CN111912373A - A method for measuring tooth profile deviation using a roughness profiler - Google Patents

Abstract

The invention discloses a tooth profile deviation measuring method by using a roughness profiler, which comprises the steps of obtaining tooth profile data of an involute cylindrical gear on the roughness profiler, establishing an involute tooth profile model according to parameters of a measured gear, solving fitting parameters by using an optimization solution idea through constructing a least square objective function of original measured data and the involute tooth profile model in a normal direction, obtaining an original measured data curve and the involute tooth profile model after orthogonal distance fitting, further calculating to obtain the tooth profile deviation of any point in the involute normal direction, and finally evaluating and calculating the deviation value to obtain the tooth profile deviation and the precision grade defined by national standards.

Description

A method for measuring tooth profile deviation using a roughness profiler

technical field

The invention belongs to the field of precision measurement, and more particularly relates to the measurement and evaluation of involute cylindrical gear tooth profile deviation, in particular to a processing method of involute tooth profile measurement data and an evaluation of involute tooth profile deviation data calculation method.

Background technique

Gear is a kind of transmission part, and the quality of gear tooth surface has a direct influence on the performance of gear transmission, such as transmission error, bearing capacity, vibration and noise, etc. Tooth profile deviation is an important parameter of gear accuracy, which needs to be obtained by evaluating gear tooth profile information. Therefore, the acquisition and processing of gear tooth profile information is extremely important.

In order to measure the tooth profile deviation, the usual practice is to form a theoretical involute by mechanical or electronic generation according to the principle of involute formation, and then record the deviation between the actual tooth profile and the theoretical involute by a probe. A typical instrument is the gear measurement center. In addition, CMM and optical measuring instruments, which are different from the principle of generative measurement, are also used in gear measurement.

Roughness profiler is a contact-type comprehensive measuring instrument, which can not only be used to detect the two-dimensional shape and position error of the workpiece, but also be widely used in the detection of surface roughness, waviness, original contour and other micro-profile parameters.

SUMMARY OF THE INVENTION

The invention provides a method for processing involute tooth profile measurement data. An involute tooth profile model is established according to the parameters of the measured gear. The objective function is to solve the fitting parameters by using the idea of optimal solution, and obtain the original measurement data curve and involute tooth profile model after fitting.

The invention provides an evaluation and calculation method for involute tooth profile deviation data. According to the obtained fitting parameters, the deviation of any point of the tooth profile in the normal direction of the involute is calculated, and the deviation value is evaluated and calculated to obtain the national Standard-defined profile deviation and accuracy class.

The invention obtains the tooth profile data of the involute cylindrical gear on the roughness profiler, establishes the involute tooth profile model according to the parameters of the measured gear, and constructs the minimum difference between the original measurement data and the involute tooth profile model in the normal direction. The square objective function is used to solve the fitting parameters by using the idea of optimal solution, and the fitted original measurement data curve and the involute tooth profile model are obtained, and then the deviation value of the tooth profile at any point on the involute normal direction is calculated. The deviation value is evaluated and calculated to obtain the tooth profile deviation and accuracy grade defined by the national standard.

Description of drawings

FIG. 1 is a schematic isometric view of a three-dimensional structure of the present invention.

Figure 2 is a side view of the structure of the present invention.

Figure 3 is a front view of the structure of the present invention.

FIG. 4 is a schematic diagram of the optimal measurement position of the gear teeth of the present invention.

5 is a schematic diagram of an involute rectangular coordinate of the present invention.

FIG. 6 is a schematic diagram of the preprocessing of the present invention.

FIG. 7 is a schematic diagram of the minimum distance point of the present invention.

FIG. 8 is a schematic diagram of an orthogonal distance fitting result of the present invention.

FIG. 9 is a schematic diagram of the calculation and evaluation of the involute profile deviation of the present invention.

