In-process measurement and correction method for machining error of face gear tooth surface considering geometric error

Abstract

The application discloses a kind of face gear tooth surface machining error on-machine measurement and correction method considering geometric error, comprising the following steps: step one: on-machine measurement geometric error compensation: 11) builds on-machine measurement platform;12) on-machine measurement geometric error modeling;13) on-machine measurement geometric error identification;14) with the linear axis several errors and rotation axis geometric error obtained by identification, compensate on-machine measurement geometric error;Step two: tooth surface error on-machine measurement: 21) planning measurement point on tooth surface, and obtaining the normal vector of each measurement point;22) establish measurement coordinate system;23) sequentially to each measurement point is measured, obtains the actual tooth surface point of face gear in each measurement point;24) according to the actual tooth surface point of face gear in each measurement point and theoretical tooth surface point, obtains the profile error and pitch error of face gear;25) according to the profile error and pitch error of face gear obtained, to face gear is carried out reverse adjustment correction.

Description

Technical Field

[0001] This invention belongs to the field of error measurement technology, specifically a method for on-machine measurement and correction of machining errors of face gear teeth considering geometric errors. Background Technology

[0002] Face gear transmission is a new type of gear transmission. Compared with bevel gears, it has advantages such as better power splitting effect, compact structure, strong load-bearing capacity, high overlap ratio, and insensitivity to installation errors. Therefore, it is widely used in the power splitting transmission device of helicopter main gearboxes. The tooth surface accuracy directly affects the service life and performance of the entire aircraft. However, face gears have a variable tooth thickness tooth profile, making the machining process relatively complex.

[0003] In existing technologies, offline measurement is generally used to inspect the machining accuracy of face gears. While this meets the inspection requirements, it requires secondary clamping between the face gear machining equipment and the face gear measuring equipment. This secondary clamping can affect the measurement accuracy due to changes in the face gear workpiece's installation, and it also reduces measurement efficiency. Chinese Patent CN114754698B discloses a face gear tooth surface measurement point planning and on-machine measurement method. Although this achieves on-machine measurement of face gears, it does not consider the influence of the grinding machine's mechanical errors on the measurement results. Therefore, the measurement results cannot accurately reflect the face gear's machining errors, and thus, on-machine correction of tooth surface machining errors is not possible. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide an on-machine measurement and correction method for the machining error of face gear teeth that takes into account geometric errors. This method can not only realize the on-machine measurement of face gear tooth surface errors, but also reduce or even eliminate the influence of geometric errors of the on-machine measurement platform on the measurement results, so that the measurement results can accurately reflect the machining error of face gear teeth, thereby enabling the correction of face gear tooth surface machining errors on the machine.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for on-machine measurement and correction of machining errors on the tooth surface of face gears, taking into account geometric errors, includes the following steps:

[0007] Step 1: In-machine measurement geometric error compensation

[0008] 11) Setting up an on-machine measurement platform: The on-machine measurement platform includes a gear grinding machine, a probe, and a signal receiving device. The probe is mounted on the A-axis of the gear grinding machine, and the signal receiving device is connected to the probe and the gear grinding machine respectively via signal lines.

[0009] 12) Modeling geometric errors in on-machine measurements

[0010] Based on the topology of the on-machine measurement platform, ideal error-free motion models of the on-machine measurement platform are established respectively. The actual motion model with errors on the in-machine measurement platform

[0011] 13) Identification of geometric errors in in-machine measurement

[0012] 131) Identification of geometric errors of linear axes

[0013] Geometric error equations for the X, Y, and Z axes of the on-machine measurement platform are constructed respectively;

[0014] The equation for the perpendicularity error between any two axes in the X-axis, Y-axis and Z-axis of the machine measurement platform is constructed.

[0015] The combined error after geometric error coupling was measured using a laser interferometer, and the geometric errors of the X-axis, Y-axis and Z-axis of the on-machine measurement platform were decoupled and separated using the 9-line method;

[0016] 132) Identification of geometric errors of rotating shafts

[0017] Using a ballbar as the measuring device, based on the functional relationship between the nominal length of the ballbar, the ballbar installation angle, the workpiece ball installation angle, the geometric error, and the measured ballbar extension during the rotation of the C-axis or A-axis of the on-machine measuring platform, inverse identification models of geometric errors for the C-axis and A-axis are established respectively. Based on the measured ballbar extension, various geometric errors of the C-axis and A-axis are identified.

[0018] 14) Use the identified linear axis errors and rotation axis geometric errors to compensate for in-machine measurement geometric errors;

[0019] Step 2: On-machine measurement of tooth surface error

[0020] 21) Plan measurement points on the tooth surface and obtain the tooth surface normal vector of each measurement point;

[0021] 22) Use a standard ball to calibrate the probe and the rotary table respectively, and establish a measurement coordinate system based on the upper surface of the inner ring of the face gear, the cylindrical surface of the inner ring, and the midpoint of the tooth groove;

[0022] 23) Measure each measurement point in sequence to obtain the coordinates of the probe at each measurement point, and then obtain the actual tooth surface points of the face gear at each measurement point;

[0023] 24) Based on the actual tooth surface points and theoretical tooth surface points of the face gear at each measurement point, the tooth profile error and tooth pitch error of the face gear are obtained;

[0024] 25) Based on the obtained tooth profile error and pitch error of the face gear, the face gear is adjusted and corrected in reverse.

