Three-dimensional tooth surface inclination deviation evaluation method

Abstract

The invention discloses a three-dimensional tooth surface inclination deviation evaluation method, and belongs to the technical field of precision measurement. The three-dimensional point cloud of the actual tooth surface is obtained through the point cloud data, the vertical distance between the discrete point of the actual tooth surface and the theoretical tooth surface is calculated, and the normal deviation is defined as the length and the perpendicular foot of the discrete point of the actual tooth surface relative to the vertical distance of the theoretical tooth surface. Converting coordinates of the rectangular coordinate system into a meshing surface coordinate system, and converting all discrete points into the meshing surface coordinate system to obtain an array; and fitting an average tooth profile plane by using the normal error point cloud data under the meshing surface coordinate system, and determining the positions of an average tooth profile trace and an average spiral trace. And evaluating the three-dimensional inclination deviation in the directions of the tooth profile and the spiral line by utilizing the slope. And according to the average tooth profile plane equation, calculating a normal vector of the average tooth profile, and taking the normal vector of the average tooth profile as a new evaluation index of the inclination deviation of the three-dimensional tooth surface. Complete tooth surface characterization can be realized by using the method.

Description

Technical Field

[0001] The invention relates to a method for evaluating the three-dimensional tooth surface inclination deviation of a cylindrical gear, and belongs to the field of precision measurement technology. Background Art

[0002] The evaluation of gear tooth surface deviation is an important part of the gear industry. Since gear transmission is achieved through the meshing line of the gear, at every moment of gear meshing transmission, the normal line of the tooth surface meshing area overlaps with the meshing line, so the tooth surface deviation is the most critical factor for the characterization of the gear tooth surface morphology.

[0003] The traditional gear evaluation method is based on GB / T10095.1, which mainly selects characteristic lines including tooth profile and helix on the tooth surface for two-dimensional evaluation. The traditional two-dimensional evaluation only evaluates one or more tooth profile lines or helix lines on the tooth surface, characterizes the characteristic lines and then reflects the morphology of the tooth surface, but this cannot fully characterize the morphology of the tooth surface, so it is extremely important to propose a three-dimensional tooth surface evaluation method. Summary of the invention

[0004] The invention discloses a method for characterizing the inclination degree of a tooth surface through a three-dimensional tooth surface inclination deviation evaluation method of a cylindrical gear, and provides a calculation and evaluation method.

[0005] To achieve the above object, the method adopted by the present invention comprises the following steps:

[0006] S1. Calculation of tooth surface normal deviation

[0007] Gear transmission is achieved through the meshing line of the gears. At the moment of gear meshing transmission, the normal line of the tooth surface meshing area overlaps with the meshing line. The evaluation of tooth surface characteristics is measured or calculated in the direction of the meshing line, that is, the normal line of the tooth surface. Normal deviation is a key factor in gear evaluation.

[0008] The three-dimensional point cloud of the actual tooth surface is obtained through the point cloud data, and the vertical distance between the discrete point P of the actual tooth surface and the theoretical tooth surface is calculated. The normal deviation is defined as the length of the vertical distance between the discrete point P (xp, yp) of the actual tooth surface and the theoretical tooth surface, the foot of the perpendicular O (xo, yo), and the positive and negative values ​​are the concave or convex sides of the theoretical tooth surface. When it is on the concave side, it is negative, and when it is on the convex side, it is positive. The coordinates of the rectangular coordinate system are converted to the meshing surface coordinate system, where X is the unfolded length, Y is the tooth width, and Z is the tooth surface deviation. The array point (X, Y, dnorm) can be obtained by converting all discrete points to the meshing surface coordinate system.

[0009]

[0010] Where: D is the distance from the discrete point to the center of the base circle;

[0011] r b is the base circle radius;

[0012] S2. Implementation of the evaluation method of three-dimensional tilt deviation

[0013] Using the normal error point cloud data in the meshing surface coordinate system, the average tooth profile plane is fitted to determine the position of the average tooth profile trace and the average helix trace. The average fitting plane is defined by three parameters, where parameter a represents the slope of the plane in the x direction and parameter b represents the slope in the y direction. The two slopes determine the angle between the plane and the tooth profile and helix direction, and the slope is used to evaluate the three-dimensional inclination deviation in the tooth profile and helix direction. According to the average tooth profile plane equation, the normal vector ρ(x hα ,z hβ ,δ h ), the average tooth profile normal vector ρ is used as a new evaluation index for the three-dimensional tooth surface inclination deviation.

[0014] Project the average tooth profile normal vector to the unfolded length and tooth width direction in the meshing surface coordinate system, transform the three-dimensional normal vector into two-dimensional, and the projected vector can be used to evaluate the inclination deviation according to GB / T10095.1.

[0015] It is required to characterize the three-dimensional tooth surface error and be compatible with the characteristics of the traditional two-dimensional gear error. The average tooth profile normal vector calculates the inclination angle of the tooth surface along the tooth profile direction and the inclination angle along the helix direction, and associates the three-dimensional tooth surface inclination deviation evaluation with the traditional tooth profile inclination deviation and helix inclination deviation to improve the three-dimensional tooth surface accuracy evaluation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of the vertical distance between the actual discrete point P on the tooth surface and the theoretical tooth surface based on three-dimensional point cloud computing.

[0017] Figure 2 is the fitted average tooth profile plane. DETAILED DESCRIPTION

[0018] The present invention is further described below with reference to the accompanying drawings, simulations and examples.

