Error identification method of double-crank RSSR mechanism measured by hobbing machine ball bar

Abstract

The present application relates to the error identification method of double-crank RSSR mechanism measured by hobbing machine ball bar, and belongs to the technical field of machine tool precision detection. It comprises: the construction of the measurement mechanism model of the hobbing machine ball bar; the degeneration of the measurement mechanism model of the hobbing machine ball bar into a double-crank spatial four-bar mechanism; taking the difference between the extreme values of the linkage mapping angle as the objective function, and taking the length conditions of the measured double-crank spatial four-bar mechanism model as the constraint, the optimal installation position parameters are obtained by optimizing the ball bar installation position parameters; measurement mechanism parameter identification and test result analysis: based on the optimal installation position parameters, the actual installation and measurement are carried out, and the actual data of the ball bar are collected; a parameter identification model is established, and the real structure parameters of the double-crank spatial four-bar mechanism model are identified by inversion, which is used to realize the parameter identification of the installation error and the machine tool motion error; the present application improves the effectiveness of the double-crank spatial four-bar mechanism synthesis and parameter identification method measured by the hobbing machine ball bar.

Description

Technical Field

[0001] This invention relates to a method for identifying errors in a double-crank RSSR mechanism measured by a ballbar gauge for a gear scraper, belonging to the field of machine tool precision testing technology. Background Technology

[0002] The spindle of the gear scraper and the rotary axis of the workpiece table both rotate a full circle and are coupled into generating motion. However, the motion accuracy of the gear scraper needs to cover these working conditions, and currently there is no mature and effective motion accuracy measurement technology or evaluation method. The ballbar is a new type of instrument for measuring the motion accuracy of machine tools, currently commonly used in multi-axis linkage measurement in machining centers. Its kinematic principle is to combine the spatial link assembly (SPS) with the machine tool kinematic chain to form a multi-degree-of-freedom spatial mechanism, establishing a multi-axis machine tool ballbar measurement mechanism model and motion geometry evaluation method. Therefore, this method is extended to gear machining tools to provide a theoretical model for the installation position design, associated motion configuration, and error identification of the ballbar measurement for gear scraper motion accuracy. However, no research reports have been found on the establishment of spatial mechanism models for ballbar measurement of gear scrapers, such as dimensional synthesis and error identification. Therefore, a method for error identification of the double-crank RSSR mechanism for ballbar measurement of gear scrapers is needed to improve the accuracy detection level of gear machining tools. Summary of the Invention

[0003] This invention provides a method for identifying errors in a double-crank RSSR mechanism measured by a ballbar gauge on a gear scraper, in order to improve the accuracy detection level of gear processing machine tools.

[0004] The technical solution of this invention is: a method for identifying errors in a double-crank RSSR mechanism measured by a ballbar measuring instrument for a gear scraper, the method comprising:

[0005] S1. Construction of the ball bar measuring mechanism model for the gear scraper: The tool spindle rotary joint, the workpiece table rotary joint, and the ball bar spatial rod of the gear scraper are combined into a multi-degree-of-freedom spatial mechanism to construct the RSPSR model of the ball bar measuring mechanism for generating gears.

[0006] S2. The ballbar measuring mechanism model of the scraper is degenerated into a double-crank spatial four-bar mechanism RSSR: the ballbar spatial bar group is treated as a rigid component and degenerated into a double-crank spatial four-bar mechanism RSSR model;

[0007] S3. Optimization of the RSSR model of the double-crank spatial four-bar linkage: Taking the minimum difference of the extreme values ​​of the link mapping angle as the objective function and the link length condition of the RSSR model of the double-crank spatial four-bar linkage as the constraint, the installation position parameters of the ball bar are optimized to obtain the optimal installation position parameters.

[0008] S4. Measurement Mechanism Parameter Identification and Test Result Analysis: Based on the optimal installation position parameters, actual installation and measurement are carried out, and actual data of the ballbar are collected; a parameter identification model is established, and the real structural parameters of the double crank spatial four-bar linkage RSSR model are identified by inversion, which is used to realize the parameter identification of installation error and machine tool motion error.

[0009] Further, S1 includes:

[0010] The ball bar measuring instrument for a gear scraper measures the two rotating shafts of the gear scraper. The measuring mechanism of the ball bar measuring instrument for a gear scraper includes components and components. ,member ,member ,member ; Specific components, parts ,member ,member ,member These correspond to the frame, base ball assembly, spindle ball assembly, measuring rod body, and data acquisition unit, respectively; the input parameters for the ball bar measuring mechanism of the scraper machine are the components. The rotation angle θ1 and the component Relative to components The rotation angles θ2, θ1, and θ2 relative to the drive rotation angles θ of the two rotary axes of the machine tool 1A and θ 2C The following relationship exists:

[0011] (1);

[0012] Where, θ C1 and θ C2 The installation phase of the fixed and moving ball points relative to the initial rotation angle of the rotary axis of the gear scraping machine;

