JP4329648B2 - Gear vibration calculation method, program, and recording medium - Google Patents

Description

  The present invention relates to a technique for calculating vibration of a gear, and more particularly to a technique for calculating vibration of a vibration transmission system including a rotating body having a gear and a support body that supports the rotating body.

  Gears are used in various machines, including automobile transmissions, to transmit torque between different axes. The gear is an element that is easy to efficiently transmit torque, but is also an element that easily becomes a source of vibration and noise. In particular, in recent years, there has been a strong demand for quietness of machines, and accordingly, reduction of gear noise has been strongly demanded in machines using gears.

  For example, in an automobile, an engine (internal combustion engine), which is a power source, is a main source of vibration and noise. However, as a result of advances in technology for reducing engine noise, transmission noise using gears is relatively low. Has been recognized prominently. For this reason, there has been a strong demand for techniques and design techniques for reducing the noise of transmissions using gears.

Against this background, Patent Document 1 discloses a technique for analyzing gear noise by paying attention to the tooth surface shape of a gear. Patent Document 2 discloses a technique for analyzing gear noise by paying attention not only to the movement of the gear itself but also to a load acting on a bearing that rotatably supports the gear.
JP-A-5-157663 JP-A-9-53702

  The inventors of the present invention have conducted research on a technique for reducing vibration and noise of a machine using a gear. As a result, for example, in a machine configured such that a rotating body having a gear is supported by a support via a bearing, the meshing excitation force of the gear vibrates the support via the bearing, Since gear noise is generated, in order to design a machine with reduced gear noise, it has been noticed that not only reduction of gear meshing vibration force but also improvement of vibration characteristics of the support are important.

  Therefore, in order to reduce gear noise in this type of machine, the meshing vibration generation force of the gear is predicted with high accuracy, and the vibration of the vibration transmission system including the rotating body having the gear and the support body that supports the rotating body is determined. Must be predicted with high accuracy.

  Against the background described above, the present invention predicts the meshing vibration force of the gear with high accuracy in the technology for calculating the vibration of the gear, and a rotating body having the gear and a support body that supports the rotating body, It is an object to predict vibrations of a vibration transmission system including a high accuracy.

In order to solve the above-mentioned problems, according to a first aspect of the present invention, there is provided a gear device in which at least two rotating bodies that mesh with each other and are rotatably supported by a support body, and at least two of them are supported. The rotating body includes two rotating shafts and two gears that rotate coaxially together with the two rotating shafts, and form a gear pair that meshes with each other at the tooth surfaces. A gear vibration calculation method for calculating vibrations of what is configured to include:
Between the tooth surfaces of the two gears, the time variation of the tangential load acting along the common tangent of both base circles of the two gears is expressed as follows: (a) the relative distance between the teeth where the two gears mesh with each other; In response to the displacement, the time variation of the response displacement load acting between the meshing tooth surfaces where the two gears mesh with each other; and (b) the meshing contact where the tooth surfaces of the two gears contact each other during the meshing. A tangential load calculating step for calculating a point as a composite value of the time variation of the dynamic load acting between the meshing tooth surfaces of the two gears in response to the time variation in the gear radial direction ;
A vibration response calculation step including a vibration response calculation step of calculating a time response of at least one of the rotating body and the support body with respect to the vibration having the gear pair as a vibration source based on the calculated tangential load time variation. A method is provided.
In order to solve the above-mentioned problem, according to a second aspect of the present invention, there is provided a gear device in which at least two rotating bodies that mesh with each other are rotatably supported by a support body, and at least two of them are rotated. The rotating body includes two rotating shafts and two gears that rotate coaxially together with the two rotating shafts, and form a gear pair that meshes with each other at the tooth surfaces. A gear vibration calculation method for calculating vibrations of what is configured to include:
Between the tooth surfaces of the two gears, the time variation of the tangential load acting along the common tangent of both base circles of the two gears is expressed as follows: (a) the relative distance between the teeth where the two gears mesh with each other; In response to the displacement, the time variation of the response displacement load acting between the meshing tooth surfaces where the two gears mesh with each other; and (b) the meshing contact where the tooth surfaces of the two gears contact each other during the meshing. A tangential load calculating step for calculating a point as a composite value of the time variation of the dynamic load acting between the meshing tooth surfaces of the two gears in response to the time variation in the gear radial direction ;
Based on the calculated tangential load time variation, the axial load calculation step of calculating the time variation of the axial load acting along the rotation axis of each gear,
Based on the calculated axial load time variation and the calculated tangential load time variation, calculate the time response of at least one of the rotating body and the support body with respect to vibration using the gear pair as a vibration source. Including a vibration response calculation step to
The tangential load calculation step includes:
The time variation of the response displacement load of each gear is the product of the time variation of the relative angular displacement between the two gears and the coupling rigidity of the two gears, and the time variation of the relative angular velocity between the two gears. And a response displacement load calculation step of calculating a sum of the product of the coupling attenuation of the two gears and a value obtained by dividing the sum by the basic circle radius of each gear;
The time variation of the dynamic load of each gear is calculated by multiplying the dynamic load of each gear by the amplitude at each meshing order i (i: 1 to n) and a periodic function selected in advance so that the time t is a variable. Dynamic load time fluctuation calculation process to calculate using
The dynamic load time variation calculation step includes:
As the meshing of the two gears progresses, the dynamic load amplitude of each gear is calculated based on the meshing transmission error curve of each gear, or the rotational speed of each gear and the tooth surface of each gear There is provided a gear vibration calculation method including a dynamic load amplitude calculation step for calculating the dynamic load amplitude of each gear based on the load applied to the gear.
The following aspects are obtained by the present invention. Each aspect is divided into sections, each section is given a number, and is described in a form that cites other section numbers as necessary. This is to facilitate understanding of some of the technical features that the present invention can employ and combinations thereof, and the technical features that can be employed by the present invention and combinations thereof are limited to the following embodiments. Should not be interpreted. That is, it should be construed that it is not impeded to appropriately extract and employ the technical features described in the present specification as technical features of the present invention although they are not described in the following embodiments.

  Further, describing each section in the form of quoting the numbers of the other sections does not necessarily prevent the technical features described in each section from being separated from the technical features described in the other sections. It should not be construed as meaning, but it should be construed that the technical features described in each section can be appropriately made independent depending on the nature.

(1) A gear device in which at least two rotating bodies that rotate in mesh with each other are rotatably supported by a support, and the at least two rotating bodies include two rotating shafts and two of them. Gear vibration calculation method for calculating vibrations of two gears which rotate together coaxially with the rotation shaft of the gears and which have a gear pair which meshes with each other at the tooth surfaces Because
Between the tooth surfaces of the two gears, the time variation of the tangential load acting along the common tangent of both base circles of the two gears is expressed as follows: (a) the relative distance between the teeth where the two gears mesh with each other; In response to the displacement, the time variation of the response displacement load acting between the meshing tooth surfaces where the two gears mesh with each other; and (b) the meshing contact where the tooth surfaces of the two gears contact each other during the meshing. A tangential load calculation step of calculating as a composite value of the time variation of the dynamic load acting between the meshing tooth surfaces of the two gears in response to the basic circle radius error of the point;
A vibration response calculation method including a vibration response calculation step of calculating a response of at least one of the rotating body and the support body with respect to vibration using the gear pair as a vibration source based on the calculated tangential load time variation. .

