angle from the reference position of the deformed workpiece and the rocking angle of the grinding unit is mathematically calculated using trigonometric functions such as the sine theorem and the cosine theorem. Thus, an outer peripheral shape specifying formula that determines the outer peripheral grinding shape of the deformed workpiece is calculated in advance. The entire grinding unit with the headstock and tailstock mounted on the table can swing about a swinging shaft disposed almost directly below the shaft center and parallel to the main shaft axis. In a state where it is arranged, that is, in a state where the irregularly shaped workpiece is arranged so as to be able to oscillate about the oscillation axis arranged almost immediately below the axis of the main shaft, the grinding unit is based on the outer peripheral shape specifying formula. By rotating the deformed workpiece continuously while swinging the outer periphery of the deformed workpiece, the outer periphery of the deformed workpiece is ground to the shape defined by the outer peripheral shape specifying formula. Since the above calculation can be performed mathematically only by using a trigonometric function, it is compared with calculating the position of the back and forth movement of the grindstone table with respect to the rotation angle of the deformed workpiece in order to carry out the grinding method of Patent Document 1. This is easy to do. That is, since the grinding (machining) program for carrying out the invention of claim 1 can be created by a mathematical method using a trigonometric function, the creation thereof is relatively easy for those skilled in the art of the invention of claim 1. Can be done.
In the invention of claim 1, the deformed workpiece to be ground has a polygonal cross section, and has the same surface portion as the number of corners of the polygon, and the deformed workpiece is moved while swinging the axis of the deformed workpiece. The method is different from the swing grinding method for deformed workpieces having a non-circular cross-section in that each surface portion is rotated within an angle corresponding to the central angle of each surface portion, and the surface portion is sequentially ground. In the invention of claim 1 as well, the outer periphery defining the relationship between the rotation angle from the reference position of each surface portion of the deformed workpiece having a polygonal cross section and the swing angle of the deformed workpiece, similarly to the deformed workpiece having a non-circular cross section. The shape specifying formula is calculated and calculated mathematically using a trigonometric function.

The invention of claim 2 is a rocking-type grinding machine for carrying out the rocking grinding method for deformed workpieces according to claim 1, comprising a spindle servomotor for driving and rotating the spindle, comprising a grinding unit which is pivotably supported around a pivot axis, and a swing servo motor for swinging the grinding unit about the said pivot axis, servo motor the swing Is configured with a pair of output shafts facing each other and arranged on the same axis, so that the axis of each oscillation servomotor is an oscillation axis, and the pair of oscillation servos Each motor has a speed reducer having an input shaft and an output shaft on the drive shaft center, and the drive shaft of each swing servo motor is connected to the input shaft of each speed reducer and arranged between the speed reducers. Both ends of the mounted grinding unit attachment Connected to the output shaft of each speed reducer, the grinding unit is integrally attached to the grinding unit mounting body, and the rotation of the drive shaft of each oscillation servo motor is decelerated to rotate the grinding unit mounting body. Thus, the grinding unit is configured to swing about the axis of each swing servomotor, and the rotation angle from the reference position of the deformed workpiece and the swing angle of the grinding unit specify the outer peripheral shape. In order to maintain the relationship specified by the equation, the spindle and swing servomotors are synchronously rotated and the deformed workpiece is ground to the shape specified by the outer peripheral shape specification equation. It is characterized by.

According to the invention of claim 2, the outer peripheral shape specifying which defines a rotation angle from the reference position of deformed workpiece polygonal section, to identify the relationship between the swing angle of the grinding unit a periphery grinding shape of the deformed workpiece so as to satisfy the formula, and a servo motor spindle for rotating the spindle of the grinding unit, is synchronized with the oscillating servo motor for swinging to the grinding unit about the pivot axis, a polygonal section The outer periphery of the deformed workpiece can be ground to the shape specified by the outer peripheral shape specifying formula by rotating it within an angle corresponding to the center angle of each polygonal surface portion of the deformed workpiece. In other words, two types of servo motors for spindles that drive and rotate the irregularly shaped workpiece and oscillation servomotors that cause the grinding unit to oscillate so that the position of the grinding point of the irregularly shaped workpiece becomes the position specified by the outer peripheral shape specification formula. By rotating the servo motor synchronously, it is possible to grind the deformed workpiece without using the master workpiece and without moving the grindstone back and forth.

  In addition, the swing servo motor is composed of a pair of output shafts facing each other on the same axis, and the rotation of the drive shaft of each swing servo motor is decelerated by each speed reducer, Is configured to rock the grinding unit mounting body integrally connected to the output shaft of each reduction gear, that is, the grinding unit. Thus, since the grinding unit is configured to swing by being driven from both sides along the axial direction, the torsional force does not act on the grinding unit at the time of swinging. As a result, even during the oscillation of the grinding unit, the grinding unit can maintain the same grinding accuracy as when it is stationary.

  In addition, the shaft centers of a total of four rotating devices of a pair of oscillating servomotors arranged with the drive shafts facing each other and each reduction gear corresponding to the pair of oscillating servomotors are all on the same axis. Since the pair of opposed servo motors and the grinding unit mounting body are substantially directly connected to each other, the accuracy of the position of the oscillation axis of the grinding unit and the oscillation angle are improved. This also contributes to maintaining the grinding accuracy of deformed workpieces.

The invention according to claim 3 is an outer peripheral surface which is a surface to be ground while continuously rotating the deformed workpiece gripped by the chuck so that the rotation axis of the deformed workpiece having a non-circular cross section is concentric with the axis of the main shaft. in grinding, the whole of the grinding unit headstock and tailstock is mounted on the table, almost around the axis and pivot axis disposed parallel to the said main shaft just below the axis of the main shaft An outer peripheral shape specifying formula that specifies the outer peripheral grinding shape of the deformed workpiece by specifying the relationship between the rotation angle of the deformed workpiece from the reference position and the swing angle of the grinding unit is calculated in advance. Then, based on the outer peripheral shape specification formula, the outer peripheral surface was specified by the outer peripheral shape specification formula by continuously rotating the deformed workpiece while swinging the grinding unit around the swing axis. Of irregularly shaped workpieces to be ground An apparatus for carrying out the dynamic grinding method, include a servo motor spindle for rotationally driving the spindle, a grinding unit which is swingably supported around the pivot axis, the grinding A swing servomotor for swinging the unit around the swing axis, and the swing servomotor is composed of a pair of opposed output shafts arranged on the same axis. Thus, the axis of each oscillation servomotor is an oscillation axis, and the pair of oscillation servomotors each include a reduction gear having an input shaft and an output shaft on the drive axis, The drive shaft of each oscillating servo motor is connected to the input shaft of each speed reducer, and both ends of the grinding unit mounting body arranged between the speed reducers are connected to the output shaft of each speed reducer. The grinding unit mounting body The grinding unit is mounted integrally, the rotation of the drive shaft of each oscillating servo motor is decelerated, and the grinding unit mounting body is rotated, so that the grinding unit rotates the axis of each oscillating servo motor. The main shaft and the rotation angle so that the rotation angle from the reference position of the deformed workpiece and the rocking angle of the grinding unit maintain the relationship specified by the outer peripheral shape specifying formula. Each of the swing servomotors is rotated synchronously so that the deformed workpiece is ground to a shape specified by the outer peripheral shape specification formula .

