JPH05116026A - Tooth surface correction method of gear - Google Patents

Abstract

PURPOSE:To provide a tooth surface correction method of a gear by which gears with a good tooth surface profile can be efficiently produced without hardly inviting the rise of manufacturing cost. CONSTITUTION:A plurality of simplified reference tooth surface profiles based on the difference in the tooth surface error distribution to the ideal tooth surface profile of a gear are set, and corrected reference tooth surface profiles approximate to the actual tooth surface profiles of the gear after these plural reference tooth surface profiles have been deformed and quenched respectively are obtained. Engagement transmission errors of the gear based on the corrected tooth surface profiles calculated by the difference between these corrected reference tooth surface profiles and the actual tooth surface profiles after quenching are calculated respectively. In such a constitution, the tooth surface of the gear is corrected to suit a corrected reference tooth surface profile in which the above engagement transmission errors are minimized.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a gear tooth surface correction method for efficiently correcting the tooth surface based on the tooth surface error of the gear after quenching.

[0002]

2. Description of the Related Art A wide variety of gears are incorporated in a power transmission system of an automobile. Of these gears, particularly gears on which a large force acts have tooth flanks formed on a helix, and are hardened after finishing to give sufficient strength.

Carbon steel, which is usually used as a gear material, has its hardness remarkably improved by quenching.
The tooth surface shape is considerably deteriorated due to heat distortion or the like during hardening of the gear that has been cut. For this reason, conventionally, the tooth surface of the gear that has been gear-cut with a hobbing machine or the like is pre-finished with a shaving cutter or the like, and by quenching this, the tooth surface error due to thermal strain is taken into consideration as much as possible. After quenching the gears, a simple inspection is performed to eliminate gears with particularly bad tooth surface shapes.

[0004]

In the present method of manufacturing a gear as described above, a tooth surface error occurs in units of several micrometers to several tens of micrometers with respect to an ideal involute tooth surface. It is well known that the error increases the meshing excitation force of the gears and is a source of vibration and noise of the power transmission system.

In order to obtain a highly accurate gear without considering the manufacturing cost and productivity, it is conceivable to grind with a gear wheel after quenching the gear. It is not possible to adopt such a method for all vehicle types for those that require importance to the car.

[0006] Conventionally, a production management method has been completely known as to how to correct the tooth surface error of a gear after quenching to what shape and to what extent before quenching can effectively reduce the meshing vibration force of the gear. There wasn't.

[0007]

It is an object of the present invention to set a plurality of reference tooth surface shapes based on the distribution of tooth surface errors with respect to an ideal tooth surface shape of a gear, and correct the tooth surface shapes in accordance with the reference tooth surface shapes. ,
An object of the present invention is to provide a tooth flank correction method for a gear, which can efficiently produce a gear having a good tooth flank shape with almost no increase in manufacturing cost.

[0008]

SUMMARY OF THE INVENTION A tooth flank correction method of a gear according to the present invention comprises a plurality of simplified reference tooth flank shapes based on differences in distribution of tooth flank errors with respect to an ideal tooth flank shape of the gear. To obtain a corrected reference tooth surface shape that approximates the actual tooth surface shape of the gear after quenching by deforming each of these plurality of reference tooth surface shapes, The gear transmission error of each gear is calculated based on the corrected tooth surface shape calculated from the difference with the actual tooth surface shape of the gear, and the gear transmission transmission error corresponds to the corrected reference tooth surface shape that minimizes the gear transmission error. The tooth flank of the gear is corrected by the above.

In the case of correcting the tooth flank shape of a gear, the method of correcting the tooth flank at the time of finishing such as shaving, which is performed before quenching of the gear, makes it easy to correct the blade shape of the shaving cutter and improve the machining efficiency. In this respect, it is more advantageous than the case of performing tooth surface modification by grinding after quenching.

[0010]

[Function] The actual tooth flank error after quenching is measured, and a plurality of simplified reference tooth flank shapes preset for this tooth flank shape are deformed to obtain the actual tooth flank shape after quenching. The approximate correction reference tooth surface shape is obtained.

Next, a corrected tooth surface shape is calculated based on the difference between the corrected reference tooth surface shape and the actual tooth surface shape,
Gear mesh transmission errors due to these modified tooth surface shapes are respectively calculated. Then, a corrected reference tooth surface shape that minimizes this meshing transmission error is selected.

After that, the tooth flanks of the gears are corrected by using a tool or the like corresponding to the selected corrected reference tooth flank shape so that the tooth flanks of the gears to be machined have the corrected tooth flank shape, and meshed. Consider to reduce the transmission error. here,
When the tooth surface shape can be corrected by changing the hardening method, the tooth surface of the gear is corrected by adopting the hardening method corresponding to the selected corrected reference tooth surface shape.