  According to this method, it is possible to calculate the vibration of a gear device in which at least two rotating bodies that rotate in mesh with each other are rotatably supported by the support.

  In this method, in order to calculate the vibration of the gear device, a tooth surface force in which two meshing gears interact with each other via meshing tooth surfaces is a common tangent of both base circles of the two gears. Calculated as a tangential load acting along In addition, the tangential load is responsive to the relative displacement between the teeth where the two gears mesh with each other, the response displacement load acting between the meshing tooth surfaces where the two gears mesh with each other, and the two gears. In response to the basic circle radius error at the meshing contact point where the tooth surfaces contact each other during meshing, the calculation is performed in consideration of both the dynamic load acting between the meshing tooth surfaces of the two gears. Further, based on the calculated tangential load, the response of at least one of the rotating body and the support body with respect to the vibration using the two gears as the excitation source is calculated.

  Therefore, according to this method, it becomes easy to predict the tooth surface force exerted by the two gears engaged with each other with high accuracy, and as a result, the rotation with respect to the vibration using the two gears as the excitation source is facilitated. It becomes easy to calculate the response of at least one of the body and the support with high accuracy.

(2) Furthermore, an axial load calculation step for calculating a time variation of an axial load acting along the rotation axis of each gear based on the calculated tangential load time variation is included, and the vibration response calculation step includes The gear vibration calculation method according to item (1), wherein the response is calculated based on the calculated axial load time variation and the calculated tangential load time variation.

  According to this method, since each gear is a helical gear, it is possible to calculate the axial load generated in the axial direction of each gear due to the presence of the torsion angle of the teeth during the meshing rotation of the gear. It becomes possible. Furthermore, by considering the calculated axial load together with the calculated tangential load, it becomes possible to calculate the vibration response of at least one of the rotating body and the support body with high accuracy.

(3) The tangential load calculation step calculates the response displacement load time variation of each gear, the product of the time variation of the relative angular displacement between the two gears, and the coupling rigidity of the two gears. 4. The gear vibration calculation method according to item (1) or (2), including a response displacement load calculation step of calculating using a value divided by the base circle radius of.

(4) In the tangential load calculation step, the response displacement load time variation of each gear is calculated by multiplying the time variation of the relative angular displacement between the two gears and the coupling rigidity of the two gears, A response displacement load calculating step of calculating a sum of a product of a temporal change in relative angular velocity between the gears and a coupling damping of the two gears by dividing the sum by the basic circle radius of each gear ( The gear vibration calculation method according to item 1) or (2).

(5) The tangential load calculation step calculates a dynamic load time variation caused by the meshing of the two gears using a dynamic load amplitude of each gear and a preselected periodic function. The gear vibration calculation method according to any one of (1) to (4), including a time variation calculation step.

(6) The dynamic load time variation calculation step includes a dynamic load amplitude calculation step of calculating the dynamic load amplitude of each gear based on the meshing transmission error curve of each gear as the meshing of the two gears progresses. The gear vibration calculation method according to item (5).

(7) The dynamic load time fluctuation calculating step calculates the dynamic load amplitude of each gear based on the rotational speed of each gear and the load applied to the tooth surface of each gear. The gear vibration calculation method according to item (5), including:

(8) The dynamic load time variation calculation step includes a periodic function definition step of defining the periodic function based on the rotational speed of each gear and the number of teeth of each gear. (5) to (7) The gear vibration calculation method according to any one of the above.

(9) The vibration response calculation step calculates the response using a finite element model that approximately represents the gear device,
The tangential load calculation step calculates the tangential load regardless of the finite element model,
The vibration response calculation step includes a load calculation step of calculating an external load input to a gear model representing each gear of the finite element model based on the calculated tangential load (1) to (8) ) The gear vibration calculation method according to any one of the items.

  According to this method, when calculating the tangential load, it is not necessary to consider the relationship between the tangential load and the finite element model for calculating the vibration response, so it is easier than when the relationship must be considered. It is possible to calculate the tangential load.

(10) The vibration response calculation step calculates the response using a finite element model that approximately represents the gear device,
The tangential load calculation step calculates the tangential load in consideration of the interaction between the rotating body and the support,
The vibration response calculation step includes a load calculation step of calculating an external load input to a gear model representing each gear of the finite element model based on the calculated tangential load (1) to (8) ) The gear vibration calculation method according to any one of the items.

  According to this method, it becomes possible to calculate the tangential load with higher accuracy than when calculating without considering the interaction between the rotating body and the support.

(11) The finite element model is defined to include a plurality of finite elements and a plurality of nodes.
The gear load calculation method according to (9) or (10), wherein the load calculation step calculates the external load with respect to at least one selected node selected in advance among the plurality of nodes.

(12) The gear model expresses that, despite the input of the external load to the real gear represented by the gear model, the real gear does not warp in a direction perpendicular to the plane perpendicular to the axis of the real gear. A rigid body model that
The at least one selected node includes a plurality of representative nodes arranged at equal intervals on the rigid model among the plurality of nodes.
The gear calculation method according to (11), wherein the load calculation step calculates the external load in association with the plurality of representative nodes.

  According to this method, it is easy to calculate the vibration response of at least one of the rotating body and the support body by jointly constructing the gear model as a rigid body model and allocating the external load to a plurality of representative nodes. Can be realized.

  In this method, it is possible to calculate the external load so that the external load is equally distributed to the plurality of representative nodes or according to a certain distribution pattern.

(13) The gear vibration calculation method according to (12), wherein the load calculation step calculates the external load so that the external load is equally distributed to the plurality of representative nodes.

  According to this method, since it is sufficient to calculate the external load so that the external load is equally distributed to a plurality of representative nodes, it is necessary to calculate the external load so that the external load is distributed according to a certain distribution pattern. In some cases, it is easier to simplify the calculation of the external load.

(14) A program executed by a computer to implement the gear vibration calculation method according to any one of (1) to (13).

  If this program is executed by a computer, the same effect can be realized according to basically the same principle as in the method according to any one of the above items (1) to (13).

  The program according to this section can be interpreted so as to include not only a combination of instructions executed by a computer to fulfill its function, but also files and data processed in accordance with each instruction.

  In addition, this program may achieve its intended purpose by being executed by a computer alone, or may be intended to achieve its intended purpose by being executed by a computer together with other programs. it can. In the latter case, the program according to this section can be mainly composed of data.

(15) A recording medium on which the program according to item (14) is recorded so as to be readable by a computer.

  If the program recorded on the recording medium is executed by a computer, the same operation and effect as the method according to any one of the items (1) to (13) can be realized.

  This recording medium can adopt various formats, for example, a magnetic recording medium such as a flexible disk, an optical recording medium such as a CD and a CD-ROM, a magneto-optical recording medium such as an MO, and an unremovable storage such as a ROM. Any of these may be adopted.

  Hereinafter, one of more specific embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a block diagram conceptually showing the hardware configuration of a gear noise CAE (Computer Aided Engineering) system 10 suitable for implementing a gear noise prediction method according to an embodiment of the present invention. The gear noise CAE system 10 is mainly configured by a computer 24 having a processor 20 and a memory 22. In the present embodiment, the gear noise prediction method is an example of the “gear vibration calculation method” in the item (1).