The invention of claim 3 differs from the invention of claim 2 in that a deformed workpiece having a non-circular cross section is an object to be ground, and is different only in that the spindle of the grinding unit is continuously rotated. 2 is the same as the odd-shaped workpiece having a polygonal cross section.

  The rocking grinding method according to the present invention mathematically calculates the relationship between the rotation angle of the deformed workpiece from the reference position and the rocking angle of the grinding unit using trigonometric functions such as the sine theorem and the cosine theorem. Thus, an outer peripheral shape specifying formula that defines the outer peripheral grinding shape of the deformed workpiece is calculated in advance. The entire grinding unit with the headstock and tailstock mounted on the table can swing about a swinging shaft disposed almost directly below the shaft center and parallel to the main shaft axis. In a state where it is arranged, that is, in a state where the irregularly shaped workpiece is arranged so as to be able to oscillate about the oscillation axis arranged almost immediately below the axis of the main shaft, the grinding unit is based on the outer peripheral shape specifying formula. In the case of a deformed workpiece having a non-circular cross section, the deformed workpiece is continuously rotated, and in the case of a deformed workpiece having a polygonal cross section, the deformed workpiece is rotated within one rotation. By grinding each surface portion sequentially, the outer periphery of the deformed workpiece is ground to the shape defined by the outer periphery shape specification formula, regardless of whether the profile is non-circular or polygonal. Since the above calculation can be performed mathematically only by using a trigonometric function, it is compared with calculating the position of the back and forth movement of the grindstone table with respect to the rotation angle of the deformed workpiece in order to carry out the grinding method of Patent Document 1. This is easy to do. That is, since the grinding (machining) program for carrying out the present invention can be created by a mathematical method using a trigonometric function, the creation thereof can be relatively easily performed by those skilled in the art of the invention of claim 1.

1 is a front view of a rocking grinder according to the present invention. It is a side view similarly. 1 is a partially enlarged view (partially enlarged sectional view showing a state in which the drive shaft 14 of the servo motor M ₁ for swinging and the support shaft portion 4 at one end of the grinding unit attachment body A are connected via the speed reducer R ₁ . ). (A), (b) is a diagram showing a sequence of grinding profiled workpiece W _1. (C), (d) is a diagram showing the sequence of grinding profiled workpiece W _1. (E), (f) are diagrams showing the sequence of grinding profiled workpiece W _1. FIG. 6 is an overall view showing the relationship between the rotation angle (θx) of the odd-shaped workpiece W ₁ and the swing angle (θy) of the headstock B. FIG. 5 is a partially enlarged view showing the relationship between the grinding point P ′ _{2 at} the virtual position of the deformed workpiece W ₁ and the two grinding points P ₁ and P ₃ before and after the grinding point P ′ ₂ and the rotational axis C′w ₁ of the deformed workpiece W ₁ . FIG. FIG. 6 is a partially enlarged view of FIG. 5 showing the relationship between the rotational axis C′w ₁ , the grinding point P ′ _2, and the rotational axis C ₃ of the grindstone G of the deformed workpiece W _{1 at} the virtual position of the deformed workpiece W ₁ . Each axis Cw ₁ , C′w _{1 of the} deformed workpiece W _{1 at} the virtual position and the actual position of the deformed workpiece W ₁ , the swing axis C ₀ of the headstock B, and the axis C _{3 of the} grindstone G It is the elements on larger scale of FIG. 5 which show the relationship of these. FIG. 5 shows the relationship among the rotational axis Cw _{1 of the} deformed workpiece W _{1 at} the actual position of the deformed workpiece W ₁ , the swing axis C ₀ of the headstock B, and the axis C ₃ of the grindstone G. It is an enlarged view. Is a diagram for determining the virtual rotation angle of the grinding point P _'2 profiled workpiece W ₁ in a virtual position (α-γ). When the deformed workpiece W ₁ arranged at the virtual position is rotated by an angle (β) around the axis C ₃ of the grindstone G and returned to the actual grinding position, the rotation axis Cw of the deformed workpiece W ₁ is returned. rotation angle of the profiled workpiece W ₁ to the arrangement position in the ₁ start state is a diagram showing that becomes (α-γ + β). FIG. 12 is a diagram schematically showing a state in which a triangle P ′ ₂ C ₃ C′w ₁ in the state of FIG. 11 is rotated by an angle (β). In the state of FIG. 11, the deformed workpiece W ₁ at the start position arranged with the long axis F perpendicular to the swing position is rotated clockwise by the swing angle (θy), and the grinding point P ₂ is set from the start position. rotation angle of the profiled workpiece W ₁ until the grinding ([theta] x) is a diagram showing that the (α-β + γ-θy ). It is a graph showing the relationship between the rotational angle of the profiled workpiece W ₁ and ([theta] x) and swing angle of the headstock B ([theta] y) _{[(θy) = f 1 (θx} ) ]. (A), (b) is a diagram showing the grinding principle of the eccentric workpiece W _2. It is a diagram illustrating a grinding principle of square cross section of the profiled workpiece W _3. (A), (b) is a plan view of the oscillating grinding machine using a master workpiece W _0, and a left side view.