[0013]

EXAMPLE In this example, 10 types of reference tooth surface shapes 1 to 10 (20 types including positive and negative reversed states) are set based on the distribution of tooth surface errors with respect to the ideal tooth surface shape of a gear. , With an ideal involute tooth surface as a reference, 5 at equal intervals in the tooth trace direction and the tooth brush direction of the tooth surface, respectively.
The amount of the tooth flank error at the coordinate position plotted point by point is represented by the determinants R _{1 to} R ₁₀ shown in the following equations _{1 to 10} , and these reference tooth flank shapes 1 to 10 are schematically shown in FIGS. Represent In this case, the absolute value of the maximum tooth surface error (indicated by a positive value) that results in insufficient machining and the maximum tooth surface error that results in excessive machining (indicated by a negative value) with respect to the ideal involute tooth surface. ), The value of the tooth surface error at each coordinate position is set so that the sum of the absolute value and the absolute value of
The corrected reference tooth surface shape is obtained by multiplying by.

[0014]

[Equation 1]

The reference tooth surface shape shown in Equation 1 corresponds to FIG. 1, and the tooth surface error at both ends in the tooth trace direction is in a state of being twisted in the reverse direction in the tooth depth direction.

[0016]

[Equation 2]

The reference tooth surface shape shown in the equation 2 corresponds to FIG. 2, and the central portion in the tooth trace direction is curved in a cylindrical shape retracted along the tooth depth direction.

[0018]

[Equation 3]

The reference tooth surface shape shown in Equation 3 corresponds to FIG. 3 and is a sine curve of 3/4 cycle along the tooth trace direction.

[0020]

[Equation 4]

The reference tooth surface shape shown in the equation 4 corresponds to FIG. 4, and is a sine curve of one cycle along the tooth trace direction.

[0022]

[Equation 5]

The reference tooth surface shape shown in the equation 5 corresponds to FIG. 5, and has a cylindrical shape in which the central portion in the toothbrush direction projects along the tooth trace direction.

[0024]

[Equation 6]

The reference tooth surface shape shown in the equation 6 corresponds to FIG. 6 and is a sine curve of 3/4 cycle along the toothbrush direction.

[0026]

[Equation 7]

The reference tooth surface shape shown in the equation 7 corresponds to FIG. 7 and is a sine curve of one cycle along the tooth brush direction.

[0028]

[Equation 8]

The reference tooth surface shape shown in the equation 8 corresponds to FIG. 8 and is curved in a spherical shape in which the central portion in the tooth trace direction and the central portion in the tooth depth direction project.

[0030]

[Equation 9]

The reference tooth surface shape shown in the equation 9 corresponds to FIG. 9 and is inclined along the tooth trace direction.

[0032]

[Equation 10]

The reference tooth surface shape shown in the equation 10 corresponds to FIG. 10 and is inclined along the tooth brush direction.

In addition to the above-mentioned ten types of reference tooth surface shapes, it is of course possible to set reference tooth surface shapes other than this, and in order to improve the measurement accuracy, the plot position of the tooth surface error is further increased. You may make it set many.

On the other hand, with reference to the ideal involute tooth surface, the actual tooth surface shape of the gear after quenching is 5 at equal intervals in the tooth trace direction and the tooth drop direction of the tooth surface.
The amount of tooth flank error at the coordinate position plotted point by point is represented by the determinant S _X shown in the following Expression 11.

[0036]

[Equation 11]

Based on the tooth flank shape of the actual gear after this quenching, the reference tooth flank shape 1 shown in the above equations 1 to 10 is given.
By multiplying the determinants R _{1 to} R ₁₀ of Nos. ₁₀ to ₁₀ with an appropriate proportionality constant h, the corrected reference tooth surface shapes approximate to the actual tooth surface of the gear are calculated. Specifically, the difference between the determinant S _X expressed by the equation 11 and the determinant R of the reference tooth surface shape expressed by the following equation 12 is calculated, and the determinant when this difference becomes the minimum Select R as the corrected reference tooth surface shape. That is, the determinant S _X and the determinant R are based on the corrected reference tooth surface shape obtained by changing the proportional constants for each ± 0.1 to the above determinants R _{1 to} R _10.
The difference between and is repeatedly calculated.

[0038]

[Equation 12]

Therefore, the difference between the determinant S _X and the determinant R is given by the following equation 13.

[0040]

[Equation 13]

The proportionality constant h that minimizes the value of the equation 13 is obtained for each determinant R _{1 to} R ₁₀ , and this is multiplied by the determinant R _{1 to} R ₁₀ of the original reference tooth surface shape to obtain the correction reference. After obtaining the tooth surface shape determinant, calculate the gear mesh transmission error based on the corrected tooth surface shape calculated from the difference between these corrected reference tooth surface shapes and the actual tooth surface shape of the gear after quenching. To do.