[0025] Furthermore, in step 12), the ideal error-free motion model of the on-machine measurement platform... for:

[0026]

[0027]

[0028]

[0029] in, This represents the ideal homogeneous transformation matrix between the probe and the face gear workpiece;

[0030] This represents the ideal homogeneous transformation matrix between the machine tool base and the face gear workpiece; T represents the ideal homogeneous transformation matrix between the machine tool base and the C-axis; pRC This represents the mounting pose matrix between the machine tool base and the C-axis; T mRC This represents the motion pose matrix between the machine tool base and the C-axis; T represents the ideal homogeneous transformation matrix between the C-axis and the face gear workpiece; pCG This represents the mounting pose matrix between the C-axis and the face gear workpiece; T mCG This represents the motion pose matrix between the C-axis and the face gear workpiece;

[0031] This represents the ideal homogeneous transformation matrix between the probe and the machine tool base; T represents the ideal homogeneous transformation matrix between the machine tool base and the X-axis; pRX This represents the mounting pose matrix between the machine tool base and the X-axis; T mRX This represents the motion pose matrix between the machine tool base and the X-axis; T represents the ideal homogeneous transformation matrix between the X and Z axes; pXZ T represents the mounting pose matrix between the X and Z axes; mXZ This represents the motion pose matrix between the X and Z axes; T represents the ideal homogeneous transformation matrix between the Z-axis and the A-axis; pZA T represents the mounting pose matrix between the Z-axis and A-axis; mZA This represents the motion pose matrix between the Z-axis and the A-axis; T represents the ideal homogeneous transformation matrix between the A-axis and the Y-axis; pAY Represents the mounting pose matrix between the A-axis and the Y-axis; T mAY This represents the motion pose matrix between the A-axis and the Y-axis; T represents the ideal homogeneous transformation matrix between the Y-axis and the probe; pYP T represents the mounting pose matrix between the Y-axis and the probe;mYP This represents the motion pose matrix between the Y-axis and the probe;

[0032] The actual motion model of the on-board measurement platform has errors. for:

[0033]

[0034]

[0035]

[0036] in, This represents the actual homogeneous transformation matrix between the probe and the face gear workpiece;

[0037] This represents the actual homogeneous transformation matrix between the machine tool base and the face gear workpiece; T represents the actual homogeneous transformation matrix between the machine tool base and the C-axis; peRC This represents the mounting pose error matrix between the machine tool base and the C-axis; T meRC This represents the motion pose error matrix between the machine tool base and the C-axis; T represents the actual homogeneous transformation matrix between the C-axis and the face gear workpiece; peCG T represents the mounting pose error matrix between the C-axis and the face gear workpiece; meCG This represents the motion pose error matrix between the C-axis and the face gear workpiece;

[0038] This represents the actual homogeneous transformation matrix between the machine tool base and the probe. T represents the actual homogeneous transformation matrix between the machine tool base and the X-axis; peRX This represents the mounting pose error matrix between the machine tool base and the X-axis; T meRX This represents the motion pose error matrix between the machine tool base and the X-axis; T represents the actual homogeneous transformation matrix between the X and Z axes; peXZ T represents the mounting pose error matrix between the X and Z axes; meXZ This represents the motion pose error matrix between the X and Z axes; T represents the actual homogeneous transformation matrix between the Z-axis and the A-axis; peZA T represents the mounting pose error matrix between the Z-axis and A-axis; meZA This represents the motion pose error matrix between the Z-axis and the A-axis; T represents the actual homogeneous transformation matrix between the A-axis and the Y-axis; peAY T represents the mounting pose error matrix between the A-axis and the Y-axis; meAY This represents the motion pose error matrix between the A-axis and the Y-axis; T represents the actual homogeneous transformation matrix between the Y-axis and the probe; peYP T represents the mounting pose error matrix between the Y-axis and the probe; meYP This represents the motion pose error matrix between the Y-axis and the probe.

[0039] Furthermore, in step 131), the geometric error equation for the X-axis is:

[0040]

[0041] E X =[δ x (X),δ y (X),δ z (X),ε x (X),ε y (X),ε z (X)]

[0042] Δ X =[Δx1(X),Δx2(X),Δx3(X),Δy1(X),Δy2(X),Δz1(X)]

[0043]

[0044] Among them, E X B represents the geometric error matrix of the X-axis; X The geometric error identification matrix representing the X-axis; Δ X The error matrix representing the X-axis; δ x (X), δ y (X) and δ z (X) represents the linear error of the X-axis in the X, Y, and Z directions, respectively; εx(X), εy(X), and ε z (X) represents the angular error of the X-axis in the X, Y, and Z directions, respectively; Δx i (X) represents the X-axis positioning error measured when the X-axis moves along the i-th measurement path; Δy i (X) and Δz i (X) represents the straightness error measured in the Y and Z directions respectively when the X-axis moves along the i-th measurement route;

[0045] The geometric error equation for the Y-axis is:

[0046]

[0047] E Y =[δ x (Y),δ y (Y),δ z (Y),ε x (Y),εy (Y),ε z (Y)]

[0048] Δ Y =[Δy4(Y),Δy5(Y),Δy6(Y),Δx4(Y),Δz4(Y),Δz5(Y)]

[0049]

[0050] Among them, E Y B represents the geometric error matrix along the Y-axis; Y The geometric error identification matrix representing the Y-axis; Δ Y The error matrix representing the Y-axis; δ x (Y), δ y (Y) and δ z (Y) represent the straightness errors of the Y-axis in the X, Y, and Z directions, respectively; ε x (Y), ε y (Y) and ε z (Y) represents the angular error of the Y-axis in the X, Y, and Z directions, respectively; Δy i (Y) represents the Y-axis positioning error measured when the Y-axis moves along the i-th measurement path; Δx i (Y) and Δz i (Y) represents the straightness error measured in the X and Z directions respectively when the Y-axis moves along the i-th measurement route;

[0051] The geometric error equation for the Z-axis is:

[0052]

[0053] E Z =[δ x (Z),δ y (Z),δ z (Z),ε x (Z),ε y (Z),ε z (Z)]

[0054] Δ Z =[Δz7(Z),Δz8(Z),Δz9(Z),Δx8(Z),Δy7(Z),Δx7(Z)]

[0055]

[0056] Among them, E Z B represents the geometric error matrix along the Z-axis; Z The geometric error identification matrix representing the Z-axis; Δ Z The error matrix representing the Z-axis; δ x (Z), δy (Z) and δ z (Z) represents the linear error of the Z-axis in the X, Y, and Z directions, respectively; ε x (Z), ε y (Z) and ε z (Z) represents the angular error of the Z-axis in the X, Y, and Z directions, respectively; Δz i (Z) represents the Z-axis positioning error measured when the Z-axis moves along the i-th measurement path; Δx i (Z) and Δy i (Z) represents the straightness error measured in the Z direction and Y direction respectively when the Z-axis moves along the i-th measurement route;

[0057] x i y i and z i These represent the X-axis, Y-axis, and Z-axis coordinates of an ideal point on the measurement line, respectively.