First, an oscillating grinder for carrying out the oscillating grinding method of the present invention will be described with reference to FIGS. Figure 1 is a front view of the oscillating grinding machine according to the present invention, FIG. 2 is a likewise a side view, FIG. 3 is a partial enlarged view of FIG. 1 (a swing servomotor M ₁ drive shaft 14 And a support shaft portion 4 at one end of the grinding unit attachment body A is a partially enlarged cross-sectional view showing a state where the support shaft portion 4 is connected via the reduction gear R ₁ . A pair of second bases 2 are fixed to the first base 1 at a predetermined interval along the axis C ₁ of the main shaft S, and a grinding unit is attached to the support 3 fixed to each second base 2. Support shaft portions 4 at both ends along the axis C ₁ of the main shaft S in the mounting body A are rotatably supported via a plurality of bearings 5. For this reason, the grinding unit attachment body A is rotatably supported by the support body 3 via the plurality of bearings 5 at the support shaft portions 4 at both ends thereof.

A cylindrical casing 8 is integrally attached to the outer end surface of the support 3 via a bolt 6 and its own fitting portion 7, and the bolt 11 and its own fitting are fitted to the outer end surface of the casing 8. A cylindrical mounting portion 13 of the oscillating servo motor M ₁ is integrally attached via the joint portion 12. The rotational axis of the oscillation servo motor M ₁ exists on the extension of the rotational axis of the grinding unit attachment A. That is, a pair of oscillating servo motors M ₁ are disposed opposite to each other with the grinding unit attachment body A interposed therebetween, and the rotation axis of the pair of oscillating servo motors M _{1 and} the rotation axis of the grinding unit attachment body A are arranged. Are arranged horizontally so as to be concentric. The axis of the pair of swing servomotors M ₁ arranged concentrically with the rotation axis of the grinding unit attachment body A is a swing axis C ₀ described later.

The drive shaft 14 of the oscillating servo motor M ₁ is connected to the support shaft portion 4 of the grinding unit attachment body A via a reduction gear R ₁ composed of a harmonic drive (registered trademark) mechanism. That is, the rotation of each drive shaft 14 of the pair of swing servo motors M ₁ is decelerated by each reduction gear R ₁ to drive the support shaft portions 4 at both ends of the grinding unit attachment body A. When the grinding unit attachment body A is driven and rotated, the grinding unit GU that is integrally attached to the upper surface of the grinding unit attachment body A has a grinding accuracy so that no torsional force acts on the grinding unit attachment body A. It is trying not to decline.

The speed reducer R ₁ is a flex spline having a web generator 16 in which a thin bearing 15 is fitted on the outer periphery of an elliptical cam and a thin cup-shaped metal elastic body, and teeth are carved on the outer periphery of the opening. 17 and a circular spline 18 in which teeth that mesh with the teeth of the flex spline 17 are formed on the inner periphery, and a swing servomotor M _{1 is provided at} the cam portion of the web generator 16. Of the circular spline 18 is fixed to the end surface of the support shaft portion 4 of the grinding unit mounting body A via a plurality of bolts 19, and the circular spline 18 is It is fixed to the end surface of the casing 8 via a plurality of bolts 20. Since the number of teeth formed on the outer periphery of the flex spline 17 is usually two less than the number of blades formed on the inner periphery of the circular spline 18, the flex of the web generator 16 causes the flex spline 17 to rotate. When the inside of the circular spline 18 is rotated while the spline 17 is elastically deformed, the rotation of the web generator 16 on the input side is decelerated and transmitted to the flex spline 17 on the output side due to the difference in the number of teeth. The The shaft centers of the web generator 16 connected to the input side and the flex spline 17 connected to the output side are concentric with each other and exist on the shaft center of the servo motor M ₁ for oscillation. The normal reduction ratio of the reduction gear R ₁ composed of a harmonic drive (registered trademark) mechanism is (1/100).

On the upper surface side of the grinding unit attachment A, the grinding unit GU is integrally attached, and in the state where the grinding unit GU is horizontally disposed, the rocking shaft is directly below the axis C ₁ of the spindle S of the grinding unit GU. A heart C ₀ is placed.

The oscillating servo motor M ₁ includes an encoder (not shown) that can detect the rotation angle of the drive shaft 14, and the number of generated pulses per rotation is (1.6 × 10 ⁷ ). Since the grinding unit mounting body A is rotated by being reduced by (1/100) by the reduction gear R ₁ , the number of pulses generated by the oscillation servo motor M ₁ for one rotation of the grinding unit mounting body A is ( 1.6 × 10 ⁹ ), and the accuracy of the rocking angle of the grinding unit mounting body A is considerably high.

Grinding unit GU mounted integrally on the upper surface of the grinding unit mount A includes a headstock B fixed to the table 21, and face the headstock B, along the direction of the axis C ₁ of the spindle S It consists of a tailstock D slidably arranged. The rotation of the pair of servo motors M ₁ is decelerated by each reduction gear R ₁ and the grinding unit mounting body A is driven and rotated, and the casing 22 of the headstock B is connected to the casing 22 via a plurality of bearings 23. The main shaft S that is rotatably supported is driven by the rotation of the main shaft servo motor M ₂ disposed on the rear end side of the main shaft S being decelerated by a speed reducer R _{2 including} a harmonic drive (registered trademark) mechanism. It is rotated. The main shaft servomotor M ₂ , the shaft centers of the input side and output side members of the reduction gear R ₂ (the web generator 16 connected to the input side, and the flex spline 17 connected to the output side) Are arranged on the axis C _{1 of the} main shaft S. The reduction gear R ₂ is different from the reduction gear R ₁ only in size and has the same structure.

The tailstock D has the same configuration as the tailstock of a normal grinder, and the spindles B and the spindles 24 and 25 of the tailstock D support the deformed workpiece W ₁ at both centers, and by the dog 26. When the deformed workpiece W ₁ is rotated integrally with the spindle S and the deformed workpiece W ₁ is ground with the grindstone G that advances and retreats in the horizontal direction perpendicular to the axis C ₁ of the spindle S, normal grinding is performed. It is the same as the board. The grindstone G is supported by a grindstone table (not shown) so as to advance and retreat with respect to the main shaft base B along a direction orthogonal to the axis C ₁ of the main shaft base B.

Hereinafter, a method for calculating the above-described outer peripheral shape specifying formula will be described. In the present invention, as shown in FIG. 4-A to Figure 4-C the rotation, together with the profiled workpiece W ₁ is rotated about the spindle axis C ₁ in the counterclockwise direction, the grinding wheel G is counterclockwise and, when grinding the profiled workpiece W _1, the spindle axis C _1, while swinging about a pivot axis C _0, the deformed workpiece W ₁ is ground. Then, the line segment connecting the rotational angle ([theta] x) relative to the spindle axis C ₁ of the profiled workpiece W _1, a vertical line passing through the pivot axis C _0, and the spindle axis C ₁ the pivot axis C ₀ L The outer peripheral shape of the deformed workpiece W ₁ is specified by the relationship with the rocking angle (θy) formed with ₁₂ . Therefore, the swing angle (θy) becomes a function of the rotation angle (θx) of the deformed workpiece W ₁ , and this function [θy = f ₁ (θx)] can be obtained. The calculation method of this function will be described below. . Incidentally, in FIG. 4-A to Figure 4-C, on the illustrated relationship, the axis C ₃ of the grinding wheel G is is shown in proximity to the outer peripheral surface of the grinding wheel G than the actual position.

