JP2009294729A - Gear design support method, gear design support apparatus, gear design support program, and storage medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a gear design support method for high-precision and easy-to-support gear design by eliminating work of evaluating prototyping a gear driving system. <P>SOLUTION: The method includes: a basic input process S101 for inputting specification information of a gear, and driving condition information such as a target speed and a load torque; a gear shape error input process S102 for inputting shape error, i.e., a gear tooth profile error, a tooth trace error, and a cumulative pitch error; an assembling error input process S103 for giving information of an eccentric error between the base circle center and rotation center of the gear; a motion equation deriving process S106 for obtaining an action line at an initial stage of contact with the base circle in the gears, calculating the value of the shape error on the tooth surface of the gear, based on the information from the gear shape error input process, calculating the value of the assembling error by eccentricity, based on the information from the assembling error input process, setting the force equilibrium formula by each gear pair having contact on the action line, and generating the motion equation; a calculation process S107 for time-sequentially solving the equation of motion; and an output process S109 for outputting the action results of a driving shaft and a driven shaft calculated. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a gear design support device, a gear design support method, and a recording medium, and more specifically, by providing basic specifications, drive conditions, and error conditions (gear shape error and eccentric assembly error) of the gear. The present invention relates to a gear design support device, a gear design support method, a gear design support program, and a recording medium that can estimate transmission characteristics of a gear mechanism system in a state close to operation and check beforehand whether there is a problem with the gear mechanism system.

In general, a gear design support device using a computer is used in designing a gear in a gear mechanism system of a precision machine product such as a copying machine or a printer.
Conventionally, there has been proposed a technique in which a meshing radius that changes due to eccentricity is obtained by an approximate expression, and a differential equation is solved to obtain rotational characteristics (gear rotational error) (Patent Document 1).
That is, by approximating the rotation radius at the meshing position between the meshing gears by the cosine theorem to obtain the rotational angle ratio of the gears meshing with each other, and solving the rotational angle ratio as a variable-separated differential equation, The maximum rotation error of the output gear with respect to the input gear is obtained, and the eccentricity tolerance in the manufacture of each of the gears is determined so that the maximum rotation error is a predetermined value or less.
Also, outside, the effective radius of the gear that changes due to eccentricity is obtained, the rotational speed is multiplied by this to obtain the linear velocity at the meshing position, and this is divided by the eccentric radius to calculate rotational fluctuations. A device that develops into a gear train and obtains a phase in which fluctuation is reduced has been proposed (Patent Document 2).
Furthermore, by calculating the action line (surface) that changes due to gear mounting eccentricity and solving the force balance equation on this line (on the surface), the rotation unevenness of the meshing period and the rotation unevenness due to the eccentricity are calculated simultaneously. The thing to do is proposed (patent document 3).
In Patent Document 3, the gear design support device models a gear transmission mechanism system installed between a drive shaft and a driven shaft, and analyzes and calculates the dynamic behavior of the driven shaft with respect to the operation of the drive shaft. The basic circle center of the gear giving the information on the basic specifications of the gear, the drive condition information, the shape error of the gear tooth profile error, the tooth trace error, etc., and the eccentric error between the basic circle center of the gear and the rotation axis center And an action line that changes due to the eccentricity of the rotation axis center, and a force balance equation is set for each tooth pair in contact with the action line to generate an equation of motion and solve the equation of motion in time series to determine the drive axis and The operation result of the driven shaft is output.
Japanese Patent No. 3521744 JP 2002-122188 A JP 2003-240064 A

However, in Patent Documents 1 and 2, geometrical analysis is performed using a radius that changes due to eccentricity. This is a static analysis, and the influence of inertia terms and rotational speed (dynamic behavior: density unevenness) is obtained. It cannot be analyzed.
In Patent Document 3, the equation of motion is constructed in consideration of the tooth shape error, eccentric assembly error, tooth pair rigidity, load torque, etc., meshed for each tooth, so that more accurate analysis is possible. However, it takes time to calculate.
In particular, it takes a long time to calculate the position of the action line accompanying the eccentric rotation with the eccentric gear and calculate the balance of force on the action line strictly. Further, in a color copier or color printer having a plurality of photosensitive drums, the number of gear drive systems is increased correspondingly, which imposes a time burden on the designer. Furthermore, the same can be said for devices that are driven by using a large number of gears by reducing the number of motors as power sources such as low-cost machines.
In view of the above situation, the present invention reduces in advance the effects of the assembly error of the gear shape error (tooth profile error, tooth trace error, cumulative pitch error) and the eccentricity error that affect the rotation transmission characteristics of the gear in advance. Predicted by time analysis, the analysis is performed in consideration of dynamic behavior (influence of inertia term and rotation speed: resonance phenomenon, etc.), thereby confirming that there is no problem with the gear mechanism system, and the gear drive system An object of the present invention is to provide a gear design support method and apparatus capable of providing gear design support with high accuracy and ease without the need for trial manufacture and evaluation.