  An input device 30 such as a keyboard and a mouse is connected to the computer 24, whereby data and commands can be input to the computer 24. The computer 24 is further connected to an output device 40 such as a monitor (for example, a display), a printer, a plotter, etc., thereby supporting messages and information on the computer 24 (for example, data input to the computer 24). The data input form (calculation result by the computer 24) is visualized and presented to the user.

  As shown in FIG. 1, an external storage device 50 is further connected to the computer 24. The external storage device 50 is used with a recording medium 52 such as a CD-ROM being detachably mounted. The recording medium 52 includes, for example, various programs and various data (for example, data for defining an FEM model) including a gear noise prediction program to be executed by the computer 24 in order to implement the gear noise prediction method. ) Is recorded. These programs and data are read from the recording medium 52 into the computer 24 and processed as necessary.

  The gear noise prediction method is executed in order to predict vibrations that occur in a working state in a manual transmission (hereinafter also referred to as “M / T”) of an automobile.

  FIGS. 2 to 4 show an example in which the M / T 60 is a type mounted on a front-wheel drive (FF) type automobile. Specifically, FIG. 2 shows an external view of the M / T 60 in a perspective view, and FIG. 3 shows a gear train accommodated in the M / T 60 in a perspective view. In FIG. 4, a plurality of mechanical elements of the M / T 60 are simplified and shown in a plan view.

  As shown in FIG. 3, in M / T 60, a plurality of rotating shafts 90 that rotate together with a plurality of gears 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84. 92 and 94 are accommodated in the case 96 shown in FIG. 2 in a state where the tooth surfaces are meshed with each other.

  As shown in FIG. 3, the gears 62, 64, 66, 68 and 70 are 1st gear, 2nd gear, 3rd gear, 4th gear and 5th gear, respectively, and the gears 74, 76, 78, 80 and 82 are respectively The gears are meshed with the gears 62, 64, 66, 68 and 70, respectively. The gear 84 is a final gear, and the gear 72 is a gear meshed with the gear 84.

  The rotation shafts 90, 92, and 94 are, for example, an input shaft 90 that is rotated by a power source (for example, an engine or an electric motor) of an automobile on which the M / T 60 is to be mounted, and the rotation (torque) of the input shaft 90. 3, among the plurality of gear pairs shown in FIG. 3, an output shaft 92 that is transmitted and rotated via a synchromesh (not shown) and a pair of drive shafts 94, 94 ( (See FIG. 4).

  3 and 4, reference numeral 98 denotes a differential gear. The differential gear 98 is installed between a pair of drive shafts 94 and 94 connected to the gear 84 and controls the difference in rotational speed between them.

  As shown in FIG. 2, the case 96 has a housing for a power source of an automobile (for example, an engine as an internal combustion engine) on which the M / T 60 is to be mounted by using a fitting such as a bolt at the mounting portion 102 of the case 96. Cylinder block) is rigidly coupled (fixed). Further, the case 96 is elastically coupled to the vehicle body via an elastic body such as rubber at the mount point PM thereof. The mount point PM is selected as a vibration measurement point for measuring the vibration of M / T60.

  As shown in FIG. 3, in the M / T 60, a rotating body 104 is formed by gears 62, 64, 66, 68 and 70 and a rotating shaft (input shaft) 90. Further, a rotating body 106 is formed by the gears 72, 74, 76, 78, 80 and 82 and a rotating shaft (output shaft) 92. Further, a rotating body 108 is formed by the gear 84 and a rotating shaft (drive shaft) 94.

  That is, in this embodiment, M / T 60 is an example of the “gear device” in the above item (1), and each of the three rotating bodies 104, 106, and 108 is an example of the “rotating body” in the same term. Yes, the case 96 is an example of the “support” in the same section.

  FIG. 4 shows the configuration of the M / T 60 on the assumption that a bench test of the M / T 60 is performed. For this reason, the “drive motor” in FIG. 4 corresponds to the “power source” in the actual machine. The “absorption motor” corresponds to a “wheel” in the actual machine. In FIG. 4, the M / T 60 is configured such that rotation transmission (torque transmission) from the input shaft 90 to the output shaft 92 is performed via a gear pair including a gear 66 (3rd gear) and a gear 78. A state in which rotation transmission (torque transmission) from the output shaft 92 to the drive shaft 94 is performed through a gear pair composed of a gear 72 and a gear 84 (final gear) is shown with particular attention.

  As shown in FIG. 4, each rotating shaft 90, 92, 94 is supported by a case 96 via an appropriate number of bearings 100, and the case 96 holds each bearing 100. In the M / T 60, a vibration transmission system 110 including three rotating bodies 104, 106 and 108 and a case 96 is configured.

  FIG. 4 shows the configuration of the M / T 60 by taking an example in which each gear 62 and the like are helical gears. Therefore, an engagement portion of the gear pair 66 and 78 involved in torque transmission from the input shaft 90 to the output shaft 92 and an engagement portion of the gear pair 72 and 84 involved in torque transmission from the output shaft 92 to the drive shaft 94 are provided. The loads F1 and F2 are generated in a direction inclined with respect to the direction perpendicular to the axis due to the presence of the twist angle ψ of each gear 62 and the like. Each of the loads F1 and F2 includes a dynamic load due to meshing of teeth in addition to a load due to input torque. This dynamic load is generated by tooth surface modification, tooth deflection, and manufacturing errors.

  Further, in FIG. 4, the rotational inertia moment of the rotating body 104 is expressed as “M1”, and the rotational inertia moment of the rotating body 106 is expressed as “M2”. Further, the coupling rigidity of the gear pairs 66 and 78 is expressed as “K1”, and the coupling rigidity of the gear pairs 72 and 84 is expressed as “K2”, respectively. Each coupling stiffness K * is, for example, when two actual elastic rotating bodies that mesh with each other are equivalently replaced with two virtual rigid rotating bodies that mesh with each other and connected to each other by a rotating spring. This corresponds to the rigidity of the rotary spring.

  The dynamic load due to the meshing of the teeth acts as a meshing excitation force of the gears (hereinafter referred to as “gear excitation force”), and the case 96 is vibrated via the bearing 100. Gear noise is generated. Therefore, in order to reduce gear noise, it is important to reduce gear excitation force and to improve the vibration characteristics (particularly vibration response characteristics) of the case 96. Therefore, designers and analysts of M / T 60 are required to predict the gear vibration force with high accuracy and to calculate the vibration response of case 96 with high accuracy.

  By the way, Honda, one of the inventors of the present invention, studied to find a method that can accurately analyze the gear vibration, and as a result, the load acting on each tooth surface when the meshing gear pair rotates. It was found that it is effective to analyze gear vibration in consideration of the dynamic load which is the fluctuation of. Furthermore, the inventor differentiated the dynamic load from the ideal basic circle radius of each gear, the rotational moment of inertia of each gear, the gear ratio, the transmission torque, and the tooth profile error with the rotation angle of the gear of interest. A new analysis theory that can be calculated using the obtained basic circle radius error, the basic circle radius error derivative obtained by differentiating the basic circle radius error with the rotation angle of the gear of interest, and the rotation angular velocity of the gear of interest. Advocated. The contents of this new analysis theory are disclosed in Japanese Patent Laid-Open No. 5-157663.

