KR100458161B1 - Method for measuring shape error of spiral bevel gear - Google Patents

Abstract

The present invention relates to a method for measuring a shape error of a spiral bevel gear, and more particularly, it is a general three-dimensional measuring device for tooth profile errors and tooth trace errors that are difficult to measure by conventional methods. The present invention relates to a method for measuring a shape error of a spiral bevel gear, which is measured by an algorithm on a computer using a Coordinate Measuring Machine (CMM). Meanwhile, the present invention relates to a method for measuring a shape error of a spiral bevel gear, which can more accurately measure a pitch error (adjacent pitch error and cumulative pitch error) of a spiral bevel gear, which has been measured by a conventional method.

Description

Method for measuring shape error of spiral bevel gears

The present invention relates to a method for measuring a shape error of a spiral bevel gear, and more particularly, it is a general three-dimensional measuring device for tooth profile errors and tooth trace errors that are difficult to measure by conventional methods. The present invention relates to a method for measuring a shape error of a spiral bevel gear, which is measured by an algorithm on a computer using a Coordinate Measuring Machine (CMM).

Meanwhile, the present invention relates to a method for measuring a shape error of a spiral bevel gear, which can more accurately measure a pitch error of a spiral bevel gear, which has been measured by a conventional method.

As is well known to those skilled in the art, Spiral Bevel Gears (SBGs) are used for the purpose of delivering high torque in a compact form and are toothed along spiral curves as compared to straight bevel gears. The gear shape of the spiral bevel gear is the most complicated shape among the gear shapes and requires precise tolerances, and its measuring method is also very important.

1A to 1C schematically illustrate the types of shape errors of spiral bevel gears, FIG. 1A shows tooth profile errors, FIG. 1B shows tooth trace errors, and FIG. 1C shows Pitch Error

However, due to the absence of a measuring method for measuring the shape error of the spiral bevel gear shown in FIG. 1, the method currently used for measurement has a problem that is limited to the pitch error.

The present invention was created in order to solve the above problems, and it is difficult to measure the tooth error and the side line error by the conventional method using an algorithm on a computer using a universal coordinate measuring machine (CMM; It is an object of the present invention to provide a method for measuring a shape error of a spiral bevel gear.

Still another object of the present invention is to provide a method for measuring a shape error of a spiral bevel gear, which can more accurately measure a pitch error of a spiral bevel gear, which has been measured by a conventional method.

1A to 1C are conceptual views illustrating a shape error of a general spiral bevel gear (SBG).

Figure 2 is an embodiment of the coordinate measurement of the spiral bevel gear using a three-dimensional coordinate measuring machine (CMM).

3 illustrates one embodiment of a spherical involute coordinate system for generating a software reference model (SMM).

4a to 4c are conceptual views showing the relationship between the rotation amount of the virtual gear model (VGM) for the SMM in the corresponding measurement item according to the present invention.

Figure 5 is an exemplary view of the measurement of the tooth error according to the method of the present invention.

Figure 6 is an exemplary view of the measurement of the side line error by the method of the present invention.

Figure 7 is an exemplary measurement of the adjacent pitch error and cumulative pitch error by the method of the present invention.

8 is a conceptual diagram showing the construction steps of the method of the present invention.

Shape error measurement method of the spiral bevel gear according to the present invention to achieve the above object,

Measuring three-dimensional coordinates of the discontinuous point of the spiral bevel gear shape processed using the three-dimensional coordinate measuring machine; Constructing a virtual gear model (VGM) of the following formula, which is a curve equation in a three-dimensional space, using a measured three-dimensional coordinate value by a general fitting method;

here,

u : Parameter for the direction of involute teeth

w : Parameter for the spiral curve direction

P _{i, j} : Unknown for n × m control points

R _{i, p} (u), R _{j, q} (w) : fitting interpolation function for u, w direction

Constructing a Software Master Model (SMM) from a given gear design data and specification in spherical involute coordinates such as the following formula;

here,

: u-direction coordinate transformation matrix

: w direction coordinate transformation matrix

Comparing the software reference model (SMM) with the virtual gear model (VGM) and rotationally converting the corresponding measurement items to minimize the following formula; And

here,

Rot (X, θ): Rotation transformation matrix for the X and θ directions

V (i): rotation coordinate center coordinate

From the difference between the software reference model and the virtual gear model, the tooth error and side line error in the corresponding measurement items are calculated as the sum of the maximum error and the minimum error.

