JP3642274B2 - Gear design method and gear - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a gear design method and a gear, and more particularly to a technique for obtaining a meshing transmission error at a load in a simple direction.
[0002]
[Prior art]
Ideally, the tooth surface of the gear has an involute tooth profile, but due to misalignment when the gear is disposed, the tooth edge of one gear abuts against the tooth surface of the other gear ( (Edge contact) may occur, and a large meshing transmission error occurs, causing gear noise, vibration, and the like. For this reason, tooth surface modification is usually performed by tooth profile modification, tooth line modification, bias, etc., but since the mesh transmission error depends on the load, the mesh transmission error considering the load deflection is obtained by calculation. In addition, it is necessary to set gear specifications and modified tooth surfaces with a small meshing transmission error (gear noise) by actually making a prototype of a gear and performing tests under various conditions. As a method for calculating the meshing transmission error at the time of load, see, for example, the paper No. 60 of “The Japan Society of Mechanical Engineers,” Volume 60, No. 575 (1994-7). Various methods such as 94-0049 have been proposed.
[0003]
The meshing transmission error is a rotation error of a pair of gears that mesh with each other, and is represented, for example, by an advance / delay amount of the driven gear when the driving gear is rotated at a constant speed. In this specification, the relationship between the meshing transmission error and the rotation angle is referred to as a meshing waveform, and in particular, the meshing waveform from the meshing start to the meshing end when meshing rotation is performed with only one tooth is referred to as a motion curve.
[0004]
[Problems to be solved by the invention]
However, when actually producing and testing multiple gears with different specifications and modified tooth surfaces, it requires enormous trial costs and man-hours, and it is difficult to test all conditions, and it is not always sufficient. A gear that satisfies the requirements cannot be obtained. In addition, when calculating the meshing transmission error at the time of load, it is generally necessary to calculate the convergence of the load torque balance, etc., and it is necessary to calculate for a long time each time the conditions such as the load torque are changed. It was not always appropriate for the study.
[0005]
The present invention has been made in view of the above circumstances, and an object of the present invention is to make it possible to quickly obtain a meshing transmission error under load by a simple calculation method.
[0006]
[Means for Solving the Problems]
In order to achieve such an object, the first invention is a method for calculating a gear transmission error at a predetermined load of a gear and designing the gear in consideration of the gear transmission error at the time of the load. A motion curve calculation step for calculating a motion curve representing the relationship between the transmission error of one tooth meshing and the rotation angle based on the tooth surface shape under no load; and (b) calculating the amount of deflection of the tooth under load. And (c) a load-time meshing transmission error calculation step for obtaining a meshing transmission error during loading based on the motion curve and the amount of deflection of the tooth during loading. It is characterized by.
[0007]
2nd invention is the gear design method of 1st invention, (a) Overlapping waveform generation process which produces | generates the overlapping waveform arrange | positioned so that the said motion curve may be shifted in the said rotation angle direction by 1 pitch of a tooth | gear, and one part may overlap. (B) The load-on-load meshing transmission error calculating step includes the step of calculating the rotation angle direction according to the number of motion curves existing between the overlapping waveform and the meshing transmission error position corresponding to the deflection amount. It is characterized in that a region is divided and a meshing transmission error under load is obtained for each region based on a motion curve existing in the region.
[0008]
According to a third aspect of the present invention, in the gear design method of the second aspect, in the region where the number of motion curves is one, the shape of the motion curve remains as it is and the relationship between the transmission error during rotation and the rotational angle represents the relationship between the rotation angle and the rotation angle. In the case where the number of motion curves is a plurality of areas, the plurality of motion curves are synthesized to obtain a meshing waveform during loading.
[0009]
A fourth invention is a gear designed and manufactured according to the gear design method of any one of the first to third inventions.
