JPH0551082B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Object of the Invention] (Industrial Application Field) The present invention relates to a method and apparatus for evaluating tooth profile and tooth trace errors on tooth surfaces of gears.

(Prior art) Devices for measuring tooth profile and tooth trace errors on gear tooth flanks measure the difference between the theoretically correct Ivolute tooth profile curve and the actual tooth profile curve, and the difference between the theoretical tooth trace curve and the actual tooth trace curve. Differences in gears are detected and displayed as tooth profile error curves and tooth lead error curves.Evaluation methods and evaluation standards are used when performing so-called evaluations such as classifying gears as good or bad or determining grades using these error curves. is determined separately. For example, in the JIS standard B1702, as shown in Figure 10, for the tooth profile inspection range e of the measured tooth profile error curve a, the maximum value of the error on the positive (+) side from the reference line s passing through the pitch point. The sum of the maximum values of errors on the negative (-) side is defined as a tooth profile error E, and the grade of the gear is determined by this tooth profile error E. If there is a pressure angle error on the tooth surface, the tooth profile error curve a will be inclined with respect to the reference line s, so the pressure angle error can be determined by drawing the average straight line m on the tooth profile error curve a and calculating from that inclination. It is prescribed that Since this evaluation method is based on the premise that the reference tooth profile is a theoretically accurate involute tooth profile, the reference line s and the average straight line m are straight lines.

On the other hand, with the recent advances in gear engineering, the design tooth profile has come to be a modified tooth profile that is a modified regular involute tooth profile, and is arbitrarily determined by the gear depending on the gear's use, specifications, etc. A wide variety of modified tooth profile patterns are used.
Moreover, the shape of the modified tooth profile is given as a diagram of a modification pattern for a regular involute tooth profile, as shown in FIG. 11, but is not given as a mathematical formula. In this way, when the design tooth profile is an arbitrary shape with the involute corrected, the JIS standard does not specify a method for determining the actual gear tooth profile error by comparing the actual tooth profile and the design tooth profile (the ISO standard still does not specify a method to determine the actual gear tooth profile error. under consideration).

In addition, according to the DIN standard, as shown in Figure 12,
Design tooth profile curve d and measured actual tooth profile error curve a
Draw an average tooth profile curve m by moving or rotating the design tooth profile curve d on the paper so that the difference between the two is minimized, and move the average tooth profile curve m in the y-axis direction based on the average tooth profile curve m. The interval between the most (+) side and the most (-) side of the tooth profile error curve a is determined as the tooth profile error f _f 〓, and the difference between the average tooth profile curve m in the y-axis direction is the pressure error f _H Then, the tooth profile error Fα is defined as Fα=√ _f 〓 ² + _H 〓 ² .

(Problems to be Solved by the Invention) However, the most difficult problem in practice with the above-mentioned DIN standard method is finding the average tooth profile curve m. The DIN standard also does not specify a specific method.

Therefore, a transparent paper on which the design tooth profile curve d is drawn is placed on top of the recording paper on which the actual tooth profile error curve a is drawn, and the evaluator appropriately overlaps the actual tooth profile error curve a and the design tooth profile curve d. The average tooth profile curve m was determined by comparing the two.

Therefore, the subjectivity of the evaluator is involved in determining the average tooth profile curve, and individual differences are large, making reliable evaluation impossible and requiring time and effort.

The above description also applies to tooth trace errors in exactly the same way.

The present invention was made in view of the above-mentioned points, and it is possible to accurately and easily obtain an average tooth profile curve or an average tooth trace curve, and to calculate the tooth profile error based on the accurate average tooth profile curve or average tooth trace curve. An evaluation method for evaluating curves or tooth trace error curves, and an evaluation method that automatically determines the average tooth profile curve or average tooth trace curve, and then calculates the tooth profile error curve or tooth trace error curve based on the average tooth profile curve or average tooth trace curve. The purpose is to provide an evaluation device for evaluation.

