CN104913931B - Another Accurate Determination Method of Evaluation Area Boundary Point in Gear Overall Error Measurement - Google Patents

Abstract

Another accurate determination method of domain for assessment circle point in Gear integrated error measuring, because same error amount is huge on the shape influence in the involute stage of unit curve, and to the engaging-in and stage of nibbling out influence very little, therefore the present invention is in the origin of determining unit curve, with engaging-in section and nibbles out based on the data of the two transition stages of section.It is treated actual measurement global error unit curve on draw a horizontal linear, using range cell peak as an offset constant at as this straight line initial position；From obtained initial position so that the distance at optimization aim position between the straight line and two intersection points for surveying unit curve is also constant；The origin of global error unit curve is accurately finally obtained, so that the domain for assessment circle point of global error unit curve is accurately determined.

Description

Another Accurate Determination Method of Evaluation Area Boundary Point in Gear Overall Error Measurement

technical field

The invention relates to a method for accurately determining the boundary point of an evaluation area on a gear overall error measurement curve, and belongs to the field of precision testing technology and instrument technology.

Background technique

The overall error measurement technology of gears was pioneered by Chinese scientific and technological personnel in the early 1970s. This technology can extract the individual errors and comprehensive errors of gears from the overall error curve of gears, and solves how to obtain all gears on one gear measuring instrument. The problem of misinformation. The overall gear error measurement method is also called the motion geometry measurement method of the transmission element. Its basic idea is to use the measured gear as a rigid transmission element and obtain The error of the gear under test. The gear precision measuring instruments based on the gear overall error measurement technology independently developed by our country, such as the CZ-450 produced by Chengdu Tools, were widely promoted and applied in our country in the 1990s, and made an important contribution to the development of my country's gear processing industry. For his contribution, the CZ-450 instrument won the second prize of the National Invention Award. The patents related to the gear measurement technology based on the overall error were purchased by the well-known German company Klingelnberg in the gear field.

The overall error technique has unique advantages. First, the overall error curve vividly reflects the gear meshing transmission process, and accurately reveals the variation law of individual gear errors and the relationship between errors, which is especially suitable for the process error analysis and dynamic performance prediction of gears. Second, the instrument using this method has the advantages of high measurement efficiency, rich measurement information, and the measurement process is closer to the state of use. Third, the instrument does not require high environmental conditions, and is especially suitable for precision testing and quality control of mass-produced gear products. In a word, under the current trend of automotive gears requiring 100% full detection, the research on the overall error measurement technology of gears has both theoretical value and great application value.

In order to meet the condition that the coincidence degree required by the overall error measurement technology is less than 1, the measurement standard components used in the existing gear overall error measuring instruments are standard worms with skipped teeth or standard gears with skipped teeth, among which the standard worm with skipped teeth is the most commonly used. The jumping standard worm is essentially a multi-head measuring worm, usually with double heads or three heads, and only the two sides of one head are reserved as the working tooth surface, and the tooth surfaces of the other heads are ground thin. The retained working tooth surface is called the measurement tooth surface, and the thinned tooth surface is called the transmission tooth surface.

The basic principle of gear overall error measurement is that the measuring tooth surface of the standard component is meshed with the measured tooth surface of the measured gear, and the point contact between the measuring tooth surface and the measured tooth surface is maintained, and the transmission error curve is recorded during the process. . However, since the coincidence degree is less than 1 when the overall error is measured, the position of the actual meshing point will extend beyond the theoretical meshing line, so the complete process of measuring the tooth surface driving the measured tooth surface to rotate can be divided into three stages: the first stage is The tooth top of the measured gear is scraping on the measured tooth surface, and the actual contact point is on the tooth top of the measured gear. This is a transitional stage, called the meshing stage; the second stage is to measure the tooth surface The stage where the involute tooth profile meshes with the involute tooth profile of the tested gear, and the actual contact point position gradually slides from the tooth top of the tested tooth surface to the tooth root of the tested tooth surface. This stage is called involute Meshing stage; the third stage is the stage where the tooth top of the measured tooth surface scrapes at the tooth root of the measured tooth surface, and the actual contact point is on the tooth top of the measurement standard element, which is also a transition stage, called meshing out stage. Figure 1 is a schematic diagram of the positional relationship between the measured tooth surface and the measured tooth surface in these three stages. In Figure 1, the tooth profile of the standard worm with skipped teeth is replaced by the straight profile of the rack.

Figure 1 also illustrates the formation process of the overall error cell curve. The unit curve of the overall error curve is shown at the bottom of Figure 1. The unit curve of the overall error curve is composed of a section of rising curve corresponding to the meshing stage, a nearly horizontal curve corresponding to the involute meshing stage and a section of falling curve corresponding to the meshing stage.