Tooth Profile Error

Tooth Trace Error

It characterized by including the step of obtaining.

In a preferred embodiment of the present invention, the single pitch error of the spiral bevel gear is

here,

: single pitch error of the i th tooth

: Pitch Circle Diameter at w = 0.5

: alignment angle of the i th tooth

n : this number

i : this index

It further includes the step of obtaining.

In a preferred embodiment of the present invention, the Is or Can be replaced with

In a preferred embodiment of the present invention, the adjacent pitch error of the i-th tooth of the spiral bevel gear ( ) And cumulative pitch error ( ) Using the single pitch error value,

The virtual gear model (VGM) may measure the processed gear tooth shape using a three-dimensional coordinate measuring machine (CMM) to measure the spiral bevel gear. The software reference model (SMM) is a reference design formula for comparison with the teeth measured by the virtual gear model (VGM), and the reference design formula consists of spherical involute teeth in the gear design specification. to be.

Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the method for measuring the shape error of the spiral bevel gear according to the present invention. In the following description of the present invention, when it is determined that detailed descriptions of related well-known technologies or configurations may unnecessarily obscure the subject matter of the present invention, the detailed description will be omitted. In addition, terms to be described below are terms defined in consideration of functions in the present invention, which may vary according to the intention or custom of a user or an operator. Therefore, the definition should be made based on the contents throughout the specification.

First, in the method of the present invention, three-dimensional coordinates of discontinuous points of a spiral bevel gear shape processed using a three-dimensional coordinate measuring machine should be measured. An embodiment of this embodiment is shown in FIG.

Using a three-dimensional coordinate value measured by the embodiment as shown in Figure 2, for example, in a three-dimensional space by a non-uniform Rational B-Spline (NURBS) fitting method We construct the Virtual Gear Model (VGM) of Equation 1 below. Here, the NURBS is a mathematical method for fitting the surface from random data, that is, the surface measurement data. The NURBS is a method of fitting a gear tooth surface from three-dimensional coordinate measurement data to construct a VGM.

Formula 1

In Formula 1 above,

u : parameter for Involute tooth direction;

w is a parameter for the spiral curve direction;

P _{i, j} : unknown for n × m control points;

R _{i, p} (u), R _{j, q} (w) : Fitting interpolation function for u, w directions.

After constructing the virtual gear model as above, a software reference model is constructed as shown in Equation 2 below in the spherical involute coordinates defined as shown in FIG. 3 from the given gear design data and specifications.

Formula 2

In Formula 2 above,

: u direction coordinate transformation matrix;

: w direction coordinate transformation matrix.

After the software reference model and the virtual gear model are constructed as described above, they are compared and rotated for the corresponding measurement item as shown in FIG. FIG. 4A shows the tooth profile alignment rotation amount, FIG. 4B shows the spiral curve profile conversion rotation amount, and FIG. 4C shows the conversion rotation amount of the pitch point.

Formula 3

In Formula 3 above,

Rot (X, θ): rotation transformation matrix for the X, θ directions;

V (i): rotation coordinate center coordinate.

From the difference between the software reference model (SMM) and the rotated virtual gear model (VGM), the tooth and side line errors in each relevant measurement are obtained by the following formulas 4 and 5 as the sum of the maximum and minimum errors: Become.

Formula 4

Formula 5

Equation 4 is a preferable formula for calculating tooth profile error, and Equation 5 is a preferable formula for calculating tooth trace error.

