JP2009070192A - Gear design support method, gear design support device, program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a gear design support method capable of supporting gear design highly precisely and easily. <P>SOLUTION: The gear design support method comprises: a basic input process 101 for inputting basic items of a target gear and its driving condition; a gear shape difference input process 103 for giving shape difference information about a gear; an assembly difference input process 105 for giving a deviation difference between a base circle center and a rotation center of the gear and information about the respective shafts inclinations; a pre-equation of motion derivation process 109 for obtaining a line of action in contact with base circles of the gears, setting a force balance equation to every pair of gears in contact on the line of action, and generating the equation of motion; a pre-calculation process 111 for solving the equation of motion time serially; an excitation extraction process 115 for calculating excitation for vibrating the gear during the calculation; a main equation of motion derivation process 117 for switching to the equation of motion using the calculated excitation; a main calculation process 119 for solving the equation of motion time serially; and an output process 123 for outputting an analysis result of a drive shaft and a driven shaft calculated by the main calculation process. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a gear design support device, a gear design support method, a program, and a recording medium that support the design of a gear in a gear mechanism system of a precision machine product, and more particularly to basic specifications, drive conditions, and error conditions (gears) of a gear. Gear design support device, gears that can estimate the transmission characteristics of the gear mechanism system in a state close to actual operation and confirm whether there is a problem related to the gear mechanism system in advance by giving a shape error, eccentricity, and assembly error) The present invention relates to a design support method program and a recording medium.

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, a technique has been proposed in which a rotation characteristic (motion curve) under no load and a deflection characteristic under load are individually obtained and combined to reduce calculation time (Patent Document 1). That is, since the gear transmission error at the time of a predetermined load of the gear is calculated and the gear is designed in consideration of the gear transmission error at the time of the load, the gear transmission error for one tooth when there is no load based on the tooth surface shape. Curve calculation step for calculating a motion curve representing the relationship between the rotation angle and the rotation angle, a deflection amount calculation step for calculating the deflection amount of the tooth under load, and a deflection amount of the tooth under load with the motion curve And a load-on-load meshing transmission error calculating step for obtaining the load-on meshing transmission error by calculation.

  In addition, it is proposed to divide the gear part and the case part that supports the gear part, obtain the bearing load when the gear is driven, and apply the load to the case bearing part to perform deformation analysis of the case. (Patent Document 2). That is, in a power transmission analysis method of a power transmission mechanism including a gear train having a plurality of gear shafts, and a case for housing the gear train by supporting the gear shafts by bearings, the gear train and the case are separated, The mesh model of the gear train and the mesh model of the case are constructed separately, and after giving the support position of the gear shaft of the gear train, the load of the support position of the gear shaft corresponding to the predetermined input torque is set. Calculate and input this calculated load to the bearing portion of the case to calculate the position after deformation of the bearing portion, and then the position of each bearing portion of the case, the support position of each gear shaft of the gear train, The transmission characteristic analysis of the gear train and the deformation analysis of the case are performed while delivering the load while making them coincide with each other.

In addition, by sequentially calculating the action line (surface) that changes due to gear mounting eccentricity and solving the force balance equation on this line (on the surface), rotation due to uneven rotation of the meshing cycle and eccentricity There has been proposed one that can calculate unevenness simultaneously (Patent Document 3). That is, the gear design support device models the 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. Giving information on specifications, drive conditions, gear tooth profile errors, tooth trace errors, etc., and information on eccentric errors between the basic center of the gear and the center of the rotation shaft, and the center of the rotation center of the gear The line of action that changes due to the eccentricity of the axis is obtained, a force balance equation is set for each pair of teeth that are in contact with the line of action, a motion equation is generated, and the equation of motion is solved in a time series to solve the drive shaft and the driven shaft. The operation result is output.
Japanese Patent No. 3642274 JP 2004-258697 A JP 2003-240064 A

However, in the case of the conventional method (Patent Document 1), since it is calculated from the rotation characteristic (motion curve) under no load and the deflection characteristic under load, it becomes a static analysis, and the influence of the inertia term and the rotation speed (dynamic behavior) ) Could not be analyzed.
Moreover, in the said conventional method (patent document 2), since the gear and the case were analyzed (FEM) with the mesh model and the amount of elastic deformation was calculated | required, there existed a problem that analysis required time.
In the conventional method (Patent Document 3), since the equation of motion is constructed in consideration of the shape error and assembly error of each tooth meshed with each tooth, the tooth pair rigidity, the load torque, etc., Although more rigorous analysis is possible, there is a problem that the calculation takes time. In particular, 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. 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.
The present invention has been made in view of the above-described conventional problems, and its purpose is to confirm whether there is a problem with the gear mechanism system, and to eliminate the work of making a prototype and evaluating the gear drive system with high accuracy. Another object of the present invention is to provide a gear design support device, a gear design support method, a program, and a recording medium that can easily support gear design.

