JPH0463323B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a gear tooth profile inspection method and apparatus for inspecting the tooth profile of a gear, particularly the shape of a tooth surface.

An example of a conventional tooth profile inspection means for a gear having an involute curve is shown in FIGS. 1A and 1B. In this figure, a disk 23 (hereinafter referred to as "base disk") having the same diameter as the basic circle diameter determined by the specifications of the gear to be measured 24 is connected to a predetermined shaft 2.
The gear to be measured 24 is similarly inserted and fixed to the shaft 25 while being held between the upper and lower centers. Further, a straightedge 28 is crimped above the base disk 23 in the drawing, and this straightedge 28 is fixed to a measuring table 21 movable in the direction of an arrow 27. For example, when measuring the tooth profile of the right tooth flank of the gear to be measured 24, while rotating the gear 24 and the base disk 23 clockwise, move the straight edge 28 to the right, and vice versa. When measuring the tooth profile of the left tooth surface of the measurement gear 24, while rotating the gear 24 and the base disk 23 counterclockwise, use the straight edge 2.
Move 8 to the left. Further, a measuring stylus 22 for tooth profile inspection is fixed to the measuring table 21 as shown in the figure. The measuring tip 22 is normally fixed at its fulcrum (the rounded part at the upper end) to the straightedge 28, and at the same time has the other tip as a free end, which allows it to rotate the gear 24 and the base disk 23 as well as the straightedge 28. As the tooth surface moves, it follows the tooth surface while in contact with the tooth surface to be measured (actually, it is pressed against the tooth surface by a spring mechanism, etc.). The plate method is well known in the field of gear tooth profile inspection (for example,
First edition published on November 30th, Nikkan Kogyo Shimbun “Gear Handbook”
(Refer to the Gear Handbook Editorial Committee).

As shown in FIG. 1B, the involute curve is an arc (F1/F2)
Since the locus of point F3 is such that is equal to the line segment (F3・F2), the point of contact between the straightedge 28 and the base disc 23 is moved to the base disc by the movement of the measuring table 21 in the direction of the arrow 27. The trajectory drawn by moving away from 23 becomes a theoretical involute curve. On the other hand,
Since the tip of the tracing stylus 22 detects the curve of the tooth surface to be measured, the tooth profile error can be obtained from both and recorded on the recorder 26. Note that this first
In the apparatus shown in the figure, the shaft 25 is usually provided with an appropriate rotation angle measuring means (not shown), and the rotation angle information about the gear to be measured 24 and the base disk 23 to be measured is sent to the recorder 26. transmitted to.

However, in the conventional tooth profile inspection means as described above, it is necessary to prepare in advance a base disk corresponding to the gear to be measured, and the gear and base disk must be set in the device, which requires such work. Another disadvantage is that analysis of the measurement data requires special skills, making it necessary to rely on skilled engineers.

An object of the present invention is to improve the drawbacks of the prior art described above, and to make it possible to perform measurements while the gear to be measured is attached to the mechanical device in which the gear is used, thereby reducing the setting work on the measuring device. In addition to eliminating the
It is an object of the present invention to provide an inexpensive gear tooth profile inspection method and device that can record and store measurement data well.

In other words, in the present invention, the actual shape of the tooth flank to be measured is measured based on a measurement coordinate system that is appropriately determined in advance in a measuring device, while the theoretical shape of the tooth flank is The calculated theoretical value and the measured value are calculated based on a theoretical coordinate system determined corresponding to the position, and the calculated theoretical value and the measured value are determined based on the positions of a pair of measuring instruments that are respectively brought into contact with the appropriate tooth grooves of the gear. This method attempts to calculate the tooth profile error of a gear by reexpressing it in the same coordinate system through coordinate transformation based on another coordinate system, and then comparing the theoretical value and the measured value. .

Hereinafter, one embodiment of the present invention will be described in detail according to one embodiment shown in FIGS. 2 to 7. Note that the embodiments described below are based on an example in which the tooth surface of a gear is represented by an involute curve.

