Minimum prediction method for tolerance of each corner of gear
The change of pressure angle is one of the factors affecting the tooth shape error. The main process cause is the tooth profile angle error of the tool. Since this error can be considered as a constant value, the young and small are generated by the linear relationship. The tooth profile error curve including only the pressure angle error is an oblique line from the second term of the formula, and the expansion angle change also affects the size of the tooth profile error. The change of the expansion angle is mainly caused by the error of the machine tool transmission chain. Generally, the gear train of the gear processing machine has a long transmission chain and many influencing factors, and inevitably, the shape error deviating from the straight line will occur. The above analysis shows that the tooth profile error curve can be decomposed into two parts: pressure angle error and tooth shape error. Similarly, the tooth-to-earth error curve can also be decomposed into a spiral angle error and a waviness error.
The spiral angle error is generally determined by the position error of the guide rail of the machine tool, and the wave error causes many reasons, such as the shape of the drive chain and the column guide. It is very meaningful to decompose the tooth-toothed tooth error into the pressure angle helix angle error and the shape waviness error according to the National Natural Science Funding Project. Based on this, the cause of the error can be analyzed and the process adjustment can be guided. In order to separate the two kinds of errors, the center line must first be determined according to the measured curve. Currently, in the field of gear testing, there are two methods for determining the center line, that is, the calculation method based on the principle of least squares method and the drawing method, graph, and cabinet.
The calculation method determines the center line as shown in the figure, so that the abscissa is the tooth-shaped unfolding length on the tooth-to-earth error curve as the tooth width, the ordinate is the tooth shape error, the tooth direction error, and the direction of the midline center line is obtained according to the principle of least squares 丫It is the only parameter that determines the error of the pressure angle or the helix angle. The addition or yang is independent of the position of the neutral line, so the concept of the center line can be extended to a parallel line cluster.
For lower-precision measurements, the midline is often determined by visual mapping. The position of the midline should be such that the error curve is equal to the area enclosed by the midline on both sides of the midline within the measurement range. The reference proposes to improve the accuracy of the mapping method by multiple approximation methods, but the process is not easy to implement. Generally, the drawing requirements of the gear tooth direction error can be satisfied by one drawing.
Where the hitting profession is in the form of a dry penalty, the shape error is changed. The distance from the first point to the middle line is the distance from the male to the middle line. When the same side of the middle line is used, the negative sign is used in the formula, and the positive side is used in the opposite side. No. The center line is the midline of the extension definition.
Prove that for straightness evaluation, the objective function is a single-valley function, which is calculated by iterative method, and its solution is convergent and unique. The iterative calculation process used in this paper is the first step to determine the midline range. For t-shirts, select the median as the initial centerline and select the initial step size as an arbitrary integer. In the second step, the midline is searched for rotation in the second step, and the Ganzhou dry turn after each rotation is calculated. If one of the angles is found, and the tenth is found, the midline can be judged to be in the range. Inside. If the third step is in the process of turning, it is judged whether the rape is less than £. The calculation accuracy, if it is, the calculation ends, if not, the fourth step is performed. In the fourth step, choose a uniform oath and repeat the second step.
Minimum area method for pressure angle or helix angle error. The center line determined by least squares regression is the best straight line in the statistical sense. The purpose of separating the pressure angle helix angle error from the tooth tooth to the error curve is to analyze The processing condition, by adjusting the factors affecting the error of the pressure angle helix angle during the machining process, minimizes the residual error, that is, the shape error is the smallest.
According to the shape and position error theory, the optimal straight line in the sense of shape error can be obtained by the minimum area method. According to the relevant literature, the results of the minimum area method and the least squares method for evaluating the shape error can be different, so the minimum area method can significantly improve the evaluation accuracy. The mathematical expression of the minimum area method is initial. The method of determining is as follows: First, the coordinate origin is translated to the first point, and a series of new coordinate values ​​are obtained. The maximum value of the result is the minimum value, l...calculation y, using the coordinate rotation method, the coordinate system is rotated evenly, although the minimum area method The calculation process is more complicated than the least squares method, but it is not difficult to implement due to the wide application of computers.
The use of the minimum area mapping rule shows more advantages, the evaluation accuracy is high, and the method is simple. The straight line connecting the two high points (or the two low points) is found in the extension, and the slope of the middle line is: because 丫2>丫, to meet the two highs or two lows of the criterion. Three or two evaluation methods to solve the example comparison of a gear helix angle of 15 degrees, left-handed, modulus m3, z40, tooth width 16mm, tested on a tooth orientation tester. It is simple and convenient to evaluate the helix angle (pressure angle) error using the minimum area method.
In this case, the results of the least squares method and the minimum area method are nearly 20 different. Therefore, the minimum area method proposed in this paper can significantly improve the accuracy of evaluation and has great practical value.
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