A method for measuring the addendum circle diameter of a cylindrical gear

Abstract

The application provides a method for measuring the tooth crest circle diameter of a cylindrical gear, comprising the following steps: S1, initially establishing a workpiece coordinate system, taking the machining reference end surface of the cylindrical gear as a reference plane A, taking the section circle of the cylindrical gear which is perpendicular to the reference plane A as a reference circle B, taking the center of the reference circle B as the origin of the workpiece coordinate system, taking the Z of the origin on the reference plane A, defining the X axis and the Y axis on the reference plane A, and defining the Z axis which is perpendicular to the reference plane A; S2, precisely establishing the workpiece coordinate system, measuring by a three-coordinate measuring machine, and taking the Cartesian coordinate system as six degrees of freedom; S3, measuring the tooth crest circle diameter of the cylindrical gear, rotating by 360 / z degrees in the measurement software, and calculating the tooth crest circle diameter of the cylindrical gear. The tooth crest circle diameter of the cylindrical gear is measured by the high-precision three-coordinate measuring machine and the measuring rod, so that each tooth crest data point of the cylindrical gear can be accurately measured, and the tooth crest circle diameter is calculated.

Description

Technical Field

[0001] This invention relates to the field of cylindrical gear measurement technology, and in particular to a method for measuring the tip circle diameter of a cylindrical gear. Background Technology

[0002] Currently, there are two commonly used methods for measuring the tip circle diameter of cylindrical gears.

[0003] The first method involves direct measurement using a general-purpose vernier caliper or outside micrometer. Specifically, the measurement is performed on the tip circle diameter of the cylindrical gear, using a vernier caliper or outside micrometer with different maximum permissible errors and scale divisions, based on the size of the gear's tip circle diameter and tolerance requirements. The measurement is taken at the tip of the gear at the midpoint of the tooth width, with at least four diameter measurement points evenly distributed around the circumference. Each measurement point is measured three times, and the arithmetic mean of the three readings at the four locations is taken as the measurement result of the tip circle diameter. However, because the scale division and maximum permissible error of the measuring equipment used in this method are essentially at the millimeter level, the uncertainty sources of this method are mainly: the operator's human eye resolution introduces an uncertainty component of at least 0.01 mm, the scale division and maximum permissible error of the measuring equipment introduce an uncertainty component of at least 0.01 mm, and the uncertainty of the measurement result is at least 0.03 mm, which is far from meeting the measurement requirements for the tip circle diameter of high-precision cylindrical gears.

[0004] The second method involves using the self-learning mode of a high-precision 3D coordinate measuring machine (CMM). Specifically, the operator manually controls the CMM probe to evenly distribute at least four measurement points along the circumference at the tooth tip, located at the midpoint of the tooth width of the cylindrical gear being measured. A corresponding coordinate system for the part is then established. The operator manually sets the starting point on the tooth tip at the midpoint of the tooth width, and the CMM automatically collects all the points on the tooth tip required for the circular element. After collection, the measurement software fits and forms a measurement circle and calculates the circle diameter. Although this method uses a high-precision CMM with μm-level precision, the initial position of the automatic execution program is set manually. The operator's visual error and the influence of the vector direction of the manually collected coordinate points by the CMM lead to inaccurate positioning of the initial measurement position. Specifically, the measurement position at the tooth tip in the midpoint of the first tooth width will result in accumulated rotational angle errors when measuring the tooth tip of each subsequent tooth. Furthermore, during the measurement of the last tooth tip, the probe may enter the tooth groove and collect empty points, causing probe collisions.

[0005] The direct measurement method using general-purpose vernier calipers or outside micrometers is time-consuming, labor-intensive, and has low versatility and accuracy due to the numerous models and specifications of the measuring equipment, unsatisfactory maximum permissible errors and graduation values, bulky size, significant temperature influence, and the need for multiple personnel to coordinate measurements. Furthermore, while the self-learning mode of a high-precision 3D coordinate measuring machine offers the advantage of high precision, inaccurate initial measurement positioning often necessitates repeated repositioning during the measurement process. This method is also time-consuming and labor-intensive. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for measuring the tip circle diameter of a cylindrical gear. By using a high-precision coordinate measuring machine with a measuring rod to measure the tip circle diameter of the cylindrical gear, the data point of each tip of the cylindrical gear can be accurately measured, thereby calculating the tip circle diameter.