[0013] Based on the DH coordinate system convention, the coordinate systems of each component of the ballbar measuring mechanism of the scraper machine are established as follows: a moving coordinate system {B; i1, j1, k1} is established through the fixed ball center E; a moving coordinate system {A; i2, j2, k2} is established through the moving ball center F; and a fixed coordinate system {B0; X; ...} is established with component l0 as the frame. f Y f Z f}, {B0; X f Y f Z f{A; i1, j1, k1} and {B; i2, j2, k2} are fixed coordinate systems, fixed on the rigid body. i1, j1, k1 and i2, j2, k2 are the axes of the motion coordinate systems established through the fixed center E and the moving center F, respectively. They translate and rotate with the rigid body, their directions changing with time, exhibiting relative motion. The length of the frame A0B0 is l0, corresponding to vector l0. The unit vectors of the two rotary joint axes on the frame are k1 and k2, with a fixed angle α0 between them. The two connecting rods B0... The lengths of E and A0F are l1 and l2, respectively, corresponding to vectors l1 and l2, and they form fixed angles α1 and α2 with their axes k1 and k2, respectively, and rotate around their respective axes by angles θ1 and θ2, respectively; the length of the link EF containing the sliding joint P is d, corresponding to vector d and the mapping angle α3, and all components form a spatial closed loop A0B0EPF; the scraper ball bar measuring mechanism model RSPSR consists of 8 structural parameters, namely l0, l1, l2, d, α0, α1, α2, α3, and the coordinate positions of the two ball centers, the fixed ball center E and the moving ball center F, are represented by R. E (x) E y E , z E ) and R F (x) F y F , z F The closed-loop vector equations of the RSPSR measuring mechanism model of the scraper ballbar are established from the vectors of each link:

[0014] (2);

[0015] Taking the molds from both sides of equation (2), we obtain the basic displacement equation of the RSPSR model of the ball bar measuring mechanism of the tooth scraper:

[0016] (3);

[0017] in:

[0018] (4);

[0019] The length of the ballbar is given by equations (3) and (4), which are the kinematic equations of the two-axis motion ballbar measuring mechanism of the scraper. The kinematic geometric relationship between its structural parameters, input drive parameters and output measurement parameters is established. There are 8 dimensional parameters of the mechanism: l0, l1, l2, d, α0, α1, α2, α3. Among them, (l0, α0) corresponds to the structural parameters of the two axes C1 and C2, respectively representing R. C1 axis and R C2The length and included angle of the common perpendicular between the axes; given the structural parameters of the measuring mechanism, with the independent variables inputting the rotation angles θ1 and θ2, solve for the output parameter d of the RSPSR measuring mechanism model of the scraper ball bar instrument;

[0020] When the two C-axis move ideally, that is, when they only rotate around their axes, the output parameter d is a function of the independent variables θ1 and θ2. Moreover, θ1 and θ2 are independent variables, and the energy numbers exhibit different functions, so the output parameter d is a different function. When the distance between the moving ball point and the stationary ball point remains unchanged, the output parameter d is a constant.

[0021] Furthermore, S2 specifically includes:

[0022] The measuring rod assembly SPS is degenerated into a single rod with two sets of SS, and the measuring mechanism model RSPSR of the scraper ballbar is degenerated into a double-crank spatial four-bar linkage RSSR, with the two axes C1 and C2 forming an active and passive constraint relationship. The double-crank spatial four-bar linkage RSSR is a single-degree-of-freedom mechanism, requiring only one rotation axis to be driven independently, while the motion of the other rotation axis is solved by the kinematics of the mechanism. However, in actual measurement, both axes are driven independently, but the rotation angles of the two axes must conform to the kinematic relationship of the RSSR mechanism.

[0023] The scraper ball bar measuring mechanism model RSPSR and the double crank spatial four-bar linkage RSSR have structural parameters, where (l0, l1, l2, d, α0, α1, α2, α3), and the coordinate parameters of the two ball points are (l1, α1) and (l2, α2). In order to solve the input and output function relationship of the double crank spatial four-bar linkage RSSR, the function relationship between the two connecting rod rotation angle variables θ1 and θ2 is derived according to equation (3):

[0024] (5)

[0025] in:

[0026] (6)

[0027] Equations (5) and (6) establish the functional relationship between the input and output parameters θ1 and θ2 of the double-crank spatial four-bar linkage RSSR. Substituting these parameters into equation (1), the driving angles θ of the two rotating shafts of the double-crank spatial four-bar linkage RSSR are obtained. 1A and θ 2C .

[0028] Furthermore, S3 specifically includes:

[0029] The RSSR model of the double-crank spatial four-bar linkage keeps the distance between the fixed ball point and the moving ball point constant, so that the actual motion range of the ballbar measuring kinematic pair P is used to measure the motion error of the two linkage axes; the rotation angle of the machine tool C1 axis corresponds to the crank B'F position of the ballbar measuring mechanism, and the rotation angle of the machine tool C2 axis corresponds to the crank O'E position of the ballbar measuring mechanism.

[0030] First, determine the coordinate positions of the X, Y, and Z axes of the machine tool to achieve precise feed by working together. Second, set the parameters of the ballbar measuring mechanism and establish a fixed coordinate system {C2; X...} at point O on the rotation axis of the tool spindle C2. f Y f Z f Establish a motion coordinate system {O'; i1, j1, k1} through the center E of the sphere, and establish a motion coordinate system {B'; i2, j2, k2} through the center F of the sphere.

[0031] The ballbar measuring mechanism of the scraper includes connecting rod BB', connecting rod OO', frame OB, connecting rod O'E, connecting rod B'F, ​​and connecting rod EF; their lengths are denoted as a0, a1, l0, l1, l2, and p, respectively; the two input parameters θ1 and θ2 represent the rotation angles of connecting rod O'E and connecting rod B'F, ​​and the rotation angles θ of the two rotating shafts of the scraper, respectively. 1A θ 2C The installation phase of the fixed and moving ball points of the ball bar relative to the initial rotation angle of the rotary axis of the gear scraping machine, i.e., the driving angle θ of the fixed and moving ball points relative to the two rotary axes of the machine tool. C1 and θ C2 ;