In order to solve the above-mentioned object, the invention according to claim 1 models a gear transmission mechanism system installed between the drive shaft and the driven shaft, and the dynamic behavior of the driven shaft with respect to the operation of the drive shaft. In the gear design support method for analyzing and calculating the basic input process, the basic input unit inputs the specification information that is the basic specification of the target gear and the drive condition information of the target speed and load torque, and the gear shape error. A gear shape error input step for inputting information on the shape error of the gear tooth profile error, tooth trace error and cumulative pitch error by the input unit, and an eccentricity between the basic circle center and the rotation center of the gear by the assembly error input unit. An action line at an initial time in contact with the basic circle of the gears is obtained from the basic input process by the assembly error input process that gives information on the error and the equation of motion derivation unit, The value of the shape error of the car tooth surface is calculated from the information given in the gear shape error input step, and the value of the assembling error due to eccentricity is calculated from the information given in the assembling error input step. A motion equation derivation step for generating a motion equation by setting a force balance equation for each tooth pair in contact on the action line based on the information, and a calculation step for solving the motion equation in time series by the calculation unit And an output step of outputting an operation result of the drive shaft and the driven shaft calculated by the calculation step by an output unit.
According to a second aspect of the present invention, the gear transmission mechanism system is a gear transmission mechanism system for driving a rotating drum that drives the rotating drum, and the driving shaft and the driven shaft are used in the output step. 2. The gear design support method according to claim 1, wherein when outputting the operation result, the output of the driven shaft is multiplied by the radius of the rotating drum and converted into a characteristic value on the surface of the rotating drum. Features.
According to a third aspect of the present invention, the equation of motion is generated by integrating the gear shape error, the assembling error due to the eccentricity, and the tooth-to-rigidity changing at the meshing position. It features a gear design support method.

According to a fourth aspect of the present invention, the tooth-to-tooth rigidity changes according to the gear shape error and the meshing position when the gear is at a constant speed, and the gear is at a constant speed. The gear design support method according to any one of claims 1 to 3, wherein the tooth-pair rigidity is treated as a constant value at the time of starting that is not.
The invention according to claim 5 is the gear design support according to any one of claims 1 to 3, wherein the transition of the meshing state of the gear adopts a value when the gear reaches a constant speed. Features method.
According to a sixth aspect of the present invention, the value of the viscosity coefficient of the equation of motion is made larger than usual when the gear starts up from a stationary state to a constant speed. It is characterized by the gear design support method described in 1.

The invention according to claim 7 is the gear design support according to any one of claims 1 to 3, wherein the analysis step and the convergence tolerance are adjusted in accordance with a load fluctuation timing when the gear is at a constant speed. The invention according to claim 8 is characterized in that the gear design support according to any one of claims 1 to 7, wherein the accuracy in solving the equation of motion is adjusted according to a band of meshing frequency. Features method.
The invention according to claim 9 is characterized by a program for causing a computer to execute the gear design support method according to any one of claims 1 to 8.
According to a tenth aspect of the present invention, there is provided a computer-readable storage medium storing the program according to the ninth aspect.

  The invention described in claim 11 models a gear transmission mechanism system installed between the drive shaft and the driven shaft, and analyzes and calculates the dynamic behavior of the driven shaft with respect to the operation of the drive shaft. In the gear design support device, basic input means for providing the basic information of the gear and the driving condition information of the target speed and load torque, the tooth profile error of the gear, the tooth trace error, the shape error of the accumulated pitch error Gear shape error input means for providing information on the assembly, assembling error input means for providing information on the eccentric error between the center of the basic circle and the rotation center of the gear, and an initial time when the basic input means contacts the basic circle of the gears. The value of the shape error of the gear tooth surface on the line is calculated from the information obtained by the gear shape error input means, and the value of the assembly error due to eccentricity is calculated by the assembly error input means. Calculated from the obtained information, and based on the calculated information, a motion equation derivation means for generating a motion equation by setting a force balance equation for each tooth pair in contact on the action line, and in time series Computation means for solving an equation of motion, and output means for outputting operation results of the drive shaft and the driven shaft calculated by the computation means are provided.

  Since it is configured as described above, according to the present invention, in the dynamic analysis calculation of the eccentric gear, which takes time to calculate in the gear simulation, the influence of the eccentricity is calculated as the position change on the action line, so that the same parameter as the gear shape error Parameters that can be analyzed by converting them up and improving the analysis efficiency (reduction of calculation time, reduction of calculation costs) in the time series calculation process, and consequently the rotation transmission characteristics of the gears. The effects of gear shape errors (tooth profile errors, tooth trace errors, cumulative pitch errors) and eccentric errors can be predicted in advance and in a short time analysis. At that time, the analysis is performed in consideration of dynamic behavior (influence of inertial term and rotational speed: resonance phenomenon, etc.), thereby confirming that there is no problem with the gear mechanism system, and testing and evaluating the gear drive system. The gear design can be supported with high accuracy and ease.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
FIG. 1 is a schematic block diagram of an embodiment of a gear design support apparatus according to the present invention.
As shown in FIG. 1, this gear design support apparatus is applied to a computer 1 such as a personal computer, and has a CPU (Central Processing Unit) 3 that performs comprehensive control via an internal bus 2 and an analysis result. RAM (Random Access Memory) 5 for temporarily storing data, CRT (Cathode Ray Tube) 7 as a display, input keyboard 9 and mouse 11 using this display, FDD (Floppy) for directly inputting / outputting data (Registered trademark) Disk Drive) 13, a printer 15 for outputting analysis results, an OS (Operating System) for basic control of the CPU 3, and a magnetic disk device (HDD: Hard) in which a gear design support program for gear design support is stored Disk Drive) 17 is connected.
In the FDD (Floppy (registered trademark) Disk Drive) 13, gear shape error data, eccentricity error data, assembly error data (axial parallelism error data), gear specification data, and the like are stored. (Registered trademark) Disk) 19 is inserted and read. Note that gear shape error data, eccentricity error data, assembly error data (axis parallelism error data), and gear specification data may be input using the input / output keyboard 9 and mouse 11.

