JP4164482B2 - Vibration analysis method - Google Patents

Description

  The present invention relates to a vibration analysis method for a structure in which a plurality of members are weakly coupled.

  In the design process of office equipment, the finite element method and the boundary element method are used to predict the noise generated outside the equipment. In vibration analysis and acoustic analysis using the finite element method and boundary element method, it is necessary to make the object including the acoustic space, the exterior of the office equipment, the inside of the equipment, etc. into finite elements. This is done by representing a finite number of rectangular parallelepipeds or a set of planar squares.

  After this modeling, the acoustic transfer function from the location of the equipment with the vibration source such as the motor to the noise observation point is calculated by the finite element method and the boundary element method.

  In statistical energy analysis (SEA), the analysis target is divided into several elements, and the vibration mode is uniformly excited in the elements, and the power flow between the elements is proportional to the energy difference. (For example, refer to Patent Document 1).

  Considering a system in which two one-degree-of-freedom systems are connected by a connecting spring, it is considered that transmission power proportional to the energy difference between the two vibration systems is generated in the vibration system. In general structures, this idea is expanded so that the energy of each mode of an independent vibration system (element) in which a large number of modes exist differs from the energy of each mode of the adjacent vibration system. We think that we are exchanging proportional transmission power.

The main variable of SEA is energy common to the physical system, and in order to perform the above-mentioned treatment, frequency average and spatial average over the whole element are performed like an octave band.
JP 11-337402 A

  However, it is difficult to accurately represent the structure as a finite element method (FEM) model in a device having a structure (weak coupling) in which a plurality of members are coupled by screws or caulking, such as office equipment. is there. In particular, the analysis result varies greatly depending on the constraint conditions of the elements of the weakly coupled portion.

  Due to the above factors, the accuracy of the vibration system of office equipment represented by finite elements greatly depends on the accuracy of modeling weakly coupled parts, and as a result, it is very difficult to express an accurate vibration system. It becomes difficult.

  In order to solve the above problem, an object of the present invention is to provide a vibration analysis method suitable for a weakly coupled structure.

In order to achieve the above object, the present invention provides:
A vibration analysis method for a structure in which a plurality of members are weakly coupled,
A statistical energy analysis method for dividing the structure into a plurality of subsystems and performing vibration analysis of each subsystem;
A sensitivity analysis method for determining the sensitivity of the internal loss factor of the subsystem derived by the statistical energy analysis method and the coupling loss factor between the subsystems;
A parameter derivation method for expressing the coupling loss coefficient using a general theory, and deriving a configuration parameter of the coupling loss coefficient obtained by the general theory;
A vibration evaluation method for evaluating vibration by applying a finite element method to the subsystem created based on the configuration parameters;
A vibration analysis method characterized by analyzing vibrations of the structure using the above.

  According to the present invention, it is possible to analyze in detail the vibration energy distributed in each subsystem, the direction in which vibration power flows between the subsystems, and the magnitude thereof.

  Exemplary embodiments of the present invention will be described in detail below with reference to the drawings. However, the dimensions, materials, shapes, relative arrangements, and the like of the components described in this embodiment are not intended to limit the scope of the present invention only to those unless otherwise specified. .

  FIG. 1 is an explanatory diagram of the internal configuration of a copying machine as an example of an image forming apparatus equipped with an automatic document feeder. This copying machine is configured by connecting an automatic document feeder B to the upper part of an image forming apparatus main body A. ing.

  Here, the overall configuration of the image forming apparatus will be briefly described first, and then the automatic document feeder will be described in detail.

[Entire configuration of image forming apparatus]
The image forming apparatus main body A integrally includes a reading device A1 and a recording device A2, and sequentially feeds a plurality of originals set on the automatic document feeder B and reads them by the reading device A1. Recording is performed on a recording medium such as plain paper or an OHP sheet by the recording apparatus A2 in accordance with the read information.

  The reading device A1 irradiates the original G, which is conveyed to a predetermined position on the platen glass 1 by the automatic original conveying device B, which will be described in detail later, with light from the light source 2, and reflects the reflected light through the mirror 3 and the lens 4. Then, image exposure is performed on the photosensitive drum.

  The recording device A2 records an image on the recording medium S by an electrophotographic image forming means in accordance with the image exposure from the reading device A1. The specific structure of the image forming means is that the surface of the photosensitive drum 5 that is driven and rotated is uniformly charged by the primary charger 6, and an electrostatic latent image is formed on the photosensitive drum 5 by the image exposure. The latent image is developed with toner by the developing means 7 to form a toner image.