  In order to achieve 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, so that the dynamics of the driven shaft with respect to the operation of the drive shaft are modeled. A gear design support method for analyzing and calculating a behavior, a basic input step of inputting basic specification information and driving condition information of a target gear by a basic input unit, and a shape of the gear by a gear shape error input unit Gear shape error input step for giving error information, assembly error input step for giving information on the eccentric error between the basic circle center and the rotation center of the gear and the inclination of each axis by the assembly error input unit, and derivation of the previous equation of motion A working line in contact with the basic circle between the gears from the information given in the basic input step and the assembly error input step, and the gear shape error input step and the assembly error A pre-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 information obtained from the force step, and a time series by the pre-calculation unit The pre-calculation step for solving the equation of motion, the excitation force extraction step for calculating the excitation force to vibrate the gear in the middle of the calculation by the excitation force extraction unit, and the calculated excitation force by the equation of motion derivation unit This equation of motion derivation step for switching to the equation of motion used, this calculation step for solving this equation of motion in time series by this calculation unit, and the drive shaft and the driven shaft calculated by this calculation step by the output unit And an output process for outputting the analysis result.

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 output shaft process includes a drive shaft and a driven shaft. When outputting the analysis result, the output of the driven shaft is multiplied by the radius of the rotating body, and converted into a characteristic value on the surface of the rotating body drum.
The invention according to claim 3 is characterized in that, when the excitation force is calculated and a simplified equation of motion using the calculation is made, the excitation force is a function of the rotation angle of the gear.
The invention according to claim 4 is characterized in that, when the excitation force is calculated and a simplified equation of motion using this is obtained, the amplitude of the excitation force is a function of the load torque of the gear. .
In the invention according to claim 5, regarding the calculation of the excitation force, the amplitude and phase of the excitation force are obtained by using quadrature detection from the total data of the tooth counterforces of the meshing gear teeth and the engagement frequency. It is characterized by that.
In the invention according to claim 6, regarding the calculation of the excitation force, the amplitude and phase of the excitation force are calculated from the total data of the tooth-to-forces of the meshing gear teeth and the engagement frequency using a fast Fourier transform. It is characterized by seeking.

The invention described in claim 7 is characterized in that the accuracy in calculating the excitation force is adjusted according to the band of the meshing frequency.
The invention according to claim 8 is characterized in that the value of the viscosity term of the equation of motion is set larger than usual when the equation of motion is switched.
According to a ninth aspect of the present invention, the gear transmission mechanism system installed between the drive shaft and the driven shaft is modeled to analyze and calculate the dynamic behavior of the driven shaft with respect to the operation of the drive shaft. A design support method, a basic input step of inputting basic specification information and driving condition information of a target gear by a basic input unit, and a gear shape which gives information on the shape error of the gear by a gear shape error input unit An error input step, an assembly error input step that gives information on the eccentric error between the basic circle center and the rotation center of the gear and the inclination of each axis by the assembly error input unit, and the basic input step by the previous motion equation derivation unit Then, an action line in contact with the basic circle between the gears is obtained from the information given in the assembly error input step, and the information obtained from the gear shape error input step and the assembly error input step is obtained. Pre-motion equation derivation step for generating a motion equation by setting a force balance equation for each tooth pair contacting on the action line based on the above, and a pre-calculation step for solving the motion equation in time series by a pre-calculation unit And an excitation force extraction step for calculating an excitation force that vibrates the gear in the middle of the calculation by the excitation force extraction unit, and a book for switching to the equation of motion using the calculated excitation force by the equation of motion derivation unit. Equation of motion derivation step, main calculation step for solving the equation of motion in time series by the present calculation unit, and output step for outputting the analysis result of the drive shaft and the driven shaft calculated by the output unit by the output unit And a program for executing on a computer a gear design support method.