[0007] The technical solution adopted by this invention to solve its technical problem is: A method for measuring the tip circle diameter of a cylindrical gear includes the following steps: S1. Initially establish the workpiece coordinate system The machining reference end face of the cylindrical gear is taken as reference plane A. The cross-sectional circle of the cylindrical surface is projected onto reference plane A as reference circle B. The center of reference circle B is taken as the origin of the workpiece coordinate system. The origin is located on reference plane A. The X-axis and Y-axis are defined on reference plane A. The direction perpendicular to reference plane A is defined as the Z-axis. S2, Fine-tuning the workpiece coordinate system The Cartesian coordinate system, measured by a coordinate measuring machine, has six degrees of freedom, with two axes and the origin position fixed. S3. Measurement of the tip circle diameter of cylindrical gears Based on the principle of circular closure, when the number of teeth of the cylindrical gear being measured is z, the middle section of the tooth width of the cylindrical gear is selected as the measurement trajectory, and the tooth tip corresponding to the bisector of the angle is defined as the measurement starting position. Then, the other tooth tips of the cylindrical gear are evenly distributed at 360° / z of the circumference. The measurement software is edited to rotate at a 360° / z angle, automatically collecting data points on the tooth tip. After the automatic execution of the data point collection, a circle is fitted and formed, and the diameter of the cylindrical gear tip circle is calculated.

[0008] In step S2, the two axes include a first axis and a second axis. The first axis is fixed in a coordinate system with reference plane A of the cylindrical gear, and the second axis is fixed in a coordinate system through a measuring bar. The origin is fixed by reference plane A and the center of reference circle B projected onto reference plane A. The steps for precisely establishing the workpiece coordinate system are as follows: C1. Fix the first axis Measure the reference plane A of the cylindrical gear and align the first axis of the workpiece coordinate system: +Z axis; C2, Placement of measuring rod Based on the gear module m and the number of teeth z, calculate the diameter of the gauge bar, select a high-precision gauge bar with the required diameter, and place the gauge bar in the tooth groove of the cylindrical gear in the specified direction. C3. Measuring rod The cross-sectional circle of the gauge bar in the tooth groove is measured by a coordinate measuring machine and projected onto the reference plane A to obtain the center C of the cross-sectional circle; C4. Fix the second shaft Project the cross-sectional circle on the cylindrical gear cylinder onto the reference plane A to obtain the center B of the reference circle. Construct a straight line L1 using the two points B and C. Rotate the line L1 by 360° / 2z through the coordinate system to obtain the straight line L2. At this time, L2 is located at the middle position of the tooth tip. The angle bisector L2 is aligned with the second axis of the workpiece coordinate system: the +X axis. C5. Fixed core By placing the origin of the coordinate system on the reference plane A, and placing the (X,Y) of the origin at the center B of the reference circle, the origin can be fixed.

[0009] In step C2, the specified direction of the cylindrical gear is: the center position of any tooth of the cylindrical gear is consistent with the X-axis position of the coordinate system of the coordinate measuring machine, that is, it is located in the same axial direction. The tooth grooves on the left and right sides of this tooth are tooth grooves in the specified direction, and a measuring rod is placed in one of the tooth grooves.

[0010] In step C2, when placing the measuring rod, first ensure that the measuring rod is tangent to the left and right tooth surfaces of the cylindrical gear, secondly ensure that the top axial end of the measuring rod is higher than the tooth tip of the cylindrical gear, and finally use modeling clay to fix the measuring rod to the tooth surface.

[0011] In step C2, the formula for calculating the diameter D of the measuring rod is as follows: Due to the limitations of the coordinate measuring machine's probe and the accuracy requirements, to ensure the accuracy of the measurement results, the measured circle must be greater than 120°, as follows: (one) In formula (1): The diameter of the tooth tip circle, Let C be the diameter of the tooth root circle, and L be the distance between the center C of the measuring rod and the tooth root. Full tooth height; The formula for calculating the diameter D of the gauge bar is as follows: (two) In equation (ii): D is the diameter of the measuring rod, H is the radius of the measuring rod, L is the distance between the center C of the measuring rod and the tooth root, and θ is the angle between the straight line L and the tooth surface, θ = 360° / 2z.

[0012] The axial tip is at least two coordinate measuring machine probes above the tooth tip.

[0013] The beneficial effects of this invention are: 1. By using a high-precision measuring rod as an aid and leveraging the high-precision measurement advantage of a coordinate measuring machine, a connection is established between the measuring rod and the addendum circle diameter of the cylindrical gear through a coordinate system, thereby accurately measuring each addendum data point of the cylindrical gear and calculating the addendum circle diameter.