Detailed ways

The invention provides a method for acquiring tooth profile data of an involute cylindrical gear on a roughness profiler. As shown in Figure 1, the roughness profiler includes a column 1, a drive box 2, a probe system 3, an axial moving table 4, and a base 5. As shown in FIG. 2 , the involute gear fixture 6 includes a motor 7 , a coupling 8 , a main shaft shaft 9 , a circular grating system 10 , and an involute gear 11 to be measured. The probe system 3 is composed of a measuring stylus and a sensor rod, which is connected to the drive box 2 so that it can move along the measured tooth surface in the X-axis plane (tangential axis). The column 1 can make the probe system 3 and the The drive box 2 moves up and down on the Z axis (vertical axis), the involute gear clamp 6 realizes the clamping of the involute gear to be measured and the rotation in the X axis plane, and the axial moving table 4 realizes the involute gear clamp. 6 The movement on the Y axis (radial axis) makes the measured involute gear 11 adjust the measurement position in the direction of its tooth width, and the circular grating system 10 is installed on the involute gear fixture 6 to detect the Measure the rotation angle of the involute gear 11 after each measurement. The left end of the main shaft shaft 9 is connected to the motor 7 through the coupling 8, and the right end is connected to the measured involute gear 11. One end of the measured involute gear 11 is limited by the shaft shoulder, and the other end is limited by the screw, nut and shaft. The sleeve is clamped and fixed in the axial direction, and the main shaft shaft 9 is supported and fixed on the axial moving table 4 through the bearing. Among them, the motor shaft, the circular grating, and the measured involute gear rotate synchronously.

In order to obtain the involute tooth profile of the measured involute gear accurately and comprehensively, it is necessary to precisely locate the measurement position after the measured involute gear is installed. After the involute gear to be tested is clamped, the gear teeth to be tested are driven to rotate to the optimal measurement position by the motor, so that the root forming point F _f on the tooth root position of the tooth surface of the tested gear and the position of the tooth tip are formed. The top forming point Fa is on _a horizontal line, as shown in Figure 4, which minimizes the measurement variation range of the stylus probe system and reduces the nonlinear error in the measurement of the involute tooth profile.

After the measured involute gear is clamped and the tooth surface measurement position is adjusted, the tooth profile data is measured. The implementation process of the measurement is as follows: the first step is to control the axial moving table, and adjust the probe to the axial center position of the tooth profile; the second step, move the probe to the tooth root forming point F of the measured tooth near _f , and continue to move 0.05mm in the direction of the tooth root, operate the profiler to make the probe measure from the current position to 0.05mm beyond the tooth tip forming point _Fa , complete the measurement of the tooth profile of the involute gear to be measured, and measure the tooth profile of the involute gear. The measurement data is stored in the computer.

The invention provides a method for processing involute tooth profile measurement data. In the first step, according to the parameters of the involute gear under test, a parametric equation is used for modeling based on the involute generation method. The involute is the trajectory of any point on the generating line when the generating line rolls purely around the base circle. The involute rectangular coordinates are shown in Figure 5. According to this definition, the rolling angle uk of any point _K on the involute can be obtained as:

In the formula: θ _k is the spread angle of point K, and α _k is the pressure angle of point K.

The involute profile parameter equation is expressed as:

Where: r _b is the radius of the base circle.

通过对式(2)中渐开线齿廓参数方程进行旋转，最终得到最佳测量位置的渐开线齿廓理论模型：Set the rotation angle of the optimal measurement position relative to the initial position of the involute profile parameter equation modeling in Eq. (2) as

By rotating the involute tooth profile parameter equation in formula (2), the theoretical model of the involute tooth profile for the optimal measurement position is finally obtained:

In formula (3), the minimum value u _min and the maximum value u _max of the rolling angle u are respectively taken at the starting point and the ending point of the involute. For an involute cylindrical gear, the starting point F of the involute is the intersection of the transition curve and the involute tooth profile:

为齿顶高系数，x为变位系数，z为齿数，d_F为F点的直径，d_b为基圆直径。where α _F is the pressure angle at point F, α _t is the end face pressure angle,

is the addendum height coefficient, x is the displacement coefficient, z is the number of teeth, _{d F} is the diameter of point F, and db is the diameter of the base circle.