Further, not only the FD (Floppy (registered trademark) Disk) 19 but also a portable recording medium such as a CD-ROM (Compact Disc Read Only Memory) or a CD-R / RW (Compact Disc Recordable / ReWritable) is used. It doesn't matter. By storing the design support program in the portable recording medium (external storage device) in this way, it is possible to carry it, and simulation can be easily performed in various places.
With such a configuration, a gear design support program stored in a magnetic disk device (HDD: Hard Disk Drive) 17 is executed, which is obtained from the dynamic analysis result of the gear as will be described later, and is effective at the time of design. Information can be supplied from CRT or printed paper.
In the above-described embodiment, an OS (Operating System) that performs basic control of a CPU (Central Processing Unit) and a program that supports design by calculating dynamic rotation characteristics of gears are included in a magnetic hard disk drive (HDD: Hard Disk Drive). 17 is provided in the computer 1, but the hard disk drive (HDD: Hard Disk Drive) 17 is an external storage device as shown in FIG. 2, and the OS and analysis program are transferred from the external storage device via the HDD interface 21. You may make it read. FIG. 2 is a schematic block diagram of a modified example of the gear design support apparatus shown in FIG.

As described above, according to the present embodiment, it can be installed in various information processing apparatuses such as computers, gear shape errors (tooth profile errors, tooth trace errors, accumulated pitch errors), eccentric errors, and assembly errors (driving shaft and follower). The effect of the parallelism error of the axis can be predicted in advance by a short analysis, and the recording medium can be brought into various places for simulation.
As a result, it is possible to provide a recording medium that can easily support gear design with high accuracy by eliminating the work of checking whether there is a problem with the gear mechanism system, making a prototype and evaluating the gear drive system.
Further, by executing a gear design support program based on an OS (Operating System) that performs basic control of the CPU 3, the CPU 3 has functional blocks as shown in FIG.

FIG. 3 is a functional block diagram when the gear design support program is executed by the computer 1 shown in FIG.
As shown in FIG. 3, the gear design support device includes a basic input unit 31 that gives basic information of a target gear and driving condition information such as target speed and load torque, and a tooth profile error of the gear. Gear shape error input unit 32 that gives information on shape errors such as tooth trace error, cumulative pitch error, etc., and an assembly error input that gives information on the eccentric error between the basic circle center and rotation center of the gear, and the inclination of each axis From the unit 33 and the basic input unit 31, the action line at the initial time contacting the basic circle of the gears is obtained, the shape error value of the gear tooth surface on the line is calculated from the gear shape error input means 32, and due to eccentricity The value of the assembling error is calculated from the assembling error input means 33, and the equation of motion is derived by setting the force balance equation for each tooth pair contacting on the action line based on the obtained information and generating the equation of motion. Part 34; A calculation unit 35 for solving the series in the equation of motion, and has calculated the drive shaft of the calculator 35 and an output unit 36 for outputting the operation result of the driven shaft, a.

Next, analysis processing for design support in the gear design support apparatus shown in FIG. 1 will be described with reference to the flowchart of FIG. FIG. 4 is a flowchart of analysis processing for design support in the gear design support apparatus shown in FIG.
In step 101 of FIG. 4, first, basic specification information of a target gear and its driving condition information are input.
Here, basic specification information includes the number of gear teeth, module, pressure angle, torsion angle, tooth width, material, moment of inertia, distance between axes, and the like. The drive condition information includes, for example, initial angles of the drive gear and the driven gear (which tooth starts to mesh with), a target speed and drive torque applied to the drive shaft, and load torque applied to the driven shaft.
Next, in step 102, information on the gear shape error (tooth profile error, tooth trace error, cumulative pitch error, tooth gap runout) is given in the gear error input process, and then in step 103, the assembly error input process is performed. Add information on eccentricity error (distance between pitch circle center and rotation axis center).
After giving these data, in step 104, in the analysis condition setting step, the analysis target operation time of the gear drive system and the analysis step (analysis time interval) are set as the analysis conditions.
Here, the gear drive system meshes the drive-side teeth and the driven-side teeth to transmit the power, and the meshing of these teeth depends on the respective rotation angles (in the case of constant speed, the time Is always changing). The contact force between teeth involved in power transmission is obtained as a product of a contact stiffness (teeth-to-stiffness) value Kt and a deflection amount ψ thereof. The influence e of the gear shape error can be dealt with by offsetting the contact position (position on the action line) compared to the case where the tooth surface position has no shape error. Further, the contact position on the action line also changes by δ due to the eccentricity error. Therefore, in step 105, a change amount δ of the tooth surface position is calculated by a method described later according to the position of the eccentric angle (the amount of eccentricity and its phase, rotation angle), and the obtained δ value is used as an offset of the shape error. In addition, the gear shape error and the eccentric assembly error can be modeled by arranging them on the same parameter.