  The invention according to claim 10 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. A design support method, a basic input step of inputting basic specification information and driving condition information of a target gear by a basic input unit, and a gear shape which gives information on the shape error of the gear by a gear shape error input unit An error input step, an assembly error input step that gives information on the eccentric error between the basic circle center and the rotation center of the gear and the inclination of each axis by the assembly error input unit, and the basic input step by the previous motion equation derivation unit And an action line in contact with the basic circle between the gears from the information given in the assembly error input step, obtained from the gear shape error input step and the assembly error input step Based on the information, a pre-motion equation derivation step that generates a motion equation by setting a force balance equation for each pair of teeth contacting on the action line, and a pre-calculation that solves the motion equation in time series by the pre-calculation unit The process and the excitation force extraction step for calculating the excitation force to vibrate the gear in the middle of the calculation by the excitation force extraction unit, and the equation of motion using this calculation equation derivation unit are switched to the equation of motion using the calculated excitation force. This equation of motion derivation step, this calculation step that solves this equation of motion in time series by this calculation unit, and the output unit that outputs the analysis results of the drive shaft and the driven shaft calculated by the calculation step And a recording medium storing a program for executing the gear design support method in a computer.

  The invention according to 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. A design support device, a basic input unit for inputting basic specification information and driving condition information of a target gear, a gear shape error input unit for providing information on the shape error of the gear, and a basic circle of the gear An assembly error input unit that gives information on the eccentricity error between the center and the rotation center and the inclination of each axis, and an action line that touches the basic circle between the gears from the information provided by the basic input unit and the assembly error input unit Pre-motion for generating an equation of motion by setting a force balance equation for each tooth pair in contact on the action line based on information obtained from the gear shape error input unit and the assembly error input unit Equation deriving section and time series A pre-calculation unit that solves the equation of motion, an excitation force extraction unit that calculates an excitation force that vibrates the gear in the middle of calculation, and an equation-of-motion equation derivation unit that switches to the equation of motion using the calculated excitation force And a main calculation unit that solves the equation of motion in time series, and an output unit that outputs an analysis result of the drive shaft and the driven shaft calculated by the main calculation unit. .

According to the present invention, the calculation of the excitation force of the meshing cycle, which takes time for calculation in the gear simulation, is repeatedly performed using an approximated simplified formula, and the calculation is performed while checking the convergence state. Analysis efficiency (reduction of calculation time, reduction of calculation cost), parameters of gear shape errors (tooth profile error, tooth trace error, accumulated pitch error) and eccentricity that affect the rotation transmission characteristics of gears. The effects of errors and assembly errors can be predicted in advance and with a short 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.

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. 14 is a functional block diagram when the gear design support program is executed by the computer 1 shown in FIG.
As shown in FIG. 14, this gear design support device includes a basic input unit 31 that provides basic information of a target gear and information on driving conditions such as target speed and load torque, and a tooth profile error of the gear. Gear shape error input unit 33 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 eccentricity error between the basic circle center and rotation center of the gear and the inclination of each axis. From the information given by the unit 35, the basic input unit 31 and the assembly error input unit 35, an action line that changes due to the eccentricity between the center of the basic circle of the gear and the center of the rotation shaft is obtained, and the error of the gear shape error input unit 33 and the assembly error Based on the information obtained from the input unit 35, a pre-motion equation deriving unit 37 for generating a motion equation by setting a force balance equation for each tooth pair contacting on the action line, and this motion equation in time series Calculate before solving 39, an excitation force extraction unit 41 that calculates an excitation force that vibrates the gear in the middle of the calculation, a motion equation deriving unit 43 that switches to an equation of motion using the calculated excitation force, and time series The calculation unit 45 that solves the equation of motion, and the output unit 47 that outputs the analysis result of the drive shaft and the driven shaft calculated by the calculation unit 45 are provided.