[0032] The ballbar measuring mechanism for a gear scraping machine includes the ballbar measuring rod assembly (SPS) and the kinematic chain of the machine tool under test. The motion synthesis of this measuring mechanism determines the installation positions of the fixed and moving ball points of the ballbar, thereby obtaining the dimensions of the measuring mechanism. The centers of the two S-joints of the ballbar are respectively installed on the fixed ball point (r) on the cutting tool O'E. Ef θ Ef , z Ef ) and the moving ball point (r) on the workbench B'F Fk θ Fk , z Fk To ensure the ballbar is installed at the extreme position of the mapping angle α3, i.e., when plane OO'E and plane OEF are coplanar, the objective function is to minimize the difference between the extreme values ​​of the link mapping angle α3, and the constraint is the length of the measuring mechanism. The ballbar installation position parameters are optimized, and the following optimization comprehensive model is established:

[0033] (7)

[0034] in:

[0035] objective function The difference in the connecting rod mapping angle α3 is minimized when the crank of the measuring mechanism rotates one revolution, where i is the number of discrete positions and n is the number of measurement positions;

[0036] Optimize variables The installation position parameters of the ballbar in the measuring mechanism are defined as shown in equation (7) of the optimization synthesis model;

[0037] Optimize constraints: For rod length l OF The minimum value is reached when the crank of the measuring mechanism moves to a position where plane O'EE and plane OEF are coplanar. and maximum value ; To calculate the time required for the measuring mechanism to achieve a full revolution The length of the rod; To determine the range of values ​​for α3 when the crank of the measuring mechanism achieves a full revolution;

[0038] In the synthesis of ballbar measuring mechanism, the input and output parameters achieve full rotation. Based on the kinematic equations of the two-axis ballbar measuring mechanism of the gear processing machine tool, the kinematic geometric relationship between structural parameters, input drive parameters and output measurement parameters must be established. The conversion of spur gear machining conditions is achieved by adjusting the tool spindle tilt angle α3, so as to meet the machining conditions of spur gears. The crank must also be present during the motion.

[0039] Furthermore, S4 specifically includes:

[0040] Substituting the input parameters of the RSSR model of the double-crank spatial four-bar linkage into equation (3), the corresponding theoretical output data are calculated. ， i=1,2,…n; simultaneously, the corresponding rotation angle data of the two axes of the scraper are given. , i=1,2,…n, representing the rotation angles of the scraper tool's rotary axis and the worktable's rotary axis at measurement point i, i=1,2,…n. The ballbar outputs the measurement data. Formula (3) is used to calculate the discrete length of the ballbar. The output data belongs to the RSSR model of a double-crank spatial four-bar linkage under given ballbar installation parameters, and has calculation conditions, while the ballbar measurement data... This is actual data, measured by a ball bar. and bar length The difference between the two reflects the error in the mechanism parameters. To obtain the actual mechanism parameters, a mechanism parameter identification model is established as follows:

[0041] (8)

[0042] In the above formula (8), For data measured by the ball bar instrument The maximum deviation between the calculated values ​​and those of the RSSR model of the double-crank spatial four-bar linkage; i is the number of discrete positions, n is the number of measured positions; the optimization variables are... Objective function For data measured by the ball bar instrument The calculated discrete bar length The absolute value of the difference; st represents the constraints on the structural parameters, and the discrete data of the ballbar theoretical values. The calculation formula is as follows:

[0043] (9)

[0044] in , The calculation formula is as follows:

[0045] (10).

[0046] The present invention also provides an error identification system for a double-crank RSSR mechanism measured by a ballbar for a gear scraper, the system comprising: a module for performing the error identification method for a double-crank RSSR mechanism measured by a ballbar for a gear scraper.

[0047] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements a method for identifying the error of a double crank RSSR mechanism measured by the ball bar of the scraper.

[0048] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements a method for identifying errors in a double-crank RSSR mechanism measured by the ballbar of the scraper.

[0049] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements a method for identifying errors in a double-crank RSSR mechanism measured by the ballbar of the scraper.

[0050] The beneficial effects of this invention are as follows: This invention constructs a unified model of the ballbar measuring mechanism for a gear scraper, providing a design method for the ballbar's measurement motion and installation position; the mechanism model and design method proposed in this invention are correct and effective. Based on the parameter identification method of the double-crank RSSR mechanism, it verifies that the actual measurement data shows stability in the face of interference factors such as installation errors, providing an effective solution for improving gear machining accuracy. Attached Figure Description

[0051] Figure 1This is a schematic diagram of the measuring structure of the ball bar instrument for the scraper machine of the present invention;

[0052] Figure 2 This is a simplified diagram of the mechanism for measuring and machining spur gears using the ball bar instrument of the scraper machine according to the present invention;

[0053] Figure 3 This is a simplified diagram of the RSPSR mechanism model measured by the ballbar of the scraper machine according to the present invention;

[0054] Figure 4 This is a simplified diagram of the mechanism for measuring the degraded RSSR using the ball bar instrument of the scraper machine according to the present invention;

[0055] Figure 5 This is a graph showing the measurement data of the ball bar instrument for the scraper machine of the present invention.

[0056] Figure 1 Chinese labels:

[0057] 101-Column, 102-Bed, 103-Worktable, 104-Slide, 105-Tool Post. Detailed Implementation

[0058] Example 1: As Figures 1-5 As shown, the method for identifying errors in a double-crank RSSR mechanism measured by a ballbar for a gear scraper includes:

[0059] S1. Construction of the ball bar measuring mechanism model for the gear scraper: The tool spindle rotary joint, the workpiece table rotary joint, and the ball bar spatial rod of the gear scraper are combined into a multi-degree-of-freedom spatial mechanism to construct the RSPSR model of the ball bar measuring mechanism for generating gears.