[0010]
【The invention's effect】
In the gear design method of the present invention, the motion curve under no load is obtained by calculation from the tooth surface shape, the amount of deflection of the tooth under load is obtained by calculation, and the motion curve and the amount of deflection of the tooth under load are calculated. Since the meshing transmission error under load is obtained by calculation based on the above, a complicated convergence calculation or the like is unnecessary, and the meshing transmission error under load can be calculated in a short time. For this reason, optimum gear design with less gear noise can be performed in a short time by obtaining the meshing transmission error at the time of loading of various gears in which the specifications of the gear and the modified tooth surface are changed extremely finely. On the other hand, if the gear design is similar to the conventional design time, the design time is greatly reduced.
[0011]
The second invention divides a region in the rotation angle direction according to the number of motion curves up to the meshing transmission error position corresponding to the deflection amount by using an overlapping waveform in which the motion curves are shifted by one pitch. In each of the third invention, when the number of motion curves is one area, the shape of the motion curve is directly used as a load mesh waveform, and the motion curve of the motion curve is obtained. In a region having a plurality of numbers, a plurality of motion curves are synthesized to obtain a meshing waveform at the time of loading. Each of them is an embodiment of the first invention, and the same effect as the first invention can be obtained.
[0012]
In addition, the gear of the fourth invention designed and manufactured according to such a gear design method can obtain substantially the same effect as the gear design method.
[0013]
DETAILED DESCRIPTION OF THE INVENTION
The present invention is preferably applied to the design of helical gears, helical bevel gears, hypoid gears and the like whose teeth are twisted in the axial direction, but other gears such as spur gears whose teeth are parallel to the gear shaft. It can also be applied to design.
[0014]
The method of the present invention is preferably executed by signal processing of a microcomputer, and a motion curve calculation means, a deflection amount calculation means for executing the motion curve calculation step, the deflection amount calculation step, and the on-load meshing transmission error calculation step, respectively. And a gear design device having a load-meshing transmission error calculation means.
[0015]
In carrying out the method of the present invention, it is desirable to design a pair of gears that are actually meshed and rotated. For example, the gears are designed to mesh with an ideal tooth surface gear having an involute tooth profile. Various aspects such as designing can be adopted.
[0016]
The tooth surface shape for determining the motion curve is determined by the gear specifications of the designed gear and the modified tooth surface, but it is also possible to consider the average error of processing during manufacturing. It is also possible to obtain a motion curve in a state closer to actual meshing rotation, for example, by adding misalignment due to load on the rotation shaft of the gear.
[0017]
An overlapping waveform in which the motion curve is shifted by one tooth pitch (angular pitch) in the rotation angle direction becomes the same waveform in one pitch period as long as there is no pitch error. It is also possible to take into account the pitch error of the processing at the time of manufacture. In this case, for example, the motion curve is arranged while being shifted by one pitch by the number of gear teeth, and shifted in the meshing transmission error direction according to the pitch error. You can do that.
[0018]
As the meshing transmission error during loading, it is appropriate to obtain a meshing waveform during loading that expresses the relationship between the meshing transmission error and the rotation angle as in the third aspect of the invention, but the maximum amplitude and average amplitude of the meshing transmission error, etc. You may make it obtain | require other physical quantities regarding a meshing transmission error.
[0019]
The technical philosophy of calculating the meshing transmission error under load based on the motion curve under no load and the amount of deflection of the tooth under load is not only the design of the gear but also the quality evaluation of the actual gear manufactured. It can also be used. In that case, measure the tooth profile of the actual gear and calculate the no-load motion curve, or if possible, rotate the mesh with only one tooth and measure the no-load motion curve. It ’s fine. The amount of tooth deflection at the time of loading can be obtained by calculation from the material, shape, etc., but it may be measured by applying load torque to an actual gear.