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. 3 is a flowchart of an analysis process for design support in the gear design support apparatus shown in FIG.
In step 101 of FIG. 3, first, basic specification information of the 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 driving condition information includes, for example, initial angles of the driving gear and the driven gear (which tooth starts to engage with which tooth), a target speed applied to the driving shaft, and a load torque applied to the driven shaft.
Next, in step 103, 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 105, the assembly error input process. To add information on the eccentricity error (distance between the center of the base (pitch) circle and the center of the rotating shaft) and the parallelism error (shaft inclination) between the driving shaft and the driven shaft.
After giving these data, in step 107, 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 the product of the contact stiffness (tooth-to-stiffness) value and the amount of deflection. The influence of the gear shape error can be dealt with by offsetting the contact position (position on the action line) as compared with the case where the tooth surface position has no shape error. Also, when an axial parallelism error occurs due to an assembly error, the tooth surface position changes according to the position of the tooth width compared to the case where there is no error, so by adding this changed amount to the offset, the gear shape Error and assembly error can be modeled.
Next, in step 109, when the meshing force acts on the action line in the process of deriving the previous equation of motion and the shaft rotates eccentrically, the action line that changes with the rotation angle is geometrically obtained sequentially for analysis ( In addition, a formula is established for each gear, and it is analyzed simultaneously (see FIG. 5). That is, an action line in contact with the basic circle between the gears is obtained from the information given in the basic input process and the assembly error input process, and the information obtained from the gear shape error input process and the assembly error input process is obtained. An equation of motion is generated by setting a force balance equation for each tooth pair originally contacting on the action line.
FIG. 4 is an explanatory diagram showing the relationship between the basic circles of the meshing gears and the action lines in contact therewith, and FIG. 5 shows the motion when formulating each gear and analyzing it in combination. It is explanatory drawing of an equation.

（１）
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は噛合っている歯面位置での駆動側と従動側の形状誤差と軸平行度誤差の和である。
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。 As shown in FIG. 5, when calculating the balance of forces between tooth surfaces on this line of action, the tooth surface shape error (gear shape error: tooth shape error, tooth trace error, etc.) and assembly error (axis parallelism error) The amount of deflection when the offset is given is calculated. 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.

(1)
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 amount of tooth surface deformation in the action line direction, and e is the sum of the shape error and the axis parallelism error on the driving and driven sides at the meshing tooth surface positions.
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.

（２）
ここで、Ｆｔｃは一定値で負荷トルクなどによって決まる値、Ｆｔｖは噛合い周期の変動成分（起振力）、ｆｍは噛合い周波数、ｔは時間、ζは変動成分の位相である。
次に、ステップ１１１において、定常状態で所定の時間を解析（時系列的に前記運動方程式を解く前計算工程）すると、図６のように噛合っている歯ごとの接触力が得られる。これらの総和が歯車を駆動する力（トルク）となる（図７参照）。図６は、噛合っている歯ごとの接触力を示す図であり、図７は、噛合っている歯ごとの接触力の総和を示す図である。
そして、この噛合い周期の変動成分が、回転ムラを生じさせる起振力（トルクムラ）である。そこで、ステップ１１３において、前計算工程が終了すると、ステップ１１５、１１７において、起振力抽出工程および本運動方程式導出工程で定常状態の解析データからこの起振力の周波数と振幅、位相を求め、運動方程式の噛合い接触力Ftを、上記（２）式のように定常値Ftcと変動成分（起振力成分Ftv）に振り分けて設定し、上記（１）式を上記（２）式へと切り替える（簡略化した起振力；図８参照）。図８は、簡略化した起振力（トルクムラ）を示す図である。 The meshing contact force Ft is obtained by pre-calculation processing for solving the above equation of motion, and is set as the following equation.

(2)
Here, Ftc is a constant value determined by the load torque and the like, Ftv is the meshing cycle fluctuation component (vibration force), fm is the meshing frequency, t is time, and ζ is the phase of the fluctuation component.
Next, in step 111, when a predetermined time is analyzed in a steady state (pre-calculation step for solving the equation of motion in time series), the contact force for each meshed tooth is obtained as shown in FIG. The sum of these becomes the force (torque) for driving the gear (see FIG. 7). FIG. 6 is a diagram showing the contact force for each meshed tooth, and FIG. 7 is a diagram showing the total contact force for each meshed tooth.
And the fluctuation component of this meshing cycle is an excitation force (torque unevenness) that causes rotation unevenness. Therefore, when the pre-calculation process is completed in step 113, in steps 115 and 117, the frequency, amplitude, and phase of this excitation force are obtained from the analysis data in the steady state in the excitation force extraction step and the motion equation derivation step. The meshing contact force Ft in the equation of motion is set by dividing into the steady value Ftc and the fluctuation component (vibration force component Ftv) as in the above equation (2), and the above equation (1) is converted into the above equation (2). Switching (simplified vibration force; see FIG. 8). FIG. 8 is a diagram showing a simplified vibration force (torque unevenness).