  To synchronize with the formation of the toner image, the recording medium S accommodated in the removable sheet cassette 8 or the sheet deck 9 is selectively separated and fed one by one by the feeding belt 10, and is inclined by the registration roller 11. The line is conveyed to the image forming unit in accordance with the image forming timing while being corrected. Then, a toner image formed on the photosensitive drum 5 is applied to the recording medium S conveyed between the photosensitive drum 5 and the transfer charger 12 by applying a bias to the transfer charger 12 to record an image. The toner remaining on the photosensitive drum 5 after the toner image is transferred is removed by the cleaning means 13.

  The recording medium S onto which the toner image has been transferred as described above is conveyed to the fixing means 15 by the conveying belt 14, where the toner image is fixed by applying heat and pressure, and the sheet discharge tray 17 is fixed by the discharge roller 16. Is discharged.

The recording apparatus A2 according to the present embodiment has a double-sided recording function. When recording on both the front and back sides of the recording medium S, the recording medium S recorded on one side as described above is discharged as a flapper. The sheet is transported to the retransmission path 19 by switching 18 and reversed by switching back in the retransmission path 19, and then transported again to the image forming means by the retransmission roller 20 and recorded on the other surface side to be recorded on the sheet discharge tray 17. To discharge.

[Automatic document feeder]
Next, the configuration of the automatic document feeder B that transports the document G to a reading position by the reading device A1 and discharges the document G to a discharge unit after reading will be described.

  FIG. 2 is an explanatory view of a main section of the automatic document feeder. The automatic document feeder B includes a document placement unit B1, a document feeding unit B2, a document transport unit B3, and a document discharge unit B4.

{Overall configuration of automatic document feeder}
(Original Feeding Section)
The document placing portion B1 is for setting a bundle of documents G with the document surface facing up on the stacking surface 21a of the document placing tray 21, and guides both sides of the set document G by abutting against the side guides 21b. .

  As shown in FIG. 2, the document feeding unit B2 separates a plurality of documents G set on the document placing tray 21 one by one from the uppermost document by a friction separation method, and feeds them by a pair of registration rollers. Is.

  The pickup roller 22 is mounted so as to be able to swing up and down by a vertical mechanism (not shown). When feeding the original, the pickup roller 22 is lowered onto the original bundle, and the intermediate plate 23 is raised to feed the original bundle. The roller 24 is pressed to enter the preliminary feeding operation.

  Thereafter, the feeding roller 24 and the pickup roller 22 are rotated by the motor M1 as a driving source to feed the document G. At this time, the second and subsequent documents to be fed along with the uppermost sheet are stopped by the friction piece 25 and remain on the document placing tray 21. Thereafter, the document is guided by the guide member 26, passes between the feeding guide member 28 constituting the feeding path 27 and the feeding guide member 29, and is guided to the registration roller pair 30 a and 30 b. The registration roller pairs 30a and 30b are stopped when the leading edge of the original reaches, and form a loop by the conveyance by the feeding roller 24 to correct the skew feeding, and then feed the original to the original conveying unit B3.

(Original transport section)
The document conveying section B3 is configured such that the conveying belt 31 is stretched by a driving roller 32a and a driven roller 32b and is pressed against the platen glass 1 by belt pressing rollers 32c, 32d, 32e, and 32f. Then, when the driving roller 32a is rotationally driven by the motor M2 as a driving source, the conveying belt 31 is rotationally driven. The original G fed by this rotation enters between the transport belt 31 and the platen glass 1 and is transported on the platen glass 1 by the frictional force of the transport belt 31. The document G transported to a predetermined position on the platen glass 1 by the transport belt 31 is stopped when the motor M2 is stopped, and an image is read by the reading device A1 described above.

  The document after image reading is further conveyed to the right side of FIG. 2 by re-driving the motor M2, guided by the jump table 33, and conveyed to the document discharge portion B4.

  When a small-size document is conveyed, if there is a subsequent document, the subsequent document is conveyed to a predetermined position by the rotation of the conveying belt 31 in the same manner as the preceding document, and then read by the reading device A1. During this reading operation, the preceding document is turned upside down by the document discharge section B4 and discharged onto the document discharge table 34 as will be described later.

(Original output)
The document discharge section B4 reversely discharges the document G after reading. As shown in FIG. 2, the driven roller 36 and the driven roller 37 are pressed against the reverse roller 35, and the reverse path P2 includes a transport roller. A pair 38a, 38b is provided.