[0020]
That is, the calculation method of the meshing transmission error at the time of loading is based on the motion curve representing the relationship between the meshing transmission error of one tooth at no load and the rotation angle, and the amount of deflection of the tooth at the time of loading. It has a load transmission error calculation process which calculates | requires the transmission error at the time of load by calculation. Preferably, the method further includes an overlapping waveform generation step for generating an overlapping waveform in which the motion curve is shifted by one pitch of the tooth in the rotation angle direction so as to be partially overlapped, and the on-load meshing transmission error calculation is performed. The step divides the region in the rotational angle direction according to the number of motion curves existing up to the meshing transmission error position corresponding to the deflection amount in the overlapping waveform, and the number of motion curves is one region. Then, the shape of the motion curve is used as it is as an on-load engagement waveform, and when the number of motion curves is a plurality of areas, the plurality of motion curves are synthesized to obtain an on-load engagement waveform.
[0021]
The above-mentioned motion curve and deflection amount can be obtained by actual measurement or calculation. As for the motion curve, a plurality of motion curves related to all teeth are obtained, and they are shifted in the rotation angle direction by one pitch of the tooth. By generating the overlapping waveform, it is possible to calculate the meshing transmission error under load with higher accuracy.
[0022]
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 is a diagram for explaining an example of a procedure for designing a gear having helically twisted teeth in the axial direction, such as a helical gear, a helical bevel gear, and a hypoid gear according to the method of the present invention. Uses a microcomputer or the like to determine gear specifications, modify the tooth surface, etc., and design the gear. The gear specifications include, for example, the number of teeth, center distance, module, pressure angle, torsion angle, tooth depth, tooth width, reference pitch circle diameter, gear ratio, material, etc. Modifications, bias, etc. In step S2, the mesh transmission error characteristic is obtained using the microcomputer or the like based on the tooth surface shape of the gear designed in step S1, and in step S3, gear noise or the like is calculated based on the mesh transmission error characteristic. When the performance evaluation is satisfied and the predetermined requirement is satisfied, the process is terminated as acceptable, but when the condition is unacceptable, the tooth surface modification or the like is changed in step S1, and the processes in step S2 and subsequent steps are repeated. The meshing transmission error characteristic is a characteristic relating to the load torque and the meshing transmission error as shown in FIG. 9, for example. In step S3, the pass / fail is determined from the magnitude of the meshing transmission error in the load torque region at the place where the gear is used. To do.
[0023]
FIG. 2 is a block diagram for explaining the basic configuration of the gear design device 10 that is preferably used when determining the meshing transmission error characteristic in the above step S2. The central processing unit 12 connected to the data bus line, a hard disk, The microcomputer includes a main storage device 14 such as a ROM and an auxiliary storage device 16 such as a RAM. The central processing unit 12 performs signal processing in accordance with a program stored in advance in the main storage device 14 while using the temporary storage function of the auxiliary storage device 16 and the like. Functionally, the motion curve calculation means 30 shown in FIG. , An overlapping waveform generation means 32, a no-load engagement waveform calculation means 34, a deflection amount calculation means 36, an on-load engagement waveform calculation means 38, and an engagement transmission error characteristic calculation means 40.
[0024]
The display device 18 shown in FIG. 2 displays an image of a cathode ray tube, a liquid crystal panel, or the like, and displays the specifications and shape of the designed gear, the motion curve required when calculating the meshing transmission error characteristic, the overlapping waveform, It displays a meshing waveform during loading, a meshing waveform during loading, a meshing transmission error characteristic, etc., or an operation procedure, a selection menu, and a guide display of contents to be input. The keyboard 20, tablet 22, and dial 24 are input operation devices, and various types of information are input, commanded, selected, and the like by an operator. The printer 26 is for printing the display contents of the display device 18 and the specifications, shapes, or meshing transmission error characteristics of the designed gear. The network controller 28 is connected to a workstation, a machine tool, or the like. It is for information transmission. Various data of a gear designed and changed by another microcomputer via the network controller 28 may be taken in, but the series of FIG. 1 including the design and change of the gear using the gear design device 10 is included. It is also possible to perform all the processes.