[0058] i = 1, 2, 3, 4, 5, 6, 7, 8, 9.

[0059] Furthermore, in step 131), the equation for the perpendicularity error between the X-axis and the Y-axis is:

[0060] S YX =θ y -θ x

[0061] S YZ =θ y -θ z

[0062] S ZX =θ z -θ x

[0063] Among them, S YX Indicates the perpendicularity error between the X-axis and the Y-axis; S YZ Indicates the perpendicularity error between the Y-axis and the Z-axis; S ZX θ represents the perpendicularity error between the Z-axis and the X-axis. x θ represents the angle of deviation between the actual trajectory and the theoretical trajectory along the X-axis. y θ represents the angle of deviation between the actual trajectory and the theoretical trajectory along the Y-axis. z This represents the deviation angle between the actual trajectory and the theoretical trajectory along the Z-axis.

[0064] Furthermore, in step 132), the functional relationship between the nominal length of the ball shaft, the ball shaft mounting angle, the workpiece ball mounting angle, the geometric error, and the measured ball shaft extension / retraction during the rotation of the rotation axis C or A is as follows:

[0065]

[0066] Wherein, the subscript R represents the axis of rotation, which can be replaced by A and C; L R Indicates the nominal length of the ballbar; ΔL R Represents the extension / retraction of the ballbar; θ R The angle between the axis of the cue stick and the axis of the worktable is denoted as the mounting angle; z Rω0 The height of the workpiece ball above the worktable surface; The angle between the coordinate vector of the center of the workpiece sphere and the positive x-axis is defined as the initial installation angle of the workpiece sphere; δx(R), δy(R), and δz(R) represent the linear errors of the R-axis in the X, Y, and Z directions, respectively; εx(R) and εy(R) represent the angular errors of the R-axis in the X and Y directions, respectively.

[0067] The beneficial effects of this invention are as follows:

[0068] This invention presents an in-machine measurement and correction method for the machining error of face gear teeth, considering geometric errors. An in-machine measurement platform is directly constructed using a gear grinding machine, with the probe mounted on the A-axis of the grinding machine, creating the necessary conditions for in-machine measurement. Before in-machine measurement of the machining error of the face gear teeth, firstly, a geometric error model between the probe and the face gear is established using the topology of the in-machine measurement platform; then, various geometric errors are identified, yielding the geometric errors of the linear axis and the rotational axis; finally, the identified linear axis and rotational axis errors are used to compensate for the geometric errors during in-machine measurement. This ensures that the influence of the geometric errors of the in-machine measurement platform on the measurement results can be reduced or even eliminated during the in-machine measurement process. After compensating for the geometric errors in the in-machine measurement, the face gear tooth surface is measured in-machine. The probe is used to measure the planned measurement points in sequence to obtain the coordinates of each measurement point, and then the actual tooth surface points of the face gear at each measurement point are obtained. Using the actual tooth surface points and the theoretical tooth surface points, the tooth profile error and tooth pitch error of the face gear are obtained. The tooth profile error and tooth pitch error are the face gear tooth surface machining errors after eliminating the influence of geometric errors. Finally, the face gear is reverse-adjusted to improve the machining accuracy of the face gear. Attached Figure Description

[0069] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0070] Figure 1 A flowchart of the method for on-machine measurement and correction of surface gear tooth surface machining error considering geometric errors in this invention;

[0071] Figure 2 This is a schematic diagram of the on-machine measurement platform;

[0072] Figure 3 This is a schematic diagram of the structure of each moving part in the on-machine measurement platform;

[0073] Figure 4 A simplified topology diagram of the on-machine measurement platform;

[0074] Figure 5 A simplified diagram of the motion of the on-machine measurement platform;

[0075] Figure 6 This is a schematic diagram of the drive train of the in-machine measurement platform;

[0076] Figure 7 A schematic diagram of the full kinematic chain of an on-machine measurement platform considering 42 geometric error elements;

[0077] Figure 8 This is a schematic diagram illustrating the principle of geometric error measurement and identification for linear axes based on the 9-line method.

[0078] Figure 9 A schematic diagram illustrating the identification of perpendicularity error between the X-axis and Y-axis;

[0079] Figure 10 A schematic diagram for identifying rotation axis errors using a ballbar;

[0080] Figure 11 Planning diagram for tooth surface measurement points;

[0081] Figure 12 This is a schematic diagram of the coordinate system for on-machine measurement of a face gear;

[0082] Figure 13 This is a schematic diagram of the measurement path;

[0083] Figure 14 This is a topological diagram of the relative error before and after geometric error compensation. Detailed Implementation

[0084] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0085] like Figure 1 As shown in the figure, this embodiment considers the on-machine measurement and correction method for the machining error of the gear tooth surface, which takes into account geometric errors, and includes the following steps.

[0086] Step 1: In-machine measurement geometric error compensation

[0087] 11) On-machine measurement platform setup: The on-machine measurement platform includes a gear grinding machine, a probe, and a signal receiving device. The probe is mounted on the A-axis of the gear grinding machine, and the signal receiving device is connected to both the probe and the gear grinding machine via signal lines, such as... Figure 2As shown.

[0088] 12) Modeling geometric errors in on-machine measurements

[0089] Based on the topology of the on-machine measurement platform, ideal error-free motion models of the on-machine measurement platform are established respectively. The actual motion model with errors on the in-machine measurement platform

[0090] like Figure 3 The diagram shown is a schematic of the on-machine measurement platform. Table 1 shows the structure of the platform. Figure 3 The corresponding component names are marked in each of the attached diagrams.