FIG. 5 is an explanatory diagram showing the relationship between the basic circle of the meshing gear and the action line in contact therewith. The action line in this initial state is obtained, and each meshing force is applied in this direction (action force, half-action force). In the case of eccentric rotation, the position of the action line changes depending on the rotation angle, but the change in the direction can be considered minute, so the position of the action line at the initial stage is fixed, and the effect of eccentricity is the tooth on the action line. It is handled as the surface position change amount δ and a numerical calculation is performed.
Here, a method for calculating the variation δ of the tooth surface position will be described below.

次に、偏心中心Ｏｅで任意の点Ｐｏをθ回転させたときの座標Ｐｅ（ｘｅ，ｙｅ）を求める。
Ｏｅからみた点Ｐｏの座標は、

となるので、偏心中心Ｏｅを中心としてθ回転させたときの座標Ｐｅは、

である。
Ｏｅ座標系からＯ座標系に

を用いて戻すと、
座標Ｐｅとして

が得られる。
偏心の有無によるＯ座標系からみた位置誤差ΔＰ（Ｐｅ−Ｐ）は、次式となる。

・・・（１） 6 and 7 are diagrams for explaining a method for calculating the variation δ of the tooth surface position.
The coordinates P (x, y) when an arbitrary point Po (xo, yo) shown in FIG.

Next, coordinates Pe (xe, ye) when an arbitrary point Po is rotated by θ at the eccentric center Oe are obtained.
The coordinates of the point Po viewed from Oe are

Therefore, the coordinates Pe when θ is rotated about the eccentric center Oe is

It is.
From Oe coordinate system to O coordinate system

And return using
As coordinates Pe

Is obtained.
The position error ΔP (Pe−P) as seen from the O coordinate system due to the presence or absence of eccentricity is expressed by the following equation.

... (1)

・Ｐｍ座標での作用線と直交する直線式ｙ２

この２つの直線の交点からδを求める。ｙ１の式を変形してｙ２に代入する（ｙ１＝ｙ２＝ｙδとする）。

これによってｙδが得られたので、ｃｏｓα＝ｙδ／δを用いてδを算出する。

・・・（２）

（１）式を（２）式に代入し、偏心回転に伴う噛み合い点誤差（作用線上のズレ）δが求められる。

As shown in FIG. 7, when θ is rotated from 0 to 2π with reference to the starting point Pm (ｍ) of the action line, the locus of the position error ΔP becomes a broken-line circle. The radius of this circle is the amount of eccentricity ε, and is arranged around the start point Pm according to the eccentric phase φ.
A straight line y2 that passes through the straight line y1 on the action line and the arbitrary point Pa of the position error ΔP that changes due to the eccentricity error and is orthogonal to the action line is formulated. Then, the deviation δ in the direction of the action line from the start point Pm of the action line (▲: when there is no error) is obtained.
・ Linear expression y1 of action line in Pm coordinate

-Linear formula y2 orthogonal to the action line in Pm coordinates

Δ is obtained from the intersection of these two straight lines. The expression of y1 is transformed and substituted for y2 (y1 = y2 = yδ).

Since yδ is obtained in this way, δ is calculated using cos α = yδ / δ.

... (2)

By substituting the equation (1) into the equation (2), the meshing point error (deviation on the action line) δ accompanying the eccentric rotation is obtained.

Returning to FIG. 4, in step 106, in the equation of motion derivation step, when the meshing force acts on this action line and eccentric rotation occurs, this action line that changes with the rotation angle is obtained geometrically and analyzed. Develop an equation for each gear, and analyze it by making it simultaneous.
That is, an action line in contact with the basic circle between the gears is obtained from information given in the basic input step (S101) and the assembly error input step (S103), and the gear shape error input step (S102) and the assembly error input step (S102). The equation of motion is generated by setting a force balance equation for each tooth pair in contact on the action line based on the information obtained from (1).
Finally, in the time series calculation process of step 107, numerical analysis of the differential equation is performed, and when the analysis end time is reached (YES in step 108), an analysis result is output (step 109).