[0014] 2. By using the machining datum as the inspection datum, the datum is unified, ensuring the accuracy and reliability of the data. The cross-sectional circle on the cylindrical gear is projected onto the datum plane A to obtain the center B of the datum circle. A straight line L1 is constructed using the two points B and C. By rotating the coordinate system, the straight line L1 is rotated 360° / 2z to obtain the straight line L2. At this time, L2 is located at the middle position of the tooth tip. The angle bisector L2 is aligned with the second axis of the workpiece coordinate system, which can make the gear angle accurately bisected. This ensures that the probe can accurately measure the middle part of the tooth tip when measuring each tooth tip. This method is accurate, efficient, convenient, and highly operable.

[0015] 3. By selecting the diameter of the measuring rod at 1 / 2 to 2 / 3 of the total tooth height, it is not only convenient to install and fix the measuring rod, but also ensures that the probe can accurately measure one-third of the measuring rod, making the center of this cross-section circle accurate and reliable. Since the measuring rod is tangent to the tooth groove surface, the line connecting the center of the measured cross-section circle and the center of the inner circle bisects the tooth groove. Using the angle bisector principle, θ = 360° / 2z, which shows that... The calculation formula is used to select the diameter of the measuring rod.

[0016] 4. Saves manpower: only one person is needed to operate the tooth tip circle diameter test, and another person is responsible for supervising the test.

[0017] 5. The operating principle is simple and easy to understand, and the operation is convenient. After training, operators can master the usage methods and techniques.

[0018] 6. Low cost and simple, only a measuring rod is needed to accurately measure the tooth tip circle diameter.

[0019] 7. Convenient measurement: Coordinate measuring personnel only need to establish the coordinate system to automatically perform accurate measurements.

[0020] 8. The method is reliable, highly accurate, and has virtually no cumulative angular error.

[0021] 9. The vector direction is accurate. During automatic measurement, the measurement software automatically adjusts the measurement vector direction so that the probe contact direction is dynamically perpendicular to the workpiece surface. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the structure of the present invention.

[0023] Figure 2 A schematic diagram of the projection of the reference circle on the cylinder of the cylindrical gear being measured.

[0024] Figure 3 This is a schematic diagram of the gauge bar installation. Detailed Implementation

[0025] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] Example 1

[0027] like Figure 1 As shown, a method for measuring the tip circle diameter of a cylindrical gear includes the following steps: S1. Initially establish the workpiece coordinate system The machining reference end face of the cylindrical gear is taken as reference plane A. The cross-sectional circle of the cylindrical surface is projected onto reference plane A as reference circle B. The center of reference circle B is taken as the origin of the workpiece coordinate system. The origin is located on reference plane A. The X-axis and Y-axis are defined on reference plane A. The direction perpendicular to reference plane A is defined as the Z-axis. S2, Fine-tuning the workpiece coordinate system The Cartesian coordinate system, measured by a coordinate measuring machine, has six degrees of freedom, with two axes and the origin position fixed. S3. Measurement of the tip circle diameter of cylindrical gears Based on the principle of circular closure, when the number of teeth of the cylindrical gear being measured is z, the middle section of the tooth width of the cylindrical gear is selected as the measurement trajectory, and the tooth tip corresponding to the bisector of the angle is defined as the measurement starting position. Then, the other tooth tips of the cylindrical gear are evenly distributed at 360° / z of the circumference. The measurement software is edited to rotate at a 360° / z angle, automatically collecting data points on the tooth tip. After the automatic execution of the data point collection, a circle is fitted and formed, and the diameter of the cylindrical gear tip circle is calculated.

[0028] In step S2, the two axes include a first axis and a second axis. The first axis is fixed in a coordinate system with reference plane A of the cylindrical gear, and the second axis is fixed in a coordinate system through a measuring bar. The origin is fixed by reference plane A and the center of reference circle B projected onto reference plane A. The steps for precisely establishing the workpiece coordinate system are as follows: C1. Fix the first axis Measure the reference plane A of the cylindrical gear and align the first axis of the workpiece coordinate system: +Z axis; C2, Placement of measuring rod Based on the gear module m and the number of teeth z, calculate the diameter of the gauge bar, select a high-precision gauge bar with the required diameter, and place the gauge bar in the tooth groove of the cylindrical gear in the specified direction. C3. Measuring rod The cross-sectional circle of the gauge bar in the tooth groove is measured by a coordinate measuring machine and projected onto the reference plane A to obtain the center C of the cross-sectional circle; C4. Fix the second shaft like Figure 2 As shown, the cross-sectional circle on the cylindrical gear is projected onto the reference plane A to obtain the center B of the reference circle. A straight line L1 is constructed using the two points B and C. By rotating the coordinate system, the straight line L1 is rotated by 360° / 2z to obtain the straight line L2. At this time, L2 is located at the middle position of the tooth tip. The angle bisector L2 is aligned with the second axis of the workpiece coordinate system: the +X axis.