  Further, a swing flapper 39, an engagement flapper 40, a follower flapper 41, and a swing guide 42 are provided for sending the document to the introduction path P1 or the discharge path P3 during discharge.

  The automatic document feeder B is attached so as to cover the upper surface of the platen glass 1 provided at the top of the image forming apparatus main body A, and as shown in FIG. 3 (side cross-sectional explanatory view of the automatic document feeder) The rear side (left side in FIG. 9) is pivotally attached to the image forming apparatus main body A by the hinge unit 43, and the front side (right side in FIG. 9) is detachably attached to the image forming apparatus main body A by, for example, a magnet catch 44. . Next, the characteristic configuration of each part of the automatic document feeder B will be sequentially described.

{Support structure of each unit}
As described above, the automatic document feeder B according to this embodiment includes the document placement unit B1, the document feeding unit B2, the document transport unit B3, the document discharge unit B4, and the like as units. As shown in FIG. 4, the units are combined and assembled to the image forming apparatus main body A via a hinge unit 43.

  As shown in FIGS. 4 and 5, a support plate 45 made of sheet metal is used, and a document feeding unit B2, a document discharge unit B4, and a hinge unit 43 as units are coupled to the support plate 45 by screws 46 or the like. The support plate 45 is attached to a monocoque frame 47 made of synthetic resin integrated with the document placement portion B1.

  Next, a specific analysis flow of a specific vibration analysis method according to the present invention will be described.

  6 (a) and 6 (b) (viewed in the direction of arrow A in FIG. 6 (a)) are sub-system division diagrams of the automatic paper feeder for copying machines (automatic document feeder B). In this embodiment, the automatic document feeder B includes a subsystem (1) (document ejection unit), a subsystem (2) (document ejection unit support unit), a subsystem (3) (document placement unit), a sub System (4) (document feeder support unit), subsystem (5) (document feeder unit), subsystem (6) (document output unit), subsystem (7) (document transport unit) Subsystem was divided into units.

  FIG. 7 shows the result of a certain frequency band of SEA analysis. The arrows connecting the subsystems indicate the transmission direction of the vibration power between the subsystems, and the thickness of the arrow indicates the relative vibration power. An arrow pointing to the subsystem from outside indicates relative vibration input power from the outside, and the thickness of the arrow indicates the magnitude of vibration input power. The size of the black circle in the square of each subsystem indicates the relative vibration energy distribution of each subsystem.

  In order to reduce the noise generated by these subsystems, specifically, an internal loss coefficient indicating a loss ratio when vibration energy in each subsystem is converted into vibration power, and energy transmitted between the subsystems. It is necessary to change the coupling loss coefficient representing the loss ratio.

  The perturbation method is used here as a method for setting the objective function for reducing the total vibration energy of the seven subsystems in FIG.

Ｐ：振動パワー、ω：角周波数、Ｌ：損失係数、Ｅ：振動エネルギ
であるが、摂動法ではこのＰの変動は無視して、それぞれのＬ（ＳＥＡの損失係数）の微少な変動による、Ｅの総和の変化に対する感度を計算する。 The basic formula of SEA is

P: Vibration power, ω: Angular frequency, L: Loss coefficient, E: Vibration energy. In the perturbation method, this variation in P is ignored, and due to a slight variation in each L (loss factor of SEA), Calculate the sensitivity to changes in the sum of E.

FIG. 8 shows an example of the sensitivity analysis result. The figure shows the relationship between the internal loss factor (ILF) and coupling loss factor (CLF) and the energy fluctuation of each subsystem. In the left graph, the horizontal axis is ILF, and in the right graph, the horizontal axis is CLF, and the vertical axis represents the energy fluctuations (ΔE1 to ΔE7) of each subsystem as each loss coefficient increases. For example, with respect to the broken line portion shown in the figure, it is shown that when the ILF of the subsystem (7) is increased, the energy ΔE7 of the subsystem (7) decreases.

Further, the coupling loss coefficient CLF [1] [7] between the subsystem (1) and the subsystem (7).
When (the coupling loss coefficient when transmitting from the subsystem (1) to the subsystem (7)) is increased, the energy ΔE7 of the subsystem (7) is increased. This indicates that the energy ΔE7 of the subsystem (7) decreases when CLF [1] [7] decreases.

As a result of the above sensitivity analysis, the internal loss coefficient ILF [7] is changed to be increased, and the coupling loss coefficient CLF [1] [7] is changed to be decreased (from the subsystem (1) to the subsystem ( 7), it was found that the sum of vibration energy of these seven subsystems can be reduced most efficiently under the constraint conditions.

