JPH0933398A - Simulation method for tooth contact transmission error of bevel gear - Google Patents

Abstract

PROBLEM TO BE SOLVED: To precisely calculate a tooth contact transmission error in the tooth contact transmission error simulation of a bevel gear. SOLUTION: The relative tooth flank error between the actual tooth flank of a ring gear 1 and the actual tooth flank of a pinion 2 when an assembling error is imparted thereto is calculated. The ring gear 1 is then rotated in a direction B around an axis A from the state where a clearance corresponding to this relative tooth flank error is present between the ring gear 1 and the pinion 2 to the state where simultaneous contact lines 3, 4 mutually contact. The ring gear rotation correction angle to the ring gear rotating angle is calculated. The calculation of the ring gear rotation correction angle is performed for all simultaneous contact lines of the ring gear 1 and the pinion gear 2. The difference between maximum value and minimum value of the ring gear rotation correction angle for a plurality of simultaneous contact lines in one pitch of the ring gear rotating angle is taken as a tooth contact transmission error.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a tooth contact transmission error simulation method for bevel gears, which is performed when designing and manufacturing bevel gears.

[0002]

2. Description of the Related Art In order to design and manufacture a higher quality bevel gear (for example, a hypoid gear), it is necessary to accurately grasp a tooth contact shape and a tooth contact transmission error directly connected to gear noise. Conventionally, such tooth contact transmission error is measured by various methods.

[0003] For example, after performing a tooth contact check of a hypoid gear in which the tooth surface of a ring gear is coated with Komeitan, using a tooth contact tester, a single tooth surface meshing tester (SFT) is used.
Is used to measure the tooth contact transmission error.

In the transmission error simulation using the Gleason system, the tooth contact transmission error is simulated by a computer by performing meshing analysis of the geometric plane of the ring gear tooth surface and the geometric plane of the pinion gear tooth surface determined by gear cutting. There is.

[0005] In addition, No. 1 of the Japan Society of Mechanical Engineers Symposium Proceedings of the Japan Society of Mechanical Engineers symposium held in Fukuoka from November 7 to 9, 1989. 890-58 307-3
On page 10, the relative tooth flank error between the actual tooth flank of the pinion and the actual tooth flank of the ring gear was measured using a three-dimensional measuring machine, and the actual tooth contact transmission error was calculated from the measured relative error. Taking measurements.

[0006]

However, when the tooth contact transmission error is measured by the one tooth surface meshing tester after the tooth contact check, a skillful function is required for observing the tooth contact. In addition, since there are individual differences in the application state and observation method of Komeitan at the time of checking the tooth contact, the tooth contact transmission error may vary depending on the measurer. Further, even if the tooth contact is the same, if the measured transmission error is different, it becomes difficult to evaluate the hypoid gear. Further, in order to measure the tooth contact transmission error after the tooth contact check, it is necessary to reset the hypoid gear from the tooth contact tester to the SFT, which makes the measurement troublesome.

Further, in the transmission error simulation by the Gleason system, since the ring gear tooth surface and the pinion gear tooth surface are calculated by gear cutting, the actual tooth contact transmission error including machining error, heat treatment distortion, etc. must be measured. I can't.

Further, in the method described in the above-mentioned collection of papers,
Since the tooth contact transmission error is obtained by approximate calculation, the value becomes inaccurate, and the tooth contact simulation cannot be performed.

An object of the present invention is that the measurement is easy and
An object of the present invention is to provide a tooth contact transmission error simulation method for bevel gears, which can measure an actual tooth contact transmission error including machining error, heat treatment distortion, etc. and can accurately determine the tooth contact transmission error. .