Next, after deriving a simplified equation of motion, in step 119, analysis is performed at high speed in this calculation process, and this equation of motion is solved in time series. Thereafter, when the analysis time ends in step 121, in step 123, the analysis results accumulated so far in time series for each step time (rotation characteristics: angular transmission error and angular velocity transmission with respect to the time of the drive shaft and the driven shaft) 9 are output to the display display 7 and the printer 15 as graphs and tables as shown in FIGS. 9A, 9B, and 9C, or are stored in the recording medium (FD) 19 as data. . FIG. 9 is a diagram showing analysis results accumulated in time series for each step time, where (a) shows angular transmission errors, and (b) and (c) show angular velocity transmission errors.
As a result, for example, the time required for an analysis for one second with a pair of gears was 13 seconds in the conventional method, compared with 98 seconds in the conventional method, but in an important frequency region (such as mesh frequency). It can be seen that the calculation time can be shortened without lowering the analysis accuracy.

As described above, according to the present embodiment, the excitation force calculation of the meshing period, which takes time to calculate in the gear simulation, is repeatedly performed using the approximate simplified formula, and the calculation is performed while checking the convergence state. This increases the analysis efficiency (reduction of calculation time and reduction of calculation cost) in the calculation process, so that the gear shape errors (tooth profile error, tooth trace error, cumulative) of parameters that affect the gear rotation transmission characteristics The effects of pitch error), eccentricity error, and assembly error 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 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 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 process, the positional deviation on the surface of the rotating drum with one rotation period of the gear and the speed unevenness on the surface of the rotating drum with the gear meshing period are output. FIG. 10 is a schematic diagram showing a gear transmission mechanism system for driving a rotating drum to which the present invention is applied.
Thereby, the positional deviation and the speed unevenness on the surface of the rotating body can be obtained by multiplying the angle transmission error and the angular speed transmission error by the rotating body radius.
Thus, according to the present embodiment, the gear transmission mechanism system is a gear transmission mechanism system for driving a rotating drum that drives the rotating drum, and the drive shaft and the driven shaft are output in the output process. When the operation result is output, the output of the driven shaft is multiplied by the radius of the rotating drum, and converted into a characteristic value (positional deviation, speed unevenness) on the surface of the rotating drum. Characteristic values (positional deviation and speed unevenness) with respect to the shape error, eccentricity error and assembly error of the gear on the surface of the rotating drum on which an image is formed are obtained.
As a result, the gear shape error, eccentricity error, and assembly error are caused by positional deviation (color misregistration in multi-color superposition), which is a characteristic value on the surface of the rotating drum, and speed fluctuation (density unevenness) in the meshing cycle. How it affects a certain banding) can be revealed in a short time by pre-analysis.

（３）
すなわち、歯車の噛合い周期の振動は、歯車の歯が衝突することで発生するので、回転角の変数とした方が、より厳密となる。これにより、解析精度の向上が期待でき、また、低周期での速度ムラが重なった場合でも変調され、実測に即した計算結果が得られる。
このように、本実施形態によれば、起振力を算出し、これを用いた簡略化した運動方程式にする場合、起振力を歯車の回転角の関数とすることで、歯車の回転位置（速度）に対応した起振力波形が設定される。
その結果、高速計算をするために必要な起振力に関して、時間軸（周波数）に関して精度よく設定することで解析の信頼性の向上を図ることができる。 In addition, when formulating using the amplitude and phase of the excitation force obtained from the pre-calculation process in step 111 of FIG. 3, the rotation angle θ of the gear is used as the independent variable of the sine function instead of the time t. Thus, the following equation (3) is set.

(3)
That is, since the vibration of the meshing period of the gear is generated by the collision of the gear teeth, it becomes more strict when the rotation angle is set as a variable. As a result, an improvement in analysis accuracy can be expected, and even when speed irregularities in low cycles overlap, a modulation result is obtained and a calculation result based on actual measurement is obtained.
As described above, according to the present embodiment, when the excitation force is calculated and a simplified equation of motion using the calculated excitation force, the rotation position of the gear is obtained by using the excitation force as a function of the rotation angle of the gear. A vibration force waveform corresponding to (speed) is set.
As a result, it is possible to improve the reliability of the analysis by accurately setting the excitation force necessary for high-speed calculation with respect to the time axis (frequency).