[0025]
FIG. 4 is a flowchart for specifically explaining the processing content executed by each function of FIG. 3. Step R2 is executed by the motion curve calculating means 30, and step R3 is executed by the overlapping waveform generating means 32. Step R4 is executed by the no-load engagement waveform calculation means 34, step R6 is executed by the deflection amount calculation means 36, steps R7 and R8 are executed by the load-time engagement waveform calculation means 38, and step R10 is the engagement transmission error characteristic. It is executed by the calculation means 40. Step R2 is a motion curve calculation step, step R3 is an overlapping waveform generation step, step R6 is a deflection amount calculation step, and steps R7 and R8 are load-meshing transmission error calculation steps.
[0026]
In step R1 of FIG. 4, various data of the gear designed and changed in accordance with the operator's command are fetched. In step R2, the meshing transmission error for one tooth at no load is calculated based on the tooth surface shape of the gear. A motion curve representing the relationship with the rotation angle is obtained by calculation and displayed on the display device 18. The gear tooth surface shape is determined by gear specifications such as pressure angle, torsion angle, tooth depth, tooth width, and tooth surface modification such as tooth profile modification, tooth line modification, bias, etc. Assuming a pair of gears, the motion curve C _M is automatically obtained according to a predetermined arithmetic expression. As shown in FIG. 5, the motion curve C _M generally has a reverse parabolic shape that turns so that the middle portion of the mesh, that is, the central portion of the tooth surface is convex. It should be noted that a motion curve C _M in a state closer to the actual meshing rotation is added to the tooth surface shape by adding a shape change due to an average error of processing at the time of manufacture or adding a misalignment to the rotating shaft of the gear. Is also possible.
[0027]
In step R3, automatically generated the motion curve C _M 1 tooth pitch (angular pitch) P only by shifting the rotational angular direction overlap partially disposed so as to overlap waveform AC _M 6 Is displayed on the display device 18. In the present embodiment, the overlapping waveform AC _M is generated by ignoring the tooth pitch error at the time of machining and arranging the motion curve C _M by shifting the rotation angle by 1 pitch P at the same meshing transmission error position. It has become. For this reason, the same waveform is repeated with one pitch P as one cycle. In the subsequent processing, a predetermined arithmetic processing may be performed by extracting only one arbitrary pitch P. One pitch (angular pitch) P is obtained from gear specifications. Incidentally, it is also possible to consider the pitch error of processing time of manufacture, its may be to overlap by shifting the transmission error direction meshing motion curve C _M according to the pitch errors if.
[0028]
In step R4, ridge overlapping waveform AC _M in FIG. 6, that is only a part of the motion curve C _M located uppermost in FIG. 6, in particular by cutting only the convex shape once song portion of the reverse parabolic A no-load engagement waveform T ₀ as shown in FIG. 7 is obtained and displayed on the display device 18. That is, in the meshing rotation at no load, the driven-side gear in meshing transmission errors shown in unloaded engagement waveform T ₀ is to periodically advance or delay with respect to the drive side gear.
[0029]
Steps R5 to R8 are portions for calculating a load engagement waveform Tn and displaying it on the display device 18. In Step R5, a load torque is set and a load engagement waveform Tn is calculated each time the load engagement waveform Tn is calculated in Steps R6 to R8. Change the torque setting. The load torque may be set or changed automatically at a predetermined interval or the number of divisions with respect to a preset maximum load torque. It may be settable.