The overall error unit curve obtained by the theoretical analysis method is called the theoretical unit curve, as shown at the bottom of Figure 1 is a theoretical unit curve. The overall error unit curve obtained by actual measurement is called the measured unit curve, as shown in Figure 2 and Figure 3. Figure 2 shows a measured overall error curve, which is composed of multiple measured unit curves. Figure 3 shows the partial measured unit curve on this overall error curve.

The pitch angle on the overall error curve refers to the angular range occupied by a unit of the measured gear on the curve, and the calculation method is pitch angle θ=(360°×number of worm teeth)/number of gear teeth, as shown in Figure 3.

To obtain the individual errors and comprehensive errors of gears from the measured overall error curve, the starting point and end point of the involute phase on the measured unit curve must first be determined, and these two points are also collectively called the evaluation area boundary point. After theoretical analysis, as shown in Figure 1, there is a definite functional relationship between the starting point A2 and the ending point A1 of the involute phase and the node P, that is, as long as any point of the three is determined to be on the measured overall error unit curve , then the corresponding positions of the boundary points of the assessment area can be calculated. Therefore, this paper uses the method of determining the origin of the measured overall error unit curve to determine the evaluation area boundary point in the gear overall error measurement. The origin of the overall error unit curve is defined as the angular position of the measured gear when the actual contact point between the measured tooth surface and the measured tooth surface coincides with the node P. On the theoretical unit curve of the overall error, the abscissa at the origin, that is, the gear rotation angle, is specified as 0. As long as the abscissa of the origin position on the measured unit curve is determined, the actual position on the measured tooth surface corresponding to each data point on the measured unit curve can be determined, and then the position of each point on the measured tooth profile can be calculated. difference.

From the above analysis, it can be seen that the accuracy of each individual error and comprehensive error of the gear obtained from the overall error curve is largely affected by the determination accuracy of the evaluation area boundary point of the overall error unit curve. The traditional methods for determining the boundary point of the evaluation area of the overall error unit curve include "facet curve fitting method" and "cross-correlation function method". The fitting method of the shuttle surface meshing curve is to first calculate the theoretical overall error unit curve, and then fit it with the measured unit curve, so as to find the start and end points of the involute phase. The cross-correlation function method also calculates the theoretical overall error unit curve first, then calculates the cross-correlation function curve of the theoretical unit curve and the measured overall error curve, and determines the involute on the measured overall error unit curve based on the extreme points of the cross-correlation function. The starting point of the line phase. These two methods both realize the automatic determination of the start and end points of the involute phase, which promotes the progress of the overall error measurement technology to a certain extent. But from the point of view of the use effect, the determination accuracy of the involute starting point of these traditional methods is still insufficient for the precise measurement of gears. In order to further improve the determination accuracy of the evaluation area boundary point of the overall error curve, an accurate determination method of the evaluation area boundary point in the gear overall error measurement of the present invention is proposed by analyzing the error source of the traditional method.

Contents of the invention

The invention proposes a method for determining the boundary point of the evaluation area of the overall error unit curve of the gear. The method realizes the overall error unit by analyzing the curve positions of the two transition stages of the overall error unit curve, the meshing in and the meshing out. Accurate calculation of the origin of the curve, thus accurately determining the boundary point of the evaluation area of the overall error unit curve.

Due to the existence of processing errors, installation errors and measurement errors in actual gears, the shape of the measured actual overall error unit curve will always deviate from the shape of the theoretical unit curve. Therefore, when determining the origin position of the measured curve, the influence of the error on the shape of the curve must be considered. Through in-depth research on the overall error curve, it is found that the same amount of error has completely different effects on the overall error curve in the direction of abscissa and ordinate. On the overall error curve, the abscissa is the rotated angle of the measured gear, in degrees; the ordinate is the error of the measured tooth surface, in microns. Taking the measured gear with modulus m=3 and number of teeth z=40 as an example, if there is an error of 10 microns near the pitch circle on the tooth surface, the ordinate of the corresponding point will change by 10 microns, accounting for about 10 microns in Figure 2. 12% of the range of the ordinate; while the variation of the abscissa of the corresponding point is only about 0.0095 degrees, accounting for about 0.002% of the range of the abscissa in Figure 2, and the difference between the two ratios is about 6000 times. However, the traditional methods including "facet curve fitting method" and "cross-correlation function method" ignore the fact that there is a huge difference between the changes of vertical and horizontal coordinates caused by the same error when performing curve fitting and cross-correlation function calculations. The important principle leads to the low accuracy of determining the starting position of the involute phase on the unit curve.

The above analysis shows that the same error value has a huge impact on the shape of the involute stage of the element curve, but has little impact on the engagement and engagement stages. The data of these two transitional stages of the meshing out segment are the main ones. Theoretical analysis and experiments prove that the effect of the method of the present invention is very good.