If the addendum chamfer is ignored, the end point of the involute is on the addendum circle. Therefore, the calculation formula of the minimum value u _min and the maximum value u _max of the roll angle u is:

Where: d _a is the diameter of the addendum circle.

The second step is measurement data preprocessing. In order to ensure the stability of the algorithm and improve the convergence speed of the algorithm, the preprocessing makes the involute tooth profile model and the original measurement data curve as fast as possible before the orthogonal distance fitting.

The original measurement data obtained by measuring the gear tooth profile by the profiler has no position information, but only length and shape information. Preprocessing In the x-direction, the raw measurement data and the midpoint position of the involute tooth profile model are aligned in translation. In the y direction, by calculating the mean difference between the involute tooth profile model and the original measurement data in the y direction, the original measurement data is aligned with the involute tooth profile model, and the preprocessed original measurement data is:

As shown in Fig. 6, through preprocessing, the position of the involute tooth profile model and the original measurement data curve can be made closer to the greatest possible extent.

The third step is to optimize the solution. The Orthogonal Distance Fitting Algorithm needs to solve the least squares solution of the preprocessed measurement data curve and the involute tooth profile model in the normal direction. By constructing the objective function, the idea of optimization is used to solve the fitting parameters to obtain the fitting result of the orthogonal distance between the preprocessed measurement data curve and the involute tooth profile model.

First, use the Levenberg-Marquardt Algorithm to solve the minimum distance point on the involute tooth profile model corresponding to each measurement data point after preprocessing, and obtain all measurement points corresponding to the involute curve The position parameter u of all minimum distance points on the tooth profile model. As shown in Figure 4, M _i is any point in the pre-processed measurement data (i=1, 2,..., n, n is the total number of measurement data), and T _i is M _i in the involute tooth The minimum distance point on the profile model, that is, the corresponding point of the orthogonal distance, x(u) is the involute tooth profile model, and d _i is the normal distance between _Mi and the minimum distance point Ti _.

The managed distance is:

Solving the position parameter u of the minimum distance point T _i can be converted into solving the extreme value of the objective function D(u):

The L-M algorithm is an improvement of the Gauss-Newton iteration method. The damping coefficient λ is introduced to make the iteration have a larger convergence interval, and the iteration formula is obtained:

和平移参数x₀、y₀，通过高斯-牛顿迭代法最优化求解，实现预处理后的测量数据曲线与渐开线齿廓模型的正交距离拟合，并求解出相关拟合参数(旋转参数

平移参数x₀、y₀，所有位置参数u′)：The LM algorithm realizes that all preprocessed measurement data points solve the position parameter u of the minimum distance point on the involute tooth profile model, and all the solved position parameters u are used as the initial iterative value of all position parameters u' of the Gauss-Newton iteration method. , while adding the rotation parameter

and translation parameters x ₀ , y ₀ are optimized and solved by Gauss-Newton iterative method to realize the orthogonal distance fitting between the preprocessed measurement data curve and the involute tooth profile model, and solve the relevant fitting parameters (rotation). parameter

Translation parameters x ₀ , y ₀ , all positional parameters u′):

Let the minimum distance corresponding point after rotation and translation processing be:

T'=R ^-1 M+X ₀ (13)

Based on the idea of orthogonal distance fitting, it is necessary to minimize the sum of the squares of the minimum distances between the involute tooth profile model after rotation and translation processing and the preprocessed measurement data, and the given point of the preprocessed measurement data is equal to Each distance between the involute tooth profile models should also be minimized. The sum of the squares of the distances between the involute tooth profile model after rotation and translation processing and the preprocessed measurement data curve is:

The first-order necessary conditions are:

Based on the idea of Gauss-Newton iteration method, the iterative formula can be obtained:

J| _k Δb=(MT′)| _k , b _k+1 =b _k +αΔb (16)

The expanded form of iterative formula (16) is:

Equation (17) is a system of linear overdetermined equations for Δb that requires a least-squares solution.