[0091] Table 1. Serial Numbers and Names of Each Section

[0092]

[0093] like Figure 4 and Figure 5 The figures show a simplified topology diagram and a simplified motion diagram of the on-machine measurement platform, respectively. During on-machine measurement, the geometric error transmission of the face gear on the on-machine measurement platform starts from each motion axis and is transmitted in a chain along the on-machine measurement probe chain and the workpiece chain, resulting in a relative pose error between the probe and the face gear at the ends of the two chains.

[0094] Specifically, the probe-side drive chain (machine base RCS → probe coordinate system PCS) is: machine base — X-axis — Z-axis — A-axis — Y-axis — probe.

[0095] The transmission chain on the side of the workpiece to be tested (machine base RCS → gear coordinate system GCS) is: machine base — C-axis — face gear.

[0096] In-machine measurement of the drive train, such as Figure 6 As shown.

[0097] Machine tool geometric errors can be divided into position-independent errors (PIGEs) and position-dependent errors (PDGEs). PIGEs are caused by assembly deviations of moving parts and are independent of the position of the motion axis; while PDGEs are repeatable errors caused by manufacturing defects of moving parts, and they change continuously with the position of the motion axis. According to the principles of spatial kinematics, each motion axis of a machine tool has six degrees of freedom under unconstrained conditions, including three linear motion degrees of freedom in the coordinate axes and three rotational motion degrees of freedom around the coordinate axes. These six errors belong to PDGEs. In addition, there is a perpendicularity error S between the X, Y, and Z motion axes. ZX S ZY S ZX These three errors belong to PIGEs. Taking the C-axis as an example, there are four PIGEs: two radial runout errors δ Cxδ Cy and deflection angle error α Cy and pitch angle error β Cx The in-machine measurement platform has a total of 42 errors, namely: 30 PDGEs and 12 PIGEs. The X-axis is mounted on the base. Assuming that there is no installation error on the X-axis, the geometric errors of the in-machine measurement platform are shown in Table 2.

[0098] Table 2 Geometric Errors of the On-Machine Measurement Platform

[0099]

[0100] δ x (X), δ y (X) and δ z (X) represents the straightness error of the X-axis in the X, Y, and Z directions, respectively; ε x (X), ε y (X) and ε z (X) represents the angular error of the X-axis in the X, Y, and Z directions, respectively;

[0101] δ x (Z), δ y (Z) and δ z (Z) represents the straightness error of the Z-axis in the X, Y, and Z directions, respectively; ε x (Z), ε y (Z) and ε z (Z) represents the angular error of the Z-axis in the X, Y, and Z directions, respectively; S ZX Indicates the perpendicularity error between the Z-axis and the X-axis; δ x (A), δ y (A) and δ z (A) represents the straightness error of axis A in the X, Y, and Z directions, respectively; ε x (A), ε y (A) and ε z (A) represents the angular error of axis A in the X, Y, and Z directions, respectively; δ Az and δ Ax These represent the radial runout errors of axis A in the Z and X directions, respectively; β Az and γ Ay These represent the perpendicularity error of the A-axis relative to the Z-axis and the perpendicularity error of the A-axis relative to the Y-axis, respectively.

[0102] δ x (Y), δ y (Y) and δ z (Y) represents the straightness error of the Y-axis in the X, Y, and Z directions, respectively; ε x (Y), ε y (Y) and ε z(Y) represents the angular error of the Y-axis in the X, Y, and Z directions, respectively; S YX Indicates the perpendicularity error between the X-axis and the Y-axis; S YZ This indicates the perpendicularity error between the Y-axis and the Z-axis;

[0103] δ x (C), δ y (C) and δ z (C) represents the straightness error of the C-axis in the X, Y, and Z directions, respectively; ε x (C), ε y (C) and ε z (C) represents the angular error of the C-axis in the X, Y, and Z directions, respectively; δ Cx and δ Cy These represent the radial runout errors of the C-axis in the X and Y directions, respectively; α Cy and β Cx These represent the perpendicularity error of the C-axis relative to the Y-axis and the perpendicularity error of the C-axis relative to the X-axis, respectively.

[0104] The kinematics of the on-machine measurement platform considering 42 geometric errors, such as Figure 7 As shown.

[0105] There is a translational offset g0 = [g] between the C-axis coordinate system and the origin of the GCS. 0x g 0y g 0z ] T There is a translational offset p0 = [p] between the Y-axis coordinate system and the origin of the PCS. 0x p 0y p 0z ] T At this point, the homogeneous transformation matrices of GCS and PCS relative to RCS are respectively:

[0106]

[0107] in, This represents the homogeneous transformation matrix of the C-axis coordinate system relative to the machine tool coordinate system; The matrix representing the homogeneous transformation of the probe coordinate system relative to the Y-axis coordinate system; g 0x g 0y and g 0z These represent the translational offsets in the X, Y, and Z directions between the C-axis coordinate system and the origin of the GCS, respectively; p 0x p 0y and p 0z These represent the translational offsets in the X, Y, and Z directions between the Y-axis coordinate system and the origin of the PCS.

[0108] The mounting pose (T) of each motion axis of the on-board measurement platform pQN), installation position error (T) peQN ), movement posture (T) mQN ), motion pose error (T) meQN The corresponding transformation matrices are shown in Table 3. In the table, Q and N represent the preceding and following components in a certain forward motion chain, respectively.