[0010]

A tooth contact transmission error simulation method for a bevel gear according to a first aspect of the present invention is a method for simulating a tooth contact transmission error between one gear and the other gear, both of which are bevel gears. , Measuring the three-dimensional shape of the actual tooth flanks of the one gear and the other gear, calculating a plurality of simultaneous contact lines between the reference tooth flanks of the one gear and the other gear, and assembling error The relative tooth flank error between the actual tooth flank of the one gear and the actual tooth flank of the other gear when given, for each of the plurality of simultaneous contact lines, Between one actual tooth surface of one gear and the actual tooth surface of the other gear opposite to this actual tooth surface, from a state in which a gap corresponding to the calculated relative tooth surface error is open, The actual tooth surface of the one gear and the other Until the state where the actual tooth surfaces of the vehicle come into contact with each other at the position of the simultaneous contact line, the one gear is rotated, and the rotation correction angle of the one gear with respect to the rotation angle of the one gear at this time is calculated, Calculating a difference between a maximum value and a minimum value of the rotation correction angle of the one gear for the plurality of simultaneous contact lines in one pitch of the rotation angle of the one gear as a tooth contact transmission error. It is characterized by.

In the tooth contact transmission error simulation method of claim 1 according to the present invention, the three-dimensional shape of the actual tooth surface of one gear and the other gear is measured, and the one gear and the other gear are also measured. A plurality of simultaneous contact lines between the reference tooth surfaces are calculated. Next, the relative tooth flank error between the actual tooth flank of one gear and the actual tooth flank of the other gear when the assembly error is given is calculated. Next, from the state in which there is a gap corresponding to the calculated relative tooth surface error between one actual tooth surface of one gear and the actual tooth surface of the other gear opposite to this actual tooth surface, One gear is rotated until the actual tooth flanks of one gear and the actual tooth flanks of the other gear come into contact with each other at the position of the simultaneous contact line. The rotation correction angle of is calculated. This step is performed for each of the plurality of simultaneous contact lines. Next, the difference between the maximum value and the minimum value of the rotation correction angle of one gear for a plurality of simultaneous contact lines in one pitch of the rotation angle of one gear is calculated. The difference calculated in this way, which is calculated as the tooth contact transmission error, becomes the transmission error.

Since the tooth contact transmission error is calculated based on the actual measurement instead of the approximate calculation as described above, the tooth contact transmission error can be accurately obtained and the tooth contact simulation can be performed. it can. Further, since it is not the calculation of the tooth surface by the gear cutting setup, it is possible to calculate the actual tooth contact transmission error including the processing error, the heat treatment distortion and the like. Further, since it is not necessary to reset the SFT from the tooth contact tester, it is easy to calculate the tooth contact transmission error.

According to another aspect of the present invention, there is provided a bevel gear tooth contact transmission error simulation method, wherein an actual rotation angle of one gear is calculated based on a rotation correction angle of the one gear for each of the plurality of simultaneous contact lines. Calculated, for each of the plurality of simultaneous contact lines, between one actual tooth flank of the one gear and the actual tooth flank of the other gear facing the actual tooth flank, From the state in which the clearance corresponding to the calculated relative tooth surface error is open, the one gear is rotated at an angle corresponding to the actual rotation angle of the one gear, and one actual gear of the one gear at this time is rotated. The clearance between the tooth surface and the actual tooth surface of the other gear facing the tooth surface is measured, and one actual tooth surface of the one gear and the other gear facing the tooth surface. It is characterized by determining the state of tooth contact with the actual tooth surface of Than it is.

In the tooth contact transmission error simulation method of claim 2 according to the present invention, for each of the plurality of simultaneous contact lines, the actual rotation angle of one gear is based on the rotation correction angle of one gear. To calculate. Next, from the state in which there is a gap corresponding to the calculated relative tooth surface error between one actual tooth surface of one gear and the actual tooth surface of the other gear opposite to this actual tooth surface, Rotate one gear at an angle corresponding to the actual rotation angle of one gear, and measure the clearance between one tooth surface of one gear and the tooth surface of the other gear opposite to this tooth surface. Then, the tooth contact state between the one tooth surface of one gear and the tooth surface of the other gear opposite to this tooth surface is determined. This step is performed for each of the plurality of simultaneous contact lines.