[0019] S1. Calculation of tooth surface normal deviation

[0020] Gear transmission is achieved through the meshing line of the gears. At the moment of gear meshing transmission, the normal line of the tooth surface meshing area overlaps with the meshing line. The evaluation of tooth surface characteristics is measured or calculated in the direction of the meshing line, that is, the normal line of the tooth surface. Normal deviation is a key factor in gear evaluation.

[0021] like Figure 1As shown, the three-dimensional point cloud of the actual tooth surface is obtained through the point cloud data, and the vertical distance between the discrete point P of the actual tooth surface and the theoretical tooth surface is calculated. The normal deviation is defined as the length of the vertical distance between the discrete point P (xp, yp) of the actual tooth surface and the theoretical tooth surface, the foot of the perpendicular O (xo, yo), and the positive and negative values ​​are the concave or convex sides of the theoretical tooth surface. When it is on the concave side, it is negative, and when it is on the convex side, it is positive. The coordinates of the rectangular coordinate system are converted to the meshing surface coordinate system, where X is the unfolded length, Y is the tooth width, and Z is the tooth surface deviation. The array point (X, Y, dnorm) can be obtained by converting all discrete points to the meshing surface coordinate system.

[0022]

[0023] Where: D is the distance from the discrete point to the center of the base circle;

[0024] r b is the base circle radius;

[0025] S2. Implementation of the evaluation method of three-dimensional tilt deviation

[0026] Using the normal error point cloud data in the meshing surface coordinate system, the average tooth profile plane is fitted as follows: Figure 2 , determine the position of the average tooth profile trace and the average helix trace. The average fitting plane is defined by three parameters, where parameter a represents the slope of the plane in the x direction and parameter b represents the slope in the y direction. The two slopes determine the angle between the plane and the tooth profile and helix direction, and the slopes are used to evaluate the three-dimensional tilt deviation in the tooth profile and helix direction. According to the average tooth profile plane equation, the normal vector ρ(x hα ,z hβ ,δ h ), the average tooth profile normal vector ρ is used as a new evaluation index for the three-dimensional tooth surface inclination deviation.

[0027] Project the average tooth profile normal vector to the unfolded length and tooth width direction in the meshing surface coordinate system, transform the three-dimensional normal vector into two-dimensional, and the projected vector can be used to evaluate the inclination deviation according to GB / T10095.1.

[0028] It is required to characterize the three-dimensional tooth surface error and be compatible with the characteristics of the traditional two-dimensional gear error. The average tooth profile normal vector calculates the inclination angle of the tooth surface along the tooth profile direction and the inclination angle along the helix direction, and associates the three-dimensional tooth surface inclination deviation evaluation with the traditional tooth profile inclination deviation and helix inclination deviation to improve the three-dimensional tooth surface accuracy evaluation system.

[0029] Compared with the traditional small module gear measurement method, this method has the following advantages:

[0030] 1. The advantage of this method is accurate error positioning.

[0031] 2. This method can be used to achieve complete tooth surface characterization.

[0032] 3. This method can be used to connect two-dimensional and three-dimensional images for comparison.

[0033] 4. This method is used to address the problem that the existing two-dimensional inclination evaluation cannot characterize the degree of tooth surface inclination.

Claims

1. A three-dimensional tooth surface inclination deviation evaluation method, characterized in that: The steps include: S1. Calculation of tooth surface normal deviation The three-dimensional point cloud of the actual tooth surface is obtained through the point cloud data, and the vertical distance between the discrete point P of the actual tooth surface and the theoretical tooth surface is calculated. The normal deviation is defined as the length of the vertical distance between the discrete point P (xp, yp) of the actual tooth surface and the theoretical tooth surface, and the foot of the perpendicular O (xo, yo). The positive and negative values ​​indicate whether the discrete point is located on the concave side or convex side of the theoretical tooth surface. When it is located on the concave side, it is negative, and when it is located on the convex side, it is positive. The coordinates of the rectangular coordinate system are converted into the meshing surface coordinate system, where X is the unfolded length, Y is the tooth width, and Z is the tooth surface deviation. All discrete points are converted into the meshing surface coordinate system to obtain the array point (X, Y, dnorm). Where: D is the distance from the discrete point to the center of the base circle; r b is the base circle radius; S2. Implementation of the evaluation method of three-dimensional tilt deviation The normal error point cloud data in the meshing surface coordinate system is used to fit the average tooth profile plane and determine the positions of the average tooth profile trace and the average helix trace. The average fitting plane is defined by three parameters, where parameter a represents the slope of the plane in the x direction and parameter b represents the slope in the y direction. The two slopes determine the angle between the plane and the tooth profile and helix directions, and the slopes are used to evaluate the three-dimensional inclination deviation in the tooth profile and helix directions. According to the average tooth profile plane equation, the normal vector ρ(x hα ,z hβ ,δ h ), the average tooth profile normal vector ρ is used as a new evaluation index for the three-dimensional tooth surface inclination deviation.

2. A three-dimensional tooth surface inclination deviation evaluation method according to claim 1, characterized in that: The average tooth profile normal vector is projected to the development length and tooth width direction in the meshing surface coordinate system, and the three-dimensional normal vector is transformed into two-dimensional. The projected vector is evaluated for inclination deviation in accordance with GB / T10095.

1.

3. A three-dimensional tooth surface inclination deviation evaluation method according to claim 1, characterized in that: The average tooth profile normal vector is used to calculate the inclination angle of the tooth surface along the tooth profile direction and the inclination angle along the helix line direction, and the three-dimensional tooth surface inclination deviation evaluation is associated with the traditional tooth profile inclination deviation and helix line inclination deviation to improve the three-dimensional tooth surface accuracy evaluation system.

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