[0109] Table 3 Geometric Errors of Motion Axles

[0110]

[0111] The motion pose error matrices for each axis in the table are as follows:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117] In summary, the ideal error-free motion model of the on-machine measurement platform for:

[0118]

[0119]

[0120]

[0121] in, This represents the ideal homogeneous transformation matrix between the probe and the face gear workpiece;

[0122] This represents the ideal homogeneous transformation matrix between the machine tool base and the face gear workpiece; T represents the ideal homogeneous transformation matrix between the machine tool base and the C-axis; pRC This represents the mounting pose matrix between the machine tool base and the C-axis; T mRC This represents the motion pose matrix between the machine tool base and the C-axis; T represents the ideal homogeneous transformation matrix between the C-axis and the face gear workpiece; pCG This represents the mounting pose matrix between the C-axis and the face gear workpiece; T mCG This represents the motion pose matrix between the C-axis and the face gear workpiece;

[0123] This represents the ideal homogeneous transformation matrix between the probe and the machine tool base; T represents the ideal homogeneous transformation matrix between the machine tool base and the X-axis; pRX This represents the mounting pose matrix between the machine tool base and the X-axis; T mRX This represents the motion pose matrix between the machine tool base and the X-axis; T represents the ideal homogeneous transformation matrix between the X and Z axes; pXZ T represents the mounting pose matrix between the X and Z axes; mXZ This represents the motion pose matrix between the X and Z axes; T represents the ideal homogeneous transformation matrix between the Z-axis and the A-axis; pZA T represents the mounting pose matrix between the Z-axis and A-axis; mZA This represents the motion pose matrix between the Z-axis and the A-axis; T represents the ideal homogeneous transformation matrix between the A-axis and the Y-axis; pAY Represents the mounting pose matrix between the A-axis and the Y-axis; T mAY This represents the motion pose matrix between the A-axis and the Y-axis; T represents the ideal homogeneous transformation matrix between the Y-axis and the probe; pYP T represents the mounting pose matrix between the Y-axis and the probe; mYP This represents the motion pose matrix between the Y-axis and the probe.

[0124] The actual motion model of the on-board measurement platform has errors. for:

[0125]

[0126]

[0127]

[0128] in, This represents the actual homogeneous transformation matrix between the probe and the face gear workpiece;

[0129] This represents the actual homogeneous transformation matrix between the machine tool base and the face gear workpiece; T represents the actual homogeneous transformation matrix between the machine tool base and the C-axis; peRC This represents the mounting pose error matrix between the machine tool base and the C-axis; T meRC This represents the motion pose error matrix between the machine tool base and the C-axis; T represents the actual homogeneous transformation matrix between the C-axis and the face gear workpiece; peCG T represents the mounting pose error matrix between the C-axis and the face gear workpiece; meCG This represents the motion pose error matrix between the C-axis and the face gear workpiece;

[0130] This represents the actual homogeneous transformation matrix between the machine tool base and the probe. T represents the actual homogeneous transformation matrix between the machine tool base and the X-axis; peRX This represents the mounting pose error matrix between the machine tool base and the X-axis; T meRX This represents the motion pose error matrix between the machine tool base and the X-axis; T represents the actual homogeneous transformation matrix between the X and Z axes; peXZ T represents the mounting pose error matrix between the X and Z axes; meXZ This represents the motion pose error matrix between the X and Z axes; T represents the actual homogeneous transformation matrix between the Z-axis and the A-axis; peZA T represents the mounting pose error matrix between the Z-axis and A-axis; meZA This represents the motion pose error matrix between the Z-axis and the A-axis; T represents the actual homogeneous transformation matrix between the A-axis and the Y-axis; peAY T represents the mounting pose error matrix between the A-axis and the Y-axis; meAY This represents the motion pose error matrix between the A-axis and the Y-axis; T represents the actual homogeneous transformation matrix between the Y-axis and the probe; peYP T represents the mounting pose error matrix between the Y-axis and the probe; meYP This represents the motion pose error matrix between the Y-axis and the probe.

[0131] 13) Identification of geometric errors in in-machine measurement

[0132] Error identification of each motion axis in machine measurement can be divided into error identification of linear axes and rotational axes.

[0133] 131) Identification of geometric errors of linear axes

[0134] Geometric error equations for the X, Y, and Z axes of the machine measurement platform are constructed respectively. For example... Figure 8 As shown, this embodiment measures and identifies the geometric errors of the X, Y, and Z axes based on the 9-line method. Known point O on the measurement line. i (x Oi ,y Oi ,z Oi Move along the measuring line a set distance to reach the ideal point P. i (x i ,y i ,z i ), i = 1, 2, 3, X-axis is measured along measurement lines 1, 2, 3, Y-axis is measured along measurement lines 4, 5, 6, and Z-axis is measured along measurement lines 7, 8, 9.

[0135] The geometric error equation for the X-axis is:

[0136]

[0137] E X =[δ x (X),δ y (X),δ z (X),ε x (X),ε y (X),ε z (X)]

[0138] Δ X =[Δx1(X),Δy1(X),Δz1(X),Δx2(X),Δy2(X),Δz3(X)]

[0139]

[0140] Among them, E X B represents the geometric error matrix of the X-axis; X The geometric error identification matrix representing the X-axis; Δ X The error matrix representing the X-axis; δ x (X), δ y (X) and δ z (X) represents the linear error of the X-axis in the X, Y, and Z directions, respectively; εx(X), εy(X), and ε z (X) represents the angular error of the X-axis in the X, Y, and Z directions, respectively; Δx i (X) represents the X-axis positioning error measured when the X-axis moves along the i-th measurement path; Δy i (X) and Δz i (X) represents the straightness error measured in the Y and Z directions respectively when the X-axis moves along the i-th measurement route;

[0141] The geometric error equation for the Y-axis is:

[0142]

[0143] E Y =[δ x (Y),δ y (Y),δ z (Y),ε x (Y),ε y (Y),ε z (Y)]

[0144] Δ Y =[Δy4(Y),Δy5(Y),Δy6(Y),Δx4(Y),Δz4(Y),Δz5(Y)]

[0145]

[0146] Among them, E Y B represents the geometric error matrix along the Y-axis; Y The geometric error identification matrix representing the Y-axis; Δ Y The error matrix representing the Y-axis; δ x (Y), δ y (Y) and δ z (Y) represent the straightness errors of the Y-axis in the X, Y, and Z directions, respectively; ε x (Y), ε y (Y) and ε z (Y) represents the angular error of the Y-axis in the X, Y, and Z directions, respectively; Δy i (Y) represents the Y-axis positioning error measured when the Y-axis moves along the i-th measurement path; Δx i (Y) and Δz i (Y) represents the straightness error measured in the X and Z directions respectively when the Y-axis moves along the i-th measurement route;