As described above, the tooth contact state is quantitatively determined by determining the tooth contact state by the clearance between the one actual tooth surface of one gear and the actual tooth surface of the other gear opposite to this tooth surface. It is possible to display the tooth contact state.

A bevel gear tooth contact transmission error simulation method according to a third aspect is characterized in that the V / H check of the one gear is performed.

With such a V / H check, a skillful function is not required for observing the tooth contact, and there is no fear that the tooth contact transmission error will differ depending on the measurer.

According to a fourth aspect of the present invention, there is provided a tooth contact transmission error simulation method for bevel gears, wherein an area of the tooth contact state portion is calculated.

As described above, by calculating the area of the tooth-contact state portion, the tooth-contact area obtained quantitatively can be added to the item of quality control as a substitute characteristic value of noise.

[0020]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a tooth contact transmission error simulation method of a bevel gear according to the present invention will be described with reference to the drawings. In the embodiments described below, it is assumed that a hypoid gear that can be used in a final reduction gear of a vehicle or the like is simulated, and that the actual work tooth flanks of the ring gear and the pinion are measured by a three-dimensional measuring machine, and otherwise the computer. Shall be done above.

FIG. 1 is a diagram for explaining a first embodiment of the present invention, and FIG. 2 is a flow chart of the first embodiment of the present invention. First, in step 10,
The ring gear reference tooth surface and the pinion reference tooth surface of the hypoid gear are calculated, respectively. Here, the ring gear reference tooth surface is a tooth surface determined by gear cutting, and the pinion reference tooth surface is a conjugate tooth surface created by the ring gear 1.

Next, in step 11, the ring gear 1 corresponding to the rotation angle of the ring gear when the ring gear reference tooth surface and the pinion reference tooth surface mesh with each other without any assembly error.
And the pinion 2 contact line, that is, the simultaneous contact line (Fig. 1
Only simultaneous contact lines 3 and 4 are shown in (a) and (b). ) Is calculated. Here, the assembly error means the ring gear 1
Error in the offset direction and / or error in the assembly direction of the pinion 2. Next, in step 12, a relative error between the ring gear reference tooth surface and the pinion reference tooth surface when a predetermined assembly error is given is calculated.

Before calculating the relative tooth flank error between the actual work tooth flank of the ring gear and the actual work tooth flank of the pinion when the assembly error is given, in step 15, the ring gear reference tooth flank and the pinion reference flank are used. Based on the tooth surface, the actual work tooth surface of the ring gear and the actual work tooth surface of the pinion are measured by a coordinate measuring machine (step 13), and the actual work tooth surface of the ring gear and the pinion are measured based on the measured values. The relative tooth flank error with respect to the actual work tooth flank is calculated (step 14).

In step 15, the relative tooth flank error between the actual work tooth flank of the ring gear and the actual work tooth flank of the pinion when an assembly error is given is calculated. This relative tooth flank error corresponds to the sum of the relative tooth flank error calculated in step 12 and the relative tooth flank error calculated in step 14.

Next, in step 16, the relative tooth flank error calculated in step 15 between the one actual tooth flank of the ring gear 1 and the actual tooth flank of the pinion facing the actual tooth flank. It is arranged so that the clearance d ₁ is vacant (FIG. 1A). From this state, the ring gear 1 is rotated about the axis A in the B direction so that the simultaneous contact line 3 of the actual tooth flank of the ring gear and the corresponding simultaneous contact line 4 of the actual tooth flank of the pinion are mutually formed. Make contact (Fig. 1 (b)).

A ring gear rotation correction angle with respect to the ring gear rotation angle at this time is calculated (step 18). Then
In step 18, it is judged whether or not the ring gear rotation correction angle has been calculated for all the simultaneous contact lines of the ring gear 1 and the pinion 2. When it is determined that the simultaneous contact lines have not been calculated for all the simultaneous contact lines, the process returns to step 16, and the ring gear rotation correction angle is calculated for the simultaneous contact lines of the ring gear 1 and the pinion 2 that have not been calculated yet.

