JPH02194311A - Tooth form error measuring method - Google Patents

Abstract

PURPOSE:To find a tooth form error with high accuracy by finding the tooth error from a specific equations based upon the measured angle of rotation of a gear to be measured, the quantity of movement of a measuring element, and the detected value of ruggedness of the tooth surface. CONSTITUTION:The measurement start point of the measuring element which detects the ruggedness of the tooth surface is set outside the basic circle of the gear to be measured, and the measuring element is scanned on the tooth surface and moved at right angles to the direction connecting the measurement start point and the center of the gear to be measured as the gear to be measured rotates. Consequently, the tooth form error is found from the equations (E: tooth form error, Vg: radius of basic circle of gear to be measured, DELTAVg: distance between basic circle and measurement start point, Xo: sum of movement quantity and detected quantity of measuring element, thetam: angle of rotation of gear to be measured) based upon the measured angle of rotation of the gear to be measured, the quantity of movement of the measuring element, and the detected value of the ruggedness of the tooth surface. Thus, the tooth form error is found with high accuracy.

Description

DETAILED DESCRIPTION OF THE INVENTION <Industrial Application Field> The present invention relates to a tooth profile error measuring method for easily and highly accurately measuring the tooth profile error of a gear.

<Prior art> Conventionally, the method of measuring tooth profile error has been to set a measuring point outside the base circle and to measure various types of errors obtained from the measuring point, etc., with the main purpose of downsizing the measuring device when measuring large gears. Japanese Patent Application No. 194360/1984 has proposed a method for determining tooth profile errors by performing arithmetic processing on measurement data.

The outline will be explained below with reference to the drawings. Figure 2 f
a) is a front view showing a schematic configuration of a tooth profile error measuring device according to a conventional tooth profile error measuring method, and FIG. The gear 5 to be measured is placed in a state where machining has been completed.The column 3 and the hob saddle 4 are provided with a column movement amount detector MA that can be attached and detached. It consists of a linear scale 6 attached to the table 2 and a detection head 7 attached to the near column 3.As shown in FIG. A rotation angle detection device B is provided. This rotation angle detection device B is Daple 2
It consists of a friction disk 8 that rotates by being rubbed against the side surface of the wheel, and a pulse generator 9 that is directly connected to the friction disk 8.
The pulse generator 9 converts the rotation angle of the friction disk 8, that is, the rotation angle of the gear 5 to be measured on the table 2, into a path. Further, a measuring element driving device C that drives a measuring element 12 that detects the unevenness of the tooth surface of the gear to be measured 5 is attached to the bob saddle 4, and the measuring element driving device C that drives the measuring element 12 that detects the unevenness of the tooth surface of the gear to be measured 5 is attached to the bob saddle 4. It consists of a scale 13 and a detection bed 14. The gauge head 2 is driven in the direction of the arrow in the figure (left and right direction in Figure 2 (left and right directions in Figure 2)) by a screw feed mechanism using a pulse motor 10 and a feed screw 11, and is a gauge head consisting of a linear scale 13 and a detection head 14. The movement amount detector 15 detects the movement amount (drive amount) of the probe 12.

An arithmetic processing device is provided for storing, calculating, outputting, etc. the measurement data for determining the tooth profile error of the gear 5 to be measured.

In the tooth profile error measuring device configured as described above, when the measuring element driving device C that drives the measuring element 12 is miniaturized and the moving distance is shortened, and the radius of the tooth root circle "6" is larger than the radius r9 of the base circle. In order to make it possible to perform measurements even on the ground, as shown in Figure 3, the probe is positioned at the measurement start point S set outside the base circle, and the moving direction of the probe is aligned between the measurement start point S and the gear to be measured. The direction is perpendicular to the center line connecting the center O. In this state, the measurement starting point S and the base circle are △r, pj
Far apart.

In this way, since the measuring stylus 12 is set outside the base circle by △r, even if the measuring stylus 12 is moved in a straight line according to the rotation angle as the gear 5 to be measured rotates, the tip of the measuring stylus 12 will not move. The problem is that the tooth surface formed by the involute tooth profile curve based on the base circle is not scanned, and the amount of error from the ideal involute tooth profile cannot be directly determined.This point is solved by the method explained below. It is solved by This will be explained based on FIG.