[0030]
In step R6, the amount of deflection F of the tooth under load is automatically obtained by calculation according to a predetermined arithmetic expression based on the material and shape of the gear. The amount of deflection F of the teeth basically consists of tooth collapse and elastic deformation of the surface. Based on the load torque set in step R5, the amount of inclination and elastic deformation may be calculated and added. In the present embodiment, the angular deviation around the center line of the gear is obtained in the same manner as the meshing transmission error. Further, for example, the maximum value or the average value of the deflection amount of each part on the trajectory of the contact point may be obtained, but it can be represented by the deflection amount of any one point on the trajectory of the contact point. In the embodiment, the deflection amount F of the tooth surface position corresponding to the turning point of the motion curve C _M , that is, the uppermost portion in FIG. 5 is obtained. Although the locus of the contact point varies depending on the load torque, for example, the locus of the contact point at the time of no load may be used.
[0031]
At step R7, the overlapping waveform AC _M in FIG. 6, with automatically setting the meshing transmission error position corresponding to the amount of deflection (angle deviation) F, motion curve C that exists until the meshing transmission error position The area in the rotation angle direction is automatically divided according to the number of _M. One-dot chain line L in FIG. 8 represents the meshing transmission error position corresponding to the deflection amount F, a motion curve C number one area E ₁ of the _M present above the the meshing transmission error position L in FIG, The number of motion curves C _M is divided into _two areas E ₂ . The number of motion curves C _M increases as the deflection amount F increases, in other words, as the load torque increases.
[0032]
In step R8, for each of the areas E _1, E _2, automatically determine the load meshing waveform Tn based on the motion curve C _M present in it, such as the area E _1, the E _2, displayed on the display device 18 To do. Specifically, for the region E ₁ where the number of motion curves C _M is one, the shape of the motion curve C _M is directly shifted to the meshing transmission error position L as the meshing waveform at the time of load, and the number of motion curves C _M is For the two regions E ₂ , the composite waveform C _M av of the two motion curves C _M above the meshing transmission error position L is obtained and shifted toward the meshing transmission error direction so as to be continuous with the meshing waveform of the region E _1. By doing so, the on-load engagement waveform Tn is obtained. Synthesized waveform C _M av is the waveform of the meshing average value of transmission errors in a plurality of motion curves C _M in the present embodiment.
[0033]
In the next step R9, it is determined whether or not the calculation of the on-load meshing waveform Tn for the predetermined load torque has been completed, and the load torque is changed until the on-load meshing waveform Tn for all the load torques is calculated. However, steps R5 to R8 are repeatedly executed. Then, when the calculation of the on-load meshing waveform Tn for all the load torques is completed, the relationship between the meshing transmission error (meshing primary component) and the load torque as shown in FIG. The representing transmission error characteristic is automatically calculated and displayed on the display device 18. “○” in FIG. 9 is a meshing transmission error characteristic obtained by calculation according to the present embodiment, and “×” is a measurement of a meshing waveform under load after actually manufacturing a gear, and a Fourier transform or the like is calculated from the measurement result. The actual measured values, which are shown for comparison, have a satisfactory relationship in terms of gear design.
[0034]
According to such a gear design method of this embodiment, when calculating the meshing transmission error characteristics for evaluation, automatically determined overlapping waveform by calculating a motion curve C _M without load from the tooth surface shape It generates the AC _M, automatically determined, by calculation load meshing waveform Tn based on that amount of deflection of the tooth at the time waveform AC _M and the load overlap such F by calculating the deflection amount F of the teeth under load Since the calculation is automatically performed, a complicated convergence calculation or the like is not required, and the on-load meshing waveform Tn and further the meshing transmission error characteristic can be calculated in a short time. For this reason, by determining the meshing transmission error characteristics of various gears with extremely fine changes to the gear specifications and modified tooth surfaces, etc., it becomes possible to perform optimal gear design with less gear noise in a short time, If the gear design is similar to the conventional design time, the design time is greatly reduced.
[0035]
Incidentally, the calculation time for obtaining the on-load meshing waveform Tn for one load torque, that is, the time required for executing steps R5 to R8 is about 2 to 3 seconds (conventionally about 1 minute). And epoch-making time reduction of multi-level calculation.