The steps of the method for determining the origin of the overall error unit curve of the present invention are as follows:

Step 1: Filter the measured actual overall error curve using a high-pass filter with a cutoff wavelength of 1 to 2 times the pitch angle of the measured gear to eliminate the influence of the gear eccentricity error;

Step 2: Obtain the total height of the measured unit curve according to the measured overall error curve through high-pass filtering, and take 50-90% of the total height as the bias constant, generally 70%;

Step 3: According to the actual parameters of the tested gear and standard components, namely the number of teeth, modulus, pressure angle, addendum height and dedendum height, calculate the theoretical overall error unit curve, and obtain the angle range of the involute stage on the unit curve ;

Step 4: According to the bias constant obtained in step 2, draw a horizontal line parallel to the horizontal axis on the theoretical unit curve at a distance of one time from the top of the unit. The horizontal coordinate position of the intersection point is recorded as X1 and X2; the length of the horizontal line segment between the two intersection points is calculated and recorded as L0, then L0=X2-X1;

Step 5: Obtain the lateral position difference between the origin X0 of the unit on the theoretical unit curve of the overall error and the above-mentioned coordinate position X2, denoted as dX, then dX=X2-X0;

Step 6: Draw a horizontal straight line on the measured overall error unit curve processed in step 1, and take the distance from the highest point of the unit as a bias constant as the initial position of the straight line; the horizontal position of the intersection point of this horizontal line and the engagement curve It is also denoted as X1, and the horizontal position of the intersection with the meshing phase curve is also denoted as X2;

Step 7: Starting from the initial position obtained in step 6, take (X2-X1-L0)→0 as the optimization target, and translate the position of this line up and down for optimization, so that the line at the optimization target position is two points away from the measured unit curve. The distance between the intersection points is also the constant L0 obtained in step 4;

Step 8: At the target position searched in step 7, move leftward from the X2 position by the lateral position difference dX obtained in step 5, and then obtain the origin coordinate X0 of the measured overall error unit curve, and the calculation formula is X0=X2-dX;

Finally, the origin of the overall error unit curve is accurately obtained, thereby accurately determining the evaluation area boundary point of the overall error unit curve.

Description of drawings

Figure 1 shows the formation process and components of the overall error unit curve.

Figure 2 is the measured overall error curve.

Figure 3 shows the local and unit curves of the measured overall error curve.

Figure 4 is the measured overall error curve after high-pass filtering to eliminate eccentricity.

Figure 5 is a portion of the measured overall error curve after high-pass filtering.

Figure 6 is the theoretical unit curve of the overall error and the calculation of L0 and dX.

Fig. 7 is the determination of the origin position on the measured overall error unit curve.

detailed description

The present invention will be further described below in conjunction with accompanying drawing:

Figure 1 shows the formation process and components of the overall error unit curve. The figure also illustrates a method of obtaining the theoretical unit curve of the overall error, that is, the analysis process of the plane rack meshing method.

Figure 2 is the measured overall error curve. Fig. 3 is a part of Fig. 2, in which the tooth pitch angle of the tested gear and the range of a unit curve are marked.

In the measured overall error curve shown in Figure 2, it can be seen that there is an eccentric error in the measured gear, and the eccentric error will affect the shape of the overall error unit curve.

Figure 4 shows the overall error curve after high-pass filtering in "step 1". The cut-off wavelength of the high-pass filter is 1 times the pitch angle of the gear under test. It can be seen from Figure 4 that the eccentricity of the gear under test is basically eliminated after high-pass filtering.

Figure 5 shows a part of the overall error curve after high-pass filtering in "step 1", where the distance between the highest point and the lowest point of a unit is called the total height of the unit curve. According to the shape of the actual curve, an appropriate height should be selected as the bias constant. The bias constant can be selected within the range of 50% to 90% of the total height of the unit, generally 70% of the total height of the unit is selected.

Figure 6 shows the theoretical overall error unit curve calculated for the actual parameters of the measured gear and the standard component in step 3. The theoretical unit curve of the overall error can be obtained by methods such as plane meshing analysis method, TCA algorithm, space entity intersection method, and finite element method. Figure 6 shows the theoretical unit curve obtained by using the space entity intersection method.

According to the offset constant obtained in step 2, draw a horizontal line parallel to the horizontal axis on the theoretical unit curve at a distance of one time the offset constant from the top of the unit, and record the horizontal coordinates of the intersection point of this horizontal line and the two transition stage curves of the unit curve Positions, denoted as X1 and X2; and then the positional relationship between the origin X0 of the unit on the overall error theoretical unit curve and the above-mentioned X1, X2 can be obtained, that is, the constant L0=X2-X1, the constant dX=X2-X0; obtain X1, The process of X2, L0 and dX is also illustrated in Fig. 6.