Meanwhile, a method of obtaining a single pitch error value in the profile direction on the pitch circle diameter (PCD) as described above is as follows. That is, the single pitch error value can be obtained from various cross sections (eg, defined by w -parameter), and the single pitch error can be obtained as shown in Equation 6 below by defining the intermediate section w = 0.5.

Formula 6

In Formula 6 above,

: single pitch error of the i th tooth;

: Pitch Circle Diameter (PCD) at w = 0.5;

is the alignment angle of the i th tooth;

n : this number;

i : This index.

On the other hand, the adjacent pitch error of the i th tooth of the spiral bevel gear ( ) And cumulative pitch error ( ) Can be obtained using Equation 7 below using the single pitch error value.

Formula 7

Each step of the method for measuring the shape error of the spiral bevel gear according to the present invention described above is clearly shown in FIG. 8.

On the other hand, Figure 5 shows a measurement example of the tooth error according to the method of the present invention, Figure 6 shows a measurement example of the side row error, Figure 7 shows a measurement example of the pitch error.

As described above, the shape error measuring method of the spiral bevel gear according to the present invention is to measure the tooth error and side line error, which are difficult to measure by the conventional method, by using an algorithm on a computer using a general-purpose three-dimensional measuring device rather than a dedicated measuring device. To provide an advantage.

In addition, the present invention provides an advantage of more accurately measuring the pitch error of a spiral bevel gear, which has been measured by conventional methods.

Although a preferred embodiment of the present invention has been described in detail above, those skilled in the art to which the present invention pertains may make various changes without departing from the spirit and scope of the invention as defined in the appended claims. It will be appreciated that modifications or variations may be made. Therefore, changes in the future embodiments of the present invention will not be able to escape the technology of the present invention.

Claims (4)

In the method for measuring various shape errors of the spiral bevel gear, Measuring three-dimensional coordinates of the discontinuous point of the processed spiral bevel gear shape using the three-dimensional coordinate measuring machine; Constructing a virtual gear model (VGM) of the following formula, which is a curve equation in three-dimensional space, by a general fitting method using the measured three-dimensional coordinate values; here, u : Parameter for the direction of involute teeth w : Parameter for the spiral curve direction P _{i, j} : Unknown for n × m control points R _{i, p} (u), R _{j, q} (w) : fitting interpolation function for u, w direction Constructing a Software Master Model (SMM), such as the following formula, from the spherical involute coordinates from the given gear design data and specifications; here, : u-direction coordinate transformation matrix : w direction coordinate transformation matrix Comparing the software reference model (SMM) with the virtual gear model (VGM) and rotating the corresponding measurement item such that the following formula is minimized; here, Rot (X, θ): Rotation transformation matrix for the X and θ directions V (i): rotation coordinate center coordinate From the difference between the software reference model and the virtual gear model, the tooth error and side line error in the corresponding measurement items are calculated as the sum of the maximum error and the minimum error. Tooth Profile Error Tooth Trace Error Obtaining by; And The single pitch error of the spiral bevel gear is here, : single pitch error of the i th tooth : Pitch Circle Diameter at w = 0.5 : alignment angle of the i th tooth n : this number i : this index To obtain; To include, The virtual gear model (VGM) is a formula consisting of measurement items of spiral bevel gears by measuring a processed tooth shape (Coth Shape Coordinate Measuring Machine) (CMM), The software reference model (SMM) is a reference tooth for comparison with the tooth measured by the virtual gear model (VGM), characterized in that the reference design formula consisting of a spherical involute tooth in the gear design specification. Shape error measurement method of spiral bevel gears. delete delete The method of claim 1, wherein the adjacent pitch error of the ith tooth surface of the spiral ) And cumulative pitch error ( ) Using the single pitch error value, Shape error measurement method of a spiral bevel gear, characterized in that it further comprises the step of obtaining using.