[0147] The geometric error equation for the Z-axis is:

[0148]

[0149] E Z =[δ x (Z),δ y (Z),δ z (Z),ε x (Z),ε y (Z),ε z (Z)]

[0150] Δ Z =[Δz7(Z),Δz8(Z),Δz9(Z),Δx8(Z),Δy7(Z),Δx7(Z)]

[0151]

[0152] Among them, E Z B represents the geometric error matrix along the Z-axis; Z The geometric error identification matrix representing the Z-axis; Δ Z The error matrix representing the Z-axis; δ x (Z), δ y (Z) and δ z (Z) represents the linear error of the Z-axis in the X, Y, and Z directions, respectively; ε x (Z), ε y (Z) and ε z(Z) represents the angular error of the Z-axis in the X, Y, and Z directions, respectively; Δzi(Z) represents the Z-axis positioning error measured when the Z-axis moves along the i-th measurement path; Δx i (Z) and Δy i (Z) represents the straightness error measured in the Z direction and Y direction respectively when the Z-axis moves along the i-th measurement route;

[0153] x i y i and z i These represent the X-axis, Y-axis, and Z-axis coordinates of an ideal point on the measurement line, respectively.

[0154] i = 1, 2, 3, 4, 5, 6, 7, 8, 9.

[0155] The equation for the perpendicularity error between any two axes in a machine measurement platform (X-axis, Y-axis, and Z-axis) is constructed. Perpendicularity errors exist between the X-axis, Y-axis, and Z-axis, and these errors include S... ZX S YX and S YZ With S YX For example, using the straightness error δ at each measuring point... y (X) and δ x (Y), the average error line of the two straightness errors is calculated using the least squares method, such as Figure 9 As shown, if the deviation angles between these two average lines and the ideal coordinate axes are denoted as θ... x and θ y Then the equation for the perpendicularity error between the X-axis and the Y-axis is:

[0156] S YX =θ y -θ x

[0157] Similarly, the equations for the perpendicularity errors between the X and Z axes, and between the Y and Z axes, are:

[0158] S YZ =θ y -θ z

[0159] S ZX =θ z -θ x

[0160] Among them, S YX Indicates the perpendicularity error between the X-axis and the Y-axis; S YZ Indicates the perpendicularity error between the Y-axis and the Z-axis; S ZX θ represents the perpendicularity error between the Z-axis and the X-axis. x θ represents the angle of deviation between the actual trajectory and the theoretical trajectory along the X-axis.y θ represents the angle of deviation between the actual trajectory and the theoretical trajectory along the Y-axis. z This represents the deviation angle between the actual trajectory and the theoretical trajectory along the Z-axis.

[0161] The combined error after geometric error coupling was measured using a laser interferometer, and the geometric errors of the X-axis, Y-axis and Z-axis of the on-machine measurement platform were decoupled and separated using the 9-line method.

[0162] 132) Identification of geometric errors of rotating shafts

[0163] like Figure 10 As shown, using a ballbar as the measuring device, based on the functional relationship between the nominal length of the ballbar, the ballbar installation angle, the workpiece ball installation angle, the geometric error, and the measured ballbar extension during the rotation of the C-axis or A-axis of the on-machine measuring platform, inverse identification models of geometric errors for the C-axis and A-axis are established respectively. Based on the measured ballbar extension, various geometric errors of the C-axis and A-axis are identified.

[0164] Specifically, in this embodiment, the functional relationship between the nominal length of the ball shaft, the ball shaft mounting angle, the workpiece ball mounting angle, the geometric error, and the measured ball shaft extension during the rotation of the C-axis or A-axis is as follows:

[0165]

[0166] Wherein, the subscript R represents the axis of rotation, which can be replaced by A and C; L R Indicates the nominal length of the ballbar; ΔL R Represents the extension / retraction of the ballbar; θ R The angle between the axis of the cue stick and the axis of the worktable is denoted as the mounting angle; z Rω0 The height of the workpiece ball above the worktable surface; The angle between the coordinate vector of the center of the workpiece sphere and the positive x-axis is defined as the initial installation angle of the workpiece sphere; δ x (R), δ y (R) and δ z (R) represents the straightness error of the R-axis in the X, Y, and Z directions, respectively; ε x (R) and ε y (R) represents the angular error of the R-axis in the X and Y directions, respectively.

[0167] The extension / retraction of a cue corresponds to five errors δ on the axis of rotation. x (R), δ y (R), δ z (R), ε x (R) and ε y (R), therefore, multiple sets of experiments are needed to identify multiple geometric error elements. The extension / retraction of the ballbar corresponding to the i-th experiment is denoted as:

[0168] ΔL Ri =b Ri e R

[0169]

[0170] Where, ΔL iR Let b be the extension / retraction of the ballbar corresponding to the i-th test of the rotating shaft R. Ri Let e ​​be the error identification model vector corresponding to the i-th test of the rotation axis R. R Let θ be the geometric error vector of the rotation axis; Ri This represents the angle between the axis of the cue stick and the axis of the worktable during the i-th test; Let z be the angle between the coordinate vector of the center of the workpiece sphere and the positive x-axis during the i-th test, defined as the initial installation angle of the workpiece sphere; Riω0 L represents the height of the workpiece ball above the worktable surface during the i-th test. Ri This represents the nominal length of the ballbar during the i-th test.

[0171] 14) Use the identified linear axis errors and rotation axis geometric errors to compensate for in-machine measurement geometric errors.

[0172] Step 2: On-machine measurement of tooth surface error

[0173] 21) Plan measurement points on the tooth surface and obtain the tooth surface normal vector of each measurement point.