[0060] S2. The ballbar measuring mechanism model of the scraper is degenerated into a double-crank spatial four-bar mechanism RSSR: the ballbar spatial bar group is treated as a rigid component and degenerated into a double-crank spatial four-bar mechanism RSSR model;

[0061] S3. Optimization of the RSSR model of the double-crank spatial four-bar linkage: Taking the minimum difference of the extreme values ​​of the link mapping angle as the objective function and the link length condition of the RSSR model of the double-crank spatial four-bar linkage as the constraint, the installation position parameters of the ball bar are optimized to obtain the optimal installation position parameters.

[0062] S4. Measurement Mechanism Parameter Identification and Test Result Analysis: Based on the optimal installation position parameters, actual installation and measurement are carried out, and actual data of the ballbar are collected; a parameter identification model is established, and the real structural parameters of the double crank spatial four-bar linkage RSSR model are identified by inversion, which is used to realize the parameter identification of installation error and machine tool motion error.

[0063] Further, S1 includes:

[0064] The established model of the ballbar measuring mechanism of the tooth scraper is as follows: RSPSR Figure 1 As shown, gear scraping involves the cutting tool and workpiece rotating at an angle to each other, with both rotating around their own axes. The cutting tool spindle and the workpiece table of the gear scraping machine can rotate in coordination—achieving the generating motion in gear machining. Figure 1 In this design, the bed 102 serves as the basic component of the machine; the column 101 and the worktable 103 are mounted on the bed 102; the slide 104 is mounted on the column 101; the tool post 105 is mounted on the slide 104; and the ballbar connects the worktable 103 and the tool post 105 to measure their relative motion. , , These are the linear feed axes along the X, Y, and Z axes of the machine tool coordinate system, respectively. A is the oscillating axis rotating around the Y-axis, corresponding to the rotary motion axis of the tool holder. It is the C-axis at the end of the worktable, that is, the workpiece spindle rotation axis, which drives the workpiece being measured to perform a circular rotational motion. It is the C-axis at the tool tip, that is, the rotation axis of the tool holder spindle, which drives the measuring head / tool ​​to rotate. This is the radial direction error / feed motion error of the ballbar, used to detect positional deviation in this measurement direction. This refers to the axial direction error / perpendicularity / positioning error of the ballbar, used to detect geometric accuracy deviations along the measurement path. For example... Figure 2 The simplified diagram shown corresponds to the machining condition of a spur gear measured by a ball bar instrument on a gear scraper. The ball bar instrument measuring mechanism of the gear scraper, which measures the two rotating shafts of the gear scraper, includes component parts and components. ,member ,member ,member ; Specific components, parts ,member ,member ,member These correspond to the frame, base ball assembly, spindle ball assembly, measuring rod body, and data acquisition unit, respectively; the input parameters for the ball bar measuring mechanism of the scraper machine are the components. The rotation angle θ1 and the component Relative to components The rotation angles θ2, θ1, and θ2 relative to the drive rotation angles θ of the two rotary axes of the machine tool 1A and θ 2C The following relationship exists:

[0065] (1);

[0066] Where, θ C1 and θ C2 The installation phase of the fixed and moving ball points relative to the initial rotation angle of the rotary axis of the gear scraping machine;

[0067] Based on the DH coordinate system convention, the coordinate systems of each component of the ballbar measuring mechanism of the scraper machine are established as follows: a moving coordinate system {B; i1, j1, k1} is established through the fixed ball center E; a moving coordinate system {A; i2, j2, k2} is established through the moving ball center F; and a fixed coordinate system {B0; X; ...} is established with component l0 as the frame. f Y f Z f}, {B0; X f Y f Z f {A; i1, j1, k1} and {B; i2, j2, k2} are fixed coordinate systems, fixed on the rigid body. i1, j1, k1 and i2, j2, k2 are the axes of the motion coordinate systems established through the fixed center E and the moving center F, respectively. They translate and rotate with the rigid body, their directions changing with time, exhibiting relative motion. The length of the frame A0B0 is l0, corresponding to vector l0. The unit vectors of the two rotary joint axes on the frame are k1 and k2, with a fixed angle α0 between them. The two connecting rods B0... The lengths of E and A0F are l1 and l2, respectively, corresponding to vectors l1 and l2, and they form fixed angles α1 and α2 with their axes k1 and k2, respectively, and rotate around their respective axes by angles θ1 and θ2, respectively; the length of the link EF containing the sliding joint P is d, corresponding to vector d and the mapping angle α3, and all components form a spatial closed loop A0B0EPF; the scraper ball bar measuring mechanism model RSPSR consists of 8 structural parameters, namely l0, l1, l2, d, α0, α1, α2, α3, and the coordinate positions of the two ball centers, the fixed ball center E and the moving ball center F, are represented by R. E (x) E y E , z E ) and R F (x) F y F , z F The closed-loop vector equations of the RSPSR measuring mechanism model of the scraper ballbar are established from the vectors of each link:

[0068] (2);

[0069] Taking the molds from both sides of equation (2), we obtain the basic displacement equation of the RSPSR model of the ball bar measuring mechanism of the tooth scraper:

[0070] (3);

[0071] in:

[0072] (4);

[0073] The length of the ballbar is given by equations (3) and (4), which are the kinematic equations of the two-axis motion ballbar measuring mechanism of the scraper. The kinematic geometric relationship between its structural parameters, input drive parameters and output measurement parameters is established. There are 8 dimensional parameters of the mechanism: l0, l1, l2, d, α0, α1, α2, α3. Among them, (l0, α0) corresponds to the structural parameters of the two axes C1 and C2, respectively representing R. C1 axis and R C2 The length and included angle of the common perpendicular between the axes; given the structural parameters of the measuring mechanism, with the independent variables inputting the rotation angles θ1 and θ2, solve for the output parameter d of the RSPSR measuring mechanism model of the scraper ball bar instrument;

[0074] When the two C-axis move ideally, that is, when they only rotate around their axes, the output parameter d is a function of the independent variables θ1 and θ2. Moreover, θ1 and θ2 are independent variables, and the energy numbers exhibit different functions, so the output parameter d is a different function. When the distance between the moving ball point and the stationary ball point remains unchanged, the output parameter d is a constant.