Profiled workpiece W _1, the central angle of 180 ° portion with respect to a rotation axis Cw ₁ is a perfect circle length from the rotation axis Cw ₁ to the outer periphery (radius) is equal to the remaining 180 ° This part is a non-perfect circle whose length from the rotation axis Cw ₁ to the outer circumference changes, and has an oval shape as a whole. Therefore, when the deformed work W ₁ is set on the spindles 24 and 25 of the headstock B and the tailstock D and rotated, the round part of the deformed work W ₁ protrudes most of the grindstone G. A portion (a portion intersecting with a horizontal plane passing through the axis C ₃ of the grindstone G in the grindstone G and hereinafter referred to as “most projecting portion Ga”) is ground, but a non-circular portion is the most projecting portion. Grinding is performed at a position shifted to either above or below Ga. In the deformed workpiece W _{1 of} this example, the distance from the rotational axis Cw ₁ to the outer periphery in the non-circular part in FIGS. 4-A (b) and 4-B (d) gradually decreases, and gradually increases. The portions are ground below and above the most protruding portion Ga of the grindstone G, respectively.

Here, in calculating the function [θy = f ₁ (θx)], in the case of grinding a particular grinding point P ₂ of the non-circular portion of the profiled workpiece W _1, the deformed workpiece W ₁ from the reference position rotation angle ([theta] x) and the swing angle of the main shaft axis C ₁ of the ([theta] y) is calculated, the rotational angle of the profiled workpiece W ₁ of a number as possible in the non-circular portion of the profiled workpiece W ₁ of different grinding point P ₂ What is necessary is just to calculate (θx) and the swing angle (θy) of the spindle axis C ₁ . In the deformed workpiece W _{1 of} this example, a straight line connecting two points where the perfect circle part and the non-perfect circle part intersect is referred to as a short axis E, and an axis line orthogonal to the short axis E and passing through the rotation axis Cw ₁ is used. This is called the long axis F. The rotation angle (θx) of the deformed workpiece W ₁ is based on the short axis E. Profiled workpiece W grinding point P ₂ of the outer circumference of the non-circular portion of ₁ is specified. When calculating the rotation angle (θx) of the deformed workpiece W _{1 at} the specific grinding point P ₂ of the deformed workpiece W ₁ and the swing angle (θy) of the spindle axis C ₁ , the true outer circumference of the deformed workpiece W ₁ is calculated. In order to approach the shape, the following calculation is performed based on two different grinding points P ₁ and P ₃ before and after the grinding point P ₂ .

5 to 9 are diagrams for calculating the rotation angle (θx) of the deformed workpiece W ₁ and the swing angle (θy) of the axis C ₁ of the headstock B. FIG. 5 is an overall view. FIG. 6 to FIG. 9 are enlarged views of each part of FIG. As shown in FIG. 5, the grinding point P ₂ of the deformed workpiece W ₁ is disposed below the most projecting portion Ga of the grindstone G, and the grinding point P ₂ is the most projecting portion of the grindstone G for convenience of calculation. The deformed workpiece W ₁ is virtually rotated about the axis C _{3 of the} grindstone so as to be positioned at Ga. This state is shown by a solid line in FIG. Further, when the grinding point P ₂ of the deformed workpiece W ₁ is arranged at the virtual position, the position of the grinding point is indicated as P ′ ₂ in order to distinguish it from the actual grinding point P _2. Since the points P ₁ and P ₃ before and after P ₂ are complicated to display, they are displayed as they are without “′”. 5 to 9, CL ₃₁ indicates an arc passing through the rotational axis Cw ₁ of the deformed workpiece W _{1 at} the grinding position with the axis C ₃ of the grindstone G as the center, and CL ₃₂ is the swing axis. An arc passing through the rotation axis Cw ₁ of the deformed workpiece W ₁ with the center C ₀ as the center is shown. The axis C′w ₁ of the deformed workpiece W _{1 at} the virtual position is located on the arc CL ₃₁ . L ₂₄ indicates a perpendicular line passing through the swing axis C ₀ .

First, referring to FIG. 5 and FIG. 6, the rotation axis C′w ₁ of the deformed workpiece W ₁ arranged at the virtual position is lowered with respect to the horizontal line L ₂₁ passing through the axis C ₃ of the grindstone G. When the perpendicular line is a line segment L ₇ , the cosine theorem is used to form the line segment L ₇ and a line segment L ₂ connecting the rotational axis C′w ₁ of the virtual position and the grinding point P ′ _2. Find the angle (α). A calculation formula for obtaining this angle (α) is shown below. Here, L ₁ , L _{3 to} L ₆ and θ _{1 to} θ ₇ are as follows. L ₂₂ indicates a line (vertical line) perpendicular to a horizontal line passing through the grinding center P ₃ of the grinding wheel G through the grinding point P ′ ₂ of the deformed workpiece W _{1 at} the virtual position.
L _1: the line segment L ₃ connecting the rotation axis C'w ₁ and the grinding point P ₁ of the profiled workpiece W _1: the line segment L ₄ connecting the rotation axis C'w ₁ and the grinding point P ₃ of the profiled workpiece W ₁ : Line segment L ₅ connecting the grinding point P ′ ₂ and the grinding point P ₃ : line segment L ₆ connecting the grinding point P ₁ and the grinding point P ′ ₂ : line segment θ ₁ connecting the grinding point P ₁ and the grinding point P ₃ : Angle θ ₂ formed by line segment L ₂ and line segment L ₃ : Angle formed by line segment L ₁ and line segment L ₂ θ ₃ : Angle formed by line segment L ₂ and line segment L ₄ θ ₄ : Line segment L ₂ a line segment L ₅ of the angle theta _5: line L ₄ and the line segment angle between L ₆ theta _6: line L ₄ and the horizontal line L ₂₁ angle theta _7: forming line segment L ₂ and the horizontal line L ₂₁ angle