[0174] Based on the tooth surface equation of the face gear, the tooth surface measurement points are planned according to the AGMA standard. The number of grid points in the tooth surface measurement area is 9×5, that is, 9 grid points are taken in the tooth width direction and 5 grid points are taken in the tooth height direction. Figure 11 As shown, 45 tooth surface points and their corresponding normal vectors were calculated and generated using MATLAB.

[0175] 22) Use a standard sphere to calibrate the probe and rotary table separately, compensating for probe anisotropy, pre-stroke error, and radius compensation. Establish a measurement coordinate system based on the upper surface of the inner ring of the face gear, the inner ring cylindrical surface, and the midpoint of the tooth groove, such as... Figure 12 As shown.

[0176] 23) Measure each measurement point in sequence to obtain the coordinates of the probe at each measurement point, and then obtain the actual tooth surface points of the face gear at each measurement point.

[0177] In this embodiment, the measurement path planning method is as follows: when measuring the tooth profile error of the opposing gear, the probe moves according to the specified measurement path, such as... Figure 13As shown. When measuring tooth pitch error, the probe marks the center points of each tooth surface at 45°. When measuring tooth profile error and tooth pitch error, the probe approaches the gear tooth surface to be measured along the normal direction of the theoretical measurement point. When the probe contacts the tooth surface, the probe stops approaching, and the probe coordinates at this time are recorded.

[0178] 24) Based on the actual tooth surface points and theoretical tooth surface points of the face gear at each measurement point, the tooth profile error and tooth pitch error of the face gear are obtained;

[0179] 25) Based on the obtained tooth profile error and pitch error of the face gear, the face gear is adjusted and corrected in reverse.

[0180] This embodiment refers to the bevel gear standard, and uses on-machine measurement software to output the tooth surface topology diagrams before and after geometric error compensation. The relative errors of each measuring point on the flank gear before and after compensation are calculated as shown in Table 4, and the relative error topology diagrams of the two are drawn. Figure 14 As shown.

[0181] Table 4. Relative errors (μm) at various measurement points on the tooth surface before and after compensation.

[0182]

[0183]

[0184] Table 5. Sum of squared tooth surface errors SSE (μm) before and after compensation 2 )

[0185]

[0186] As shown in Table 5, the sum of squared errors (SSE) of the compensated front tooth surface is 28668.2426 μm. 2 After compensation, it was reduced to 28456.3136μm. 2 The measurement accuracy was improved by 7.428%. In summary, these results demonstrate that geometric error compensation effectively improves the measurement accuracy across the entire tooth surface.

[0187] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for on-machine measurement and correction of machining errors of face gear teeth considering geometric errors, characterized in that: Includes the following steps: Step 1: In-machine measurement geometric error compensation 11) Setting up an on-machine measurement platform: The on-machine measurement platform includes a gear grinding machine, a probe, and a signal receiving device. The probe is mounted on the Y-axis of the gear grinding machine, and the signal receiving device is connected to the probe and the gear grinding machine respectively via signal lines. 12) Modeling geometric errors in on-machine measurements Based on the topology of the on-machine measurement platform, ideal error-free motion models of the on-machine measurement platform are established respectively. The actual motion model with errors on the in-machine measurement platform ; 13) Identification of geometric errors in in-machine measurement 131) Identification of geometric errors of linear axes Geometric error equations for the X, Y, and Z axes of the on-machine measurement platform are constructed respectively; The equation for the perpendicularity error between any two axes in the X-axis, Y-axis and Z-axis of the machine measurement platform is constructed. The combined error after geometric error coupling was measured using a laser interferometer, and the geometric errors of the X-axis, Y-axis and Z-axis of the on-machine measurement platform were decoupled and separated using the 9-line method. 132) Identification of geometric errors of rotating shafts Using a ballbar as the measuring device, based on the functional relationship between the nominal length of the ballbar, the ballbar installation angle, the workpiece ball installation angle, the geometric error, and the measured ballbar extension during the rotation of the C-axis or A-axis of the on-machine measuring platform, inverse identification models of geometric errors for the C-axis and A-axis are established respectively. Based on the measured ballbar extension, various geometric errors of the C-axis and A-axis are identified. The functional relationship between the nominal length of the ball shaft, the ball shaft mounting angle, the workpiece ball mounting angle, the geometric error, and the measured ball shaft extension / retraction during the rotation of the C-axis or A-axis is as follows: In this context, the subscript R represents the axis of rotation, which can be replaced by A and C; Indicates the nominal length of the ballbar; This represents the extension / retraction of the ball bar. The angle between the axis of the cue stick and the axis of the worktable is denoted as the installation angle; The height of the workpiece ball above the worktable surface; The angle between the coordinate vector of the center of the workpiece sphere and the positive x-axis is defined as the initial installation angle of the workpiece sphere. , and This represents the straightness error of the R-axis in the X, Y, and Z directions, respectively. and These represent the angular errors of the R-axis in the X and Y directions, respectively; 14) Use the identified geometric errors of the linear axis and the rotation axis to compensate for the geometric errors in in-machine measurement; Step 2: On-machine measurement of tooth surface error 21) Plan measurement points on the tooth surface and obtain the tooth surface normal vector of each measurement point; 22) Use a standard ball to calibrate the probe and the rotary table respectively, and establish a measurement coordinate system based on the upper surface of the inner ring of the face gear, the cylindrical surface of the inner ring, and the midpoint of the tooth groove; 23) Measure each measurement point in sequence to obtain the coordinates of the probe at each measurement point, and then obtain the actual tooth surface points of the face gear at each measurement point; 24) Based on the actual tooth surface points and theoretical tooth surface points of the face gear at each measurement point, the tooth profile error and tooth pitch error of the face gear are obtained; 25) Based on the obtained face gear tooth profile error and pitch error, the face gear is reverse-adjusted and corrected.