[0075] Furthermore, S2 specifically includes:

[0076] The measuring rod assembly SPS is degenerated into a one-bar, two-bar (SS) structure, and the scraper ballbar measuring mechanism model RSPSR is degenerated into a double-crank spatial four-bar (RSSR) mechanism, with the two axes C1 and C2 forming an active and passive constraint relationship; for example Figure 4 As shown, the double-crank spatial four-bar linkage RSSR is a single-degree-of-freedom mechanism, requiring only one rotation axis to be driven independently, while the motion of the other rotation axis is solved by kinematics. However, in actual measurement, both axes are driven independently, but their rotation angles must conform to the kinematic relationship of the RSSR mechanism. Figure 3 and Figure 4 In the diagram, A and B are the two rotary axes of the machine tool: the motion law of the two rotary axes of the machine tool was analyzed, and the RSPSR measuring mechanism model of the ball bar instrument of the gear scraper was established;

[0077] The scraper ball bar measuring mechanism model RSPSR and the double crank spatial four-bar linkage RSSR have structural parameters, where (l0, l1, l2, d, α0, α1, α2, α3), and the coordinate parameters of the two ball points are (l1, α1) and (l2, α2). In order to solve the input and output function relationship of the double crank spatial four-bar linkage RSSR, the function relationship between the two connecting rod rotation angle variables θ1 and θ2 is derived according to equation (3):

[0078] (5)

[0079] in:

[0080] (6)

[0081] Equations (5) and (6) establish the functional relationship between the input and output parameters θ1 and θ2 of the double-crank spatial four-bar linkage RSSR. Substituting these parameters into equation (1), the driving angles θ of the two rotating shafts of the double-crank spatial four-bar linkage RSSR are obtained. 1A and θ 2C .

[0082] Furthermore, S3 specifically includes:

[0083] The RSSR model of the double-crank spatial four-bar linkage keeps the distance between the fixed ball point and the moving ball point constant, so that the actual motion range of the ballbar measuring kinematic pair P is used to measure the motion error of the two linkage axes; the rotation angle of the machine tool C1 axis corresponds to the crank B'F position of the ballbar measuring mechanism, and the rotation angle of the machine tool C2 axis corresponds to the crank O'E position of the ballbar measuring mechanism.

[0084] First, determine the coordinate positions of the X, Y, and Z axes of the machine tool to achieve precise feed by working together. Second, set the parameters of the ballbar measuring mechanism and establish a fixed coordinate system {C2; X...} at point O on the rotation axis of the tool spindle C2. f Y f Z f Establish a motion coordinate system {O'; i1, j1, k1} through the center E of the sphere, and establish a motion coordinate system {B'; i2, j2, k2} through the center F of the sphere, as follows. Figure 2 As shown, no further details will be provided;

[0085] The ballbar measuring mechanism of the scraper includes connecting rod BB', connecting rod OO', frame OB, connecting rod O'E, connecting rod B'F, ​​and connecting rod EF; their lengths are denoted as a0, a1, l0, l1, l2, and p, respectively; the two input parameters θ1 and θ2 represent the rotation angles of connecting rod O'E and connecting rod B'F, ​​and the rotation angles θ of the two rotating shafts of the scraper, respectively. 1A θ 2C The installation phase of the fixed and moving ball points of the ball bar relative to the initial rotation angle of the rotary axis of the gear scraping machine, i.e., the driving angle θ of the fixed and moving ball points relative to the two rotary axes of the machine tool. C1 and θ C2 ;

[0086] Table 1 lists the main technical specifications of the CNC gear scraping machine tool and the technical parameters of the RENISHAW ballbar.

[0087] The ballbar measuring mechanism for a gear scraping machine includes the ballbar measuring rod assembly (SPS) and the kinematic chain of the machine tool under test. The motion synthesis of this measuring mechanism determines the installation positions of the fixed and moving ball points of the ballbar, thereby obtaining the dimensions of the measuring mechanism. The centers of the two S-joints of the ballbar are respectively installed on the fixed ball point (r) on the cutting tool O'E. Ef θ Ef , zEf ) and the moving ball point (r) on the workbench B'F Fk θ Fk , z Fk To ensure the ballbar is installed at the extreme position of the mapping angle α3, i.e., when plane OO'E and plane OEF are coplanar, the objective function is to minimize the difference between the extreme values ​​of the link mapping angle α3, and the constraint is the length of the measuring mechanism. The ballbar installation position parameters are optimized, and the following optimization comprehensive model is established:

[0088] (7)

[0089] in:

[0090] objective function The difference in the connecting rod mapping angle α3 is minimized when the crank of the measuring mechanism rotates one revolution, where i is the number of discrete positions and n is the number of measurement positions;

[0091] Optimize variables The installation position parameters of the ballbar in the measuring mechanism are defined as shown in equation (7) of the optimization synthesis model;

[0092] Optimize constraints: For rod length l OF The minimum value is reached when the crank of the measuring mechanism moves to a position where plane O'EE and plane OEF are coplanar. and maximum value ; To calculate the time required for the measuring mechanism to achieve a full revolution The length of the rod; To determine the range of values ​​for α3 when the crank of the measuring mechanism achieves a full revolution;

[0093] In the synthesis of ballbar measuring mechanism, the input and output parameters achieve full rotation. Based on the kinematic equations of the two-axis ballbar measuring mechanism of the gear processing machine tool, the kinematic geometric relationship between structural parameters, input drive parameters and output measurement parameters must be established. The conversion of spur gear machining conditions is achieved by adjusting the tool spindle tilt angle α3, so as to meet the machining conditions of spur gears. The crank must also be present during the motion.

