Simulation modeling method for undeformed cuttings in honing and cutting process of internal gearing powerful gear honing

Abstract

The invention discloses a simulation modeling method for undeformed cuttings in the honing process of internal meshing powerful gear honing, which comprises the following steps of: firstly, analyzing a space coordinate motion relationship between a honing tool and a gear workpiece in the machining process of internal meshing powerful gear honing, and establishing a coordinate transformation mathematical model between a honing tool coordinate system and a gear workpiece coordinate system; then obtaining tooth surface point cloud data of the workpiece tooth socket and the honing wheel working tooth, establishing a three-dimensional model of the workpiece tooth socket and the honing wheel working tooth, and obtaining a three-dimensional simulation model with mutually matched spatial poses of the workpiece tooth socket and the honing wheel working tooth; and finally, motion parameters of a workpiece tooth groove and honing wheel working teeth are solved, honing process simulation is conducted, and an undeformed cutting model is obtained. According to the method, the high-precision three-dimensional simulation model is constructed by utilizing the point cloud data, accurate matching of the honing wheel and the workpiece space poses is realized, the undeformed cutting model is efficiently generated, and a reliable basis is provided for gear honing machining optimization.

Description

Technical Field

[0001] The invention relates to the field of gear grinding, and in particular to a simulation modeling method for undeformed chips in an internal meshing power honing process. Background Art

[0002] High-speed precision gears are key core transmission components in key areas such as new energy vehicles and aerospace. The machining accuracy of gears directly affects the noise, efficiency and service life of gear transmission. As an efficient and precise machining process, gear honing has significant advantages in removing gear surface errors and improving gear surface quality. During the gear honing process, the machining accuracy of the gear is affected by the change in honing force, and the change in honing force can be reflected by the geometric data of the undeformed chips. Therefore, conducting research on the simulation modeling method of undeformed chips in the internal meshing high-power honing process is of great significance for controlling the honing force and improving the gear machining quality.

[0003] At present, in the field of gear cutting, certain progress has been made in the modeling research of undeformed chips. However, the research focus is mostly on traditional machining processes such as gear turning and gear planing, while the research on the modeling of undeformed chips in the high-precision machining process of internal meshing power honing is still scarce. Summary of the Invention

[0004] The present invention provides a method for simulating and modeling undeformed chips in an internal meshing power honing process, which can automatically generate undeformed chips.

[0005] The technical solution adopted to achieve the purpose of the present invention is as follows, that is, a method for simulating and modeling undeformed chips in the internal meshing power honing process, comprising the following steps:

[0006] Step 1: Analyze the spatial coordinate motion relationship between the honing tool and the gear workpiece during the internal meshing power honing process, and establish a coordinate transformation mathematical model between the honing tool coordinate system and the gear workpiece coordinate system;

[0007] Step 2: Obtain the tooth surface point cloud data of the workpiece tooth groove and the honing wheel working teeth, establish a three-dimensional model of the workpiece tooth groove and the honing wheel working teeth, and obtain a three-dimensional simulation model in which the spatial poses of the two match each other;

[0008] Step 3: Solve the motion parameters of the workpiece tooth groove and the honing wheel working teeth, simulate the honing process, and obtain the undeformed chip model.

[0009] Preferably, in step 1, a coordinate transformation mathematical model between the honing tool coordinate system and the gear workpiece coordinate system is derived and established, and the specific process is as follows:

[0010] (1) Analyze the internal meshing power honing process and establish the honing wheel motion coordinate system S h, the honing wheel stationary coordinate system S1, the gear coordinate system S2, the workpiece stationary coordinate system S3 and the workpiece motion coordinate system S g Five coordinate systems.

[0011] Among them, the coordinate system S h (O h -X h ,Y h ,Z h ) is fixed on the honing wheel, Z h The axis coincides with the honing wheel axis; coordinate system S h Around Z h Axis rotation Then we get the coordinate system S1 (O1-X1, Y1, Z1); after the coordinate system S1 rotates Σ around the X1 axis, we get the coordinate system S2 (O2-X2, Y2, Z2); the coordinate system S2 is translated along the X2 axis by a center distance a gh Get S3(O3-X3,Y3,Z3); coordinate system S3 rotates around the Z3 axis Then the workpiece motion coordinate system S is obtained g (O g -X g ,Y g ,Z g ), Z g The axis coincides with the workpiece axis.