（４）
このように、本実施形態によれば、起振力を算出し、これを用いた簡略化した運動方程式にする場合、起振力の振幅を負荷トルクの関数とすることで、本計算工程中で、負荷トルクが変化する場合でも、それに合わせて一定値Ftcと変動成分（起振力）Ftvの大きさを変えるようになる。
その結果、高速計算をするために必要な起振力に関して、負荷トルクが変化した場合でも精度よく設定することで解析の信頼性の向上を図ることできる。 Further, when formulating using the amplitude and phase of the excitation force obtained from the pre-calculation process in step 111 of FIG. 3, the amplitude (vibration force) is defined as a function of the load torque.
That is, if the load torque used in the previous calculation process is used as it is, the obtained amplitude can be used as it is. However, if the load torque changes during this calculation process, the constant value Ftc and the fluctuation component (vibration) Force) Change the size of Ftv. Specifically, as shown in the following formula (4), Ftc and Ftv are defined as a function of the load torque T, and the detailed relationship is obtained by performing analysis and evaluation in advance and set.

(4)
As described above, according to the present embodiment, when the excitation force is calculated and a simplified equation of motion using this is calculated, the amplitude of the excitation force is used as a function of the load torque. Thus, even when the load torque changes, the magnitudes of the constant value Ftc and the fluctuation component (vibration force) Ftv are changed accordingly.
As a result, the reliability of the analysis can be improved by accurately setting the excitation force necessary for high-speed calculation even when the load torque changes.

Further, FIG. 11 shows how to determine the excitation force, which is a variable component of the meshing cycle, from the relationship of the sum of the time VS contact forces obtained in the previous calculation step in step 111 of FIG. As described above, calculation is performed using quadrature detection. FIG. 11 is an explanatory diagram in the case of obtaining the excitation force, which is a variation component of the meshing cycle, using quadrature detection.
This is one of the well-known techniques for quadrature detection, which is mainly a type of radio wave detection method, and is a detection method that demodulates one signal by shifting it by a quarter cycle. This method can be used for a mesh whose frequency is known in advance, such as the meshing frequency, and the calculation load required for the processing is relatively small, which is advantageous for speeding up.
As described above, according to the present embodiment, regarding the calculation of the excitation force, the amplitude and phase of the excitation force are obtained from the total data of the tooth-to-forces of the meshing gear teeth and the engagement frequency using orthogonal detection. Thus, the present invention is applied to a mesh whose frequency is known in advance, such as a meshing frequency.
As a result, the reliability of the analysis can be improved by simply and accurately setting the amplitude value of the excitation force without applying a calculation load for the excitation force necessary for high-speed calculation.

Further, FIG. 12 shows how to determine the excitation force that is the fluctuation component of the meshing cycle from the relationship of the sum of the time VS contact force obtained in the previous calculation step in step 111 of FIG. Thus, the calculation is performed using the fast Fourier transform. FIG. 12 is an explanatory diagram in the case of obtaining the excitation force that is the fluctuation component of the meshing cycle by using the fast Fourier transform.
This is a fast Fourier transform, which is a well-known technique, and performs processing for extracting how many frequency components are included in a signal. As a result, not only the meshing period but also harmonics such as the secondary component and tertiary component can be detected, so that the accuracy of the simplified mathematical formula is improved.
As described above, according to the present embodiment, the calculation of the excitation force is performed using the fast Fourier transform (FFT) from the total data of the tooth pair forces of the meshing gear teeth and the meshing frequency. By obtaining the amplitude and phase of the vibration force, processing is performed to extract how many frequency components are included in the signal.
As a result, it is possible to improve the reliability of analysis by accurately setting the amplitude value of the excitation force with respect to the excitation force necessary for high-speed calculation.

Further, in the excitation force calculation step of step 115 in FIG. 3, the accuracy in calculating the excitation force is adjusted according to the band of the meshing frequency. This is necessary because if the meshing frequency increases due to the gears becoming faster or using small module teeth, etc., the effect of this will decrease (the tolerance for rotational unevenness will increase). This means that it is not necessary to calculate the vibration force strictly.
In general, since a tendency as shown in FIG. 13 is observed, the analysis time can be shortened by controlling the extraction accuracy of the excitation force according to the band of the meshing frequency. FIG. 13 is a diagram showing an allowable value of rotation unevenness according to the mesh frequency band.
As described above, according to the present embodiment, when the meshing frequency is increased by adjusting the accuracy in calculating the excitation force according to the meshing frequency band, the degree of influence of the meshing frequency decreases. Therefore, it is not necessary to calculate the vibration force more strictly than necessary. As a result, the analysis cost (required analysis time etc.) can be reduced.