[Structure of the invention]

(Means for Solving the Problems) The method for evaluating the tooth profile and tooth trace error of a gear according to the present invention is based on the method of evaluating the tooth profile and tooth trace error of one tooth of the gear to be evaluated. From the design data that defines the design shape of the tooth trace, which is the line of intersection with the surface, a regression line that fits the design shape is found by the least squares method, and the gear to be evaluated is evaluated.
A regression line that applies to the actual tooth profile error curve or tooth trace error curve of the tooth flank of each tooth is found by the least squares method, and the regression line of the above designed tooth profile curve or designed tooth trace curve and the above actual When the designed tooth profile curve or designed tooth trace curve is moved so that the regression line of the tooth profile error curve or the tooth trace error curve matches, the designed tooth profile curve or the designed tooth trace curve is defined as the average tooth profile curve or the average tooth trace curve, The actual tooth profile error curve or tooth trace error curve is evaluated based on this average tooth profile curve or average tooth trace curve.

The gear tooth profile and tooth trace error evaluation device of the present invention is capable of evaluating the tooth profile of one tooth of a gear to be evaluated in the direction from the tooth bottom to the tooth tip, and the tooth trace which is the intersection line between the tooth flank and the pitch surface. A design data input means 4 for inputting design data defining a design shape, and data on an actual tooth profile error curve or tooth trace error curve of a tooth flank or tooth trace of one tooth to be evaluated for the gear to be evaluated. The error curve data input means 5 to be input, the regression line of the designed tooth profile curve or the designed tooth trace curve input by the design data input means 4, and the actual tooth profile error curve input by the error curve data input means 5. Alternatively, each regression line of the tooth trace error curve is determined by the least squares method, and the coordinate transformation of the design tooth profile curve or the regression line of the design tooth trace curve is performed so that both regression lines match, and the average tooth profile curve or the average Arithmetic control means 6 for determining a tooth trace curve and evaluating an actual tooth profile error curve or tooth trace error curve based on the average tooth profile curve or average tooth trace curve.
It is equipped with the following.

(Function) The method of evaluating the tooth profile and tooth trace error of a gear according to the present invention is to obtain a regression line using the least squares method from the designed tooth profile curve or the designed tooth trace curve, and to obtain the minimum regression line from the actual tooth profile error curve or tooth trace error curve. A regression line is obtained by the square method, and the average tooth profile curve or average tooth trace curve is obtained by performing coordinate transformation of the designed tooth profile curve or the set tooth trace curve so that both regression lines match. The actual tooth profile error curve or tooth trace error curve is evaluated based on the average tooth trace curve.

The gear tooth profile and tooth trace error evaluation device of the present invention uses the arithmetic control means 6 to calculate a regression line from the designed tooth profile curve or the designed tooth trace curve input by the design data input means 4 by the method of least squares. A regression line is determined by the least squares method from the actual tooth profile error curve or tooth trace error curve inputted by the error curve data input means 5, and a designed tooth profile curve or settings are made so that both regression lines match. The average tooth profile curve or average tooth trace curve is automatically obtained by performing coordinate transformation of the tooth trace curve, and then the actual tooth profile error curve or tooth trace error curve is evaluated based on this average tooth profile curve or average tooth trace curve. do.

(Embodiment) Hereinafter, the configuration of an embodiment of the present invention will be described with reference to FIGS. 1 to 7.

FIG. 1 shows the configuration of the evaluation device, which is composed of a computer system 1, a keyboard 2 and a digitizer 3 connected to the computer system 1, and the keyboard 2 or digitizer 3 is connected to one of the gears to be evaluated. Design data input means 4 for inputting design data defining the tooth profile from the bottom to the tip of the tooth flank of one tooth or the design shape of the tooth trace of the intersection line between the tooth flank and the pitch face; evaluation of the gear to be evaluated; The computer system 1 is configured as an error curve data input means 5 for inputting data of the actual tooth profile error curve or tooth trace error curve of the tooth profile or tooth trace of the tooth surface of the first tooth to be used. It is configured as an arithmetic control means 6 that performs arithmetic operations based on data to evaluate a tooth profile error curve or a tooth trace error curve.

Next, an evaluation method using this evaluation device will be explained.

A diagram of a design tooth profile curve d that defines the design shape of the tooth profile of the tooth surface of the gear to be evaluated is input into the computer system 1 as coordinate values digitized by the digitizer 3 (as shown in FIG. 2).

Then, the computer system 1 finds a regression line Ld that applies to the designed tooth profile curve d based on a program using the least squares method (as shown in FIG. 2).