6, the triangle P 'vertices C'w ₁ of ₂ P ₃ C'w ₁ part, and the triangle P ₁ P' respectively Applying the law of cosines to the vertex C'w ₁ of ₂ C'w _1, below Thus, the line segments L ₄ and L ₅ are obtained.
L ₄ ² = L ₂ ² + L ₃ ² −2L ₂ L ₃ cos θ ₁ , L ₅ ² = L ₁ ² + L ₂ ² −2L ₁ L ₂ cos θ _2, and L ₄ and L ₅ are obtained.
L ₄ = (L ₂ ² + L ₃ ² -2L ₂ L ₃ cos θ ₁ ) ^1/2
L ₅ = (L ₁ ² + L ₂ ² -2L ₁ L ₂ cos θ ₂ ) ^1/2
The angle θ ₃ is obtained by applying the cosine theorem to the vertex P ′ ₂ of the triangle P ′ ₂ P ₃ C′w ₁ ,
From L ₃ ² = L ₂ ² + L ₄ ² −2L ₂ L ₄ cos θ ₃ , cos θ ₃ = (L ₂ ² + L ₄ ² −L ₃ ² ) / 2L ₂ L _4, and the angle θ ₃ is Street.
θ ₃ = cos ⁻¹ [(L ₂ ² + L ₄ ² −L ₃ ² ) / 2L ₂ L ₄ ] Equation (1)
Similarly, the angle θ ₄ is obtained by applying the cosine theorem to the vertex P ′ ₂ of the triangle P ₁ P ′ ₂ C′w ₁ ,
From L ₁ ² = L ₂ ² + L ₅ ² −2L ₂ L ₅ cos θ ₄ , cos θ ₄ = (L ₂ ² + L ₅ ² −L ₁ ² ) / 2L ₂ L ₅
θ ₄ = cos ⁻¹ [(L ₂ ² + L ₅ ² −L ₁ ² ) / 2L ₂ L ₅ ].

Also, applying the cosine theorem to the vertex P ′ ₂ of the triangle P ₁ P ′ ₂ P ₃ ,
From L ₆ ² = L ₄ ² + L ₅ ² −2L ₄ L ₅ cos (θ ₃ + θ ₄ ), the length of the line segment L ₆ is obtained as follows.
L ₆ = [L ₄ ² + L ₅ ² −2L ₄ L ₅ cos (θ ₃ + θ ₄ )] ^1/2
Applying the cosine theorem to the vertex P ₃ of the triangle P ₁ P ′ ₂ P ₃ ,
From L ₅ ² = L ₄ ² + L ₆ ² -2L ₄ L ₆ cos θ ₅ ,
cos θ ₅ = (L ₄ ² + L ₆ ² −L ₅ ² ) / 2L ₄ L ₆
θ ₅ = cos ⁻¹ [(L ₄ ² + L ₆ ² −L ₅ ² ) / 2L ₄ L ₆ ] Equation (2)
It becomes.

Since the following equations (3) and (4) hold, θ ₆ = 90 ° −θ ₅ ... Equation (3)
θ ₇ = θ ₆ −θ ₃・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Equation (4)
Since the angles (θ ₃ ), (θ ₅ ), (θ ₆ ), and (θ ₇ ) are obtained from (Equation 1) to (Equation 4), the target angle (α) is obtained from the equation (5). It becomes.
α = 180 ° −90 ° −θ ₇・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Formula (5)

Next, referring to FIG. 8, a line segment L ₈ connecting the axis C ₃ of the grindstone G and the workpiece rotation axis Cw _{1 at} the instantaneous grinding position of the grinding point P ₂ , and the axis C of the grindstone G An angle (β) formed by a line segment L ′ ₈ connecting ₃ and the workpiece rotation axis C′w _{1 at the} virtual position is obtained. In FIG. 7, the angle formed by the horizontal line L ₂₁ and the line segment L ′ ₈ connecting the axis C ₃ of the grindstone G and the workpiece rotation axis C′w _{1 at the} virtual position is defined as (θ ₈ ). Assuming that the angle formed by L ₂₁ and the line segment L ₈ connecting the axis C ₃ of the grindstone G and the workpiece rotation axis Cw _{1 at} the moment of grinding at the grinding point P ₂ is (θ ₉ ), The angle (β) is the sum of the angle (θ ₈ ) and the angle (θ ₉ ).
β = θ ₈ + θ ₉・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Equation (6)

In FIG. 7, the length of a line segment L ₉ connecting the axis C ₃ of the grindstone G and the grinding point P ′ ₂ of the deformed workpiece W _{1 at} the virtual position is the same as the radius r of the grindstone, and the angle (θ ₈ ) is obtained as follows.
First, applying the cosine theorem to the vertex P ′ ₂ of the triangle P ′ ₂ C ₃ C′w ₁ ,
L ′ ₈ ² = L ₂ ² + L ₉ ² −2L ₂ L ₉ cos (180−θ ₇ ), and the length of the line segment L ′ ₈ is as follows.
L ′ ₈ = [L ₂ ² + L ₉ ² −2L ₂ L ₉ cos (180−θ ₇ )] ^1/2
Applying the cosine theorem to the vertex C ₃ of the triangle P ′ ₂ C ₃ C′w ₁ ,
L ₂ ² = L ₉ ² + L ′ ₈ ² −2L ₉ L ′ ₈ cos θ ₈
cos θ ₈ = (L ₉ ² + L ′ ₈ ² −L ₂ ² ) / 2L ₉ L ′ ₈
θ ₈ = cos ⁻¹ [(L ₉ ² + L ′ ₈ ² −L ₂ ² ) / 2L ₉ L ′ ₈ ]... (7)
It becomes.