[0029] C5. Fixed core

[0030] By placing the origin of the coordinate system on the reference plane A, and placing the (X,Y) of the origin at the center B of the reference circle, the origin can be fixed.

[0031] In step C2, the specified direction of the cylindrical gear is: the center position of any tooth of the cylindrical gear is consistent with the X-axis position of the coordinate system of the coordinate measuring machine, that is, it is located in the same axial direction. The tooth grooves on the left and right sides of this tooth are tooth grooves in the specified direction, and a measuring rod is placed in one of the tooth grooves.

[0032] In step C2, when placing the measuring rod, first ensure that the measuring rod is tangent to the left and right tooth surfaces of the cylindrical gear, secondly ensure that the top axial end of the measuring rod is higher than the tooth tip of the cylindrical gear, and finally use modeling clay to fix the measuring rod to the tooth surface.

[0033] In step C2, the formula for calculating the diameter D of the measuring rod is as follows: like Figure 3 As shown, based on the probe limitations and measurement accuracy requirements of the coordinate measuring machine, to ensure the accuracy of the measurement results, the measured circle must be greater than 120°, as follows: (one) In formula (1): The diameter of the tooth tip circle, Let C be the diameter of the tooth root circle, and L be the distance between the center C of the measuring rod and the tooth root. Full tooth height; The formula for calculating the diameter D of the gauge bar is as follows: (two) In equation (ii): D is the diameter of the measuring rod, H is the radius of the measuring rod, L is the distance between the center C of the measuring rod and the tooth root, and θ is the angle between the straight line L and the tooth surface, θ = 360° / 2z.

[0034] The axial tip is at least two coordinate measuring machine probes above the tooth tip.

[0035] By using a high-precision measuring rod and leveraging the high-precision measurement advantage of a coordinate measuring machine, a connection is established between the measuring rod and the addendum circle diameter of the cylindrical gear through a coordinate system, thereby accurately measuring each addendum data point of the cylindrical gear and calculating the addendum circle diameter.

[0036] By using the machining datum as the inspection datum, the datum is unified, ensuring the accuracy and reliability of the data. The cross-sectional circle on the cylindrical gear is projected onto the datum plane A to obtain the center B of the datum circle. A straight line L1 is constructed using the two points B and C. By rotating the coordinate system, the straight line L1 is rotated 360° / 2z to obtain the straight line L2. At this time, L2 is located at the middle position of the tooth tip. The angle bisector L2 is aligned with the second axis of the workpiece coordinate system, which can make the gear angle accurately bisected. This ensures that the probe can accurately measure the middle part of the tooth tip when measuring each tooth tip. This method is accurate, efficient, convenient, and highly operable.

[0037] By selecting the diameter of the measuring rod at 1 / 2 to 2 / 3 of the total tooth height, it is not only convenient to install and fix the measuring rod, but also ensures that the probe can accurately measure one-third of the measuring rod, making the center of this cross-section circle accurate and reliable. Since the measuring rod is tangent to the tooth groove surface, the line connecting the center of the measured cross-section circle and the center of the inner circle bisects the tooth groove. Using the angle bisector principle, θ = 360° / 2z. Figure 2 It can be seen that through The calculation formula is used to select the diameter of the measuring rod.

[0038] To save manpower, only one person is needed to operate the tooth tip circle diameter test, and another person is responsible for supervising the test.

[0039] The operating principle is simple and easy to understand, and the operation is convenient. After training, operators can master the usage methods and techniques.

[0040] It is low-cost and simple, requiring only a measuring rod to accurately measure the tooth tip circle diameter.

[0041] Measurement is convenient; coordinate measuring machine operators only need to establish a coordinate system to automatically perform accurate measurements.

[0042] The method is reliable, highly accurate, and has virtually no cumulative angular error.

[0043] The vector direction is precise, and during automatic measurement, the measurement software automatically adjusts the measurement vector direction so that the probe touch direction is dynamically perpendicular to the workpiece surface.