[0094] Furthermore, S4 specifically includes:

[0095] Substituting the input parameters of the RSSR model of the double-crank spatial four-bar linkage into equation (3), the corresponding theoretical output data are calculated. ， i=1,2,…n; simultaneously, the corresponding rotation angle data of the two axes of the scraper are given. , i=1,2,…n, representing the rotation angles of the scraper tool's rotary axis and the worktable's rotary axis at measurement point i, i=1,2,…n. The ballbar outputs the measurement data. Formula (3) is used to calculate the discrete length of the ballbar. The output data belongs to the RSSR model of a double-crank spatial four-bar linkage under given ballbar installation parameters, and has calculation conditions, while the ballbar measurement data... This is actual data, measured by a ball bar. and bar length The difference between the two reflects the error in the mechanism parameters. To obtain the actual mechanism parameters, a mechanism parameter identification model is established as follows:

[0096] (8)

[0097] In the above formula (8), For data measured by the ball bar instrument The maximum deviation between the calculated values ​​and those of the RSSR model of the double-crank spatial four-bar linkage; i is the number of discrete positions, n is the number of measured positions; the optimization variables are... Objective function For data measured by the ball bar instrument The calculated discrete bar length The absolute value of the difference; st represents the constraints on the structural parameters, and the discrete data of the ballbar theoretical values. The calculation formula is as follows:

[0098] (9)

[0099] in , The calculation formula is as follows:

[0100] (10).

[0101] The optimization variables in equation (8) are x=(a0, a1, l0, l1, l2, α0, θ). C1 θ C2 ) T Let the true parameters of the ballbar measuring mechanism be set after identification, and substitute them into equations (9) and (10) to obtain the output bar length of the ballbar under the identification parameters. The installation position of the ballbar on the tool spindle and the workpiece table, and the corresponding machine tool structural parameters.

[0102] Table 2 shows the structural parameters and initial parameter identification results of the RSSR of the ball bar double crank measuring mechanism under the machining of spur gears.

[0103] Based on the RSSR (Roller-Screen Measure) mechanism for the tool spindle and workpiece table and its dimensional parameters in Table 2, the actual measurement results were analyzed. The output rod length of the ball bar under the identification parameters The analysis yielded the following relationships: Figure 5 As shown, Figure 5 The test results are for machining spur gears.

[0104] As shown in the figure, the ballbar can achieve double-crank motion under given installation position parameters; and the actual measurement results... Computational data under identification parameters The good fit between the curves indicates that the size parameters of the proposed mechanism model are accurately and effectively identified.

[0105] The above provides a detailed description of the error identification method for double-crank RSSR mechanisms measured by a ballbar on a gear scraping machine, as provided in this invention. Since this method is based on the principles of differential geometry of mechanism motion, it designs the relevant technical parameters for machining spur gears on a gear scraping machine, and then performs motion synthesis and measurement accuracy error identification using a ballbar on the gear scraping machine. This method has broad applicability to different design parameters of different machine tools. This theoretical analysis demonstrates the effectiveness of the method for synthesizing and identifying parameters of multi-condition spatial RSSR mechanisms measured by a ballbar on gear machine tools, and also provides a new approach for enriching and developing the theory and application of spatial mechanism science.

[0106] The present invention also provides an error identification system for a double-crank RSSR mechanism measured by a ballbar for a gear scraper, the system comprising: a module for performing the error identification method for a double-crank RSSR mechanism measured by a ballbar for a gear scraper.

[0107] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements a method for identifying the error of a double crank RSSR mechanism measured by the ball bar of the scraper.

[0108] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements a method for identifying errors in a double-crank RSSR mechanism measured by the ballbar of the scraper.

[0109] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements a method for identifying errors in a double-crank RSSR mechanism measured by the ballbar of the scraper.

[0110] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for identifying errors in a double-crank RSSR mechanism measured by a ballbar measuring instrument for a gear scraper, characterized in that: The method includes: S1. Construction of the ball bar measuring mechanism model for the gear scraper: The tool spindle rotary joint, the workpiece table rotary joint, and the ball bar spatial rod of the gear scraper are combined into a multi-degree-of-freedom spatial mechanism to construct the RSPSR model of the ball bar measuring mechanism for generating gears. S2. The ballbar measuring mechanism model of the scraper is degenerated into a double-crank spatial four-bar mechanism RSSR: the ballbar spatial bar group is treated as a rigid component and degenerated into a double-crank spatial four-bar mechanism RSSR model; S3. Optimization of the RSSR model of the double-crank spatial four-bar linkage: Taking the minimum difference of the extreme values ​​of the link mapping angle as the objective function and the link length condition of the RSSR model of the double-crank spatial four-bar linkage as the constraint, the installation position parameters of the ball bar are optimized to obtain the optimal installation position parameters. S4. Measurement Mechanism Parameter Identification and Test Result Analysis: Based on the optimal installation position parameters, actual installation and measurement are carried out, and actual data of the ballbar are collected; a parameter identification model is established, and the real structural parameters of the double crank spatial four-bar linkage RSSR model are identified by inversion, which is used to realize the parameter identification of installation error and machine tool motion error.