In addition, the tooth profile of the tooth surface of the gear to be evaluated is measured using a general tooth profile measuring machine, and the diagram of the tooth profile error curve a drawn on a recording paper is digitized by the digitizer 3 and input into the computer system 1 as coordinate values. (as shown in Figure 3).

Then, the computer system 1 finds a regression line La that applies to the tooth profile error curve a based on a program using the least squares method (as shown in FIG. 3).

Next, computer system 1 calculates the regression line
The coordinate transformation values (the amount of translation in the y-axis direction and the rotation angle) of the regression line Ld necessary to make Ld coincide with the regression line La are determined.

Then, the coordinates of the designed tooth profile curve d are transformed based on the values of the coordinate transformation, and the designed tooth profile curve d of the coordinates resulting from the coordinate transformation is stored as an average tooth profile curve m (shown in FIG. 4).

The average tooth profile curve m obtained in this way is translated in parallel to the y-axis direction, and the most (+) of the tooth profile error curve a is
The spacing between when they touch on the side and when they touch on the most (-) side is determined as the tooth profile shape error f _f 〓 (shown in FIG. 5).

The difference in slope between the regression line Ld and the regression line La is determined as the pressure angle error f _H 〓 (shown in Figure 6).

Then, the tooth profile error Fα is calculated as Fα=√ _f 〓 ² + _H 〓 ² , and this tooth profile error Fα
The tooth profile is evaluated based on the size of the gear, and the quality of the gear is inspected.

FIG. 7 shows a flowchart of a program of the computer system 1 for determining the above-mentioned average tooth profile curve m.

Perform initial settings, determine whether it is a modified tooth profile, and if YES, set c = 0, d = 0, NO
If so, design tooth profile data {xi, yi} (i=1~
n), the regression line Ld is determined from the following equation.

ycx+d Σg ₀ (xi)=Zs, ΣIg ₀ (xi)=Zss c=6 [2Zss-(n+1)Zs]/Δx(n-1)・n
(n+1) d=1/n {Zs-3/n+1 [2Zss-(n+1)Zs]
} Next, the tooth profile error curve data {xi, yi} (i=
1 to n), the regression line La is determined from the following equation.

y=ax+b Σyi=Ys, Σiyi=Yss a=6 [2Yss-(n+1)Ys]/Δx(n-1)・n
(n+1) b=1/n{Ys-3/n+1 [2Yss-(n+1) Ys]} Next, the amount of parallel movement of the regression line Ld in the y-axis direction required to overlap the regression line Ld with the regression line La. δ,
Find the rotation angle θ.

δ=b−d θ=tan ⁻¹ a−tan ⁻¹ c Next, the coordinates of the average tooth profile curve m are calculated. This is the coordinate of the average tooth profile m, which is obtained by rotating the coordinates {xi, g ₀ (xi)} of the design tooth profile curve d by θ and translating the coordinates of the average tooth profile curve m by δ in the y-axis direction. } is calculated.

xi'=xicosθ+ _g0 (xi)sinθg(xi')=-xisinθ+ _g0 (xi)cosθ+δ The tooth profile error has been explained above, but the same applies to the tooth trace error.

Note that when the designed tooth profile curve d and the tooth profile error curve a are given as coordinate value data, the keyboard 2 is used instead of the digitizer 3 as in the above embodiment.
It can be entered directly from

In addition, as shown in FIG. 8, the voltage (or current) proportional to the tooth profile error measured by the analog tooth profile measuring device 7 is sampled at regular sampling intervals by the A-D converter 8 and digitalized. , and input it directly into the computer system 1 for storage. In this case,
The effort of inputting the tooth profile error curve measured as in the above embodiment using the digitizer 3 can be saved.
In this case, the tooth profile measuring device 7 and the A-D converter 8 are configured as the error curve data input means 5.