[0012] (2) Use the motion transformation matrix to describe the various motions required for the honing process: The honing wheel rotation motion matrix is M 1h , the axis angle adjustment motion matrix is M 21 , the center distance adjustment motion matrix is M 32 and the workpiece rotation motion matrix is M g3 According to the principle of homogeneous coordinate transformation, the coordinate system of the honing wheel motion S can be obtained. h Transform to the workpiece motion coordinate system S g Mathematical model of coordinate transformation:

[0013] M gh =M g3 M 32 M 21 M 1h

[0014] Among them, M g3 、M 32 、M 21 and M 1h The transformation matrices are expressed as:

[0015]

[0016] Where, is the workpiece rotation angle; a ghis the distance between the honing wheel and the workpiece axis; Σ is the axial angle between the honing wheel and the workpiece, is the rotation angle of the honing wheel.

[0017] Preferably, in step 2, a three-dimensional model of the workpiece tooth groove and the honing wheel working tooth is established to obtain a three-dimensional simulation model in which the spatial postures of the two match each other. The specific process is as follows:

[0018] (1) Based on the coordinate transformation mathematical model, numerical calculations are performed using mathematical software to obtain the tooth surface point cloud data of the workpiece tooth groove and the honing wheel working tooth.

[0019] (2) The tooth surface point cloud data of the workpiece tooth groove is imported into the 3D modeling software, and mesh processing and surface wizard are performed to obtain the surface solid model. The surface solid model is then filled and thickened to obtain the 3D solid model of the workpiece tooth groove.

[0020] (3) According to the tooth surface point cloud data of the honing wheel working teeth, the left and right tooth profile data points of the front and rear end surfaces of the honing wheel working teeth are obtained, and the tooth profile sketch block of the honing wheel working teeth is established through the data points.

[0021] Then, based on the three-dimensional solid model of the workpiece tooth groove, two front and rear reference planes are established according to the left and right tooth profile line data points of the front and rear end faces, and a tooth profile sketch block is inserted; the left and right tooth top lines and tooth root line data points of the honing wheel working teeth are obtained, and four honing wheel working tooth profile guide lines are generated through the data points; finally, the lofting processing is performed to establish a three-dimensional solid model of the honing wheel working teeth, and then a three-dimensional simulation model with matching spatial postures of the two is obtained.

[0022] Preferably, the process of solving the motion parameters of the workpiece tooth groove and the honing wheel working teeth in step 3 to obtain the undeformed chip model is:

[0023] (1) Use mathematical software to obtain the rotation axis coordinates of the workpiece tooth groove and the honing wheel working tooth at the initial position; calculate the angle that the workpiece single tooth groove rotates from engagement to engagement, which is called the engagement angle:

[0024] Where, The workpiece bite angle, For the bite angle.

[0025] (2) The time t required to hone a single tooth groove once o Discretize into m time periods, determine the relevant motion parameters of the workpiece and the honing wheel in a single time period t, and the relevant motion parameters include the workpiece rotation angle Honing wheel rotation angle Axial translation of the honing wheel along the Z axis of the coordinate system δ z , the radial translation of the honing wheel along the X-axis of the coordinate system δ x .

[0026] Since the workpiece tooth groove and the honing wheel working tooth do not begin to mesh at the initial position, a certain angle allowance needs to be added. Therefore, the time required to hone a single tooth groove is:

[0027] Wherein, k is the angle magnification coefficient;

[0028] ω g is the workpiece angular velocity:

[0029] Where Z h is the number of teeth on the honing wheel, Z g is the number of workpiece teeth, ω h is the angular velocity of the honing wheel, v z is the axial oscillation speed of the honing wheel, β g is the workpiece helix angle, r g is the radius of the workpiece pitch circle. If the rotation direction of the honing wheel and the workpiece is the same, use "+". If the rotation direction is opposite, use "-".