ただし、ｍ、Ｊは歯車の質量と慣性モーメント、θは回転角、ｃは粘性係数、ｒｂは基礎円半径、Ｆｔは噛合い接触力、Ｔは駆動トルクや負荷トルク、Ｏｇは基礎円中心（ギヤ重心）、Ｏｊは回転軸、Ｆｊｘ、Ｆｊｙは軸受け反力、αｗは噛合い圧力角、φは偏心角、εは偏心量、Ｋｔは接触剛性（歯対剛性）、ξは歯面同士の接触位置、ｎは噛合っている歯数、ｉはその何番目かを示す。ψは作用線方向の歯面変形量、ｅは作用線上での形状誤差ｅｏと組み付け誤差δ（偏心）の和である（ｅ＝ｅｏ＋δ）。
この式において、偏心して回転する場合変化する、φ、αｗを逐次求めて運動方程式を修正し、時系列的に解いていく。歯面変形量ψは、駆動歯車と従動歯車の噛合っている歯面の移動量の差分から求められる。 FIG. 8 is an explanatory diagram of the equation of motion, and formulas are created for each gear and are analyzed simultaneously. Deflection when offset of tooth surface shape error eo (gear shape error: tooth profile error, tooth trace error, cumulative pitch error) and eccentric assembly error δ is given when calculating the balance of forces between tooth surfaces on this line of action Calculate the amount. And the balance of this force is calculated | required for every minute time (every analysis step), and calculation is advanced. As a numerical solution method, a general Euler method, a Runge-Kutta method, a Newmark β method, etc. for solving a differential equation can be used.
That is, with respect to a certain arbitrary gear, an equation of motion is established in the rotational direction (θ) and the translational direction (x, y) using the symbols in FIG.

Where m and J are the gear mass and moment of inertia, θ is the rotation angle, c is the viscosity coefficient, rb is the basic circle radius, Ft is the meshing contact force, T is the driving torque and load torque, and Og is the center of the basic circle ( Gear center of gravity), Oj is the rotation axis, Fjx, Fjy is the bearing reaction force, αw is the meshing pressure angle, φ is the eccentric angle, ε is the eccentricity, Kt is the contact stiffness (tooth-to-rigidity), and ξ is between the tooth surfaces The contact position, n is the number of meshed teeth, and i is the number. ψ is the tooth surface deformation amount in the action line direction, and e is the sum of the shape error eo and the assembly error δ (eccentricity) on the action line (e = eo + δ).
In this equation, φ and αw, which change when rotating eccentrically, are successively obtained to correct the equation of motion, and are solved in time series. The tooth surface deformation amount ψ is obtained from the difference in the amount of movement of the tooth surfaces engaged with the drive gear and the driven gear.

When the predetermined time is analyzed in the steady state, the contact force for each meshing tooth is obtained as shown in FIG. The sum of these becomes the force (torque) that drives the gear (FIG. 10). And the fluctuation component of this meshing cycle is an excitation force (torque unevenness) that causes rotation unevenness. After that, when the analysis time ends, the analysis results (rotation characteristics: angular transmission error and angular velocity transmission error with respect to the time of the drive axis and driven axis) accumulated in time series so far are displayed as graphs and tables. The data is output to a display or a printer, or stored in a recording medium as data (see FIG. 11).
As explained above, in the dynamic analysis calculation of the eccentric gear, which takes time to calculate in the gear simulation, the influence of the eccentricity is calculated as the position change on the action line, and converted to the same parameter as the gear shape error and analyzed It is possible to increase the analysis efficiency (reduction of calculation time, reduction of calculation cost) in the time series calculation process (step 107) (for example, the time required for one second of analysis with a pair of gears is conventional) The method, which was 50 seconds, is 13 seconds according to the present invention, and the calculation time can be greatly shortened).
As a result, it is possible to predict the effects of gear shape errors (tooth profile error, tooth trace error, cumulative pitch error) and eccentricity errors, which affect the rotation transmission characteristics of the gear, in advance and in a short time analysis. At that time, the analysis is performed in consideration of dynamic behavior (influence of inertial term and rotation speed: resonance phenomenon, etc.), thereby confirming that there is no problem with the gear mechanism system, and making a prototype and evaluating the gear drive system. The gear design can be supported with high accuracy and ease.

The above-described embodiment can be applied to a gear transmission mechanism system for driving a rotating drum (for example, a photosensitive drum, a printing drum, an image forming drum, etc.) as shown in FIG.
In the output process at that time, the positional deviation on the surface of the rotating drum in the rotation cycle of the gear and the speed unevenness on the surface of the rotating drum in the gear meshing cycle are output. FIG. 12 is a schematic diagram showing a gear transmission mechanism system for driving a rotating drum to which the present invention is applied.
The positional deviation and the speed unevenness on the surface of the rotating body can be obtained by multiplying the angle transmission error or the angular speed transmission error by the rotating body radius.
As described above, according to the present embodiment, the gear transmission mechanism system is a gear transmission mechanism system for driving the rotating drum that drives the rotating drum, and in the output step (step 109), the drive shaft and the driven shaft are driven. When the operation result is output, the output of the driven shaft is multiplied by the radius of the rotating drum, and converted into characteristic values (positional deviation, speed unevenness) on the surface of the rotating drum, and output. Characteristic values (positional deviation and speed unevenness) with respect to the assembly error of the gear shape error and the eccentricity error on the surface of the formed rotating drum are obtained.
As a result, the assembly error of the gear shape error and the eccentricity error is caused by positional deviation (color deviation in multi-color superposition), which is a characteristic value on the surface of the rotating drum, and speed fluctuation in the meshing cycle (due to uneven density) How it affects a certain banding) can be revealed in a short time by pre-analysis.

