A predictive control method for tooth surface texture of internal meshing power honing helical gears

Abstract

The present invention relates to a method for predicting and controlling the tooth surface texture of an internal meshing power honing helical gear, and belongs to the field of mechanical processing technology. The operating steps are as follows: according to the spatial coordinate system of the power honing machine tool of the internal gear honing wheel, the contact line equation of the workpiece gear tooth surface is calculated; the workpiece tooth surface contact line is meshed, and the cutting speed direction of the abrasive at each contact point is calculated; the tooth surface mesh is further finely divided to simulate the two-dimensional texture trajectory generated by the movement of the abrasive; the texture cross-sectional characteristics of the abrasive on the tooth surface are calculated; the three-dimensional arc texture of the honing tooth surface is approximately simulated by using the method of discrete abrasive movement trajectory; the topological modification of the workpiece tooth surface is achieved through the multi-axis linkage of the honing machine, and the tooth surface texture after modification is predicted; the size of the axis intersection angle is changed to obtain different modified tooth surface textures. Compared with the conventional microscope measurement method, the present invention saves two-thirds of the time, and the prediction accuracy can reach 90%; it provides theoretical and technical support for honing modification.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical processing technology, and in particular relates to a three-dimensional modeling and control method for the surface texture of a gear before and after internal meshing power honing and shaping processing. Background Art

[0002] Gears are one of the most critical transmission components in high-end mechanical equipment, directly impacting their performance and reliability. Currently, gear manufacturing is moving towards high precision, low noise, high strength, and lightweight design. This is particularly true in the new energy vehicle sector, which places stricter demands on reducing gear noise. Existing research indicates that a combination of shaping and texturing can significantly reduce gear transmission noise. This is because the tooth surface texture of internal meshing power honing, before and after the shaping process, is distributed in an arc-shaped pattern on both sides of the pitch circle. This irregular tooth surface texture avoids periodic resonance and significantly reduces gear noise during operation. However, currently, predicting the three-dimensional texture model before and after honing presents significant challenges.

[0003] During honing and shaping, the honing wheel inevitably needs to be dressed. The traditional method of dressing the honing wheel at a fixed axis angle results in uncertain changes in the tooth surface texture before and after honing, resulting in a lack of means to predict and control the three-dimensional texture morphology after shaping. Generally speaking, for regular parallel textures, it is easy to derive the three-dimensional texture morphology of the workpiece surface by solving the motion trajectory equation of the abrasive particles on the mold surface. However, the irregular and asymmetric arcuate texture unique to honing tooth surfaces means that the motion trajectory equation of the abrasive particles is difficult to solve, and it is impossible to predict the three-dimensional texture morphology of the workpiece gear surface. To meet the requirements of vibration and noise reduction under specific working conditions, texture design and optimization are necessary. Therefore, it is crucial to predict the tooth surface texture morphology before and after shaping and to implement a dressing process and parameters that can control the direction of herringbone textures at any angle. Summary of the Invention

[0004] In order to overcome the problem that the three-dimensional model of the tooth surface texture before and after tooth surface modification is difficult to predict and control, the present invention provides a simple-to-operate three-dimensional modeling and control method for the tooth surface texture of internal meshing power honing helical gears from the perspective of numerical simulation.

[0005] A method for predicting and controlling the tooth surface texture of an internal meshing power honing helical gear is provided. The three-dimensional modeling and control method is applicable to a power honing machine tool. The operation steps are as follows:

[0006] (1) Establish the workpiece tooth surface contact line equation

[0007] According to the spatial coordinate system of the internal gear honing wheel power honing machine, the contact line equation on the workpiece tooth surface is established;

[0008] The tooth surface of the gear being processed is the workpiece tooth surface. The workpiece tooth surface is a standard involute helical surface. The contact line equation of the workpiece tooth surface is as follows:

[0009]

[0010] In formula (1), r w is the position vector of the workpiece gear, r b1 is the base circle radius, σ0 is the involute starting angle, θ is the helix incremental angle, λ is the involute incremental angle, v wh is the cutting velocity vector of the tooth contact point, w ow is the workpiece gear angular velocity vector in the workpiece gear coordinate system, w ow is the angular velocity vector of the honing wheel in the workpiece gear coordinate system, n w is the normal vector of the workpiece gear, r ow is the workpiece gear position coordinate vector in the workpiece gear coordinate system, r oh is the position coordinate vector of the honing wheel in the workpiece gear coordinate system, and p is the lead;

[0011] (2) Calculate the cutting speed direction of the abrasive at each contact point

[0012] According to the conjugate meshing relationship between the honing wheel and the processed gear, the rotation angle of the gear pair when meshing in and out is determined By dividing the rotation angle equally, multiple contact lines on the workpiece tooth surface are obtained according to the workpiece tooth surface contact line equation (1). Grid points are formed by taking points at equal intervals along the tooth width direction, that is, each grid point is the contact point between the abrasive and the workpiece gear; the cutting speed direction at each grid point represents the cutting movement direction of the abrasive on the honing wheel surface on the workpiece tooth surface, that is, the cutting speed formula of the abrasive at each contact point on the workpiece tooth surface is as follows:

[0013]

[0014] In formula (2), (x w ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece, ν wh is the cutting speed value of the abrasive at any position on the workpiece tooth surface, ω w is the angular velocity of the gear being processed, ω h is the angular velocity of the honing wheel, Σ wh is the axial angle between the honing wheel and the workpiece gear, E wh is the center distance between the honing wheel and the workpiece gear; the calculation formula for the direction of the cutting speed of the abrasive at any position on the workpiece tooth surface is:

[0015]

[0016] In formula (3), α is the cutting speed direction of the abrasive at any contact point on the workpiece tooth surface, v l The cutting speed of the contact point on the pitch circle of the gear being processed is different because the cutting speed and direction of the abrasive at any contact point on the tooth surface of the gear being processed are different. On the pitch circle of the gear being processed, the cutting speed direction of the contact point is 0 degrees.