In order to compare the theoretical involute curve value (hereinafter referred to as "theoretical involute value") and the measured value, it is necessary to express both values in the same coordinate system. However, the theoretical involute value is
Generally, it is determined based on the base circle of the gear,
On the other hand, the actual measured value is arbitrarily determined by the measuring device. Therefore, in order to express both using the same coordinates, it is necessary to define another coordinate system that corresponds to both the coordinate system in which the theoretical involute value is expressed and the coordinate system in which the measured value is expressed, and then perform coordinate transformation as appropriate. Bye. Therefore, in the present invention,
Let us introduce a coordinate system determined by rollers R1 and R2, which are measuring tools shown in FIG. 2, and use this to perform the coordinate transformation. In FIG. 2, the center positions of rollers R1 and R2 are
Coordinates A1i (x1i, y1i) of any n points on the outer circumference,
A2i (x2i, y2i) is read (for example, in the device shown later in FIG. 6, the probe PB is moved to the position of these rollers R1 and R2 and a part of the outer circumference is traced; by the way, in FIG. 6,
For convenience of illustration, the width of the positioning table 4 in the x direction is shown to be narrower than the distance between these rollers R1 and R2, but the actual width of the positioning table 4 is smaller than the distance between these rollers R1 and R2. R
(the probe PB is movable to the positions of these rollers R1 and R2), and is determined by circular approximation using the method of least squares.
Note that the coordinates (x, y) have an origin at 0 [x, y] and are appropriately determined by the measuring device. In this way, first, the coordinates P1 (u ₁ , v ₁ ) of the center of roller R1 are becomes. Here, S _k =Σ(x1i-1) _Uk (y1i-1) _U1 = ₁ /nΣx1i, ₁ = 1/nΣy1i. Similarly, the center coordinates P2 (u ₂ , v ₂ ) of the roller R2 can also be determined. Incidentally, the radius of these rollers Rj (j = 1, 2) is calculated by the following formula, where rj is It can be found at However, in reality, the diameters of these rollers R1 and R2 are actually measured, and the measured values are later used in equation (6) or equation (7).

Note that the coordinate system determined by rollers R ₁ and R ₂ may be determined arbitrarily as long as the coordinates can be converted between the theoretical involute value and the measured value described above, but here, for the sake of explanation, the coordinate system that connects the centers P1 and P2 will be used. The description will be made using a coordinate system centered on the midpoint M of the line segment.

Center coordinates of rollers R1 and R2 obtained as described above
From P1 (u ₁ , v ₁ ) and P2 (u ₂ , v ₂ ), find the coordinates M (u, v) of the midpoint M of the line segment connecting P1 and P2 and express it in a matrix. becomes. Furthermore, the angle β between the line segment and the coordinate axis x is expressed as β=tan _U-1 (v ₁ −v ₂ /u ₁ −u ₂ ) (3).

Next, the theoretical involute value is generally the base circle
Since it is expressed based on BC, the relationships among the various quantities required for the coordinate transformation described later are determined in advance. In this example, since the number of teeth existing between the rollers R1 and R2 is an odd number, there is a tooth CT located in the center, and hereinafter, this will be used as the object of inspection to find the relationship between the above various quantities. do. Note that the teeth to be inspected may be set in advance, and the positions of the rollers R1 and R2 may be determined accordingly.

The module of gear G is m, the number of teeth is Z, and the pressure angle on the pitch point is α. Then, the basic circle shown in Figure 3
The radius RC of BC is RC=mZ/2cosα. ...(4) becomes. On the other hand, a line segment connecting the intersection point PC of the tooth surface of the tooth CT (more precisely, its extension line) and the base circle BC and the gear center OG, as well as a line segment connecting the midpoint M and the gear center OG, The angle Ψ is Ψ=x+4Wtanα ₀ /2Z+tanα ₀ −α ₀ (5). However, W is a dislocation coefficient.

Next, if the pressure angle at the intersection of the tooth surface of the tooth CP and the roller R1 is α _p , then this tangent tanα _p is the angle θ _p in the figure, that is, the line segment between the intersection and the gear center OG, and the line segment from the intersection to the The angle between the tangent to the base circle BC and the line segment at the gear center can be found by solving the equation tan=(θ _p +x/2−Ψ)=θ _p +D/2RC (6) . However, D
is the diameter of roller R1. Therefore, gear center
The distance R between OG and the center P1 of roller R1 is It can be expressed as

On the other hand, the angle φ formed between the R and the line segment defined by the gear center OG and the midpoint M is as follows: φ=πZ _k /Z (8). Here, Z _k represents the number of teeth existing between rollers R1 and R2. Therefore, the midpoint M and the gear center
The distance from OG is =Rcosφ...(9).