[0030] Single time period: t = t o / m

[0031] Workpiece rotation angle:

[0032] Honing wheel rotation angle:

[0033] Axial translation of the honing wheel along the Z axis of the coordinate system: δ z =v z t

[0034] Radial translation of the honing wheel along the X-axis of the coordinate system: δ x =v x t

[0035] Where, v x is the radial feed speed of the honing wheel.

[0036] (3) Based on the three-dimensional simulation model with matching spatial postures described in step 2, the initial workpiece and honing wheel are named workpiece No. i and honing wheel No. i, respectively; then, their rotation axes are established and named workpiece rotation axis and honing wheel rotation axis, respectively.

[0037] A Boolean addition operation is performed on workpiece No. i and honing wheel No. i to obtain the undeformed chips and save them, and then the Boolean addition operation command is withdrawn; then the honing wheel No. i is rotated and translated according to the motion parameters to obtain the honing wheel No. i+1; then a Boolean subtraction operation is performed on workpiece No. i and honing wheel No. i to obtain the workpiece that has been honed once, and the workpiece that has been honed once is rotated to obtain the workpiece No. i+1.

[0038] Based on the steps described above, secondary development was carried out to build automatic cycle logic, which can then obtain all undeformed chips when honing a single tooth groove and the final machined tooth groove. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Flow chart of the method of the present invention

[0040] Figure 2 Schematic diagram of the spatial coordinate system of the honing wheel and the workpiece during gear honing

[0041] Figure 3 Point cloud diagram of the tooth surface of the honing wheel working teeth and workpiece tooth grooves

[0042] Figure 4 Schematic diagram of the process of building a three-dimensional solid model of the workpiece tooth groove

[0043] Figure 5 Schematic diagram of the process of building a 3D solid model of the honing wheel working teeth

[0044] Figure 6 Three-dimensional simulation models with matching spatial poses

[0045] Figure 7 This is the running interface diagram of the honing process simulation

[0046] Figure 8 Schematic diagram of the undeformed chips generated for the third honing of the tooth groove

[0047] Figure 9 Schematic diagram of the workpiece tooth groove after honing DETAILED DESCRIPTION

[0048] The present invention will be described below with reference to the accompanying drawings and embodiments to illustrate the technical solution, but the scope of protection of the present invention is not limited to the embodiments shown. Without departing from the above technical concept of the present invention, various substitutions and modifications based on common technical knowledge and customary means in the field should be included in the scope of protection of the present invention.

[0049] like Figure 1 As shown, this embodiment provides a method for simulating and modeling undeformed chips in the honing process of internal meshing power honing, which can be used to simulate the honing process and obtain an undeformed chip model.

[0050] The basic parameters of the workpiece and honing wheel used in this embodiment are shown in Table 1.

[0051] Table 1 Basic parameters of workpiece and honing wheel

[0052]

[0053] The honing simulation process parameters used in this embodiment are shown in Table 2.

[0054] Table 2 Honing simulation process parameters

[0055]

[0056] The specific operation process of simulation modeling is as follows:

[0057] (1) Analyze the spatial coordinate motion relationship between the honing tool and the gear workpiece during the internal meshing power honing process and obtain the coordinate transformation mathematical model.

[0058] (1.1) Analyze the internal meshing power honing process and establish five coordinate systems, see Figure 2 , including the honing wheel motion coordinate system S h , the honing wheel stationary coordinate system S1, the gear coordinate system S2, the workpiece stationary coordinate system S3 and the workpiece motion coordinate system S g .

[0059] Among them, the coordinate system S h (O h -X h ,Y h ,Z h ) is fixed on the honing wheel, Z h The axis coincides with the honing wheel axis; coordinate system S h Around Z h Axis rotation Then we get the coordinate system S1 (O1-X1, Y1, Z1); after the coordinate system S1 rotates Σ around the X1 axis, we get the coordinate system S2 (O2-X2, Y2, Z2); the coordinate system S2 is translated along the X2 axis by a center distance a gh Get S3(O3-X3,Y3,Z3); coordinate system S3 rotates around the Z3 axis Then the workpiece motion coordinate system S is obtained g (O g -X g ,Y g ,Z g ), Z g The axis coincides with the workpiece axis.