Next, in FIG. 8, a perpendicular is drawn from the swing axis C ₀ to the vertical line L ₂₃ passing through the axis C ₃ of the grindstone G, and the intersection of the perpendicular and the vertical line L ₂₃ is defined as Q. If the intersection of the line segment C ₀ Q and the vertical line L ₂₂ is J , the length of the line segment C ₀ Q is equal to the line segment L ₁₀ equal to the radius r of the grindstone G and the round part of the deformed workpiece W _1. Is the sum of the line segment L ₁₁ equal to the radius of. L ₁₂ is a line segment connecting the oscillation axis C ₀ and the workpiece rotation axis Cw _{1 at} the moment of grinding at the grinding point P ₂ , and L ₁₃ is the axis C ₃ of the grindstone G. This is a line segment connecting the swing axis C ₀ . A line segment L ₁₃ connecting the axis C ₃ of the grindstone G and the pivot axis C _0, and a line segment L ₁₄ connecting the axis C ₃ of the grindstone G and the point Q (the length of the line segment L ₁₂ is equal). ) Is (θ ₁₀ ), and the intersection angle between the line segment L ₁₃ and the horizontal line L ₂₁ is (θ ₁₁ ), the angle (θ ₁₁ ) is as follows.

tan θ ₁₀ = (L ₁₀ + L ₁₁ ) / L ₁₄
θ ₁₀ = tan ⁻¹ [(L ₁₀ + L ₁₁ ) / L ₁₄ ] (8)
θ ₁₁ = 90 ° −θ ₁₀・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Equation (9)

Further, the line segment L ₁₃ becomes L ₁₃ = L ₁₄ / cos θ ₁₀ from (L ₁₄ = L ₁₃ cos θ ₁₀ ).
Further, the intersection angle (θ ₁₂ ) between the line segment L ₈ and the line segment L ₁₃ is obtained as follows by applying the cosine theorem to the vertex C ₃ of the triangle C ₀ C ₃ Cw ₁ .
L ₁₂ ² = L ₈ ² + L ₁₃ ² -2L ₈ L ₁₃ cos θ ₁₂
cos θ ₁₂ = (L ₈ ² + L ₁₃ ² −L ₁₂ ² ) / 2L ₈ L ₁₃
θ ₁₂ = cos ⁻¹ [(L ₈ ² + L ₁₃ ² −L ₁₂ ² ) / 2L ₈ L ₁₃ ] · Expression (10)

θ ₉ = θ ₁₁ −θ ₁₂・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Equation (11)
Therefore, the objective β (= θ ₈ + θ ₉ ) is obtained from the equations (7) to (11).

Next, referring to FIG. 9, the swing angle (θy) is calculated. In the triangle C ₀ C ₃ Q, since the angle (θ ₁₀ ) formed by the line segment C ₀ C ₃ and the line segment C ₃ Q has already been obtained by the equation (8), the line segment C ₀ Q and the line segment C The formation angle (θ ₁₃ ) with ₀ C ₃ is as follows.
θ ₁₃ = 180 ° −90 ° −θ ₁₀ (12)
The angle (θ ₁₄ ) formed by the line segment C ₀ C ₃ and the vertical line L ₂₄ passing through the swing axis C ₀ is as follows.
θ ₁₄ = 90 ° −θ ₁₃・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Equation (13)

Further, in order to obtain the angle (θ ₁₅ ) formed by the line segment C ₀ Cw ₁ and the line segment C ₀ C ₃ , the two line segments L ₈ and L ₁₂ of the triangle C ₀ C ₃ Cw ₁ are obtained. By applying the sine theorem, (L ₈ / sin θ ₁₅ = L ₁₂ / sin θ ₁₂ ) and (sin θ ₁₅ = L ₈ sin θ ₁₂ / L ₁₂ ) are obtained, and the angle (θ ₁₅ ) is as follows. .
θ ₁₅ = sin ⁻¹ (L ₈ sin θ ₁₂ / L ₁₂ ) (14)
From the equations (13) and (14), the swing angle (θy) is as follows.
θy = θ ₁₅ −θ ₁₄・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Equation (15)

Next, with reference to FIGS. 10 to 13, obtaining the swing angle ([theta] y) rotation of the profiled workpiece W ₁ with respect to the angle at the time of grinding the grinding point P _'2 profiled workpiece W ₁ ([theta] x). FIG. 10 is a diagram for obtaining a virtual rotation angle (α−γ) of the grinding point P ₂ . In FIG. 10, at the virtual position of the deformed workpiece W ₁ , the angle (α) is the line segment L ₇ (the line segment included in the long axis F of the deformed workpiece W ₁ with the long axis F perpendicular to the virtual position). , An angle formed by the rotational axis C′w ₁ of the virtual position and the line segment L ₂ connecting the grinding point P ′ ₂ . The angle (γ) is an angle formed by the long axis F of the deformed workpiece W _{1 at} the virtual position and the line segment L ₂ . 10, there is shown profiled workpiece W ₁ arranged to the start position in the virtual position by a one-dot chain line, deformed workpiece W ₁ that virtual ground virtual grinding point P _'2 are virtual profiled workpiece W ₁ This means that the position is rotated by (α−γ) with respect to the start position. That is, the virtual rotation angle of the deformed workpiece W ₁ virtually cutting the virtual grinding point P ′ ₂ is (α−γ).

FIG. 11 shows that when the deformed workpiece W ₁ arranged at the virtual position is rotated by an angle (β) around the axis C ₃ of the grindstone G and returned to the grinding position at the moment of the grinding point P ₂ , rotation angle of the profiled workpiece W ₁ to the location that is positioned in the start state to the rotation axis Cw ₁ profiled workpiece W ₁ is a diagram showing that becomes (α-γ + β), FIG. 12, the state of FIG. 11 FIG. 6 is a diagram schematically showing a state in which a triangle P ′ ₂ C ₃ C′w ₁ is rotated by an angle (β). In FIG. 11, the intersection angle between the line segment L ₂ and the line segment L ′ ₈ is (δ), and the intersection point between the line segment L ₇ and the straight line (horizontal line) L ₂₁ is V (see FIGS. 11 and 12). In the triangle VC′w ₁ P ′ ₂ , [α + (δ + θ ₈ ) + 90 ° = 180 °] is established, and the following equation is established.
α + δ + θ ₈ = 90 ° ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Formula (16)

On the other hand, in FIG. 12, the angles θ ₈ , θ ₉ , α, and δ are as illustrated. In FIG. 12, L ′ ₂₁ is a straight line generated by rotating a horizontal line L ₂₁ passing through the axis C ₃ of the grindstone G by an angle (β) around the axis C ₃ , 'and _21, the intersection of the perpendicular L ₂₅ passing through the rotation axis Cw ₁ profiled workpiece W _1, which is ground by the grinding point P ₂ is T, the straight line L from the rotation axis Cw _1' L beat ₂₁ Let U be the intersection of the perpendicular and the straight line L ′ ₂₁ . Further, the straight line L ₂₆ passes through the rotation axis Cw ₁ profiled workpiece W _1, a parallel straight line (auxiliary line) to the horizontal line L _21. The angle formed by the intersection of the straight line L ₈ and the straight line L ₂₆ is equal to the intersection angle (θ ₉ ) between the straight line L ₈ and the horizontal line L _21, and is an unknown line segment Cw ₁ T and line segment Cw. Assuming that the angle formed with ₁ U is (θ ₁₆ ), the straight line L ₂₅ and the straight line L ₂₆ are orthogonal to each other, and the following expression is established.
θ ₁₆ + α + δ−θ ₉ = 90 ° ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Equation (17)