Further, when switching from the pre-calculation step (calculation based on the detailed equation of motion) of step 111 in FIG. 3 to the main calculation step (calculation based on the simplified equation of motion) of step 119, only the vicinity of the viscosity term of the equation of motion. I try to increase the value. As a result, when a discontinuous variable between the detailed calculation result and the simplified calculation result is generated, the vibration is suppressed by increasing the viscosity term so that vibration does not occur. However, since the vibration generating force component is given directly, even if the viscosity term is increased only at this time, the influence is small.
As described above, according to this embodiment, when the equation of motion is switched, the value of the viscosity term of the equation of motion is set to be larger than usual, so that a detailed calculation result (pre-calculation step) and a simplified calculation result are obtained. If a discontinuous variable occurs in (this calculation step), the vibration is suppressed from occurring there.
As a result, it is possible to smoothly switch the equations of motion necessary for high-speed calculation, and to prevent a state where the calculation stops in the middle (divergence due to difficulty in convergence).

It is a schematic block diagram of an embodiment of a gear design support device according to the present invention. It is a schematic block diagram of the modification of the gear design support apparatus shown in FIG. It is a flowchart of the analysis process for the design support in the gear design support apparatus shown in FIG. It is explanatory drawing which shows the relationship between the basic | foundation circle | round | yen of the meshing gear and the action line which touches it. It is explanatory drawing of an equation of motion, when formula is created for every gear and it is made simultaneous and it analyzes. It is a figure which shows the contact force for every tooth | gear engaged. It is a figure which shows the sum total of the contact force for every tooth | gear engaged. It is a figure which shows the simplified vibration force (torque nonuniformity). It is a figure which shows the analysis result accumulate | stored for every step time in time series, (a) is an angle transmission error, (b), (c) is a figure which shows an angular velocity transmission error. It is the schematic which shows the gear transmission mechanism system for the rotary body drum to which this invention is applied. It is explanatory drawing in the case of calculating | requiring the excitation force which is a fluctuation | variation component of a meshing period using a quadrature detection. It is explanatory drawing in the case of calculating | requiring the excitation force which is a fluctuation | variation component of a meshing period using a fast Fourier transform. It is a figure which shows the allowable value of the rotation nonuniformity according to the zone | band of the meshing frequency. It is a functional block diagram at the time of running a gear design support program by the computer 1 shown in FIG.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Computer, 2 ... Internal bus, 3 ... CPU, 7 ... Display display, 9 ... Keyboard, 11 ... Mouse, 15 ... Printer, 17 ... HDD, 21 ... HDD interface, 31 ... Basic input part, 33 ... Gear shape error Input part 35 ... Error input part 37 ... Pre-motion equation deriving part 39 ... Pre-computation part 41 ... Excitation force extraction part 43 ... This motion equation deriving part 45 ... This calculation part 47 ... Output part

Claims (11)