[0044] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the tip circle diameter of a cylindrical gear, characterized in that: Includes the following steps: S1. Initially establish the workpiece coordinate system The machining reference end face of the cylindrical gear is taken as reference plane A. The cross-sectional circle of the cylindrical surface is projected onto reference plane A as reference circle B. The center of reference circle B is taken as the origin of the workpiece coordinate system. The origin is located on reference plane A. The X-axis and Y-axis are defined on reference plane A. The direction perpendicular to reference plane A is defined as the Z-axis. S2, Fine-tuning the workpiece coordinate system The Cartesian coordinate system, measured by a coordinate measuring machine, has six degrees of freedom, with two fixed axes and the origin. The two axes include a first axis and a second axis. The first axis is fixed by the reference plane A of the cylindrical gear, and the second axis is fixed by the coordinate system through a gauge bar. The origin is fixed by the reference plane A and the center of the reference circle B projected onto the reference plane A. The steps for precisely establishing the workpiece coordinate system are as follows: C1. Fix the first axis Measure the reference plane A of the cylindrical gear and align the first axis of the workpiece coordinate system: +Z axis; C2, Placement of measuring rod Based on the gear module m and the number of teeth z, calculate the diameter of the gauge bar, select a high-precision gauge bar with the required diameter, and place the gauge bar in the tooth groove of the cylindrical gear in the specified direction. C3. Measuring rod The cross-sectional circle of the gauge bar in the tooth groove is measured by a coordinate measuring machine and projected onto the reference plane A to obtain the center C of the cross-sectional circle; C4. Fix the second shaft Project the cross-sectional circle on the cylindrical gear cylinder onto the reference plane A to obtain the center B of the reference circle. Construct a straight line L1 using the two points B and C. Rotate the straight line L1 by 360° / 2z through the coordinate system to obtain the straight line L2. At this time, L2 is located at the middle position of the tooth tip. The angle bisector L2 is aligned with the second axis of the workpiece coordinate system: the +X axis. C5. Fixed core By placing the origin of the coordinate system on the reference plane A, and placing the (X,Y) of the origin at the center B of the reference circle, the origin can be fixed. S3. Measurement of the tip circle diameter of cylindrical gears Based on the principle of circular closure, when the number of teeth of the cylindrical gear being measured is z, the middle section of the tooth width of the cylindrical gear is selected as the measurement trajectory, and the tooth tip corresponding to the bisector of the angle is defined as the measurement starting position. Then, the other tooth tips of the cylindrical gear are evenly distributed at 360° / z of the circumference. The measurement software is edited to rotate at a 360° / z angle, automatically collecting data points on the tooth tip. After the automatic execution of the data point collection, a circle is fitted and formed, and the diameter of the cylindrical gear tip circle is calculated.

2. The method for measuring the tip circle diameter of a cylindrical gear as described in claim 1, characterized in that: In step C2, the specified direction of the cylindrical gear is: the center position of any tooth of the cylindrical gear is consistent with the X-axis position of the coordinate system of the coordinate measuring machine, that is, it is located in the same axial direction. The tooth grooves on the left and right sides of this tooth are tooth grooves in the specified direction, and a measuring rod is placed in one of the tooth grooves.

3. The method for measuring the tip circle diameter of a cylindrical gear as described in claim 1, characterized in that: In step C2, when placing the measuring rod, first ensure that the measuring rod is tangent to the left and right tooth surfaces of the cylindrical gear, secondly ensure that the top axial end of the measuring rod is higher than the tooth tip of the cylindrical gear, and finally use modeling clay to fix the measuring rod to the tooth surface.

4. The method for measuring the tip circle diameter of a cylindrical gear as described in claim 1, characterized in that: In step C2, the formula for calculating the diameter D of the measuring rod is as follows: Due to the limitations of the coordinate measuring machine's probe and the accuracy requirements, to ensure the accuracy of the measurement results, the measured circle must be greater than 120°, as follows: (one) In formula (1): The diameter of the tooth tip circle, Let C be the diameter of the tooth root circle, and L be the distance between the center C of the measuring rod and the tooth root. Full tooth height; The formula for calculating the diameter D of the gauge bar is as follows: (two) In equation (ii): D is the diameter of the measuring rod, H is the radius of the measuring rod, L is the distance between the center C of the measuring rod and the tooth root, and θ is the angle between the straight line L and the tooth surface, θ = 360° / 2z.

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