Because the involute meshing stage of the overall error curve obtained by actual measurement is very sensitive to errors, the curve at this stage changes drastically, so the method of the present invention avoids using the data of the involute meshing section to participate in the calculation of the involute start and end points, Instead, only the data for the transition curves of the engagement phase and the engagement phase apply. For this reason, step 7 of the present invention has used optimization algorithm, and this algorithm optimizes the position of the vertical direction of auxiliary horizontal straight line, is the optimized initial position with the highest point of the distance unit as the bias constant, with (X2-X0-L0) →0 is the optimization target, and finally the optimal target position is obtained. This optimization problem is essentially an extremum and unique minimization problem, and common optimization algorithms such as Newton's method and gradient descent method can be used.

FIG. 7 shows the process of finally obtaining the origin coordinate X0 of each overall error unit curve in Step 6, Step 7 and Step 8.

For each measured unit curve, firstly, start from the maximum height of the unit in step 6, and shift downwards by an offset constant obtained in step 2, and use this position as the starting position of the optimization algorithm; secondly, start from the maximum height of the unit Starting from the initial position of the optimization algorithm, with (X2-X1-L0)→0 as the optimization target, the position of this straight line is translated up and down for optimization, so that the distance between the two intersection points of the straight line at the optimized target position and the measured unit curve is L0 obtained in step 4; finally, at the searched target position, move leftward from the X2 position by the lateral position difference dX obtained in step 5 to obtain the origin coordinate X0 of the measured overall error unit curve, and the calculation formula is X0= X2-dX;

In the method of the present invention, the constant L0 and dX that determine the positional relationship between the unit origin and the two transition curves are all obtained by the theoretical unit curve of the overall error, and these two constants are not affected by the random error in the gear machining and measurement process. influences. The task of finding the vertical position of the constant L0 on the measured unit curve is completed by an optimization algorithm, which only uses the data of the transition curves on both sides that are insensitive to random errors, and does not use the data of the transition curves that are particularly sensitive to random errors. Data for the involute meshing phase. The horizontal position of the transition curves of the engagement curve and the engagement curve is very little affected by random errors, and the absolute value of the slope of the two curves is very large, even if the value in the vertical direction changes, the position in the horizontal direction The impact is still small. Combining the above factors, the method proposed by the present invention completely avoids the use of data in the involute meshing stage that is particularly sensitive to random errors, and the accuracy of the boundary point position of the evaluation area of the determined overall error unit curve is very high, which can meet the precision requirements of automobile gears. measurement requirements.

Claims (1)

1. another accurate determination method of domain for assessment circle point in Gear integrated error measuring, it is characterised in that：This method Realize that step is as follows,

Step one：The actual measurement global error unit curve obtained to measurement is 1 times~2 times of tested gear using cutoff wavelength The high-pass filter of angular pitch is filtered, to eliminate the influence of gear eccentricity error；

Step 2：The total height of actual measurement unit curve is obtained according to the actual measurement global error unit curve through high-pass filtering, this is taken The 50~90% of individual total height are offset constant；

Step 3：It is the number of teeth, modulus, pressure angle, height of teeth top and height of teeth root for the actual parameter for being tested gear and standard component, Global error theoretical units curve is calculated, the angular range in involute stage on theoretical units curve is obtained；

Step 4：The offset constant obtained according to step 2, one times of offset constant at the top of range cell on theoretical unit curve Place makees a horizontal line parallel to transverse axis, records the friendship of two transition stage curves of this horizontal line and theoretical units curve The horizontal coordinate position of point, is designated as X1 and X2；The horizontal line section length between two intersection points is calculated, L0 is designated as, then L0=X2- X1；

Step 5：Obtain the horizontal position between the origin X0 and above-mentioned coordinate position X2 of unit on global error theoretical units curve Difference is put, dX is designated as, then dX=X2-X0；

Step 6：A horizontal linear is drawn on the actual measurement global error unit curve handled by step one, it is single with distance First peak is the initial position as this straight line at an offset constant；The level of this horizontal line and engaging-in intersections of complex curve Position is designated as X1 ', and X2 ' is designated as with the horizontal level of nibbling out stage intersections of complex curve；

Step 7：The initial position obtained from step 6, with (X2 '-X1 '-L0) → 0 be optimization aim, upper and lower translation this The position of bar straight line is optimized so that two intersection points of the straight line and actual measurement global error unit curve at optimization aim position Between distance be also obtained constant L0 in step 4；

Step 8：The target location searched in step 7, from X2 ' positions move to left a step 5 in obtained lateral attitude Poor dX, just obtains surveying the origin X0 of global error unit curve, calculation formula is X0=X2 '-dX；

The final origin for accurately obtaining actual measurement global error unit curve, so that global error unit curve is accurately determined Domain for assessment circle point.