One of the means for predicting the mechanical shape by changing the coupling loss coefficient CLF [1] [7] small is a method of obtaining the coupling loss coefficient from the forced vibration response by the finite element method.

FIG. 9 is a diagram showing a state in which the subsystem (1) and the subsystem (7) are mechanically coupled. The response of the subsystem (7) and the subsystem (1) due to the vibration of the subsystem (1) is predicted by the finite element method, the vibration power for exciting the subsystem (1), and the subsystem (7) By calculating the vibration energy generated, the coupling loss coefficient CLF [1] [7
] And CLF [7] [1]. Then, as shown in FIG. 10, a shape in which the coupling loss coefficient CLF [1] [7] is minimized within the product restrictions can be obtained by solving the objective function by the optimization algorithm.

  FIG. 11 is a graph showing the noise reduction effect for each 1/3 octave band when the present embodiment is applied to the models before and after improvement. In addition, the horizontal axis of the figure represents the noise frequency, and the vertical axis represents the noise level of each frequency band. From this result, it can be confirmed that the noise level is reduced in a wide frequency band.

As noted above,
(1) Define subsystem coupling (SEA),
(2) SEA analysis is performed on the subsystem configuration, and the internal loss coefficient of each subsystem and the coupling loss coefficient between subsystems defining the coupling are determined (SEA).
(3) In order to minimize vibration energy of each subsystem, a more efficient loss factor is selected based on the coupling of subsystems, the internal loss factor obtained by SEA analysis, and the coupling loss factor (
Loss factor sensitivity analysis method),
(4) Obtain a shape that optimizes the selected loss factor by optimizing the parameters of the forced vibration response analysis by the finite element method (parameter optimization),
By following this flow, it is possible to reduce the noise of the product.

  In the first embodiment, the improvement flow obtained by the parameter optimization method using the finite element method (4) has been described. In the second embodiment, an improvement plan can be derived by a simpler method for the loss factor to be noticed determined by the sensitivity analysis method of (3) above, and a specific subsystem shape for noise countermeasures can be created. A method will be described (FIG. 12 shows an improvement flow according to the second embodiment).

  First, a method for expressing the coupling loss coefficient applied in this embodiment will be described. Based on wave theory, the coupling loss coefficient can be expressed by the following equation.

ここで、η_ｉｊ：要素ｉから要素ｊへの結合損失係数、ｃ_ｇｉ:要素ｉの曲げ波群速度
、Ｌ：結合長さ、τ_ｉｊ：エネルギ透過率、ω：角周波数、Ｓ_ｉ：要素ｉの表面積、ｎ_ｉ：要素ｉのモード密度である。

Here, η _ij : Coupling loss coefficient from element i to element j, c _gi : Bending wave group velocity of element i, L: Coupling length, τ _ij : Energy transmittance, ω: Angular frequency, S _i : Element i surface area, n _i : mode density of element i.

Regarding the coupling loss _coefficient , c _gi is uniquely determined by the material. L is the coupling length when all the couplings between the subsystems are regarded as line couplings, and τ _ij varies depending on the coupling angle between the elements, but can be regarded as uniformly 90 degrees. As other elements, There is a plate thickness ratio.

  The internal loss factor of each subsystem in the present embodiment can be calculated from a mathematical formula, but in order to obtain better calculation accuracy, a constant numerical value under the same conditions was used from the experimental database. .

FIG. 13 shows the result of predicting the coupling loss coefficient CLF [1] [7] by this wave theory. In the figure, the horizontal axis indicates the vibration frequency between subsystems, and the vertical axis indicates the coupling loss coefficient CLF [1] [7] of each vibration frequency. The coupling loss number obtained by actual measurement agrees well with the predicted value.

FIG. 14 shows a coupling parameter that reduces the coupling loss coefficient CLF [1] [7] using the wave theory described above, and the vibration power for the subsystem created based on the derived coupling parameter. The transmission state (actually measured value) is expressed. According to the figure, since the coupling loss coefficient CLF [1] [7] has decreased, it can be confirmed that the positive and negative directions of the transmitted vibration power are reversed. From this result, it is shown that the method of deriving the coupling parameter by the wave theory well represents the tendency of the actual measurement value.