When it is determined in step 18 that the ring gear rotation correction angles have been calculated for all the simultaneous contact lines, the tooth contact transmission error is calculated in step 19, and this processing step is ended. This tooth contact transmission error can be obtained by calculating the difference d ₃ between the maximum value and the minimum value of the ring gear rotation correction angle for a plurality of simultaneous contact lines at one pitch d ₂ of the ring gear rotation angle. Yes (see Figure 3). Here, 1 pitch d ₂ is the ring gear 1
Let z be the number of teeth in

## EQU1 ## It is represented by d ₂ = 2π / z.

In this example, since the tooth contact transmission error is calculated based on actual measurement, not the approximate calculation, the tooth contact transmission error can be accurately obtained and the tooth contact simulation can be performed. it can. Further, since it is not the calculation of the tooth surface by the gear cutting setup, it is possible to calculate the actual tooth contact transmission error including the processing error, the heat treatment distortion and the like. Further, since the calculation is performed on the computer without resetting the SFT from the tooth contact tester, it does not take time to calculate the tooth contact transmission error.

FIG. 4 is a diagram for explaining the second embodiment of the present invention, and FIG. 5 is a flow chart of the second embodiment of the present invention. First, in step 20,
As shown in FIG. 6, the ring gear actual rotation angle is calculated based on the ring gear correction angle calculated in the first embodiment. Here, the actual rotation angle of the ring gear is, in the meshing range d ₄ of one tooth surface of the ring gear,
The ring gear rotation correction angle for one pitch d ₂ of the ring gear rotation angle and the ring gear rotation correction angle of the tooth flanks before and after the ring gear rotation angle.

Next, in step 21, between the one actual tooth surface of the ring gear 1 and the actual tooth surface of the pinion facing this actual tooth surface, the relative tooth surface calculated in step 15 (FIG. 2). Arrangement is performed so that the clearance d ₁ corresponding to the error is vacant (FIG. 4A). From this state, the ring gear 1 is rotated about the axis A in the B direction at the ring gear actual rotation angle corresponding to the simultaneous contact lines 3 and 4 (FIG. 4B).

Next, in step 22, the clearance between the corresponding simultaneous contact lines 3 and 4 is calculated. Then
In step 23, it is judged whether or not this clearance has been calculated for all the simultaneous contact lines of the ring gear 1 and the pinion 2. When it is determined that the simultaneous contact lines have not been calculated for all the simultaneous contact lines, the process returns to step 21, and the clearance is calculated for the simultaneous contact lines of the ring gear 1 and the pinion 2 which have not been calculated yet.

When it is determined in step 23 that the clearances have been calculated for all the simultaneous contact lines, the tooth contact state is determined in step 24, and this processing step is terminated. As for the tooth contact state in step 24, as shown in FIG. 4 (c), the above-mentioned clearance is displayed on the tooth surface of the ring gear, and the clearance (6 μm in this example) of a predetermined distance or less is displayed as the tooth contact portion. Judge by. . In FIG. 4C, the broken line is the simultaneous contact line, and the solid line is the tooth contact portion.

In this example, the tooth contact state is determined from the clearance between the one actual tooth surface of the ring gear 1 and the actual tooth surface of the pinion 2 that faces the tooth surface, so that a quantitative tooth contact is obtained. The status can be displayed.

If desired, the tooth contact state is determined in this manner, and then "The Gleason Work" by Gleason Co.
"Testing and Inspecting Bevel and Hypoid Gear of s"
The V / H check as described in "s" is performed on the computer. Thus, by performing the V / H check on the computer without using a tooth contact tester as in the conventional case, the tooth contact can be observed. There is no need for a skilled function, and there is no fear that the tooth contact transmission error will differ depending on the measurer.