[0060] (1.2) Use the motion transformation matrix to describe the various motions required for the honing process: The honing wheel rotation motion matrix is M 1h , the axis angle adjustment motion matrix is M 21 , the center distance adjustment motion matrix is M 32 and the workpiece rotation motion matrix is M g3 According to the principle of homogeneous coordinate transformation, the coordinate system of the honing wheel motion S can be obtained. h Transform to the workpiece motion coordinate system S g Mathematical model of coordinate transformation:

[0061] M gh=M g3 M 32 M 21 M 1h

[0062] Among them, M g3 、M 32 、M 21 and M 1h The transformation matrices are expressed as:

[0063]

[0064] Where, is the workpiece rotation angle; a gh is the distance between the honing wheel and the workpiece axis; Σ is the axial angle between the honing wheel and the workpiece, is the rotation angle of the honing wheel.

[0065] (2) Obtain the tooth surface point cloud data of the workpiece tooth groove and the honing wheel working tooth, establish a three-dimensional model of the workpiece tooth groove and the honing wheel working tooth, and obtain a three-dimensional simulation model in which the spatial postures of the two match each other.

[0066] (2.1) Based on the coordinate transformation mathematical model, numerical calculations are performed using Matlab mathematical software to obtain the tooth surface point cloud data of the workpiece tooth groove and the honing wheel working tooth, see Figure 3 .

[0067] (2.2) See Figure 4 , import the tooth surface point cloud data of the workpiece tooth groove into the Solidworks 3D modeling software, perform mesh processing and surface wizard to obtain the surface solid model, and then fill and thicken the surface solid model to obtain the 3D solid model of the workpiece tooth groove.

[0068] (2.3) See Figure 5 According to the tooth surface point cloud data of the honing wheel working tooth, the left and right tooth profile data points of the front and rear end surfaces of the honing wheel working tooth are obtained, and the tooth profile sketch block of the honing wheel working tooth is established through the data points.

[0069] Then, based on the three-dimensional solid model of the workpiece tooth groove, two front and rear reference planes are established according to the left and right tooth profile data points of the front and rear end faces, and the tooth profile sketch block is inserted; the left and right tooth top lines and tooth root line data points of the honing wheel working teeth are obtained, and four honing wheel working tooth profile guide lines are generated through the data points; finally, the lofting process is performed to establish the three-dimensional solid model of the honing wheel working teeth, and then a three-dimensional simulation model with matching spatial postures of the two is obtained, such as Figure 6 shown.

[0070] (3) See Figure 7 , the motion parameters of the workpiece tooth groove and the honing wheel working teeth are solved, the honing process is simulated, and the undeformed chip model is obtained.

[0071] (3.1) The rotation axis coordinates of the workpiece tooth groove at the initial position (0,0,0) and (0,0,100) and the rotation axis coordinates of the honing wheel working tooth at the initial position (95.5198,-1.5164036,-9.88435734) and (95.5198,1.5164036,9.88435734) are obtained by Matlab mathematical software respectively; the angle that the workpiece single tooth groove rotates from engagement to exit is calculated, which is called the engagement angle:

[0072]

[0073] Where, The workpiece bite angle, For the bite angle.

[0074] (3.2) The time t required to hone a single tooth groove once o Discrete into 35 time periods, determine the relevant motion parameters of the workpiece and the honing wheel in a single time period t, the relevant motion parameters include the workpiece rotation angle Honing wheel rotation angle Axial translation of the honing wheel along the Z axis of the coordinate system δ z , the radial translation of the honing wheel along the X-axis of the coordinate system δ x .

[0075] Since the workpiece tooth groove and the honing wheel working teeth do not begin to mesh at the initial position, a certain angle allowance needs to be added. Therefore, the time taken to hone a single tooth groove once is:

[0076]

[0077] Wherein, k is the angle magnification coefficient;

[0078] ω g is the workpiece angular velocity:

[0079] Where Z h is the number of teeth on the honing wheel, Z g is the number of workpiece teeth, ω h is the angular velocity of the honing wheel, v z is the axial oscillation speed of the honing wheel, β g is the workpiece helix angle, r g is the radius of the workpiece pitch circle. If the rotation direction of the honing wheel and the workpiece is the same, use "+". If the rotation direction is opposite, use "-".