Set the stop condition as:

|b _k+1 -b _k |＜ε (18)

决定着拟合的精度，进而影响着齿廓偏差计算的结果。由此，迭代的停止条件为：For the fitting parameter b that needs to be solved, in the final solution result

It determines the accuracy of fitting, and then affects the result of tooth profile deviation calculation. Thus, the stopping condition of the iteration is:

平移参数x₀、y₀和所有位置参数u′。为了保留测量齿廓在整个齿轮上的相对位置，最终的拟合结果对渐开线齿廓模型旋转

对原始测量数据平移x₀、y₀，最终得到渐开线齿廓模型与预处理后的测量数据的正交距离拟合结果，如图8所示(偏差放大)。The solved fitting parameter b contains the optimal rotation parameter for the orthogonal distance fitting

Translation parameters x ₀ , y ₀ and all positional parameters u'. In order to preserve the relative position of the measured tooth profile on the entire gear, the final fitting result is rotated on the involute tooth profile model

The original measurement data is shifted by x ₀ and y ₀ , and finally the orthogonal distance fitting result between the involute tooth profile model and the preprocessed measurement data is obtained, as shown in Figure 8 (bias magnification).

The invention provides a method for evaluating and calculating involute tooth profile deviation data. The first step is to calculate the normal deviation of the tooth profile after ODF processing according to all the position parameters u obtained by the ODF algorithm:

表示在计值范围L_α内，包容实际齿廓迹线的，与平均齿廓迹线完全相同的两条迹线间的距离，且两条曲线与平均齿廓迹线的距离为常数；齿廓倾斜偏差

表示在计值范围L_α内，两端与平均齿廓迹线相交的两条设计齿廓迹线间的距离，如图9所示。In the second step, the normal deviation result of the tooth profile after ODF processing is calculated according to formula (22), and the calculation and evaluation are carried out based on the definition in the current national standard GB/T10095.1-2008 for the precision manufacturing of cylindrical gears. Among them, the tooth profile deviation is calculated according to the regulations on tooth profile deviation in the current national standard GB/T10095.1-2008 for the precision of cylindrical gears: the total tooth profile deviation (F _α ) is expressed in the calculation range L _α , including the actual tooth profile The distance between the two design tooth profile traces of the trace; tooth profile shape deviation

Represents the distance between two traces that are exactly the same as the average tooth profile trace within the value range L _α , including the actual tooth profile trace, and the distance between the two curves and the average tooth profile trace is constant; Profile tilt deviation

Indicates the distance between two designed tooth profile traces whose ends intersect with the average tooth profile trace within the value range L _α , as shown in Figure 9.

齿廓倾斜偏差

三个项目的单项精度，完成对被测渐开线齿轮的精度评价。In the third step, according to the calculation results, based on the precision of cylindrical gears, the current national standard GB/T10095.1-2008 is made to look up the table to obtain the total tooth profile deviation (F _α ), tooth profile shape deviation

Tooth profile inclination deviation

The single precision of the three items completes the precision evaluation of the measured involute gear.

Claims (2)

1. A tooth profile deviation measuring method using a roughness profiler is characterized in that: establishing an involute tooth profile model according to parameters of a measured gear, and solving fitting parameters by using an optimization solution idea through constructing a least square objective function of original measurement data and the involute tooth profile model in a normal direction to obtain a fitted original measurement data curve and the involute tooth profile model;

and calculating to obtain the deviation of any point of the tooth profile in the normal direction of the involute according to the fitting parameters obtained by solving, and evaluating and calculating the deviation value to obtain the tooth profile deviation and the precision grade defined by the national standard.

2. The method of tooth profile deviation measurement using a roughness profiler as set forth in claim 1, wherein: the method comprises the steps of obtaining tooth profile data of an involute cylindrical gear on a roughness profiler, establishing an involute tooth profile model according to parameters of a measured gear, constructing a least square objective function of original measured data and the involute tooth profile model in a normal direction, solving fitting parameters by using an optimization solving idea to obtain a fitted original measured data curve and the involute tooth profile model, further calculating to obtain tooth profile arbitrary point deviation in the involute normal direction, and finally evaluating and calculating the deviation value to obtain tooth profile deviation and precision grade defined by national standards.

Images