First, assuming a circle (measurement circle, radius r9 + △r9) whose radius is larger by Δr than the base circle (radius rg), set the measurement starting point S on this measurement circle, and place the measuring point at these 8 points. 12
Install the tip of the.

Now, it is assumed that the gear 5 to be measured is rotating counterclockwise, and one representative tooth surface I will be considered.

As shown in FIG. 4, the reference position is when the base end of the representative tooth surface (2) is on the center line L2 passing through the measurement starting point S.

From this reference position, the contact between the tip of the probe 12 and the representative tooth surface ■, that is, the start of tooth profile error measurement, occurs at 8 points, and at this time, the gear 5 to be measured is θ away from the reference position. As it rotates, the tooth surface becomes ■.

This θ can be expressed by the following equation (1).

After the measurement starts, for example, the rotation angle θ (specifically, rotation speed) of the gear 5 to be measured is measured by the rotation angle detection device B, and the measurement drive device C (pulse motor 10 and feed screw 11) A method of driving the measuring head 2 while applying a control signal to the measuring head 12 so that the measured amount of the measuring head 12 becomes 0 according to the output of the measuring head 12 (JP-A-56-64-610 Let us consider the situation in which the measurement was continued in the previous publication, and the tooth surface (■) was further rotated by an angle θ and became the tooth surface (-9).

In this state, the position of the tip of measuring stylus 2 is set as point P in the direction perpendicular to the center line 2 at the measurement starting point S.

The sum of the measured values detected by the probe movement amount detector 15 and probe 12 at this time is X. Assuming that, the angles θ, θ, and θ in FIG. 4 are given by the following equations (2) to (4), respectively.

θ−θ]−θ (2) Where θ is the 50 rotation angle of the gear to be measured detected by the rotation angle detection device B, and θ2 is the unwinding angle of the pincushion that determines the irregular tooth profile as shown in Figure 4. If the tooth surface ■ is an ideal involute tooth profile, the following equation (5) holds true.

θ1+θ, 202
...(5) However, if there is a concave tooth profile error at point I on the tooth surface ■, θ103〉θ2, and conversely, if there is a convex tooth profile error at point 1], θ1''-θ
3×θ2.

Therefore, each measured quantity θ7 and X. θ found from
1+θ3. The tooth profile error can be grasped by the magnitude relationship of θ2.

Here, if the representative tooth surface ■ is an ideal involute tooth surface, the U coordinate value U of point P with respect to the U-■ coordinate system is given by the following equation (6) from the involute curve formula and the coordinate transformation formula. .

u=r, ((excitation θ2−θ2・(2)θ2)・(g)θ.

”=((g)θ2”−θ2・Yuθ2)・Yuθ,+
(61 Therefore, the differential coefficient d of U with respect to θ
u/dθ.

is the following equation (7).

du d, = -r, ((6111θ2-62・work θ2)・t
Anθ1”-((2)θ2+θ2・粲θ2)・(9)θ
, + (7) Now, as θ2−θ, −θmdθ1 (
By substituting into formula 7), taking into account the sign, du becomes the following formula (8)
becomes.

du=rg((mθ2−θ2・workθ21tAnθ.

”-1 θ2 + θ2・Gallery θ2)・(1) θ1)(θ2−0
3-θ1) Therefore, the tooth profile error E in the normal direction of the tooth surface (2) is approximately given by the following equation (9), as shown in FIG.

E=duXcaoθ 9 ((廁θ2-02・慟θ2)・ゆうθ.

+(Working θ21-θ,・Reduction θ2)・Working θ1)(θ2-03
-θ1)・(Capital)θ3 <Problems to be Solved by the Invention> When examining the measurement accuracy using the conventional tooth profile error measurement method, the following results are obtained, for example.

Now, as an example, the torsion angle β=-7625'46#,
Pressure angle a-20°, base circle radius r-1,707,826
61106.4.1 for +++n measured gears
Under the condition of 0mm, the amount of probe movement is (1,OOnm
Let us consider the situation when the condition is (i+tooth profile error amount).

l) Angle θ when tooth profile error is 0 (Xo-1,00),
For example, θ = θ - θ 0.363'2153 - 0.29333520.069
It should be 8801 radians.