From the equations (16) and (17), the following relationship is established.
α + δ + θ ₈ = θ ₁₆ + α + δ−θ ₉ = 90 °... (18)
From the equations (6) and (18), the angle (θ ₁₆ ) is derived as follows.
θ ₁₆ = θ ₈ + θ ₉ = β (19)

As a result, as is apparent from FIG. 11, the rotation angle θ ′ (x) of the deformed workpiece W _{1 with} respect to the perpendicular passing through the rotation axis Cw ₁ of the deformed workpiece W _{1 at} the moment when the grinding point P ₂ is being ground is , the virtual rotation angle of the profiled workpiece W ₁ that virtual ground virtual grinding point _{P '2 (α-γ)} , the angle of returning from a virtual position of the profiled workpiece W ₁ until the moment grinding position of the grinding point P ₂ (beta) The angle is added.
θ ′ (x) = (α−γ + β) (20)

As is apparent from FIG. 13, the rotation angle θ ′ (x) is based on the normal line passing through the rotation axis Cw ₁ of the deformed workpiece W _{1 at} the moment when the grinding point P ₂ is ground. a rotational angle of the workpiece W _1, profiled workpiece W _1, since the ground while swinging about the pivot axis C _0, the moment of grinding the grinding point P ₂ are the profiled workpiece W ₁ Must be based on a line segment L ₁₂ connecting the rotation axis Cw ₁ and the oscillation axis C ₀ (the deformed workpiece W _{1 serving as} a reference for the rotation angle is indicated by a two-dot chain line in FIG. 13). The line segment L ₁₂ is swung by an angle (θy) with respect to the start position of the deformed workpiece W _{1 in which} the long axis F is vertical. Therefore, the value obtained by subtracting the swing angle (θy) from the above-described rotation angle θ ′ (x) is the true rotation angle [θ (x)] of the deformed workpiece W ₁ .
θ (x) = θ ′ (x) −θ (y) = α−γ + β−θ (y) (21)

Then, the grinding point of many of the peripheral profiled workpiece W ₁ (countless), and a rotational angle ([theta] x) and the swing angle of the profiled workpiece W ₁ ([theta] y), obtained as described above. In the case of the deformed workpiece W ₁ , if the cumulative rotation angle of the deformed workpiece W ₁ and the swing angle (θy) of the headstock B are taken on the horizontal axis and the vertical axis, respectively, the function [θy = f ₁ (θx) ] Is as shown in FIG. As described above, when specifying the outer peripheral shape of the deformed workpiece W ₁ , the larger the number of selected grinding points, the more the function [θy = f ₁ (θx)] for specifying the outer peripheral shape is approaching the outer peripheral shape of the W ₁ truth, grinding accuracy is improved.

1 to 3, the outer peripheral shape of the deformed workpiece W ₁ is specified while rotating the servo motor M ₂ for the spindle at a constant speed, that is, while keeping the change in the rotation angle of the deformed workpiece W ₁ with respect to time constant. When the oscillating servo motor M ₁ is rotated at a non-constant speed so as to satisfy the function [θy = f ₁ (θx)], the outer periphery of the deformed workpiece W ₁ is ground into a set shape. The

As described above, the combined use of the swing servomotor M ₁ and reduction gear R _1, theoretically, with respect to one rotation of the grinding unit attachment body A which is attached a grinding unit GU, the oscillating servo motor M ₁ Since the number of generated pulses is (1.6 × 10 ⁹ ), the accuracy of the rocking angle of the grinding unit GU is considerably high. As a result, the grinding accuracy of the deformed workpiece W ₁ is increased, Grinding is possible according to the target shape.

Further, FIG. 15 showing a grinding principle of the eccentric workpiece W ₂ (a), (b), the eccentric workpiece W ₂ are both along the eccentric portion W ₂ a concentric portion W ₂ b are axially circularity The center C′w ₂ of the eccentric part W ₂ a is eccentric by the amount of eccentricity (e) with respect to the center (axial center) Cw ₂ of the concentric part W ₂ b. . In FIG. 15A, the extension line of the line connecting the axes Cw ₂ and C′w ₂ of the eccentric part W ₂ a and the concentric part W ₂ b is the axis C _{3 of the} grindstone G (see FIG. 2) . shows a state where the eccentric to the reference position the workpiece W ₂ is disposed through, FIG. 15 (b), the headstock B (eccentric workpiece W ₂₎ is the reference in a state where the eccentric workpiece W ₂ is rotated by the rotation angle ([theta] x) It shows a state of swinging by a swing angle (θy) with respect to the position. In FIGS. 15A and 15B, P ₂ represents a grinding point.

Further, the rotation angle of the eccentric workpiece W ₂ ([theta] x), the headstock B (eccentric workpiece W ₂₎ oscillation angle ([theta] y) and the relationship of the reference position (the outer circumferential shape specific formula) [[theta] y = f ₂ ([theta] x )], the procedure of profiled workpiece W ₁ mentioned above, it is possible to mathematically calculated using the cosine theorem, trigonometric functions such as sine theorem. When the oscillation servo motor M ₁ is rotated at a constant speed while the spindle servo motor M ₂ is rotated at a constant speed so as to satisfy the above-described outer peripheral shape specification formula [θy = f ₂ (θx)], an eccentric workpiece is obtained. the outer periphery of the eccentric portion W ₂ a of the W ₂ is ground as the outer peripheral shape specifying formula [θy = f ₂ (θx)]. The concentric part W ₂ b of the eccentric workpiece W ₂ is ground at a fixed position without swinging the headstock B.

Further, the deformed workpiece that can be ground by the rocking grinding method according to the present invention is not limited to the deformed workpiece W ₁ and the eccentric workpiece W ₂ that are partially deformed with respect to a perfect circle, but a deformed workpiece having a polygonal cross section. Even workpieces can be ground. FIG. 16 shows the grinding principle of the deformed workpiece W _{3 having} a square cross section, and the rotation angle θ (x of the deformed workpiece W ₃ with respect to the reference position where each surface of the deformed workpiece W ₃ is horizontal or vertical. ) And the swing angle θ (y) of the headstock B at the time when the rotation angle of the deformed workpiece W ₃ is θ (x) (the outer peripheral shape specifying formula) [θy = f ₃ (θx)] The headstock B may be swung so as to satisfy the function [θy = f ₃ (θx)], calculated in advance in the same manner as in the case of the deformed workpiece W ₁ and the eccentric workpiece W ₂ described above. . In the case of irregular workpiece W ₃ of polygonal section, depending on the number of polygons, and reload the profiled workpiece W _3, it is necessary to successively grind the surfaces. In FIG. 16, P ₂ represents a grinding point, and Cw ₃ represents the axis of the deformed workpiece W ₃ .