このように、噛合い位置で変化する歯車形状誤差や偏心組み付け誤差と、歯対剛性に関して、歯対剛性を任意の定数を掛けて小さく一定値とし、歯車形状誤差と偏心組み付け誤差の端部（噛合い始め側と終り側）にも定数をかけて小さくするようにして統合して運動方程式を生成することで、接触位置に関する変数が３つから２つになり、繰り返して実施する収束計算が短くできる。
その結果、歯車シミュレーション計算時間に要する時間を短縮化することで解析作業の効率向上を図ることができる。 Next, another example of a method for calculating the meshing contact force Ft when deriving the equation of motion in step 106 in FIG. 4 will be described.
This integrates the sum e of the contact stiffness Kt that changes at the contact position ξ and the shape error eo + the eccentric assembly error δ in order to shorten the calculation.
Specifically, in the case of the above formula (3), there are three variables (Kt, ψ and e) depending on the contact position ξ, and the contact stiffness Kt, shape error eo + eccentric assembly error δ with respect to the meshing contact position ξ. Each relationship of the sum e is shown in FIG.
On the other hand, the calculation time in the convergence calculation can be shortened by collecting the variables into two (ψ and e ′). In FIG. 14, Kt is set to a constant value Kt0, and this is changed from a broken line in the graph to a solid line by giving a coefficient for reducing the end of e (meshing start side and meshing end side). . By using this result, it is possible to execute without greatly changing the calculation result.
In this case, the meshing contact force Ft is expressed by the following equation.

As described above, the gear shape error and the eccentric assembly error that change at the meshing position and the tooth pair rigidity are set to a small constant value by multiplying the tooth pair rigidity by an arbitrary constant, and the end of the gear shape error and the eccentric assembly error ( By generating a motion equation by integrating and reducing the constant on the meshing side and the meshing side, the number of variables related to the contact position will be changed from three to two. Can be shortened.
As a result, the efficiency of the analysis work can be improved by reducing the time required for the gear simulation calculation time.

Next, an example of a mode for shortening the calculation time in the time series calculation step (step 107) of FIG. 4 will be described.
FIG. 15 is a flowchart showing the processing flow of the time series calculation step in the flowchart of FIG. 4, and FIG. 16 is a flowchart showing a first modification for shortening the calculation time.
In FIG. 15, when the time series calculation process is started, the differential equation at that time is solved according to the time series (step 201). , And return to step 201 to solve the differential equation at the time point of advance.
The tooth-pair rigidity changes depending on the gear shape error and the meshing position when it is in a constant speed region (steady speed region), and is treated as a constant value at the time of startup. In a region where the speed is not constant as at the time of starting, a complicated response is shown due to the influence of the inertial force due to the starting acceleration and the characteristics of the drive motor. If the calculation is performed in consideration of the gear shape error and the tooth-to-rigidity, it takes a long time to calculate and no work such as image generation is performed in this region (transient state). Therefore, in the first modified example shown in FIG. 16, at the initial stage of analysis (at the time of start-up), the gear shape error is set to zero, and the tooth-pair rigidity is calculated with a constant value so that it does not change at the meshing position (contact position). In addition, the calculation time can be shortened by switching slowly when the steady state is reached.

That is, after the start of the time series calculation process, if it is a steady speed region (Yes in step 301), the differential equation at that time is solved (step 302), and if convergence is determined (Yes in step 304), the data is Save (step 305), advance by the step time (step 306), return to step 301, and in the case of start-up that is not in the steady speed range (No in step 301), there is no shape error at that time, and the tooth-to-rigidity is A constant differential equation is solved (step 303-1).
Tooth rigidity changes with gear shape error and meshing position when it is in a constant speed region (steady speed region), and is treated as a constant value at startup, so that inertial force and drive motor at startup The calculation when the behavior is complicated due to the influence of the above becomes a simplified equation of motion that does not consider the gear shape error and the tooth pair rigidity. As a result, especially at the time of start-up that requires calculation time (when it is not the target of analysis), high-speed calculation is possible by eliminating the cause of rotation unevenness, and the efficiency of analysis work can be improved.

FIG. 17 is a flowchart showing a second modification for shortening the calculation time.
In this modification, the gear tooth transition (change in meshing state) is considered only when the gear is in a constant speed region (steady speed region). Accordingly, the number of teeth simultaneously engaged changes depending on the contact state (engagement position). For example, when the meshing rate is 2.5, the time during which the two teeth mesh with each other is the same as the time during which the three teeth mesh, and this varies depending on the meshing position. In a region where the speed is not constant as at the time of starting, a complicated response is shown due to the influence of the inertial force due to the starting acceleration and the characteristics of the drive motor. If calculation is performed taking into account the gear tooth transition (meshing state transition) here, it takes time to calculate, and in this region (transient state), image generation and other work are not performed, so detailed analysis is also necessary. Absent. At the initial stage of the analysis, calculation is performed by treating the gear tooth transition (meshing state transition) as fixed (for example, the three teeth are always meshing), and when the steady state is reached By switching, the calculation time can be shortened.