2. The method for error identification of a double-crank RSSR mechanism measured by a ball bar instrument for a scraper according to claim 1, characterized in that: S1 includes: The ball bar measuring instrument for a gear scraper measures the two rotating shafts of the gear scraper. The measuring mechanism of the ball bar measuring instrument for a gear scraper includes components and components. ,member ,member ,member ; Specific components, parts ,member ,member ,member These correspond to the frame, base ball assembly, spindle ball assembly, measuring rod body, and data acquisition unit, respectively; the input parameters for the ball bar measuring mechanism of the scraper machine are the components. The rotation angle θ1 and the component Relative to components The rotation angles θ2, θ1, and θ2 relative to the drive rotation angles θ of the two rotary axes of the machine tool 1A and θ 2C The following relationship exists: （1）； Where, θ C1 and θ C2 The installation phase of the fixed and moving ball points relative to the initial rotation angle of the rotary axis of the gear scraping machine; Based on the DH coordinate system convention, the coordinate systems of each component of the ballbar measuring mechanism of the scraper machine are established as follows: a moving coordinate system {B; i1, j1, k1} is established through the fixed ball center E; a moving coordinate system {A; i2, j2, k2} is established through the moving ball center F; and a fixed coordinate system {B0; X; ...} is established with component l0 as the frame. f Y f Z f }, {B0; X f Y f Z f {A; i1, j1, k1} and {B; i2, j2, k2} are fixed coordinate systems, fixed on the rigid body. i1, j1, k1 and i2, j2, k2 are the axes of the motion coordinate systems established through the fixed center E and the moving center F, respectively. They translate and rotate with the rigid body, their directions changing with time, exhibiting relative motion. The length of the frame A0B0 is l0, corresponding to vector l0. The unit vectors of the two rotary joint axes on the frame are k1 and k2, with a fixed angle α0 between them. The two connecting rods B0... The lengths of E and A0F are l1 and l2, respectively, corresponding to vectors l1 and l2, and they form fixed angles α1 and α2 with their axes k1 and k2, respectively, and rotate around their respective axes by angles θ1 and θ2, respectively; the length of the link EF containing the sliding joint P is d, corresponding to vector d and the mapping angle α3, and all components form a spatial closed loop A0B0EPF; the scraper ball bar measuring mechanism model RSPSR consists of 8 structural parameters, namely l0, l1, l2, d, α0, α1, α2, α3, and the coordinate positions of the two ball centers, the fixed ball center E and the moving ball center F, are represented by R. E (x) E y E , z E ) and R F (x) F y F , z F The closed-loop vector equations of the RSPSR measuring mechanism model of the scraper ballbar are established from the vectors of each link: （2）； Taking the molds from both sides of equation (2), we obtain the basic displacement equation of the RSPSR model of the ball bar measuring mechanism of the tooth scraper: （3）； in: （4）； The length of the ballbar is given by equations (3) and (4), which are the kinematic equations of the two-axis motion ballbar measuring mechanism of the scraper. The kinematic geometric relationship between its structural parameters, input drive parameters and output measurement parameters is established. There are 8 dimensional parameters of the mechanism: l0, l1, l2, d, α0, α1, α2, α3. Among them, (l0, α0) corresponds to the structural parameters of the two axes C1 and C2, respectively representing R. C1 axis and R C2 The length and included angle of the common perpendicular between the axes; given the structural parameters of the measuring mechanism, with the independent variables inputting the rotation angles θ1 and θ2, solve for the output parameter d of the RSPSR measuring mechanism model of the scraper ball bar instrument; When the two C-axis move ideally, that is, when they only rotate around their axes, the output parameter d is a function of the independent variables θ1 and θ2. Moreover, θ1 and θ2 are independent variables, and the energy numbers exhibit different functions, so the output parameter d is a different function. When the distance between the moving ball point and the stationary ball point remains unchanged, the output parameter d is a constant.

3. The method for error identification of a double-crank RSSR mechanism measured by a ball bar instrument for a scraper according to claim 2, characterized in that, S2 specifically includes: The measuring rod assembly SPS is degenerated into a single rod with two sets of SS, and the measuring mechanism model RSPSR of the scraper ballbar is degenerated into a double-crank spatial four-bar linkage RSSR, with the two axes C1 and C2 forming an active and passive constraint relationship. The double-crank spatial four-bar linkage RSSR is a single-degree-of-freedom mechanism, requiring only one rotation axis to be driven independently, while the motion of the other rotation axis is solved by the kinematics of the mechanism. However, in actual measurement, both axes are driven independently, but the rotation angles of the two axes must conform to the kinematic relationship of the RSSR mechanism. The scraper ball bar measuring mechanism model RSPSR and the double crank spatial four-bar linkage RSSR have structural parameters, where (l0, l1, l2, d, α0, α1, α2, α3), and the coordinate parameters of the two ball points are (l1, α1) and (l2, α2). In order to solve the input and output function relationship of the double crank spatial four-bar linkage RSSR, the function relationship between the two connecting rod rotation angle variables θ1 and θ2 is derived according to equation (3): (5)； in: (6)； Equations (5) and (6) establish the functional relationship between the input and output parameters θ1 and θ2 of the double-crank spatial four-bar linkage RSSR. Substituting these parameters into equation (1), the driving angles θ of the two rotating shafts of the double-crank spatial four-bar linkage RSSR are obtained. 1A and θ 2C .