By the way, as described above, in order to compare the theoretical involute value and the actually measured value, it is necessary to express both values using the same coordinate system as a reference. As shown in Figure 4, which will be described later, the theoretical involute value is the tooth surface of the tooth CT (more precisely, its extension line).
A coordinate system (hereinafter referred to as " Theoretical coordinate system
) (X, Y) as a reference. Therefore, for example, actual measured values can be expressed in this theoretical coordinate system (X,
Y), both will be expressed in the same coordinate system and can be compared. This coordinate transformation will be explained below.

First, the coordinates (x, y) of the probe PB shown in Fig. 5 (hereinafter referred to as "measurement coordinate system") are expressed as and the gear center OG is perpendicular to this at the midpoint M.
When converted to a coordinate system (x', y') consisting of the y'-axis passing through and whose origin is 0 [x', y'], x y = cosβ-sinβ sinβ cosβ-x'-y'+u v ... ...(10) Therefore, x′ y′=cosβ sinβ −sinβ cosβ−(x−u) −(y−v)……(11)

Next, the origin 0 [x', y'] of the coordinate system (x', y')
is translated to the gear center OG, and if this coordinate system is (X', Y') and the origin is 0 [X', Y'], then X'Y'=x'y'+Y=x'y'+O Y...(12) becomes. Furthermore, if this coordinate system (X', Y') is rotated by the angle Ψ, the theoretical coordinate system (X, Y)
Therefore, X′ Y′=cosΨ−sinΨ sinΨ cosΨX Y(13), and from this, further, X Y=cosΨ sinΨ −sinΨ cosΨX′ Y′ ...(14). In other words, in this equation (14), equation (12),
By successively substituting equation (11), we get: , can be converted to the theoretical coordinate system (X, Y). In this equation (15), Ψ can be determined by determining the gear G based on equation (5), and β can be determined by determining the center coordinates P of rollers R1 and R1 based on equations (1) and (3). ₁ (u ₁ , v ₁ ),
P ₂ (u ₂ , v ₂ ), and similarly u,
v can be determined using equation (2), and Y can be obtained using equations (6) to (9).
It can be obtained from the formula.

Using the above calculation formula, the same theoretical coordinate axes (X,
The theoretical involute value and the measured value can be compared using Y) as a reference, but as shown in Figure 5, what is actually measured by the probe PB is the contact point between the probe PB and the tooth surface of the tooth CT. rather than the coordinates of
As shown by arrow F in the figure, the center OP of probe PB
The coordinates (X _p , Y _p ) of (Note that "X _p ", "Y _p "
represents the value in the theoretical coordinate system (X, Y))
On the other hand, the theoretical involute value is generally expressed in polar coordinates, so this polar coordinate and the above (X _p , Y _p )
It is necessary to seek a relationship with The calculation formula for this conversion is described below.

In FIG. 5, the theoretical involute value IT (Xt, Yt) in the coordinate system (X, Y) of point IT is Xt Yt=sinθ−cosθ cosθ sinθRC RC·θ (16). However, θ is relative to the pressure angle α, and θ=
It is determined by the relationship of tanα. The coordinates (X _p , Y _p ) of the center OP of the probe PB in this state are: becomes. However, d is the diameter of the tip sphere of the probe PB. Substituting equation (16) into equation (17), we get becomes. This formula converts the theoretical involute value expressed in polar coordinates into coordinates (X _p , Y _p ). By comparing the value of this equation (18) with the measured value obtained by equation (15), the tooth profile error can be determined. The above is the basic principle of the present invention.

Next, a configuration example of a gear tooth profile inspection device according to the present invention will be explained with reference to FIG.

In this FIG. 6, the probe PB mentioned above is
A plunger-type digital length measuring device (hereinafter referred to as ``y length measuring device'') is placed and fixed on a positioning table 4 movable in the x direction of the measurement coordinate system (x, y), and detects the position in the y direction. 7), and a spring mechanism (not shown) applies downward pressure during measurement. The positioning table 4 is equipped with digital length measuring devices (hereinafter referred to as "x length measuring devices") 5 and 6, so that the position in the x direction can be detected.