That is, after the start of the time series calculation process, if it is a steady speed region (Yes in step 301), the differential equation at that time is solved (step 302), and if convergence is determined (Yes in step 304), the data is Save (step 305), advance by step time (step 306), return to step 301, and in the case of start-up that is not in the steady speed range (No in step 301), a differential equation with fixed meshing teeth at that time Is solved (step 303-2).
When gear tooth transition (meshing state transition) shows complex behavior due to inertial force at start-up and influence of drive motor by considering only when it is in constant speed range (steady speed range) This calculation is a simplified equation of motion that does not take into account tooth transition (meshing state transition). As a result, especially at the time of start-up that requires calculation time (when it is not the target of analysis), high-speed calculation is possible by eliminating the cause of rotation unevenness, and the efficiency of analysis work can be improved.

FIG. 18 is a flowchart showing a third modification for reducing the calculation time.
At the time of startup from the stationary state to the constant speed region (steady speed region), the value of the viscosity term (viscosity coefficient C) of the equation of motion is made larger than usual. In a region where the speed is not constant as at the time of starting, a complicated response is shown due to the influence of the inertial force due to the starting acceleration and the characteristics of the drive motor. Here, by increasing the value of the viscosity term, it is possible to expect a function of reducing high-frequency vibration that takes time for calculation.
That is, after the start of the time series calculation process, if it is a steady speed region (Yes in step 301), the differential equation at that time is solved (step 302), and if convergence is determined (Yes in step 304), the data is Save (step 305), advance step time (step 306), return to step 301, and in the case of start-up that is not in the steady speed range (No in step 301), the differential equation with a larger viscosity term at that time is Solve (step 303-3).
When starting up from a stationary state to a constant speed range (steady speed range), the value of the viscosity term (viscosity coefficient C) in the equation of motion is made larger than usual so that the influence of inertia force and drive motor in this range In this case, the calculation when the complicated behavior is shown is simplified (in order to quickly suppress the vibration component generated at the start-up by the viscosity term). As a result, especially at the time of start-up that requires calculation time (when it is not the target of analysis), high-speed calculation is possible by eliminating the cause of rotation unevenness, and the efficiency of analysis work can be improved.

FIG. 19 is a flowchart showing a fourth modification for shortening the calculation time.
The analysis step and convergence tolerance are adjusted according to the load fluctuation timing in the constant speed region (steady speed region). When the timing of load fluctuation is known in advance in a constant speed range (for example, paper carry-in timing in the image generation device or operation timing of other processes), analysis parameters (analysis step, convergence) can be analyzed in detail before and after Change the tolerance. By doing in this way, it becomes possible to carry out highly accurate calculation efficiently without becoming difficult to converge.
That is, after the start of the time series calculation process, if it is the timing of load fluctuation (Yes in step 401), the differential equation at that time is solved (step 402), and if it is determined that the convergence has occurred (Yes in step 404), the data Is saved (step 405), the step time is advanced (step 406), and the process returns to step 401. If the load fluctuation timing is not reached (No in step 401), the differential equation with a larger viscosity term at that time is solved. (Step 403).
By adjusting the analysis step and the convergence tolerance in accordance with the load fluctuation timing in the constant speed region (steady speed region), it is not difficult to converge (the calculation diverges) during the calculation. As a result, in order to perform high-speed calculations, especially when the timing of load fluctuations that require calculation time is known, the time required for convergence calculation can be reduced by finely adjusting the analysis steps there, etc. In this case, it is possible to improve the efficiency of the analysis work by adjusting the analysis conditions only in the vicinity where the load fluctuation is applied, instead of making the analysis step finer or reducing the tolerance.

Further, in step 106 in FIG. 4, the accuracy in calculating the equation of motion is adjusted according to the band of the meshing frequency. This is because, when the meshing frequency increases due to the high speed of gears or the use of small module teeth, the degree of influence of rotation unevenness in the meshing cycle of the gears decreases (the human eye). This means that it is not necessary to calculate the rotational unevenness more strictly than necessary.
Since a tendency as shown in FIG. 20 is generally observed, the analysis time can be shortened by controlling the extraction accuracy of the excitation force in accordance with the mesh frequency band.
By adjusting the accuracy when solving the equation of motion according to the mesh frequency band, for example, the banding frequency that is easy to recognize by the human eye is increased in analysis accuracy, and conversely in the inconspicuous frequency region, the analysis accuracy To reduce the calculation time. As a result, the analysis cost (required analysis time etc.) can be reduced.