4. The method for error identification of a double-crank RSSR mechanism measured by a ball bar instrument for a scraper according to claim 1, characterized in that, S3 specifically includes: The RSSR model of the double-crank spatial four-bar linkage keeps the distance between the fixed ball point and the moving ball point constant, so that the actual motion range of the ballbar measuring kinematic pair P is used to measure the motion error of the two linkage axes; the rotation angle of the machine tool C1 axis corresponds to the crank B'F position of the ballbar measuring mechanism, and the rotation angle of the machine tool C2 axis corresponds to the crank O'E position of the ballbar measuring mechanism. First, determine the coordinate positions of the X, Y, and Z axes of the machine tool to achieve precise feed by working together. Second, set the parameters of the ballbar measuring mechanism and establish a fixed coordinate system {C2; X...} at point O on the rotation axis of the tool spindle C2. f Y f Z f Establish a motion coordinate system {O'; i1, j1, k1} through the center E of the sphere, and establish a motion coordinate system {B'; i2, j2, k2} through the center F of the sphere. The ballbar measuring mechanism of the scraper includes connecting rod BB', connecting rod OO', frame OB, connecting rod O'E, connecting rod B'F, ​​and connecting rod EF; their lengths are denoted as a0, a1, l0, l1, l2, and p, respectively; the two input parameters θ1 and θ2 represent the rotation angles of connecting rod O'E and connecting rod B'F, ​​and the rotation angles θ of the two rotating shafts of the scraper, respectively. 1A θ 2C The installation phase of the fixed and moving ball points of the ball bar relative to the initial rotation angle of the rotary axis of the gear scraping machine, i.e., the driving angle θ of the fixed and moving ball points relative to the two rotary axes of the machine tool. C1 and θ C2 ; The ballbar measuring mechanism for a gear scraping machine includes the ballbar measuring rod assembly (SPS) and the kinematic chain of the machine tool under test. The motion synthesis of this measuring mechanism determines the installation positions of the fixed and moving ball points of the ballbar, thereby obtaining the dimensions of the measuring mechanism. The centers of the two S-joints of the ballbar are respectively installed on the fixed ball point (r) on the cutting tool O'E. Ef θ Ef , z Ef ) and the moving ball point (r) on the workbench B'F Fk θ Fk , z Fk To ensure the ballbar is installed at the extreme position of the mapping angle α3, i.e., when plane OO'E and plane OEF are coplanar, the objective function is to minimize the difference between the extreme values ​​of the link mapping angle α3, and the constraint is the length of the measuring mechanism. The ballbar installation position parameters are optimized, and the following optimization comprehensive model is established: （7）； in: objective function The difference in the connecting rod mapping angle α3 is minimized when the crank of the measuring mechanism rotates one revolution, where i is the number of discrete positions and n is the number of measurement positions; Optimize variables The installation position parameters of the ballbar in the measuring mechanism are defined as shown in equation (7) of the optimization synthesis model; Optimize constraints: For rod length l OF The minimum value is reached when the crank of the measuring mechanism moves to a position where plane O'EE and plane OEF are coplanar. and maximum value ; To calculate the time required for the measuring mechanism to achieve a full revolution The length of the rod; To determine the range of values ​​for α3 when the crank of the measuring mechanism achieves a full revolution; In the synthesis of ballbar measuring mechanism, the input and output parameters achieve full rotation. Based on the kinematic equations of the two-axis ballbar measuring mechanism of the gear processing machine tool, the kinematic geometric relationship between structural parameters, input drive parameters and output measurement parameters must be established. The conversion of spur gear machining conditions is achieved by adjusting the tool spindle tilt angle α3, so as to meet the machining conditions of spur gears. The crank must also be present during the motion.

5. The method for error identification of a double-crank RSSR mechanism measured by a ball bar instrument for a scraper according to claim 2, characterized in that, S4 specifically includes: Substituting the input parameters of the RSSR model of the double-crank spatial four-bar linkage into equation (3), the corresponding theoretical output data are calculated. ， i=1,2,…n; simultaneously, the corresponding rotation angle data of the two axes of the scraper are given. , i=1,2,…n, representing the rotation angles of the scraper tool's rotary axis and the worktable's rotary axis at measurement point i, i=1,2,…n. The ballbar outputs the measurement data. Formula (3) is used to calculate the discrete length of the ballbar. The output data belongs to the RSSR model of a double-crank spatial four-bar linkage under given ballbar installation parameters, and has calculation conditions, while the ballbar measurement data... This is actual data, measured by a ball bar. and bar length The difference between the two reflects the error in the mechanism parameters. To obtain the actual mechanism parameters, a mechanism parameter identification model is established as follows: （8）； In the above formula (8), For data measured by the ball bar instrument The maximum deviation between the calculated values ​​and those of the RSSR model of the double-crank spatial four-bar linkage; i is the number of discrete positions, n is the number of measured positions; the optimization variables are... Objective function For data measured by the ball bar instrument The calculated discrete bar length The absolute value of the difference; st represents the constraints on the structural parameters, and the discrete data of the ballbar theoretical values. The calculation formula is as follows: （9）； in , The calculation formula is as follows: （10）。 6. An error identification system for a double-crank RSSR mechanism measured by a ballbar measuring instrument for a tooth scraper, characterized in that, The system includes a module for performing the error identification method for a double crank RSSR mechanism measured by a ballbar for a scraper as described in any one of claims 1 to 5.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the error identification method for the double crank RSSR mechanism measured by the ball bar instrument of the scraper as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the error identification method for the double crank RSSR mechanism measured by the ball bar instrument of the scraper as described in any one of claims 1 to 5.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the error identification method for the double crank RSSR mechanism measured by the ball bar instrument of the scraper as described in any one of claims 1 to 5.

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