11) Here, the tooth profile error (change in U coordinate value) is 10
μm (Assuming that Xo = 1.00 + 0.011, let's see how much the tooth profile error is evaluated when using the method of the present invention.

Now, Xo=1. When OO+0.01, θ=0.36
32162 θ=0.2933305 dθ=θ−θ−θ.

From these values, du calculated using equation (8) in the specification of this application becomes du = o, 0102 clause, and a measurement error of 2% occurs against the tooth profile error of 0.01n + m + assumed in advance. You can see that

111) Also, the tooth profile error is 150 μm (Xo=1.
0O-0,05), then similarly to 11), it becomes duany, 0506++uu. In this case, it can be seen that a measurement error of 1.2% occurs compared to the pre-assumed tooth profile error of -0.05+n+ul.

As described above, in tooth profile error measurement using the conventional method, there is always a problem that there is a measurement m difference of several percent.

Means for Solving the Problems and Their Effects> The tooth profile error measuring method according to the present invention sets the measurement start point of the measuring stylus for detecting the unevenness of the tooth surface at a position outside the base circle of the gear to be measured. As the gear to be measured is rotated, the probe is moved in a direction perpendicular to the direction connecting the measurement start point and the center of the gear to be measured while scanning the tooth surface. The tooth profile error is determined by the following equation from the rotation angle of the gear to be measured, the amount of movement of the measuring stylus, and the detected value of the unevenness of the tooth surface.

E= r9[(C10(θ2-θ1)”-02...si
n(θ2-θ1)l-cmθ3+(success θ2-θ1)-θ
2・(9)(θ2-θ1)) fiber θ3](θ2-θ3-0
1)・(10 Where, E: Tooth profile error r: Radius of the base circle of the gear to be measured Δr; Distance between the base circle and the measurement start point xo: Sum of the amount of movement of the contact point and the amount detected by the contact point θ: Example: Hereinafter, one embodiment of the tooth profile error measuring method according to the present invention will be explained in detail. Consider the cause,
The meaning of formula (10) improved in the present invention will be explained with reference to FIG. 1. Note that the symbols used in the explanation of the prior art will be used as they are here, and detailed explanation will be omitted.

In Figure 1, ■ is a minute portion of the ideal involute tooth surface when the gear rotation angle is θ, and ■ is a minute portion of the tooth surface of the gear to be measured that includes a tooth profile error, and the position of ■ is dθ (wθ2−θ3−θ0.θ2.θ
3. θ1 are f3), f41. The gear is in a state of rotation by an amount (given by each equation of f2)). Here, point P is the point to be measured on the tooth surface ■, and point P' indicates the position of point P when rotated by dθ.

By the way, as mentioned above, since the measurement of the tooth profile error evaluation point is carried out on the straight line l in Fig. 1, the p/point cannot be measured, and the points that can actually be measured are the tooth surface ■ and This is the Q point where the direct vfie intersects. Therefore, the index giving the tooth profile error and the value to be found in step 17 are based on the value of PQ instead of du in Figure 1, and PQ in B gives the amount of tooth profile error on the straight line l. . That is, the cause of the measurement error in the conventional method is that du in the figure is determined as an approximate value of the value PQ that should actually be determined.

Therefore, in order to solve the accuracy problems of the conventional method,
If PQ is found instead of du in FIG. 1, then PQ can be found by the following procedure. In FIG. 1, the U coordinate value u and V coordinate value V of point P with respect to the UV coordinate system are given by the following equations from the involute curve equation and the coordinate transformation equation.

(6)′ Therefore, the differential coefficient of U with respect to 01 d u / dv1
The differential coefficient d v / dv1 for θ of °V (the differential coefficient d v / dv1 is obtained as shown below).

...(7)■ To the website, type 7 and the deco on the forehead...(7)' Now θ2-θ3-θmdθ, the tooth profile error amount du' on the straight line I (i.e., PQ in Fig. 1) ) is determined by the following formula, taking into account the sign.

du' =-du-dv --θ =rg[(ca6(θ2-θl)+θ2・Success θ2-θ1
)) + - θ3 (Shi θ2 - θ1) - θ2 - cso (θ2 -
θ1))](]θ2-θ3-01...[11) Therefore, the tooth profile error E in the normal direction of the tooth surface It will be done.