1 is a schematic configuration block diagram of an embodiment of a gear design support device according to the present invention. The schematic block diagram of the modification of the gear design assistance apparatus shown in FIG. FIG. 3 is a functional block diagram when a gear design support program is executed by the gear design support device shown in FIG. 1. The flowchart of the analysis process for the design support in the gear design support apparatus shown in FIG. Explanatory drawing which shows the relationship between the basic | foundation circle | round | yen of the meshing gear and the action line which touches it. The figure for demonstrating the calculation method of variation | change_quantity (delta) of a tooth surface position. The figure for demonstrating the calculation method of variation | change_quantity (delta) of a tooth surface position. Explanatory drawing of an equation of motion. The figure which shows the contact force for every tooth | gear engaged. The figure which shows the sum total of the contact force for every tooth | gear which has engaged. The figure which shows the analysis result accumulate | stored for every step time. 1 is a schematic diagram showing a gear transmission mechanism system for driving a rotating drum to which the present invention is applied. The figure which shows each relationship of the sum of the contact rigidity with respect to a meshing contact position, shape error + eccentric assembly error (the 1). The figure which shows each relationship of the sum of the contact rigidity with respect to a meshing contact position, shape error + eccentric assembly error (part 2) The flowchart which shows the flow of a process of the time series calculation process in the flowchart of FIG. The flowchart which shows the 1st modification for shortening calculation time. The flowchart which shows the 2nd modification for shortening calculation time. The flowchart which shows the 3rd modification for shortening calculation time. The flowchart which shows the 4th modification for shortening calculation time. The figure which shows the allowable value of the rotation nonuniformity according to the zone | band of the meshing frequency.

Explanation of symbols

  1 Computer, 2 Internal bus, 3 CPU, 5 RAM, 7 CRT, 9 Keyboard, 11 Mouse, 13 FDD, 15 Printer, 17 Magnetic disk unit, 19 FD, 31 Basic input section, 32 Gear shape error input section, 33 Assembly Error input unit, 34 equation of motion derivation unit, 35 calculation unit, 36 output unit

Claims (11)

In a gear design support method for modeling a gear transmission mechanism system installed between a drive shaft and a driven shaft, and analyzing and calculating the dynamic behavior of the driven shaft with respect to the operation of the drive shaft,
A basic input step of inputting the specification information which is the basic specification of the gear to be processed and the driving condition information of the target speed and load torque by the basic input unit;
A gear shape error input step of inputting information on the shape error of the gear tooth shape error, the tooth trace error, and the cumulative pitch error by the gear shape error input unit;
An assembly error input step for providing information on an eccentric error between the center of the basic circle and the rotation center of the gear by an assembly error input unit;
The motion equation deriving unit obtains an initial action line in contact with the basic circle between the gears from the basic input process, and a shape error value of the gear tooth surface on the action line is given in the gear shape error input process. And the value of the assembly error due to eccentricity is calculated from the information given in the assembly error input step, and the force of each tooth pair in contact on the action line is calculated based on the calculated information. An equation of motion derivation step for generating an equation of motion by setting a balance equation;
A calculation step of solving the equation of motion in time series by a calculation unit;
An output step of outputting an operation result of the drive shaft and the driven shaft calculated by the calculation step by an output unit;
A gear design support method comprising:   The gear transmission mechanism system is a gear transmission mechanism system for driving a rotating drum that drives a rotating drum, and when the operation result of the driving shaft and the driven shaft is output in the output step, The gear design support method according to claim 1, wherein the output of the shaft is multiplied by the radius of the rotating drum, and the characteristic value on the surface of the rotating drum is converted and output.   3. The gear design support method according to claim 1, wherein the equation of motion is generated by integrating the gear shape error, the assembling error due to eccentricity, and the tooth-to-rigidity changing at the meshing position.   The tooth pair rigidity is changed according to the gear shape error and the meshing position when the gear is at a constant speed. The gear design support method according to any one of claims 1 to 3, wherein the rigidity is handled as a constant value.   The gear design support method according to any one of claims 1 to 3, wherein a value when the gear is at a constant speed is adopted as the transition of the meshing state of the gear.   4. The gear design support according to claim 1, wherein the value of the viscosity coefficient of the equation of motion is made larger than usual when the gear starts up from a stationary state to a constant speed. 5. Method.   The gear design support method according to any one of claims 1 to 3, wherein an analysis step and a convergence tolerance are adjusted in accordance with a load fluctuation timing when the gear is at a constant speed.   The gear design support method according to any one of claims 1 to 7, wherein an accuracy in solving the equation of motion is adjusted according to a band of a meshing frequency.   A program for causing a computer to execute the gear design support method according to any one of claims 1 to 8.   A computer-readable storage medium storing the program according to claim 9. In a gear design support device that models a gear transmission mechanism system installed between a drive shaft and a driven shaft and analyzes and calculates the dynamic behavior of the driven shaft with respect to the operation of the drive shaft.
Basic input means for giving specification information which is a basic specification of the gear and driving condition information of target speed and load torque;
Gear shape error input means for giving information on the shape error of the gear tooth profile error, tooth trace error, and cumulative pitch error;
Assembly error input means for providing information on an eccentric error between the center of the basic circle and the center of rotation of the gear;
From the basic input means, an action line at the initial time contacting the basic circle of the gears is obtained, the shape error value of the gear tooth surface on the line is calculated from the information obtained by the gear shape error input means, and is eccentric. The value of the assembling error is calculated from the information obtained by the assembling error input means, and based on the calculated information, a force balance equation is set for each tooth pair in contact on the action line, and the equation of motion is calculated. Means for deriving the equation of motion to be generated;
A calculation means for solving the equation of motion in time series,
Output means for outputting the operation results of the drive shaft and the driven shaft calculated by the calculation means;
A gear design support device comprising:

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