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 a dynamic behavior of the driven shaft with respect to the operation of the driving shaft,
A basic input process for inputting basic specification information of the gear to be processed and its driving condition information by the basic input unit;
A gear shape error input step for providing information on the shape error of the gear by a gear shape error input unit;
An assembly error input step for giving information on the eccentricity error between the basic circle center and the rotation center of the gear and the inclination of each axis by the assembly error input unit;
From the information given in the basic input step and the assembly error input step, a line of action in contact with the basic circle of the gears is obtained by the front motion equation derivation unit, and from the gear shape error input step and the assembly error input step A pre-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 obtained information;
A pre-calculation step of solving the equation of motion in time series by a pre-calculation unit;
An excitation force extraction step for calculating an excitation force for vibrating the gear in the middle of the calculation by the excitation force extraction unit;
This motion equation derivation unit switches this motion equation to the motion equation using the calculated excitation force,
This calculation process for solving this equation of motion in time series by this calculation unit,
A gear design support method comprising: an output step of outputting an analysis result of the drive shaft and the driven shaft calculated in the calculation step by an output unit.   The gear transmission mechanism system is a gear transmission mechanism system for driving a rotating drum that drives a rotating drum, and when the analysis result of the driving shaft and the driven shaft is output in the output process, the driven shaft is driven. The gear design support method according to claim 1, wherein the output of the shaft is multiplied by the radius of the rotating body to convert to a characteristic value on the surface of the rotating drum and output.   3. The gear design support method according to claim 1, wherein when the excitation force is calculated and a simplified equation of motion using the calculation is made, the excitation force is a function of a rotation angle of the gear. .   The said excitation force is calculated, and when making it into the simplified equation of motion using this, the amplitude of an excitation force is made into a function of the load torque of a gearwheel, The Claim 1 characterized by the above-mentioned. Gear design support method.   5. The amplitude and phase of the excitation force are obtained by using orthogonal detection from the sum total data of the tooth-to-forces of the meshing gear teeth and the engagement frequency with respect to the calculation of the excitation force. The gear design support method according to any one of the above.   With respect to the calculation of the excitation force, the amplitude and phase of the excitation force are obtained from the total data of the tooth-to-forces of the meshing gear teeth and the engagement frequency by using a fast Fourier transform. 5. The gear design support method according to any one of 4 above.   The gear design support method according to any one of claims 1 to 6, wherein the accuracy in calculating the excitation force is adjusted according to the band of the meshing frequency.   The gear design support method according to any one of claims 1 to 7, wherein the value of the viscosity term of the equation of motion is set larger than usual when the equation of motion is switched.   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 a dynamic behavior of the driven shaft with respect to the operation of the driving shaft. A basic input step of inputting basic specification information and driving condition information of the target gear, a gear shape error input step of providing information on the shape error of the gear by a gear shape error input unit, and an assembly error input unit. An eccentricity error between the basic circle center and the rotation center of the gear, an assembly error input step that gives information on the inclination of each axis, and a basic motion equation derivation unit, given by the basic input step and the assembly error input step From the information, an action line in contact with the basic circle between the gears is obtained, and contact is made on the action line based on the information obtained from the gear shape error input step and the assembly error input step. A pre-equation equation derivation step for generating a motion equation by setting a force balance formula for each tooth pair, a pre-calculation step for solving the equation of motion in a time series by a pre-calculation unit, and a vibration force extraction unit An excitation force extraction step for calculating an excitation force that vibrates the gear in the middle, an equation for derivation of the equation of motion for switching to an equation of motion using the calculated excitation force, and a calculation unit for calculating the equation of motion A gear design support method comprising: a main calculation step for solving the equation of motion in time series; and an output step for outputting an analysis result of the drive shaft and the driven shaft calculated by the output unit by an output unit. A program to run on.   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 a dynamic behavior of the driven shaft with respect to the operation of the driving shaft. A basic input step of inputting basic specification information and driving condition information of the target gear, a gear shape error input step of providing information on the shape error of the gear by a gear shape error input unit, and an assembly error input unit. An eccentricity error between the basic circle center and the rotation center of the gear, an assembly error input step that gives information on the inclination of each axis, and a basic motion equation derivation unit, given by the basic input step and the assembly error input step From the information, an action line in contact with the basic circle between the gears is obtained, and contact is made on the action line based on the information obtained from the gear shape error input step and the assembly error input step. A pre-equation equation derivation step for generating a motion equation by setting a force balance formula for each tooth pair, a pre-calculation step for solving the equation of motion in a time series by a pre-calculation unit, and a vibration force extraction unit An excitation force extraction step for calculating an excitation force that vibrates the gear in the middle, an equation for derivation of the equation of motion for switching to an equation of motion using the calculated excitation force, an equation for derivation of the equation of motion, A gear design support method comprising: a main calculation step for solving the equation of motion in time series; and an output step for outputting an analysis result of the drive shaft and the driven shaft calculated by the output unit by an output unit. A recording medium on which a program to be executed is recorded. 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,
A basic input unit for inputting basic specification information of the target gear and its driving condition information;
A gear shape error input unit for giving information on the shape error of the gear;
An eccentricity error between the basic circle center and the rotation center of the gear, and an assembly error input unit that gives information on the inclination of each axis;
An action line in contact with the basic circle between the gears is obtained from information given by the basic input unit and the assembly error input unit, and based on information obtained from the gear shape error input unit and the assembly error input unit. A pre-motion equation derivation unit that generates a motion equation by setting a force balance equation for each tooth pair in contact on the action line;
A pre-calculation unit for solving the equation of motion in time series,
An excitation force extraction unit for calculating an excitation force for vibrating the gear in the middle of the calculation;
This motion equation derivation unit that switches to the equation of motion using the calculated excitation force,
This calculator that solves this equation of motion in time series,
A gear design support apparatus, comprising: an output unit that outputs an analysis result of the drive shaft and the driven shaft calculated by the calculation unit.

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