E = du'
(9) θ3 (Success θ2-θ1)-θ2・(2)(θ2-1
! 71)) Corridor θ31 (θ2-03-〇1)... An example is shown below.

By the way, the differences between the conventional method and the method of the present invention are based on the measurement position, the specifications of the gear to be measured, the measured values of various detectors (gear rotation angle detector, probe movement amount detector, etc.) Obtained value "l ro FΔrgF θ1p θ2j
The structure of the various detectors and the operating procedures for obtaining measured values from these detectors are the same as those of the prior art. Therefore, a detailed explanation of the equipment configuration for measurement, the measurement procedure, etc. will be omitted, and the conventional method and the method of the present invention will be explained by substituting the actually obtained measured values into the above-mentioned calculation formula. The tooth profile error was calculated from each and compared.

As an example, the torsion angle β = 7"23'46'
Pressure angle α = 20', base circle radius r = 1707.82
Δr = 1 (16,410
mm, and the amount of probe movement is 100III++ tooth profile error amount, the following is a comparison.

In other words, when the tooth profile error amount is -0.01m+n, du approximately determined by the conventional method is 0.01016+
Compared to am, there is an error of 1.6% from the true value.
ma, which had an error of only 1% from the true value, indicating a clear reduction in measurement error. Furthermore, when the tooth profile error amount = -0.05 mm, in the conventional method, du = -0.05062 mm, which is 1.
There is an error of 4%, whereas in the method of the present invention, du=
-0,04978ram, which is 0644% of the true value
Even in this example, a clear reduction in measurement error was observed, demonstrating the advantage of the measurement method according to the present invention.

<Effects of the Invention> According to the tooth profile error measuring method of the present invention, the measuring element is positioned outside the base circle of the gear to be measured, and the measuring element is scanned and moved while rotating the gear to be measured. Various measured values obtained with
When calculating the tooth profile error of the gear to be measured through calculation using the calculation formula, the approximation accuracy of the calculation formula has been greatly improved, making it possible to obtain the tooth profile error with extremely high accuracy.

[Brief explanation of the drawing]

FIG. 1 is an explanatory diagram showing the improved principle of the tooth profile error measuring method according to the present invention, FIG. Fig. 4 is an explanatory diagram of the installation location of the tooth profile error, and Fig. 4 is an explanatory diagram of the measurement principle of tooth profile error. Processing device, r is the radius of the base circle, Δr is the amount of deviation between the measurement start point and the base circle, rb is the radius of the root circle, S is the measurement start point, M. ■ is the tooth profile curve. Mitsubishi Heavy Industries, Ltd.

Claims (1)

[Scope of Claims] The measuring point of the measuring stylus that detects the unevenness of the tooth surface is set at a position outside the base circle of the gear to be measured, and the gear to be measured is rotated from there, and as the gear is rotated, the measurement point is The measuring stylus is moved in a direction perpendicular to the direction connecting the measurement start point and the center of the gear to be measured while scanning the tooth surface, thereby measuring the rotation angle of the gear to be measured and the movement of the measuring stylus. A method for measuring tooth profile error, characterized in that the tooth profile error is determined by the following equation from the detected values of the amount and the unevenness of the tooth surface. E=r_g[{cos(θ_2-θ_1)+θ_2・s
in(θ_2−θ_1)}・cosθ_3+{sin(
θ_2-θ_1)-θ_2・cos(θ_2-θ_1)
}・sinθ_3](θ_2-θ_3-θ_1) Here, θ_1={√[(r_g+Δr_g)^2-r_g^2
]/r_g}-tan^-^1{√[(r_g+Δr_
g) ^2-r_g^2]/r_g}+θ_m θ_2=√[X_o^2+(r_g+Δr_g)^2-
r_g^2]/r_g θ_3=tan^-^1{[r_g^2・θ_2-(r
＿g+Δr_g)・X_o]/(r_g^2−X_o^
2)} E: Tooth profile error r_g: Radius of the base circle of the gear to be measured Δr_g: Distance between the base circle and the measurement start point corner