FIG. 7 is a flow chart of the tooth contact transmission error and the tooth contact state output by the tooth contact error simulation. First, in step 30, gear specifications and three-dimensional tooth surface shape data are input to a computer. Next, in step 31, a predetermined assembly error is input to the computer. Next, at step 32, a tooth contact transmission error simulation including the processing steps of the first and second embodiments is performed.
Next, in step 33, the tooth contact transmission error and the tooth contact state calculated in step 32 are output, and this processing step ends.

FIG. 8 is a diagram showing the relationship between the tooth contact transmission error value calculated by the flowchart of FIG. 7 and the tooth contact transmission error value measured by SFT. In this example, a tooth abradant made of white alumina abrasive (WA) and a tooth abradant made of cubic boron nitride (CBN) are shown in FIG.
The tooth contact transmission error value was calculated on the computer in accordance with the flowchart of 1. and the tooth contact transmission error value was measured by SFT. Further, in FIG. 8, the tooth contact transmission error calculated by the computer in the X-axis direction is represented by Y
The tooth contact transmission error measured by STF in the axial direction was plotted. As can be seen from the figure, Y = 0.609X for both the WA tooth grind and the CBN tooth grind.
It is found that the tooth contact transmission error calculated by the computer and the tooth contact transmission error measured by the STF are highly consistent with each other.

FIG. 9 (a) is a diagram showing the relationship between the ring gear rotation angle and the tooth contact transmission error obtained by the flow chart of FIG. 7, and FIG. 9 (b) is obtained by the flow chart of FIG. It is a figure which shows a tooth-contact state. In FIG. 9A, the solid line portion corresponds to the ring gear actual rotation angle. The circle in FIG. 9B corresponds to the tooth contact portion, and the clearance between one actual tooth surface of the ring gear and the actual tooth surface of the pinion facing this is less than or equal to a predetermined distance (this example). Indicates 6 μm). In this example,
In FIG. 9B, the number of circles (this corresponds to the tooth contact portion) displayed on the tooth surface is calculated, and the area of the tooth contact portion is calculated by multiplying the number by the unit area of the circle. For example, it can be calculated in step 32 (FIG. 7). By calculating the area of the tooth-contacting portion in this manner, the tooth-contacting area obtained quantitatively can be added to the item of quality control as a substitute characteristic value of noise.

FIG. 10 is a flowchart for distinguishing a good hypoid gear from a defective hypoid gear by making a quantitative determination of the gear. In this example, this flowchart is used as a tool for gear quality control. First,
In step 40, the actual tooth flank of the ring gear and the actual tooth flank of the pinion are measured using a coordinate measuring machine.
Next, in step 41, tooth contact transmission error, tooth contact position, and tooth contact area, which can be calculated using the above-described embodiment, are calculated. In step 42, it is determined whether the hypoid gear is a good product or a defective product based on the tooth contact transmission error, the tooth contact position, and the tooth contact area calculated in step 41, and this processing step is ended, and the product is determined to be a good product. Ship the determined hypoid gear.

FIG. 11 is a flow chart for defining the optimum tooth flank of the gear. The term "optimal tooth surface" as used herein refers to a tooth surface in which the tooth contact transmission error is not easily affected by the assembly error, that is, the tooth contact transmission error is insensitive to the assembly error. First, in step 50, an arbitrary tooth surface error measured by the three-dimensional measuring machine is input to the computer. Next, in step 51, the tooth contact transmission error is calculated using the flowchart of FIG. Then, in step 52,
It is determined whether or not the calculated tooth contact transmission error is the optimum tooth surface that is insensitive to the assembly error. If it is determined that the tooth surface is not the optimum tooth surface, the tooth surface shape is changed in step 53, and the process returns to step 50. If it is determined that the tooth flank is the optimal tooth flank, the optimal tooth flank is defined in step 54, and this processing step is ended. In this way, it is possible to define the optimum tooth surface in which the tooth contact transmission error is insensitive to the assembly error.