For example, in the case of the determinant S _B in which the tooth flank error of the actual gear after quenching is expressed by equation 14, each determinant R ₁ ~
The value of the proportional constant h that minimizes the above-mentioned difference corresponding to R ₁₀ is as shown in Table 1 below. Then, the gear engagement transmission error is calculated based on the corrected tooth surface shape calculated from the difference between the corrected reference tooth surface shape and the actual tooth surface shape of the gear after quenching. The result is shown in Table 1 above. Is also shown.

[0043]

[Equation 14]

[0044]

[Table 1]

As is clear from Table 1, the determinant R ₆ of the equation ₆ is multiplied by the proportional constant h of 6.9 (micrometer) to the corrected reference tooth surface shape, and the meshing transmission error is reduced to the minimum value of 0. It can be 28 micrometers. The determinant S _O fixes tooth surface shape corresponding to the determinant R ₆ of 6 referred to below several 15.

[0046]

[Equation 15]

Using the shaving cutter corresponding to the equation (15), the tooth flank error of the gear that has been subjected to the correction finishing process on the gear before quenching is as shown in the determinant S _F of the following equation (16), and the meshing thereof is shown. The transmission error was 0.21 micrometers. That is, the mesh transmission error can be made considerably smaller than the mesh transmission error before correction of 0.77 micrometer.

[0048]

[Equation 16]

In this embodiment, the tooth surface of the gear before quenching is corrected and finished by the shaving cutter according to the tooth surface error of the gear after quenching. However, the quenching method may be devised or after quenching. The tooth surface may be corrected by the grinding process. Here, when the tooth surface is corrected by grinding after quenching, the gear should be ground to the corrected tooth surface shape without grinding to the regular involute tooth surface, so that a good mesh transmission error can be accommodated to some extent. Therefore, the grinding time can be significantly shortened.

Further, in this embodiment, the least squares method shown in the equation 13 is the minimum value of the difference between the determinant S _X representing the actual tooth flank shape of the gear after quenching and the determinant R of the reference tooth flank shape. However, it is of course possible to use other well-known calculation methods.

[0051]

According to the gear tooth surface correcting method of the present invention,
Approximate a plurality of simple reference tooth surface shapes based on the tooth surface shape of the gear after quenching, calculate the meshing transmission error in this case, and perform correction processing that corresponds to the optimum corrected reference tooth surface shape. Since the gear tooth surface of the gear can be efficiently corrected, it is possible to reliably reduce the mesh transmission error.

[Brief description of drawings]

FIG. 1 is a schematic view showing an example of a reference tooth surface shape according to the present invention together with FIGS.

FIG. 2 is a schematic view showing an example of a reference tooth surface shape according to the present invention together with FIGS. 1 and 3 to 10.

FIG. 3 is a schematic view showing an example of a reference tooth surface shape according to the present invention together with FIGS. 1, 2 and 4 to 10.

FIG. 4 is a schematic view showing an example of a reference tooth surface shape according to the present invention, together with FIGS. 1 to 3 and FIGS. 5 to 10.

FIG. 5 is a schematic view showing an example of a reference tooth surface shape according to the present invention together with FIGS. 1 to 4 and 6 to 10.

FIG. 6 is a schematic view showing an example of a reference tooth surface shape according to the present invention, together with FIGS. 1 to 5 and FIGS. 7 to 10.

FIG. 7 is a schematic view showing an example of a reference tooth surface shape according to the present invention together with FIGS. 1 to 6 and 8 to 10.

FIG. 8 is a schematic view showing an example of a reference tooth surface shape according to the present invention, together with FIGS. 1 to 7, 9 and 10.

9 is a schematic view showing an example of a reference tooth surface shape according to the present invention together with FIGS. 1 to 8 and FIG.

FIG. 10 is a schematic view showing an example of a reference tooth surface shape according to the present invention together with FIGS. 1 to 9.

Claims (1)

[Claims] 1. A plurality of simplified reference tooth surface shapes based on a difference in tooth surface error distribution with respect to an ideal tooth surface shape of a gear are set, and the plurality of reference tooth surface shapes are respectively transformed. Calculated from the difference between the corrected reference tooth surface shape and the actual tooth surface shape of the hardened gear after obtaining the corrected reference tooth surface shape that approximates the actual tooth surface shape of the gear after quenching The gear transmission error of the gear is calculated based on the corrected tooth surface shape, and the tooth surface of the gear is corrected according to the corrected reference tooth surface shape that minimizes the gear transmission error. To correct the tooth flank of the gear.