  In the present embodiment, the gear vibration force is predicted with high accuracy by this new analysis theory. In this new analysis theory, the dynamic load is generated between the meshing tooth surfaces of the two gears in response to the gear radial variation of the meshing contact points where the tooth surfaces of the two gears contact each other during meshing. It means the load that acts.

  The gear noise prediction method has been developed as a tool that supports the design of the structure of the M / T 60 so as to meet the requirements for light weight and low noise of the M / T 60. More specifically, in this gear noise prediction method, the gear noise generated in the vibration transmission system 110 is considered in consideration of the gear vibration force, the time variation of the bearing load acting on the bearing 100, and the vertical vibration of the mount point PM. It is executed in order to predict it as a time variation of acceleration.

  FIG. 5 conceptually shows a series of operations performed by a designer and an analyst using the gear noise CAE system 10 in a process diagram.

  In the series of operations, first, in step A, gear specification values (for example, pressure angle, torsion angle, gear ratio, number of teeth, basic circle radius, rotational speed, rotational inertia moment, etc.) are input as design variables. In addition, tooth surface calculation is performed. By this tooth surface calculation, the shape of the ideal tooth surface (mechanistically defined tooth surface) of each gear is calculated. That is, a tooth surface having no modified tooth surface error is obtained by calculation.

  By the way, Honda, one of the present inventors, has proposed a new tooth profile theory, the contents of which are disclosed in Japanese Patent Laid-Open No. 9-53702.

  Briefly, according to the new tooth profile theory, for each gear, a stationary coordinate system fixedly assumed with reference to the two axes of the gear pair and the common perpendicular of the two axes, In addition to the rotational coordinate system that rotates with each gear assumed for the gear, the stationary coordinate system is another coordinate system that is rotationally transformed so that one coordinate axis thereof is parallel to the working surface of the gear pair. Thus, one having a certain relative positional relationship with the rotating coordinate system is provided, and another coordinate system is used as the intermediate coordinate system.

  According to this new tooth profile theory, as in the conventional tooth profile theory, the tooth profile curve of each gear can be described directly as a function of the rotation angle in the original stationary coordinate system without mediating the pitch rotator, It can also be described directly as a function of the rotation angle in the rotating coordinate system. Furthermore, according to the new tooth profile theory, the tooth surface shape of the gear is directly described on each basic coordinate system, so that the contact problem of all kinds of gear pairs from the cylindrical gear to the hypoid gear can be solved in the static space. Using a defined unified concept (for example, an action plane, a tooth right-angle plane, a pressure angle, a torsion angle, etc.), it becomes possible to describe it uniformly by a common relatively simple expression. Further, according to the new tooth profile theory, the tooth surface shape of the gear can be accurately described even when the angular velocity ratio of the gear pair changes due to the error or deflection of the tooth surface.

  Furthermore, according to this new tooth profile theory, not only the movement of the gear pair itself but also the load acting on the bearing that rotatably supports the gear pair is taken into account, so that the load fluctuation is accurate for the entire gear movement system. Described in Furthermore, according to this new tooth profile theory, the contact point trajectory of the gear (the trajectory drawn as the contact point of the tooth surface pair meshing with each other progresses) and the common normal inclination so that the fluctuation of the bearing load becomes substantially zero. By setting the angle (normal line at each contact point with respect to the pair of tooth surfaces engaged with each other), the gear pair can be reduced in noise.

  Next, in Step B, the tooth surface modification error of each gear (crowning, end relief, etc., the amount of change of the modified tooth surface that has undergone tooth profile modification from the ideally defined tooth surface) is a design variable. After the input, the gear vibration force generated from the gear due to the meshing of the modified gear is calculated. Of the frequency of the gear vibration force, the target is a component of high frequency and minute amplitude, and specifically, the meshing primary and secondary components (for example, 1 to 3 kHz). In the calculation of the gear vibration force, the aforementioned rotational moment of inertia M * and rigidity K * (bending, shearing, Hertz) are taken into consideration.

  By the way, according to the above-described new analysis theory, if the basic circle radius error of each gear is mainly found, it is possible to calculate the dynamic load of each gear and the gear vibration force. On the other hand, according to the above-mentioned new tooth profile theory, it is an ideal correspondence of the meshing transmission error, that is, the actual correspondence between one rotation angle of two gears meshing with each other and the rotation angle of the other gear. If the difference corresponding to the deviation from is found, the above-mentioned basic circle radius error can be measured.

  Furthermore, according to the new tooth profile theory, it is possible to accurately obtain the trajectory drawn by the contact points where the tooth surfaces meshing with each other come into contact with each other, that is, the contact point trajectory. The contact point trajectory extends along the meshing direction in which the contact point, that is, the meshing point proceeds on the tooth surface. On the other hand, the meshing transmission error described above depends on the shape of the contact point locus on the tooth surface of the actual meshing tooth surface with a modification error, that is, roundness. Further, the contact point locus on the tooth surface is geometrically specified by the combination of the meshing progress direction and the tooth profile roundness of the actual meshing tooth surface in the meshing progress direction. Hereinafter, a parameter describing the degree of the tooth profile roundness (for example, the difference between the ideal tooth surface and the actual tooth surface) is referred to as a tooth profile round parameter, which corresponds to a meshing transmission error curve described later.

  Therefore, when the new analysis theory and the new tooth profile theory are combined, the gear vibration force is accurately described by the tooth profile roundness parameter as shown in FIG. Based on the knowledge described above, the gear vibration force is calculated in step B in FIG.

  When the calculation of the gear vibration force according to the new tooth profile theory is completed, as shown in FIG. 5, the response of the vibration transmission system 110 to the vibration with the gear pair as the vibration source is calculated in step C. The response of the vibration transmission system 110 conceptually corresponds to a signal obtained by amplifying or attenuating the gear vibration force according to the frequency response characteristic (vibration characteristic) of the vibration transmission system 110.

  In this vibration response calculation, a mechanism motion in consideration of elastic characteristics using an FEM model that approximately represents the overall shape of the case 96 and the shape of the periphery of each bearing 100 in the case 96 by a large number of finite elements. Analysis is performed. In this vibration response calculation, the vibration response of the vibration transmission system 110 is considered in consideration of the dynamic characteristics of the rotating shafts 90, 92, 94 and the case 96 (for example, the elastic vibration characteristics of the rotating shafts 90, 92, 94 and the case 96). It is possible to calculate.

  Further, in this vibration response calculation, the rigidity of the three rotating bodies 104, 106, 108 (for example, the rigidity of the disc such as the gear 62 and the rigidity of the rotating shaft 90), the initial alignment, and the like are selected. Therefore, this vibration response calculation can be effectively used as a tool for optimizing each design variable in order to design the M / T 60 so as to meet the purpose of light weight and low noise.

  When this vibration response calculation is executed, gear noise, load fluctuation of the bearing 100, load fluctuation at the mount point PM (vibration acceleration fluctuation), and the like are calculated. In FIG. 13, the calculation result about the frequency characteristic of the bearing load acting on the bearing 100 that supports the output shaft 92 and the calculation result about the frequency characteristic of the vertical vibration acceleration at the mount point PM of the M / T 60 are as follows. It is represented by a graph.