2. The method for on-machine measurement and correction of gear tooth surface machining error considering geometric errors according to claim 1, characterized in that: In step 12), the ideal error-free motion model of the on-board measurement platform is... for: in, This represents the ideal homogeneous transformation matrix between the probe and the face gear workpiece; This represents the ideal homogeneous transformation matrix between the machine tool base and the face gear workpiece; This represents the ideal homogeneous transformation matrix between the machine tool base and the C-axis. This represents the mounting pose matrix between the machine tool base and the C-axis; This represents the motion pose matrix between the machine tool base and the C-axis; This represents the ideal homogeneous transformation matrix between the C-axis and the face gear workpiece; This represents the mounting pose matrix between the C-axis and the face gear workpiece; This represents the motion pose matrix between the C-axis and the face gear workpiece; This represents the ideal homogeneous transformation matrix between the probe and the machine tool base; This represents the ideal homogeneous transformation matrix between the machine tool base and the X-axis. This represents the mounting pose matrix between the machine tool base and the X-axis; This represents the motion pose matrix between the machine tool base and the X-axis; This represents the ideal homogeneous transformation matrix between the X-axis and the Z-axis. This represents the mounting pose matrix between the X and Z axes; This represents the motion pose matrix between the X and Z axes; This represents the ideal homogeneous transformation matrix between the Z-axis and the A-axis; This represents the mounting pose matrix between the Z-axis and the A-axis; This represents the motion pose matrix between the Z-axis and the A-axis; This represents the ideal homogeneous transformation matrix between the A-axis and the Y-axis; This represents the mounting pose matrix between the A-axis and the Y-axis; This represents the motion pose matrix between the A-axis and the Y-axis; This represents the ideal homogeneous transformation matrix between the Y-axis and the probe; This represents the mounting pose matrix between the Y-axis and the probe; This represents the motion pose matrix between the Y-axis and the probe; The actual motion model of the on-board measurement platform has errors. for: in, This represents the actual homogeneous transformation matrix between the probe and the face gear workpiece; This represents the actual homogeneous transformation matrix between the machine tool base and the face gear workpiece; This represents the actual homogeneous transformation matrix between the machine tool base and the C-axis. This represents the mounting posture error matrix between the machine tool base and the C-axis; This represents the motion pose error matrix between the machine tool base and the C-axis; This represents the actual homogeneous transformation matrix between the C-axis and the face gear workpiece; This represents the mounting pose error matrix between the C-axis and the face gear workpiece; This represents the motion pose error matrix between the C-axis and the face gear workpiece; This represents the actual homogeneous transformation matrix between the machine tool base and the probe. This represents the actual homogeneous transformation matrix between the machine tool base and the X-axis. This represents the mounting pose error matrix between the machine tool base and the X-axis; This represents the motion pose error matrix between the machine tool base and the X-axis; This represents the actual homogeneous transformation matrix between the X-axis and the Z-axis. This represents the mounting pose error matrix between the X and Z axes; This represents the motion pose error matrix between the X and Z axes; This represents the actual homogeneous transformation matrix between the Z-axis and the A-axis; This represents the mounting pose error matrix between the Z-axis and the A-axis; This represents the motion pose error matrix between the Z-axis and the A-axis; This represents the actual homogeneous transformation matrix between the A-axis and the Y-axis; This represents the mounting pose error matrix between the A-axis and the Y-axis; This represents the motion pose error matrix between the A-axis and the Y-axis; This represents the actual homogeneous transformation matrix between the Y-axis and the probe; This represents the mounting pose error matrix between the Y-axis and the probe; This represents the motion pose error matrix between the Y-axis and the probe.

3. The method for on-machine measurement and correction of gear tooth surface machining error considering geometric errors according to claim 1, characterized in that: In step 131), the geometric error equation for the X-axis is: in, The geometric error matrix representing the X-axis; The geometric error identification matrix representing the X-axis; The error matrix representing the X-axis; , and These represent the linear errors of the X-axis in the X, Y, and Z directions, respectively. , and These represent the angular errors of the X-axis in the X, Y, and Z directions, respectively. Indicates the X-axis along the first i The X-axis positioning error measured during the movement of the measurement route; and Indicates the X-axis along the first i The straightness error measured in the Y and Z directions respectively during the movement of the measurement route; The geometric error equation for the Y-axis is: in, Represents the geometric error matrix along the Y-axis; The geometric error identification matrix representing the Y-axis; Represents the error matrix along the Y-axis; , and These represent the linear errors of the Y-axis in the X, Y, and Z directions, respectively. , and These represent the angular errors of the Y-axis in the X, Y, and Z directions, respectively. Indicates the Y-axis along the first i The Y-axis positioning error measured during the movement of the measurement route; and Indicates the Y-axis along the first i The straightness error measured in the X and Z directions respectively during the movement of the measurement route; The geometric error equation for the Z-axis is: in, Represents the geometric error matrix along the Z-axis; The geometric error identification matrix representing the Z-axis; Represents the error matrix along the Z-axis; , and These represent the linear errors of the Z-axis in the X, Y, and Z directions, respectively. , and These represent the angular errors of the Z-axis in the X, Y, and Z directions, respectively. Indicates the Z-axis along the first i The Z-axis positioning error measured during the movement of the measurement route; and Indicates the Z-axis along the first i The straightness error measured in the Z and Y directions respectively during the movement of the measurement route; , and These represent the X-axis, Y-axis, and Z-axis coordinates of an ideal point on the measurement line, respectively. i =1,2,3,4,5,6,7,8,9.

4. The method for on-machine measurement and correction of gear tooth surface machining error considering geometric errors according to claim 1, characterized in that: In step 131), the equation for the perpendicularity error between the X-axis and the Y-axis is: in, This indicates the perpendicularity error between the X-axis and the Y-axis; This indicates the perpendicularity error between the Y-axis and the Z-axis; This indicates the perpendicularity error between the Z-axis and the X-axis; This represents the deviation angle between the actual trajectory and the theoretical trajectory along the X-axis; This represents the deviation angle between the actual trajectory and the theoretical trajectory along the Y-axis; This represents the deviation angle between the actual trajectory and the theoretical trajectory along the Z-axis.

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