On the other hand, the positioning table 4 is moved by driving the stepping motor 3 by controllers 1 and 2 in the x and y directions, which are control devices. The outputs of the x-length measuring devices 5 and 6 are input to a counter 8, where the x value is measured, and the output of the y-length measuring device 7 is similarly input to a counter 9. ing. The outputs of these counters 8 and 9 are input to the input interface 1.
After being adjusted to an appropriate signal by signals 0, 11, and 12, the signal is input to the arithmetic unit 13. Note that the above-mentioned equations (1) to (18) are input and stored in the calculation device 13, and information such as the number of teeth Z and module m regarding the gear G to be measured and the positions of the rollers R1 and R2 are also input and stored in the calculation device 13. Information is input and stored by appropriate means, and the entire device is also controlled.

The output of the arithmetic unit 13 is output and displayed on an X-Y plotter 15, which is an output device, via an output interface 14.

Next, the overall operation of the above embodiment will be explained. First, the probe PB is set by the controllers 1 and 2 to the position of the tip Q of the tooth CT shown in FIG.
The pressure angle α _k at this position is the tooth tip diameter, that is, in FIG. 5, it passes through point Q and the gear center OG
(See Figure 4) Diameter of a circle centered at d _k = {Z+
2(W+1)}m, it is expressed as α _k =cos _U-1 (2RC/d _k ) (19), and this tangent corresponds to θ in equation (18). When the probe PB is moved toward the tooth bottom from this position, the pressure angle α gradually decreases from α _k . Therefore, we set the minute angle △ as appropriate.
The tangent of α, △θ=tan△α, is sequentially calculated by θk corresponding to α _k (“θ” in the figure at point Q in Figure 5).
Sampling is performed by subtracting from k) = tanα _k . That is, θ ₁ = θ _k , θ ₂ = θ _k −△θ, θ ₃
Sampling is performed at N points: =θ _k -2Δθ...θ _N =θ _k -(N-1)Δθ (hereinafter referred to as "θ _i ").

On the other hand, the tooth profile error εi in the normal direction of the tooth surface is equal to the above θi
εi=(Yi−Ypi)sinθi...(20) This is shown in FIG. here,
Yi is a value obtained by converting the measured value using equation (15), and Ypi is a theoretical involute value using equation (18). Therefore, as shown in FIG. 7, when moving the positioning table 4 in the x direction and setting it at the position θi, the actual measurement value Xi is compared with the theoretical involute value Xpi, and Xi= Xpi
Then, the value of the y length measuring device 7 is sent to the arithmetic unit 1 via the counter 9 and the input interfaces 10 and 12.
3 and calculate Yi according to formula (15). At the same time, Ypi is calculated using equation (18) based on θi corresponding to Yi. εi is calculated from these Yi and Ypi based on equation (20). By performing the above operations for each θi, the tooth profile error curve is
- It can be output to the Y plotter 15.

Generally, the tooth profile error curve takes the kamiai length on the horizontal axis. The kami-eye length ei from the tooth tip Q shown in Fig. 5 as the origin to any point on the tooth surface is determined as follows: ei=RC(θi− _θk ) (21). That is, instead of plotting εi for each θi, ei is obtained from equation (21) and εi is plotted against this ei. The computations necessary for this plotting are performed by the arithmetic unit 13.

The results of the above calculations are appropriately adjusted by the output interface 14 and then output to the X-Y plotter 15 to plot a tooth profile error curve.
An example of this tooth profile error curve is shown in FIGS. 9 and 10. Both plots were drawn for the same object to be measured, but Fig. 9 is the one measured by the conventional means shown in Fig. 1, and Fig. 10 is the one measured by the present invention. . The gear to be measured has external teeth, module m=6, number of teeth Z=48, pressure angle α=20°, standard, and hobbed.
Although the two cannot be simply compared because the measurement positions in the tooth line direction are different, the results are similar. Tooth profile errors are generally analyzed after removing fine irregularities caused by tooth surface roughness, but in the device according to the present invention, such work can be easily performed by passing the data through a filter using calculations.

Note that the above embodiment is an example in which the object to be measured is the left tooth surface of an external gear and the number of teeth existing between rollers R1 and R2 is an odd number. By making this change, it is possible to perform measurements in the same way, for example, even when the right tooth surface of the internal gear and the number of teeth between the rollers R1 and R2 is an even number. Furthermore, by appropriately changing equation (18), measurements can be made in the same way not only when the tooth surface is an involute curve but also when the tooth surface has other shapes. It is not limited to.
Further, the theoretical involute value may be converted to the measurement coordinate system, and any other coordinate system may be used as long as it is the same as the actual measurement value.