  Thereafter, in step D in FIG. 5, the vibration characteristics of M / T are evaluated by the designer based on the result of the vibration response calculation. At this time, the evaluation items include the magnitude of gear noise (for example, the magnitude of acoustic radiation power), the magnitude of load fluctuation of the bearing 100, the magnitude of load fluctuation (vibration acceleration fluctuation) at the mount point PM, and the like.

  Subsequently, in step E, conformity design of M / T 60 is performed based on the evaluation result. Specifically, after changing various design variables, the step C is executed again to perform the vibration response calculation until the evaluation results satisfactory for all the evaluation items are obtained.

  This completes a series of operations performed by the designer and the analyst using the gear noise CAE system 10.

  Steps A to C and E described above are executed by executing the gear noise prediction program. The details of the gear noise prediction program are conceptually represented in the flowchart of FIG.

  When this gear noise prediction program is executed, first, in step S1 (hereinafter, simply expressed as “S1”, the same applies to other steps), the above-mentioned gear specification values are obtained for the gear pair of interest. Representing data is input to the computer 24 via the input device 30.

  Next, in S2, the above-described tooth surface calculation is performed based on the data representing the input gear specification value. By the tooth surface calculation, the aforementioned meshing traveling direction is calculated for each gear. The meshing direction is acquired according to the above-mentioned new tooth profile theory as described in JP-A-9-53702.

  Specifically, when the meshing traveling direction of the gear Gear1 is acquired, for example, each speed ratio of the gears Gear1 and Gear2 when the gear pair Gear1 and Gear2 of this time rotates while satisfying the tooth surface contact motion condition. Find γ. The rotation angle θ1 of the gear Gear1 is described based on the angular velocity ratio γ and the rotation angle θ2 of the gear Gear2. In the intermediate coordinate system, the contact point locus between the meshing tooth surfaces and the meshing tooth surface at the contact point The inclination angle of the common normal is described by a first function having the rotation angle θ1 as an auxiliary variable. In the stationary coordinate system, based on the first function and the relative positional relationship between the stationary coordinate system and the intermediate coordinate system, the contact point trajectory and the common normal inclination angle are respectively the rotation angle θ1 as an auxiliary variable. It is described by two functions. Thereby, the contact point locus and the common normal inclination angle of the gear Gear1 in the stationary coordinate system are acquired. From the acquired information on the contact point locus, the meshing traveling direction of the gear Gear1 is acquired.

  Subsequently, in S3, data representing various constants necessary for execution of S4 and S5 described later is appropriately input for the current gear pair.

  Thereafter, in S4, the gear vibration force is calculated for the current gear pair according to the new tooth profile theory. In S4, the gear vibration force is calculated regardless of the finite element model described later. The calculation theory will be described below.

  As illustrated in FIG. 8, for the current gear pair Gear1 and Gear2, a coordinate system defined by their two gear axes and their common perpendicular is used. The coordinate system set for one gear Gear1 is defined by the u1c axis, the v1c axis, and the Z1 axis. The coordinate system set for the other gear Gear2 is defined by the u2c axis, the v2c axis, and the Z2 axis.

  In the example shown in FIG. 8, both gears Gear1 and Gear2 are helical gears, and the teeth of the gear Gear1 have a twist angle ψb1 and the teeth of the gear Gear2 have a twist angle ψb2. In FIG. 8B, the pitch circle radius of the gear Gear1 is represented by “Rp1” and the basic circle radius is represented by “Rb1”, while the pitch circle radius of the gear Gear2 is represented by “Rp2” and the basic circle radius is “Rb2”. ], Respectively.

  As shown in FIG. 8 (b), when the shaft torque Ts is transmitted between the gear pair Gear1 and Gear2 this time, the tooth surface force Fq is applied to each tooth with which the gears Gear1 and Gear2 mesh with each other. It occurs along the common tangent of both base circles of the two gears Gear1, Gear2. This tooth surface force Fq is called a tangential load. Each tooth that the gears Gear1 and Gear2 mesh with each other also generates an axial load Fz that is an axial component that acts on each gear Gear1 and Gear2 in the direction along the rotation axis due to the presence of the twist angle ψ. To do. The tangential load Fq includes, in addition to a load Fqs corresponding to the shaft torque Ts (corresponding to a response displacement load described later), a dynamic load Fqd generated by meshing of teeth.

In FIG. 8 (b), the per gear Gear2, tangential load Fq, the helix angle [psi, the resultant force _{F N} and the axis load Fz, and tangential load Fq and axis load Fz, respectively, "Fq2", "ψb2", "Fz2 ”And“ F _N2 ”.

  In S4, the tangential load Fq and the axial load Fz are calculated for each gear by combining the aforementioned new tooth form theory and the conventional tooth form theory. Hereinafter, the theory that the tangential load Fq2 and the axial load Fz2 are obtained by calculation for the gear Gear2 will be described with reference to FIGS.

  In FIG. 9, the time variation Fq2 (t) of the tangential load Fq2 is the sum of the time variation Fq2s (t) of the response displacement load Fq2s and the time variation Fq2d (t) of the dynamic load Fq2d. Is calculated as The sum is an example of the “composite value” in item (1). Here, the response displacement load Fq2s is a component of the driving torque acting on the gear Gear2 in the tangential load Fq2, and is calculated according to the conventional tooth profile theory, whereas the dynamic load Fq2d is calculated according to the new tooth profile theory. The

  Specifically, the response displacement load Fq2s is calculated assuming a model in which two gears Gear1 and Gear2 are connected to each other by a rotary spring having a spring constant K and a rotary damper having a damping coefficient C. . Torque transmission between the two gears Gear1 and Gear2 is expressed by the rotary spring and the rotary damper. That is, the response displacement load Fq2s is calculated according to the conventional tooth profile theory.

  Specifically, the response displacement load Fq2s is expressed by the equation (2) in FIG. 9, and the product of the relative angular displacement between the two gears Gear1 and Gear2 and the spring constant K, and the two gears. It is calculated by dividing the sum of the product of the relative angular velocity between Gear1 and Gear2 and the damping coefficient C by the basic circle radius Rb2 of the gear Gear2.

  In Equation (2), “θ1 (t)” represents the time variation of the rotational displacement of the gear Gear1, “θ2 (t)” represents the time variation of the rotational displacement of the gear Gear2, and “ω1 (t)” is The time variation of the rotational speed of the gear Gear1 is represented, and “ω2 (t)” represents the time variation of the rotational speed of the gear Gear2. Therefore, the relative angular velocity is

  θ1 (t) −θ2 (t)

And the relative angular velocity is

  ω1 (t) −ω2 (t)

It is represented by

  In addition, the response displacement load Fq2s is a relative displacement of the gear Gear2 due to the drive torque acting on the gear Gear2 (elastic displacement, the state of which is described by the relative rotational displacement and the relative rotational speed). This means that the load is generated in the gear Gear2 in response to the dynamic load Fq2d, and is classified as a static load component of the tangential load Fq2.

  The dynamic load Fq2d of the gear Gear2 is calculated according to the aforementioned new tooth profile theory. Here, the time variation Fq2d (t) of the dynamic load Fq2d is expressed by a periodic function whose amplitude is the component of each meshing degree of the dynamic load time variation Fq2d (t). Therefore, the dynamic load time fluctuation Fq2d (t) is expressed by the equation (3) in FIG.