The present invention is not limited to the above embodiment, but various modifications and changes can be made. For example,
In the above embodiment, the tooth contact transmission error simulation was performed for the hypoid gear, but the tooth contact transmission error simulation can be applied to the Zellore bevel gear and the spiral gear.

[Brief description of drawings]

FIG. 1A and FIG. 1B are diagrams for explaining a first embodiment of the present invention.

FIG. 2 is a flowchart of the first embodiment of the present invention.

FIG. 3 is a diagram showing a relationship between a ring gear rotation angle, a ring gear rotation correction angle, and a tooth contact transmission error.

4 (a), (b) and (c) are diagrams for explaining a second embodiment of the present invention.

FIG. 5 is a flowchart according to a second embodiment of the present invention.

FIG. 6 is a diagram showing a relationship between a ring gear rotation angle, a ring gear rotation correction angle, and a ring gear actual rotation angle.

FIG. 7 is a flowchart of output of tooth contact transmission error and tooth contact state by tooth contact error simulation.

8 is a diagram showing a relationship between a transmission error value calculated by the flowchart of FIG. 7 and a transmission error value measured by SFT.

9A is a diagram showing a relationship between a ring gear rotation angle and a tooth contact transmission error obtained by the flowchart of FIG. 7, and FIG. 9B is a tooth contact state obtained by the flowchart of FIG. FIG.

FIG. 10 is a flowchart for distinguishing a non-defective product from a hypoid gear and a defective product by quantitatively determining a gear.

FIG. 11 is a flowchart for defining an optimum tooth flank of a gear.

[Explanation of symbols]

 1 Ring gear 2 Pinion 3,4 Simultaneous contact line 5 Tooth surface A axis B Ring rotation direction

Claims (4)

[Claims] 1. When simulating a tooth contact transmission error between one gear and the other gear, which are both bevel gears, while measuring the three-dimensional shapes of actual tooth surfaces of the one gear and the other gear, , Calculate a plurality of simultaneous contact lines between the reference tooth surfaces of the one gear and the other gear, and the actual tooth surface of the one gear and the actual tooth surface of the other gear when an assembly error is given. A relative tooth flank error between the tooth flank is calculated, and for each of the plurality of simultaneous contact lines, one actual tooth flank of the one gear and the other of the other facing the actual tooth flank. Between the actual tooth surface of the gear, from the state in which there is a gap corresponding to the calculated relative tooth surface error, the actual tooth surface of the one gear and the actual tooth surface of the other gear is the Move one of the gears until they touch each other at the simultaneous contact line. Rotate, calculate the rotation correction angle of one gear with respect to the rotation angle of the one gear at this time, in one pitch of the rotation angle of the one gear, of the one gear of the plurality of simultaneous contact lines A tooth contact transmission error simulation method for a bevel gear, comprising calculating a difference between a maximum value and a minimum value of a rotation correction angle as a tooth contact transmission error. 2. For each of the plurality of simultaneous contact lines, an actual rotation angle of one gear is calculated based on a rotation correction angle of the one gear, and each of the plurality of simultaneous contact lines is calculated. On the other hand, there is a gap corresponding to the calculated relative tooth surface error between the one actual tooth surface of the one gear and the actual tooth surface of the other gear facing the actual tooth surface. From this state, the one gear is rotated at an angle corresponding to the actual rotation angle of the one gear, and one actual tooth surface of the one gear at this time and the other gear facing the tooth surface. The clearance between the actual tooth flank of the one gear and the actual tooth flank of the other gear opposite to this tooth flank The judgment is made according to claim 1.
A tooth contact transmission error simulation method for a bevel gear described. 3. A tooth contact transmission error simulation method for a bevel gear according to claim 2, wherein the V / H check of the one gear is performed. 4. The tooth contact transmission error simulation method for a bevel gear according to claim 2, wherein the area of the tooth contact state portion is calculated.