[0080] Single time period: t = t o / m=0.04502ms

[0081] Workpiece rotation angle:

[0082] Honing wheel rotation angle:

[0083] Axial translation of the honing wheel along the Z axis of the coordinate system: δ z =v z t=0.1125μm

[0084] Radial translation of the honing wheel along the X-axis of the coordinate system: δ x =v x t=0.4502nm

[0085] Where, v x is the radial feed speed of the honing wheel.

[0086] (3.3) Based on the three-dimensional simulation model with matching spatial postures described in step 2, the initial workpiece and honing wheel are named workpiece No. i and honing wheel No. i, respectively; then, their rotation axes are established and named workpiece rotation axis and honing wheel rotation axis, respectively.

[0087] A Boolean addition operation is performed on workpiece No. i and honing wheel No. i to obtain the undeformed chips and save them, and then the Boolean addition operation command is withdrawn; then the honing wheel No. i is rotated and translated according to the motion parameters to obtain the honing wheel No. i+1; then a Boolean subtraction operation is performed on workpiece No. i and honing wheel No. i to obtain the workpiece that has been honed once, and the workpiece that has been honed once is rotated to obtain the workpiece No. i+1.

[0088] Based on the steps described above, secondary development is carried out to build automatic cycle logic, which can obtain all the undeformed chips and the final processed tooth groove when honing a single tooth groove. Figure 8 and Figure 9 shown.

Claims

1. A simulation modeling method for undeformed chips in the internal meshing power honing process, characterized in that: The following steps are involved: Step 1: Analyze the spatial coordinate motion relationship between the honing tool and the gear workpiece during the internal meshing power honing process, and establish a coordinate transformation mathematical model between the honing tool coordinate system and the gear workpiece coordinate system; Step 2: Obtain the tooth surface point cloud data of the workpiece tooth groove and the honing wheel working teeth, establish a three-dimensional model of the workpiece tooth groove and the honing wheel working teeth, and obtain a three-dimensional simulation model in which the spatial poses of the two match each other; Step 3: Solve the motion parameters of the workpiece tooth groove and the honing wheel working teeth, simulate the honing process, and obtain the undeformed chip model.

2. The method for simulating and modeling undeformed chips during internal meshing power honing according to claim 1, characterized in that: In step 1, the coordinate transformation mathematical model between the honing tool coordinate system and the gear workpiece coordinate system is derived and established. The specific process is as follows: (1) Analyze the internal meshing power honing process and establish the honing wheel motion coordinate system S h , the honing wheel stationary coordinate system S1, the gear coordinate system S2, the workpiece stationary coordinate system S3 and the workpiece motion coordinate system S g Five coordinate systems; Among them, the coordinate system S h (O h -X h ,Y h ,Z h ) is fixed on the honing wheel, Z h The axis coincides with the honing wheel axis; coordinate system S h Around Z h Axis rotation Then we get the coordinate system S1 (O1-X1, Y1, Z1); after the coordinate system S1 rotates Σ around the X1 axis, we get the coordinate system S2 (O2-X2, Y2, Z2); the coordinate system S2 is translated along the X2 axis by a center distance a gh Get S3(O3-X3,Y3,Z3); coordinate system S3 rotates around the Z3 axis Then the workpiece motion coordinate system S is obtained g (O g -X g ,Y g ,Z g ), Z g The axis coincides with the workpiece axis; (2) Use the motion transformation matrix to describe the various motions required for the honing process: The honing wheel rotation motion matrix is M 1h , the axis angle adjustment motion matrix is M 21 , the center distance adjustment motion matrix is M 32 and the workpiece rotation motion matrix is M g3 According to the principle of homogeneous coordinate transformation, the coordinate system of the honing wheel motion S can be obtained h Transform to the workpiece motion coordinate system S g Mathematical model of coordinate transformation: M gh =M g3 M 32 M 21 M 1h Among them, M g3 、M 32 、M 21 and M 1h The transformation matrices are expressed as: Where, is the workpiece rotation angle; a gh is the distance between the honing wheel and the workpiece axis; Σ is the axial angle between the honing wheel and the workpiece, is the rotation angle of the honing wheel.