Further, in the deformed workpiece polygonal section, each surface is given in the profiled workpiece W _2, not limited to the plane grinding of irregular workpiece polygonal section that each surface is in convex or concave possible It is.

  Furthermore, another modified workpiece that can be ground by the rocking grinding method according to the present invention includes a gourd-shaped workpiece.

A: Grinding unit mounting body
B: Headstock
C ₀ : Oscillation axis
C ₁ : Spindle axis
C _3: grinding wheel in the axial
Cw ₁ , Cw ₃ : Rotational axis of deformed workpiece
Cw ₂ : Rotational axis of eccentric work
G: Whetstone
GU: Grinding unit
M ₁ : Servo motor for oscillation
M ₂ : Servo motor for spindle
P ₂ : Grinding point
R ₁ and R ₂ : Reducer
S: Main spindle of grinding unit
W ₁ : Oval shaped workpiece
W ₂ : Eccentric work (deformed work)
W ₂ a: Eccentric part of eccentric work
W ₂ b: Concentric part of eccentric work
W ₃ : Deformed workpiece with a square cross section
θx: Rotation angle of deformed workpiece
θy: Oscillation angle of grinding unit or headstock
16: Reducer web generator (input shaft)
17: Reducer flex spline (output shaft)
21: Table of grinding unit

Claims (3)

Rotate the deformed workpiece gripped by the chuck within an angle corresponding to the central angle of each polygonal section of the sectional shape so that the rotation axis of the deformed workpiece with a polygonal cross section is concentric with the axis of the main shaft Letting each of the outer peripheral surfaces be ground while sequentially changing each surface portion to be ground,
The entire grinding unit with the headstock and tailstock mounted on the table can swing about a swinging shaft centered almost directly below the shaft center of the main shaft and parallel to the shaft center of the main shaft. ,
By calculating in advance an outer peripheral shape specifying formula that specifies the relationship between the rotation angle from the reference position of each surface portion of the deformed workpiece and the rocking angle of the grinding unit and determines the outer peripheral grinding shape of each surface portion of the deformed workpiece. Leave
Based on the outer peripheral shape specification formula, each surface portion is moved within an angle corresponding to the center angle while each surface portion of the deformed workpiece is sequentially changed while the grinding unit is swung around the swing axis. A rocking grinding method for deformed workpieces, characterized in that each surface portion is rotated and ground to the shape specified by the outer peripheral shape specifying formula. An oscillating grinder for carrying out the oscillating grinding method for a deformed workpiece according to claim 1 ,
A grinding unit that includes a spindle servo motor for driving and rotating the spindle, and is supported so as to be swingable about the swing axis;
A rocking servo motor for rocking the grinding unit about the rocking axis;
The oscillating servo motor is configured by a pair of opposed output shafts arranged on the same axis, so that the axis of each oscillating servo motor is an oscillating axis. Each of the pair of swing servomotors includes a reduction gear having an input shaft and an output shaft on the drive shaft center,
The drive shaft of each oscillating servo motor is connected to the input shaft of each speed reducer, and both ends of the grinding unit mounting body arranged between the speed reducers are connected to the output shaft of each speed reducer. ,
The grinding unit is integrally attached to the grinding unit mounting body, the rotation of the drive shaft of each swing servo motor is decelerated, and the grinding unit mounting body is rotated, whereby the grinding unit is It is configured to swing around the axis of the servo motor.
The main shaft and swing servomotors are rotated synchronously so that the rotation angle from the reference position of the deformed workpiece and the rocking angle of the grinding unit maintain the relationship specified by the outer peripheral shape specifying formula. Then, the irregularly shaped workpiece swinging type grinding machine is configured to grind the irregularly shaped workpiece into a shape specified by the outer peripheral shape specifying formula. When grinding the outer peripheral surface, which is the surface to be ground, while continuously rotating the deformed workpiece gripped by the chuck so that the rotation axis of the deformed workpiece having a non-circular cross section is concentric with the axis of the main shaft,
The entire grinding unit with the headstock and tailstock mounted on the table can swing about a swinging shaft centered almost directly below the shaft center of the main shaft and parallel to the shaft center of the main shaft. ,
Preliminarily calculating an outer peripheral shape specifying formula that determines the outer peripheral grinding shape of the deformed workpiece by specifying the relationship between the rotation angle from the reference position of the deformed workpiece and the rocking angle of the grinding unit,
Based on the outer peripheral shape specifying formula, the irregularly shaped workpiece is continuously rotated while the grinding unit is swung around the swing axis, and the outer peripheral surface is ground to the shape specified by the outer peripheral shape specifying formula. An apparatus for carrying out a swing grinding method for deformed workpieces,
A grinding unit that includes a spindle servo motor for driving and rotating the spindle, and is supported so as to be swingable about the swing axis;
A rocking servo motor for rocking the grinding unit about the rocking axis;
The oscillating servo motor is configured by a pair of opposed output shafts arranged on the same axis, so that the axis of each oscillating servo motor is an oscillating axis. Each of the pair of swing servomotors includes a reduction gear having an input shaft and an output shaft on the drive shaft center,
The drive shaft of each oscillating servo motor is connected to the input shaft of each speed reducer, and both ends of the grinding unit mounting body arranged between the speed reducers are connected to the output shaft of each speed reducer. ,
The grinding unit is integrally attached to the grinding unit mounting body, the rotation of the drive shaft of each swing servo motor is decelerated, and the grinding unit mounting body is rotated, whereby the grinding unit is It is configured to swing around the axis of the servo motor.
The main shaft and swing servomotors are rotated synchronously so that the rotation angle from the reference position of the deformed workpiece and the rocking angle of the grinding unit maintain the relationship specified by the outer peripheral shape specifying formula. Then, the irregularly shaped workpiece swinging type grinding machine is configured to grind the irregularly shaped workpiece into a shape specified by the outer peripheral shape specifying formula.

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