[0036]
In addition, since the meshing performance (meshing transmission error characteristic) can be taken into consideration at the stage of gear specification design, it is easy to design a low-noise gear while changing the gear specifications.
[0037]
In addition, when calculating the meshing waveform Tn and the meshing transmission error characteristic of this embodiment, instead of taking in the data of the designed gear, it is actually meshed by measuring and inputting the shape data of the actual gear product. It is possible to easily and quickly obtain the meshing waveform Tn and the meshing transmission error characteristic under load without rotating, and quality evaluation such as gear noise can be easily performed.
[0038]
On the other hand, by measuring and inputting low-noise gear shape data, etc., and determining the meshing torque waveform Tn and meshing transmission error characteristics, the characteristics of the low-noise gear can be easily derived. It can also be used for evaluation.
[0039]
As mentioned above, although the Example of this invention was described in detail based on drawing, this is an embodiment to the last, and this invention implements in the aspect which added various change and improvement based on the knowledge of those skilled in the art. Can do.
[Brief description of the drawings]
FIG. 1 is a flowchart illustrating an overall flow when designing a gear according to a method of the present invention.
FIG. 2 is a block diagram illustrating a configuration of a gear design apparatus that is preferably used when obtaining a meshing transmission error characteristic in step S2 of FIG.
3 is a block diagram illustrating functions provided in the apparatus of FIG. 2. FIG.
FIG. 4 is a flowchart for specifically explaining a flow of signal processing when obtaining a meshing transmission error characteristic using the apparatus of FIG. 2;
FIG. 5 is a diagram showing an example of a motion curve calculated in step R2 of FIG.
6 is a diagram illustrating an example of an overlapping waveform generated in step R3 in FIG.
7 is a diagram showing an example of a no-load meshing waveform calculated in step R4 of FIG.
FIG. 8 is a diagram for specifically explaining the contents of signal processing when obtaining a load-time meshing waveform in steps R5 to R8 in FIG. 4;
FIG. 9 is a diagram showing a contact transmission error characteristic obtained by calculation according to the flowchart of FIG. 4 in comparison with an actual measurement value.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 10: Gear design apparatus 30: Motion curve calculation means 32: Overlapping waveform generation means 36: Deflection amount calculation means 38: Unloaded engagement waveform calculation means C _M : Motion curve AC _M : Overlapping waveform L: Deflection amount Tn: Under load Meshing waveform step R2: Motion curve calculating step R3: Overlapping waveform generating step R6: Deflection amount calculating step R7, R8: Loaded meshing transmission error calculating step

Claims (4)

A method of calculating a meshing transmission error at a predetermined load of a gear and designing the gear in consideration of the meshing transmission error at the load,
A motion curve calculation step for calculating a motion curve representing a relationship between a meshing transmission error for one tooth at the time of no load and a rotation angle based on a tooth surface shape;
A deflection amount calculating step for calculating a deflection amount of the tooth at the time of loading;
Based on the motion curve and the amount of deflection of the tooth at the time of loading, a load-time meshing transmission error calculating step for calculating a meshing transmission error at the time of loading,
A gear design method comprising: An overlapping waveform generation step of generating an overlapping waveform in which the motion curve is shifted by one pitch of the tooth in the rotation angle direction and arranged so as to partially overlap;
The on-load meshing transmission error calculating step divides the region in the rotation angle direction according to the number of motion curves existing between the overlapping waveform and the meshing transmission error position corresponding to the deflection amount. 2. The gear design method according to claim 1, wherein a transmission error at the time of load is obtained based on a motion curve existing in the region every time. In the region where the number of motion curves is one, the shape of the motion curve is directly used as a loading mesh waveform representing the relationship between the transmission error during loading and the rotation angle. The gear design method according to claim 2, wherein a plurality of motion curves are synthesized to obtain a meshing waveform during loading. A gear designed and manufactured according to the gear design method according to claim 1.

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