In addition, as shown in FIG. 9, in the case of a measuring machine that is equipped with a computer and automatically measures the tooth surface of a gear, the computer system shown in each of the embodiments in FIGS. 1 and 8 above can be used. It is possible to share both the measurement function and the evaluation function by sharing input devices. This measuring device was proposed by the applicant (Japanese Patent Application Laid-Open No. 150304/1983), and includes an A/D axis detector 13 that detects the movement of the measuring stylus 12 in contact with the measuring gear 11; θ-axis rotary encoder 1 that detects the rotation angle of measurement gear 11
4. A to detect the amount of axial movement of the measurement gear 11
An axis linear encoder 15, a T-axis linear encoder 1 that detects the amount of movement in the tangential direction of the measurement gear 11.
6. A digital signal from the R-axis linear encoder 17 that detects the amount of movement of the measuring gear 11 in the radial direction is input to the CPU 19 via the interface 18, and from this CPU 19 to the interface 18.
The θ-axis servo motor 21, the A-axis servo motor 22, the T-axis servo motor 23, and the R-axis servo motor 24 are driven via the servo drive devices 20, 20. In addition, the CPU 19 has an X-Y plotter 2.
5, a data typewriter 26, a floppy disk 27, and a doublet 28 are connected.

〔Effect of the invention〕

According to the present invention, a regression line is obtained from the designed tooth profile curve or the designed tooth trace curve by the least squares method,
A regression line is determined by the least squares method from the actual tooth profile error curve or tooth trace error curve, and the coordinate transformation of the designed tooth profile curve or set tooth trace curve is performed so that both regression lines match, and the average tooth profile curve or Since the average tooth trace curve is determined, the average tooth profile curve or average tooth trace curve can be accurately and easily determined, and the actual tooth profile error curve or tooth trace error curve is calculated based on this average tooth profile curve or average tooth trace curve. This eliminates the skill level and individual differences of the evaluators, making the evaluation easy and hassle-free.

Furthermore, since the average tooth profile curve or the average tooth trace curve is automatically determined by the arithmetic control means, the evaluation time is quick and the evaluation does not take much time.

[Brief explanation of the drawing]

FIG. 1 is a configuration diagram showing an embodiment of the method and apparatus for evaluating gear tooth profile and tooth trace errors of the present invention;
2 to 6 are explanatory diagrams showing its operation, FIG. 7 is a flowchart of the program, FIG. 8 is a configuration diagram showing another embodiment of the present invention, and FIG. 9 is a further embodiment of the present invention. Fig. 10 is an explanatory diagram of tooth profile error in a gear with an involute tooth profile, Fig. 11 is an explanatory diagram of a modified tooth profile pattern,
FIG. 12 is an explanatory diagram of a tooth profile error in a gear with a modified tooth profile. 4...Design data input means, 5...Error curve data input means, 6...Arithmetic control means.

Claims (1)

[Scope of Claims] 1. From design data that defines the tooth profile of one tooth surface of the gear to be evaluated in the direction from the tooth bottom to the tooth tip or the design shape of the tooth trace which is the intersection line between the tooth surface and the pitch surface. A regression line that applies to the design shape is determined by the least squares method, and a regression line that applies to the actual tooth profile error curve or tooth trace error curve of the tooth flank or tooth trace of one tooth that is being evaluated for the gear to be evaluated. is determined by the least squares method, and the designed tooth profile curve or designed tooth trace curve is calculated so that the regression line of the above designed tooth profile curve or designed tooth trace curve matches the regression line of the above actual tooth profile error curve or tooth trace error curve. The design tooth profile curve or designed tooth trace curve when moving is set as the average tooth profile curve or average tooth trace curve, and the actual tooth profile error curve or tooth trace error curve is evaluated based on this average tooth profile curve or average tooth trace curve. A method for evaluating tooth profile and tooth trace errors of gears. 2 Design data input means for inputting design data defining the tooth profile of one tooth surface of the gear to be evaluated in the direction from the tooth bottom to the tooth tip and the design shape of the tooth trace, which is the intersection line between the tooth surface and the pitch surface. and an error curve data input means for inputting data of an actual tooth profile error curve or a tooth trace error curve of the tooth profile or tooth trace of one tooth to be evaluated for the gear to be evaluated; find the regression line of the designed tooth profile curve or designed tooth trace curve inputted by the least squares method and the regression line of the actual tooth profile error curve or tooth trace error curve inputted by the error curve data input means, respectively; The average tooth profile curve or the average tooth trace curve is obtained by performing coordinate transformation of the regression line of the designed tooth profile curve or the designed tooth trace curve so that both regression lines match, and using the average tooth profile curve or the average tooth trace curve as a reference. A gear tooth profile and tooth trace error evaluation device comprising: arithmetic control means for evaluating an actual tooth profile error curve or tooth trace error curve;