  Hereinafter, various symbols in the expression (3) will be described.

  Fq2d1: meshing primary component of the dynamic load time variation Fq2d (t) of the gear Gear2

  Fq2d2: meshing secondary component of dynamic load time variation Fq2d (t) of gear Gear2

  Fq2dn: meshing nth-order component of the dynamic load time variation Fq2d (t) of the gear Gear2

  N2: Number of teeth of gear Gear2

  ω2_: Average rotation speed of the gear Gear2

  φ21: Phase of meshing primary component of meshing of dynamic load time variation Fq2d (t) of gear Gear2

  φ22: Phase of the meshing secondary component of the dynamic load time variation Fq2d (t) of the gear Gear2

  φ2n: meshing of the dynamic load time variation Fq2d (t) of the gear Gear2 and the phase of the nth-order component

  By the way, the frequency of the component (for example, the meshing primary and secondary components) which is particularly dominant in the dynamic load time variation Fq2d (t) is about 1 to 3 [kHz], while the M / T 60 is mounted. For example, in the case of an in-line four-cylinder engine, the engine torque fluctuation frequency is 6,000 [rpm] and 200 [Hz], and the dynamic load time fluctuation Fq2d (t) and the engine The frequency band is different from the torque fluctuation. On the other hand, the torque fluctuation of the engine means the fluctuation of the driving torque of the gear Gear2.

  Therefore, when calculating the tangential load Fq2 from the response displacement load Fq2s and the dynamic load Fq2d, it is not necessary to consider the coupled vibration between the response displacement load Fq2s and the dynamic load Fq2d. Therefore, in this embodiment, the tangential load Fq2 is calculated by the sum of the response displacement load Fq2s and the dynamic load Fq2d.

  In S4, the time variation Fz2 (t) of the axial load Fz2 of the gear Gear2 is also calculated. The axial load time variation Fz2 (t) is calculated using the tangential load time variation Fq2 (t) and the torsion angle ψb2 as represented by Expression (4) in FIG.

  In the above, the theory that the tangential load Fq and the axial load Fz are obtained by calculation in S4 has been described. Hereinafter, the execution contents of S4 will be described over time by referring to FIG.

  In S41, first, in S41, the aforementioned tooth profile roundness parameter is defined for each gear.

  The tooth profile roundness parameter is the meshing traveling direction in which the meshing contact point between the gears Gear1 and Gear2 travels on the meshing tooth surface of each gear as the meshing of the two gears Gear1 and Gear2 progresses (in the traveling direction of the meshing contact point). For example, as shown in FIG. 6, it is defined by an inclination angle η with respect to the direction perpendicular to the axis) and an engagement transmission error curve of each gear (for example, the rotational displacement of one gear and the other in accordance with the rotational displacement). The curve representing the relationship with the rotational displacement generated in the gear).

  The meshing transmission error curve is in contact with a base disk having the same diameter as the ideal base circle and the cylindrical surface of the base disk, as described in Japanese Patent Laid-Open No. 5-157663 with reference to FIG. A straight ruler having a straight edge, and a pivot type or linear type measuring element that translates integrally with the straight ruler, the contact point of which is brought into contact with the actual tooth surface of the gear to be measured. It is possible to measure using a measuring device.

  When measuring the shape of the actual tooth surface using this measuring device, the contact point of the probe is moved on the actual tooth surface along the acquired meshing advance direction (contact point locus). The gear to be measured and the measuring element are relatively displaced in the rotation axis direction of the gear to be measured.

  Next, in S42, the amplitude Fq * di (i = 1 to n) of the dynamic load Fq * d (*: 1, 2) is calculated for each gear. The amplitude Fq * di can be calculated using the above defined tooth profile roundness parameter. This is because the tooth profile roundness parameter reflects the meshing transmission error curve described above, and thus the basic circle radius error described above.

  The amplitude Fq * di of each meshing degree i of the dynamic load Fq * d is calculated based on the rotational speed of each gear and the load applied to the tooth surface of each tooth surface. The load is generated, for example, by torque transmitted from the counterpart gear to each gear. Specifically, the amplitude Fq * di can be calculated according to the above-described new analysis theory disclosed in, for example, the above-mentioned Japanese Patent Application Laid-Open No. 5-157663.

  When the calculation of the amplitude Fq * di is completed, in S43, the time variation Fq * d (t) of the dynamic load Fq * d of each gear is calculated using the equation (3) in FIG. Subsequently, in S44, the time variation Fz * (t) of the axial load Fz * of each gear is calculated using the equation (4) in FIG. This completes the execution of S4.

  Thereafter, in S5, the response of the M / T 60 case 96 to the vibration using the current gear pair as a vibration source is calculated by mechanism motion analysis in consideration of the elastic characteristics. This calculation is performed by using, for example, a method for analyzing rigid body displacement and elastic vibration of an object, which is disclosed in Japanese Patent Laid-Open No. 2000-305922.

  In S5, first, in S51, an overall model of FEM, that is, one that approximately represents M / T 60 by a plurality of finite elements is defined. The three-dimensional shape shown in FIGS. 2 and 3 is approximately expressed by the defined overall model.

  Next, in S52, the time variation Fq * s (t) of the response displacement load Fq * s of each gear is calculated using the equation (2) in FIG. Subsequently, in S53, the time variation Fq * (t) of the tangential load Fq * of each gear is calculated using the equation (1) in FIG.

  After that, in S54, an external load input to a gear model (or a rotating body model) that approximately represents each gear is calculated. The external load is a translational force and a moment acting on each gear by the meshing of teeth. These translational forces and moments are calculated based on the tangential load Fq * and axial load Fz * calculated for each gear and the gear specifications including the pressure angle and the torsion angle of each gear tooth.

  An example of the gear model is shown in a plan view in FIG. 10 (a) and in a side view in FIG. 10 (b). In FIG. 10, of the two gears meshing with each other, the gear attached coaxially with the input shaft 90 is indicated as “Body 1”, the gear attached coaxially with the output shaft 92 is indicated as “Body 2”, and Case 96 is described as “Body3”. The whole coordinate system xyz is fixed to Body3.

  In this embodiment, as shown in FIG. 10 (b), with respect to Body1, four representative nodes # 1-1 to # 1-4 out of a plurality of nodes assigned to Body1 are circles of Body1. It is set to be arranged at equal angular intervals on the circumference. On the other hand, with respect to Body2, four representative nodes # 2-1 to # 2-4 among the plurality of nodes assigned to it are set so as to be arranged at equal angular intervals on the circumference of Body2. . These Body1 and Body2 are meshed with each other at the representative nodes sharing the same number.

In this embodiment, in order to simplify the calculation of vibration response, it is assumed that both Body1 and Body2 are rigid disk models. Furthermore, in order to simplify the calculation of the vibration response, as shown in FIG. 10B, for example, the tangential load F ₂₁ acting on the body 1 from the body 2 to the body 1 includes four representative nodes # 1-1 to # 1 to It is assumed that # 1-4 are equally distributed.

  Furthermore, in this embodiment, in order to simplify the calculation of the vibration response, as illustrated in FIG. 11, it is assumed that the rotating shaft that rotates together with each gear is a rigid body model, like each gear. Yes. In the example shown in FIG. 11, the upper rotating shaft is an input shaft, and driving torque is input to the input shaft from the outside, and the driving torque is transmitted to the lower rotating shaft by a gear pair. The lower rotation shaft is an output shaft, and the output shaft rotates a motor element (corresponding to the absorption motor in FIG. 4) that simulates a dynamometer.

