Internal Gear Measurement Based On Logistic Regression

The accuracy of gear affects the transmission quality of the whole transmission system,so it is necessary to measure the gear deviation,and it is also an important prerequisite to improve the gear manufacturing level.Because of the compact structure of internal gears with small and medium modulus,it is inconvenient to use traditional gear detection methods to measure internal gears with small and medium modulus.Using machine vision and image processing methods to measure the deviation of internal gears can solve this problem well.In this paper,an internal gear measurement method based on logistic regression is proposed.The existing logistic regression algorithm is applied to sub-pixel edge location,and the tooth profile of the collected internal gear image is extracted by this sub-pixel edge location algorithm.According to the extracted sub-pixel tooth profile points,the calculation model of total deviation of internal gear tooth profile and the calculation model of single tooth pitch deviation are established.The main tasks of this paper are as follows:(1)The parallel backlight vision measurement system is used to collect the images of internal gears.There are only foreground and background in the images.The gray value of each pixel is regarded as the probability of the background.The probability of pixels in the images is classified by using the idea of classification,and a sub-pixel edge location algorithm based on logical regression is proposed.The algorithm has high precision and stable measurement results,and can solve the problem of complex light intensity calibration and reduce the calculation amount.(2)Every point on the actual gear tooth profile can be regarded as a point on involute with the same base circle but different initial phase angles.According to the geometric characteristics of involute,the calculation model of total deviation of internal gear tooth profile and the calculation model of single pitch deviation are established.Because the lens size of the vision measurement system is limited,the inner gear can not be completely in the visual field of the system,so the center of the gear is located by the outer arc of the gear.Sub-pixel edge location algorithm is used to extract the edge of the outer arc in the local image of the internal gear,and the fixed radius least square method is used to fit the outer arc of the internal gear to get the center position of the internal gear.In order to reduce the calculation error,the tooth profile and outer circular arc of internal gear are extracted continuously and sectionally,the initial phase angle of each point is calculated,and the tooth profile total deviation measurement model and single tooth pitch deviation measurement model based on the initial phase angle are established.(3)The internal gear measurement algorithm based on logistic regression proposed in this paper can measure the deviation of the internal gear with known precision grade.The existing vision measurement hardware system is used to collect images of internal gears with 8-stage accuracy,and the sub-pixel edge location algorithm is used to extract the outer circular arc and tooth profile edge points of internal gears.The measurement model of internal gear deviation is established,and the obtained sub-pixel edge points are brought into the measurement model to calculate the deviation of internal gears.Comparing the calculation results with the standard deviation of 8-stage internal gears,the effectiveness of the proposed internal gear deviation detection algorithm can be verified,and the total tooth profile deviation and single tooth pitch deviation of internal gears with small and medium modulus can be measured.