As described above, in addition to the efficient selection of the loss factor by the sensitivity analysis described in the first embodiment of the present invention, the coupling loss coefficient is expressed using the wave theory that is a general-purpose theory, and obtained by the wave theory. By deriving the coupling parameters, it is possible to easily determine the countermeasure shape of the subsystem. In addition, by evaluating the effect of this countermeasure shape with the aid of the finite element method, it is possible to grasp the transmission state of vibration power and predict the effect of noise countermeasures as a whole system, and the product can be made quieter. .

  As described above, for each parameter of coupling loss and internal loss between subsystems so that the vibration energy distribution of each subsystem is minimized, the sensitivity to changes in overall energy should be obtained, and attention should be paid to measures for vibration and noise. The coupling loss coefficient between each subsystem and the internal loss coefficient were determined. In addition, the countermeasure shape of each subsystem was created based on the sensitivity results of the above parameters and the coupling parameters derived by the coupling parameter evaluation method based on the wave theory. In addition, by applying a series of analysis processes such as predicting the effect of countermeasure shapes of each subsystem using the finite element method, the factor prediction and improvement of vibration and noise can be performed efficiently and effectively. became.

Internal configuration explanatory diagram of a copying machine as an example of an image forming apparatus equipped with an automatic document feeder Main section explanatory drawing of automatic document feeder Side cross-sectional explanatory diagram of automatic document feeder Exploded perspective view of each unit such as the document feeder and document discharge unit Explanation of the state in which units such as the document feeder and document discharge unit are connected and fixed by a support plate A diagram for explaining subsystem division of an automatic paper feeder for an copying machine (automatic document feeder) The figure explaining the magnitude of vibration power between subsystems and the transmission direction Diagram explaining loss factor sensitivity analysis Diagram illustrating coupling between subsystems Diagram explaining the shape with reduced coupling loss between subsystems The figure explaining the effect before and after the countermeasure of the noise level which concerns on Example 1 of this invention. The figure explaining the flow of the improvement method which concerns on Example 2 of this invention Diagram explaining the comparison between the measured coupling loss factor between subsystems and the coupling loss factor derived by wave theory The figure explaining transmission of the vibration power which applied Example 2 of the present invention.

Explanation of symbols

A Image forming apparatus main body A1 Reading apparatus A2 Recording apparatus B Automatic document conveying apparatus B1 Original placing section B2 Original feeding section B3 Original conveying section B4 Original discharge section G Original M1, M2, M3 Motor P1 Introduction path P2 Reverse path P3 Ejection Pass S Recording medium 21 Document placement tray 21a Loading surface 21b Side guide 22 Pickup roller 23 Middle plate 24 Feed roller 25 Friction piece 26 Guide member 27 Feed path 28 Feed guide member 29 Guide members 30a and 30b during feeding Roller 31 Conveying belt 32a Drive roller 32b Followed rollers 32c, 32d, 32e, 32f Belt pressing roller 33 Jump stand 34 Document discharge stand 35 Reversing roller 36 Followed roller 37 Followed rollers 38a, 38b Conveying roller pair 39 Swing flapper 40 Engagement flapper

Claims (5)

A vibration analysis method for a structure in which a plurality of members are weakly coupled,
A statistical energy analysis method for dividing the structure into a plurality of subsystems and performing vibration analysis of each subsystem;
A sensitivity analysis method for determining the sensitivity of the internal loss factor of the subsystem derived by the statistical energy analysis method and the coupling loss factor between the subsystems;
A parameter derivation method for expressing the coupling loss coefficient using a general theory, and deriving a configuration parameter of the coupling loss coefficient obtained by the general theory;
A vibration evaluation method for evaluating vibration by applying a finite element method to the subsystem created based on the configuration parameters;
The vibration analysis method characterized by analyzing the vibration of the said structure using.   The vibration analysis method according to claim 1, wherein the weak coupling is a structure in which the plurality of members are coupled by screws or caulking. The coupling loss factor expressed using the wave theory, vibration analysis method according to claim 1, characterized in that the aid of coupling parameter derivation method for deriving the binding parameters between the obtained subsystem by the wave theory. The vibration analysis method according to any one of claims 1 to 3 , wherein the vibration analysis method is adapted to a sheet feeding device having the structure.
The sheet feeding device has a structure composed of a resin monocoque frame and a reinforcing member made of a thin metal plate bis-coupled to the resin monocoque frame, and the structure includes a first driving source. A vibration analysis method characterized by holding a main unit, a second main unit having a driving source, and a third main unit having a conveyor belt body. 5. The vibration analysis method according to claim 4 , wherein the first main unit has a function of feeding a document, and the second main unit has a function of discharging the document.

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