  Further, in the example shown in FIG. 11, any of the rotating shafts is elastically supported between the case 96 at both ends of the respective gears. However, with respect to the input shaft, elastic support points are arranged at a position a distance a away from the gear and a distance b on the other side, whereas the output shaft is The elastic support points are respectively arranged at a position separated from the gear by a distance c on one side and a position separated by a distance d on the other side.

  When the external load is calculated as described above, in S55 in FIG. 7, based on the defined finite element model, by considering the calculated external load, the mechanism motion in consideration of the elastic characteristics. The vibration response is calculated by analysis. Thereafter, in S56, the calculation result is visualized and output to the user via the output device 40.

  The user determines whether or not the current design of the M / T 60 is appropriate by referring to the calculation result. Thereafter, in S6, it is determined whether recalculation is necessary. If the user determines that the current design is not valid, the user inputs a command to the computer 24 indicating that recalculation is necessary. In this case, the determination in S6 is YES, and the execution of the gear noise prediction program is resumed from the step according to the user's request. On the other hand, when the user determines that the current design is appropriate, the user inputs a command to the computer 24 indicating that recalculation is not necessary. In this case, the determination in S6 is NO, and the execution of the gear noise prediction program is completed.

  The present inventors executed this gear noise prediction program using the model shown in FIG. 11 in order to confirm the validity of the calculation by this gear noise prediction program. To simplify the confirmation work, the number of teeth is selected to be 5, and the dynamic load is defined to reflect only the meshing primary component, and the amplitude of the dynamic load is 33.3 [kgf]. Set to. Other specifications for the gears are as follows.

  Pressure angle: 20 [°]

  Twist angle: 31.3 [°]

  Gear ratio: 1: 1

  Basic circle radius: 30 [mm]

  Rotation speed: 3,000 [rpm]

  a: 158.5 [mm]

  b: 46 [mm]

  c: 179 [mm]

  d: 50 [mm]

  FIG. 12 is a graph showing the calculation result as the time variation of the torque acting on the output shaft in FIG. Although it is assumed that the driving torque input to the input shaft in FIG. 11 is constant, the torque output from the output shaft varies with time as a result of the torque variation due to the dynamic load of the gears being added to the output shaft. is doing. The amplitude of the fluctuation corresponds to the product of the amplitude of the dynamic load and the base circle radius, which indicates that the calculation result is valid.

  FIG. 13 is a graph showing another example of the calculation result obtained by executing this gear noise prediction program. In this example, the calculation results are the frequency characteristics of the bearing load acting on the bearing 100 that supports the output shaft 92 at M / T60, and the frequency characteristics of the vibration acceleration generated in the vertical direction at the mount point PM at M / T60. Is included.

  As is clear from the above description, in this embodiment, S41 to S45 in FIG. 7 cooperate with each other to constitute an example of the “tangential load calculation step” in the above item (1), and S51 to S53 cooperate with each other. Thus, an example of the “vibration response calculation step” in the same section is configured.

  Further, in the present embodiment, S46 in FIG. 7 constitutes an example of the “axial load calculation step” in the item (2), and S51 to S53 cooperate with each other as an example of the “vibration response calculation step” in the same term. It constitutes.

  Furthermore, in this embodiment, S43 in FIG. 7 constitutes an example of the “response displacement load calculation step” in each of the items (3) and (4), and S44 is “dynamic load” in the item (5). An example of “time fluctuation calculation step” is configured, and S42 is an example of “dynamic load amplitude calculation step” in each of the items (6) and (7), and is multiplied by the dynamic load amplitude in S44. The part defining the periodic function constitutes an example of the “periodic function defining step” in the item (8).

  Further, in the present embodiment, S51 to S53 in FIG. 7 constitute an example of the “vibration response calculation step” in the item (9), S52 constitutes an example of the “load calculation step” in the term, and S41 Thru | or S45 mutually constitutes an example of the "tangential load calculation process" in the same term.

  Furthermore, in this embodiment, S52 in FIG. 7 constitutes an example of the “load calculation step” in each of the items (11), (12), and (13), and the gear noise prediction program described above is An example of the “program” according to the item 14) is configured, and the recording medium 52 is an example of the “recording medium” according to the item (15).

  In addition, in this embodiment, in order to simplify the calculation of the vibration response, the gear is represented by a rigid disk model that does not represent its tooth profile, and on the circumference of the rigid disk model. The translational force and the moment as an external load are equally distributed to a plurality of representative nodes arranged at equal angular intervals in FIG.

  On the other hand, when it is necessary to improve the calculation accuracy of the vibration response, for example, the gear is represented by an elastic disk model that does not represent its tooth profile, and assigned to the elastic disk model. Of the multiple original nodes, select the closest original node that does not match or match the actual meshing point with the other gear, treat the selected original node as a pseudo meshing point, and use it as the pseudo meshing point. It is possible to calculate the external load so that the external load acts intensively.

  If it is necessary to further improve the accuracy of calculation of vibration response, for example, the gear is represented by an elastic precision model that expresses the tooth profile more precisely, and the other of the elastic faithful models It is possible to calculate the external load so that the external load acts intensively at a point that matches the actual meshing point with the gear.

  As mentioned above, although one embodiment of the present invention was described in detail based on a drawing, this is an illustration, and it is various based on the knowledge of those skilled in the art including the aspect described in the section of the [Disclosure of the Invention]. The present invention can be implemented in other forms that have been modified or improved.

It is a block diagram which represents notionally the hardware constitutions of the gear noise CAE system suitable for implementing the gear noise prediction method according to one Embodiment of this invention. It is a perspective view which shows the external appearance of the manual transmission supported by design by the gear noise CAE system shown in FIG. FIG. 3 is a perspective view showing a gear train housed in a case of the manual transmission shown in FIG. 2. It is a top view which simplifies and shows the manual transmission shown in FIG. FIG. 3 is a process diagram for explaining a series of operations performed by a designer to design the manual transmission shown in FIG. 2 using the gear noise CAE system shown in FIG. 1. It is a perspective view for demonstrating the concept of the tooth profile roundness parameter utilized in step A and B in FIG. 2 is a flowchart conceptually showing the contents of a gear noise prediction program executed by a computer in FIG. 1. FIG. 8 is a perspective view and a side view for mainly explaining a coordinate system used in the gear noise prediction program of FIG. 7 and a force acting between tooth surfaces. It is a figure which shows the type | formula for demonstrating the theory utilized in S4 in FIG. It is the top view and side view which show the gear model utilized in S5 in FIG. It is the front view and side view which show the gear model utilized in S5 in FIG. It is a graph which shows an example of the calculation result acquired by execution of the gear noise prediction program of FIG. It is a graph which shows another example of the calculation result acquired by execution of the gear noise prediction program of FIG.