3. The method for simulating and modeling undeformed chips during internal meshing power honing according to claim 1, characterized in that: In step 2, a three-dimensional model of the workpiece tooth groove and the honing wheel working tooth is established to obtain a three-dimensional simulation model in which the spatial postures of the two match each other. The specific process is as follows: (1) Based on the coordinate transformation mathematical model, numerical calculation is performed by mathematical software to obtain tooth surface point cloud data of the workpiece tooth groove and the honing wheel working tooth; (2) Importing the tooth surface point cloud data of the workpiece tooth groove into the 3D modeling software, performing mesh processing and surface wizard to obtain a surface solid model, and then filling and thickening the surface solid model to obtain a 3D solid model of the workpiece tooth groove; (3) According to the tooth surface point cloud data of the honing wheel working tooth, the left and right tooth profile data points of the front and rear end surfaces of the honing wheel working tooth are obtained, and the tooth profile sketch block of the honing wheel working tooth is established through the data points; Then, based on the three-dimensional solid model of the workpiece tooth groove, two front and rear reference planes are established according to the left and right tooth profile line data points of the front and rear end faces, and a tooth profile sketch block is inserted; the left and right tooth top lines and tooth root line data points of the honing wheel working teeth are obtained, and four honing wheel working tooth profile guide lines are generated through the data points; finally, the lofting processing is performed to establish a three-dimensional solid model of the honing wheel working teeth, and then a three-dimensional simulation model with matching spatial postures of the two is obtained.

4. The method for simulating and modeling undeformed chips during internal meshing power honing according to claim 1, characterized in that: In step 3, the process of solving the motion parameters of the workpiece tooth groove and the honing wheel working teeth to obtain the undeformed chip model is as follows: (1) Use mathematical software to obtain the rotation axis coordinates of the workpiece tooth groove and the honing wheel working tooth at the initial position; calculate the angle that the workpiece single tooth groove rotates from engagement to engagement, which is called the engagement angle: Where, The workpiece bite angle, is the bite angle; (2) The time t required to hone a single tooth groove once o Discretize into m time periods, determine the relevant motion parameters of the workpiece and the honing wheel in a single time period t, and the relevant motion parameters include the workpiece rotation angle Honing wheel rotation angle Axial translation of the honing wheel along the Z axis of the coordinate system δ z , the radial translation of the honing wheel along the X-axis of the coordinate system δ x ; Since the workpiece tooth groove and the honing wheel working tooth do not begin to mesh at the initial position, a certain angle allowance needs to be added. Therefore, the time required to hone a single tooth groove is: Wherein, k is the angle magnification coefficient; ω g is the workpiece angular velocity: Where Z h is the number of teeth on the honing wheel, Z g is the number of workpiece teeth, ω h is the angular velocity of the honing wheel, v z is the axial oscillation speed of the honing wheel, β g is the workpiece helix angle, r g is the workpiece pitch circle radius, "+" is used when the honing wheel and the workpiece rotate in the same direction, and "-" is used when they rotate in opposite directions; Single time period: t = t o / m Workpiece rotation angle: Honing wheel rotation angle: Axial translation of the honing wheel along the Z axis of the coordinate system: δ z =v z t Radial translation of the honing wheel along the X-axis of the coordinate system: δ x =v x t Where, v x is the radial feed speed of the honing wheel; (3) Based on the three-dimensional simulation model with matching spatial postures described in step 2, the initial workpiece and the honing wheel are named workpiece No. i and honing wheel No. i, respectively; then, the rotation axes of the two are established, and are named workpiece rotation axis and honing wheel rotation axis, respectively; Perform a Boolean addition operation on workpiece No. i and honing wheel No. i to obtain undeformed chips and save them, then withdraw the Boolean addition operation command; then rotate and translate the honing wheel No. i according to the motion parameters to obtain the honing wheel No. i+1; then perform a Boolean subtraction operation on workpiece No. i and honing wheel No. i to obtain the workpiece that has been honed once, and rotate the workpiece that has been honed once to obtain the workpiece No. i+1; Based on the steps described above, secondary development was carried out to build automatic cycle logic, which can then obtain all undeformed chips when honing a single tooth groove and the final machined tooth groove.

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