As described above, according to the present invention, it is possible to perform measurements while the gear is attached to the mechanical device in which the gear is used, without considering the positional relationship between the measuring device and the gear to be measured. It is possible to eliminate the work of setting up the measuring device, and it is possible to perform simple and good measurements without requiring any special technology.Furthermore, by being equipped with a storage device, it is possible to record and save measurement data easily. It has excellent effects in that it can be carried out at a low cost and can be provided at a low cost.

[Brief explanation of the drawing]

Fig. 1A is an explanatory diagram showing an overview of a conventional tooth profile inspection means, Fig. 1B is a diagram showing an involute curve, Fig. 2 is an explanatory diagram showing the positional relationship for coordinate transformation, and Fig. 3 is an explanatory diagram showing a gear. Fig. 4 is an explanatory drawing showing the relationship between the quantities required for the coordinate transformation shown above, Fig. 4 is an explanatory drawing showing the state of the coordinate transformation, Fig. 5 is an explanatory drawing showing the positional relationship of the probe on the tooth surface, and Fig. 6 is an explanatory drawing showing the relationship between the quantities required for the coordinate transformation. FIG. 7 is a block diagram showing an example of the configuration of the tooth profile inspection device according to the invention, FIG. 7 is a schematic flowchart showing the procedure for calculating the tooth profile error, FIG. FIG. 9 is a diagram showing an example of measurement using conventional means, and FIG. 10 is a diagram showing an example of measurement according to the present invention. G...gear, CT...teeth having the tooth surface to be measured,
x, y...measurement coordinate system, x', y'...coordinate system that is the basis of coordinate transformation, X, Y...theoretical coordinate system, R1,
R2...roller which is a measuring tool, PB...probe,
1, 2... Controller, 5, 6, 7... Length measuring device which is a measuring device, 8, 9... Counter, 13... Arithmetic device, 15... X-Y plotter which is an output device.

Claims (1)

[Scope of Claims] 1. Based on a theoretical coordinate system in which the center of the gear of the gear to be measured is the origin of the coordinates, a step of calculating a theoretical shape of the tooth surface to be measured; and a step of calculating the theoretical shape of the tooth surface to be measured, based on the amount of displacement of the probe that moves to follow the tooth surface to be measured, based on an arbitrary measurement coordinate system separate from the theoretical coordinate system. a step of measuring the actual shape of the tooth surface to be measured; and a step of measuring the actual shape of the tooth surface to be measured; a step of introducing a third coordinate system determined by the positions of the pair of measuring instruments brought into contact; and a step of changing from the theoretical coordinate system to the measurement coordinate system based on the introduced third coordinate system; Perform coordinate transformation calculations from the measured coordinate system to the theoretical coordinate system,
A method for inspecting a tooth profile of a gear, comprising: determining a shape error between the theoretical shape and the actual shape of the tooth surface to be measured based on the converted coordinate system. 2 Based on a theoretical coordinate system with the gear center of the gear to be measured as the origin of the coordinates, the theoretical coordinate of the tooth surface to be measured with the intersection of the base circle of the gear to be measured and the tooth surface to be measured of the same gear as the base point. a first calculation means for calculating a shape; and a probe that is two-dimensionally displaced following the tooth surface to be measured, and with an arbitrary measurement coordinate system different from the theoretical coordinate system as a reference, tooth flank shape measuring means for measuring the actual shape of the tooth flank to be measured based on the amount of displacement of the probe; A pair of measuring tools, a relationship between a third coordinate system determined by the installation position of the measuring tools and the theoretical coordinate system, and a relationship between the third coordinate system and the measurement coordinate system are stored. a storage means; and a storage means, based on each relationship between the stored third coordinate system, the theoretical coordinate system, and the measurement coordinate system, from the theoretical coordinate system to the measurement coordinate system, or from the measurement coordinate system to the theoretical coordinate system. a second calculation means for calculating a shape error between the theoretical shape and the actual shape of the tooth surface to be measured based on the transformed coordinate system; Gear tooth profile inspection device.