Explanation of symbols

10 gear noise CAE system 24 computer 52 recording medium 60 manual transmission 96 case 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84 gear 90, 92, 94 rotating shaft 100 bearing 104, 106 , 108 Rotating body 110 Vibration transmission system

Claims (17)

A gear device in which at least two rotating bodies that rotate in mesh with each other are rotatably supported by a support, and the at least two rotating bodies include two rotating shafts and the two rotating shafts. And a gear vibration calculation method for calculating vibrations of two gears that rotate together coaxially together and that form a gear pair that meshes with each other at the tooth surfaces. ,
Between the tooth surfaces of the two gears, the time variation of the tangential load acting along the common tangent of both base circles of the two gears is expressed as follows: (a) the relative distance between the teeth where the two gears mesh with each other; In response to the displacement, the time variation of the response displacement load acting between the meshing tooth surfaces where the two gears mesh with each other; and (b) the meshing contact where the tooth surfaces of the two gears contact each other during the meshing. A tangential load calculating step for calculating a point as a composite value of the time variation of the dynamic load acting between the meshing tooth surfaces of the two gears in response to the time variation in the gear radial direction ;
A vibration response calculation step including a vibration response calculation step of calculating a time response of at least one of the rotating body and the support body with respect to the vibration having the gear pair as a vibration source based on the calculated tangential load time variation. Method.   Furthermore, based on the calculated tangential load time variation, an axial load calculation step of calculating a time variation of the axial load acting along the rotation axis of each gear is included, and the vibration response calculation step includes the calculation The gear vibration calculation method according to claim 1, wherein the time response is calculated based on the calculated axial load time variation and the calculated tangential load time variation.   The tangential load calculation step calculates the response displacement load time variation of each gear, the product of the time variation of the relative angular displacement between the two gears and the coupling rigidity of the two gears, and the basic circle of each gear. The gear vibration calculation method according to claim 1, further comprising a response displacement load calculation step of calculating using a value divided by the radius.   In the tangential load calculation step, the response displacement load time variation of each gear is calculated by multiplying the time variation of the relative angular displacement between the two gears and the coupling rigidity of the two gears, and the two gears. A response displacement load calculating step for calculating a sum of a product of a temporal variation in relative angular velocity between the two and a product of coupling damping of the two gears by dividing the sum by a basic circle radius of each gear. 3. The gear vibration calculation method according to 2. The tangential load calculation step is selected in advance so that the time variation of the dynamic load of each gear is a variable with the amplitude of each dynamic load of each gear at each meshing order i (i: 1 to n) and time t. The gear vibration calculation method according to claim 1, further comprising a dynamic load time variation calculation step that uses a product with a periodic function .   The dynamic load time variation calculation step includes a dynamic load amplitude calculation step of calculating an amplitude of a dynamic load of each gear based on an engagement transmission error curve of each gear as the engagement of the two gears progresses. 5. The gear vibration calculation method according to 5.   The dynamic load time fluctuation calculating step includes a dynamic load amplitude calculating step of calculating an amplitude of a dynamic load of each gear based on a rotation speed of each gear and a load applied to a tooth surface of each gear. Item 6. The gear vibration calculation method according to Item 5. The periodic function is defined such that the sum of the product of the angular velocity and time t and the phase is a variable.
The dynamic load time variation calculation step substitutes the product of the rotational speed of each gear and the number of teeth of each gear into the angular velocity of the periodic function for each meshing order i of the dynamic variation of the dynamic load of each gear, and The time variation of the dynamic load of each gear is calculated for each meshing order i by substituting the phase of the component at each meshing order i of the temporal variation of the dynamic load of each gear into the phase of the periodic function. Item 8. The gear vibration calculation method according to any one of Items 5 to 7. The vibration response calculation step calculates the time response using a finite element model that approximately represents the gear device,
The tangential load calculation step calculates the tangential load regardless of the finite element model,
9. The vibration response calculating step includes a load calculating step of calculating an external load input to a gear model representing each of the finite element models based on the calculated tangential load. The gear vibration calculation method according to any one of the above. The vibration response calculation step calculates the time response using a finite element model that approximately represents the gear device,
The tangential load calculation step calculates the tangential load in consideration of the interaction between the rotating body and the support,
9. The vibration response calculating step includes a load calculating step of calculating an external load input to a gear model representing each of the finite element models based on the calculated tangential load. The gear vibration calculation method according to any one of the above. The finite element model is defined to include a plurality of finite elements and a plurality of nodes,
The gear vibration calculation method according to claim 9 or 10, wherein the load calculation step calculates the external load with respect to at least one selected node selected in advance among the plurality of nodes. The gear model is a rigid model that expresses that the real gear does not warp in a direction perpendicular to the plane perpendicular to the axis of the real gear despite the input of the external load to the real gear represented thereby. And
The at least one selected node includes a plurality of representative nodes arranged at equal intervals on the rigid model among the plurality of nodes.
The gear vibration calculation method according to claim 11, wherein the load calculation step calculates the external load in association with the plurality of representative nodes.   The gear vibration calculation method according to claim 12, wherein the load calculation step calculates the external load so that the external load is equally distributed to the plurality of representative nodes.   The gear vibration calculation method according to claim 1, wherein the time response includes a time variation of a torque acting on the rotating shaft. A gear device in which at least two rotating bodies that rotate in mesh with each other are rotatably supported by a support, and the at least two rotating bodies include two rotating shafts and the two rotating shafts. And a gear vibration calculation method for calculating vibrations of two gears that rotate together coaxially together and that form a gear pair that meshes with each other at the tooth surfaces. ,
Between the tooth surfaces of the two gears, the time variation of the tangential load acting along the common tangent of both base circles of the two gears is expressed as follows: (a) the relative distance between the teeth where the two gears mesh with each other; In response to the displacement, the time variation of the response displacement load acting between the meshing tooth surfaces where the two gears mesh with each other; and (b) the meshing contact where the tooth surfaces of the two gears contact each other during the meshing. A tangential load calculating step for calculating a point as a composite value of the time variation of the dynamic load acting between the meshing tooth surfaces of the two gears in response to the time variation in the gear radial direction ;
Based on the calculated tangential load time variation, the axial load calculation step of calculating the time variation of the axial load acting along the rotation axis of each gear,
Based on the calculated axial load time variation and the calculated tangential load time variation, calculate the time response of at least one of the rotating body and the support body with respect to vibration using the gear pair as a vibration source. Including a vibration response calculation step to
The tangential load calculation step includes:
The time variation of the response displacement load of each gear is the product of the time variation of the relative angular displacement between the two gears and the coupling rigidity of the two gears, and the time variation of the relative angular velocity between the two gears. And a response displacement load calculation step of calculating a sum of the product of the coupling attenuation of the two gears and a value obtained by dividing the sum by the basic circle radius of each gear;
The time variation of the dynamic load of each gear is calculated by multiplying the dynamic load of each gear by the amplitude at each meshing order i (i: 1 to n) and a periodic function selected in advance so that the time t is a variable. Dynamic load time fluctuation calculation process to calculate using
The dynamic load time variation calculation step includes:
As the meshing of the two gears progresses, the dynamic load amplitude of each gear is calculated based on the meshing transmission error curve of each gear, or the rotational speed of each gear and the tooth surface of each gear A gear vibration calculation method including a dynamic load amplitude calculation step of calculating the dynamic load amplitude of each gear based on the load applied to the gear.   A program executed by a computer to implement the gear vibration calculation method according to any one of claims 1 to 15.   The recording medium which recorded the program of Claim 16 so that computer reading was possible.

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