[0017] (3) Simulating the two-dimensional texture trajectory generated by abrasive motion

[0018] By further dividing the tooth surface grid finely, and according to the cutting speed direction of each contact point, the two-dimensional texture trajectory generated by the abrasive particles moving along the cutting speed direction is simulated; the specific operation is as follows:

[0019] By finely dividing the grid, the workpiece rotation angle is divided into 50 equal parts in the tooth profile direction, that is, 50 contact lines are formed on the tooth surface, and the gear width is divided into 55 equal parts along the tooth direction. According to the movement direction of the abrasive grains of the honing wheel when meshing with the workpiece tooth surface, the direction of the cutting speed at many contact points is used to simulate the two-dimensional texture trajectory generated by the movement of the abrasive grains;

[0020] (4) Calculate the texture cross-sectional characteristics of the abrasive particles on the workpiece tooth surface

[0021] Assuming that the center points of the spherical abrasive particles are all on the grid points, the texture cross-sectional features of the abrasive particles on the workpiece tooth surface, the interference depth associated with any grid point within the spherical particle area, and the trajectory of a small distance moving in the direction of the cutting speed are calculated;

[0022] To simplify the calculation model of the honing tooth surface texture, the factors affecting machining chatter, assembly and motion deviation of the machining axis, and thermal deformation of the honing wheel and the machined gear are ignored. All abrasive particles are assumed to be rigid bodies, all of which are spherical particles with equal diameters and firmly fixed on the honing wheel with a diameter of 0.3 mm. The center of the abrasive particle is used as the location of the contact line grid point on the machined gear. The fracture and wear of the abrasive particles during the honing process are ignored. The formula for the interference depth of the abrasive particles on the workpiece tooth surface is as follows:

[0023]

[0024] In formula (4), h i is the interference depth, d gr is the diameter of the spherical abrasive particles, r i Any position in the interference area between the abrasive and the workpiece tooth surface;

[0025] (5) Using the method of discrete abrasive particle motion trajectory to approximate the three-dimensional arc texture of the tooth surface

[0026] The semicircular pit trajectory of the abrasive particles moving a small distance in the direction of the cutting speed at the contact point position at each grid point is calculated. By using the method of discretizing the abrasive particle motion trajectory, countless discrete semicircular pit straight line trajectories are approximated to countless complete arc-shaped semicircular pit curves, thereby approximately simulating the three-dimensional arc texture of the honing tooth surface.

[0027] (6) Realize flexible topological modification and predict the tooth surface texture after modification

[0028] According to the parameters of the standard diamond dressing wheel and the standard workpiece gear, that is, in formula (1), r d =r w Based on the coordinate transformation, the tooth surface equation of the honing wheel is derived, and then the tooth surface equation of the modified workpiece is derived. The formula is as follows:

[0029]

[0030] in,

[0031]

[0032]

[0033] In formula (5), r h is the position coordinate vector of the honing wheel, n h is the normal vector of the honing wheel, r w1 and is the position coordinate vector of the workpiece gear after modification, n w1 is the normal vector of the workpiece gear after modification, To adjust the wheel rotation angle, is the honing wheel rotation angle, Σ hd is the axis angle between the dressing wheel and the honing wheel, the M matrix is ​​the coordinate transformation matrix, and E hd is the center distance between the dressing wheel and the honing wheel, is the swing axis of the honing wheel frame, Σ wh is the axial angle between the honing wheel and the workpiece gear, Lz is the oscillation distance of the honing wheel;

[0034] To achieve flexible topological modification of the workpiece gear tooth surface, the multi-axis linkage relationship during the honing machine operation is expressed as a polynomial. By optimizing the polynomial coefficients, the standard honing wheel can be used to modify the working gear surface in any topological manner, thus achieving arbitrary topological modification of the workpiece tooth surface without the need for a customized diamond dressing wheel.

[0035] The feed rate of the honing wheel radial feed axis, the rotation angle of the cross axis between the honing wheel and the workpiece gear, and the rotation angle of the honing wheel tool holder swing axis are defined as fifth-order polynomials about the axial motion of the honing wheel axial feed axis. The numerical method of the least squares estimation algorithm based on the sensitivity matrix is ​​adopted to solve the polynomial coefficients of these additional motions through multiple closed-loop iterations. The polynomial coefficients are substituted into formula (5), and the obtained r w1 With n w1 This is the tooth surface equation of the workpiece after modification, which is replaced by r in step (1) w With n w , recalculate the contact line equation after modification, repeat steps (2), (3), and (5) to obtain the new modified texture, and compare it with the tooth surface texture before modification to verify the degree of influence of the minor modification on the tooth surface texture; the formula is as follows:

[0036]

[0037] In formula (6), the polynomial coefficients a0~a5, b0~b5 and c0~c5 are the dynamic parameters used to modify the topological structure during the honing process, a total of 18; Lz is the axial feed of the honing wheel, is the swing axis angle of the honing wheel tool holder;

[0038] (7) Changing the size of the axis angle to obtain different modified tooth surface textures

[0039] By changing the helix angle of the honing wheel, the axial angle between the honing wheel and the gear being processed is changed, and the texture of the workpiece gear tooth surface can be controlled;

[0040] The specific operation is as follows: During the dressing process of the honing wheel using the dressing wheel, the angle of the honing wheel inclination swing axis is adjusted, that is, the axial angle of the honing wheel is adjusted by the dressing wheel; the helix angle of the honing wheel is directly changed by the dressing of the dressing wheel, and in the gear honing project, the axial angle between the workpiece gear and the honing wheel is indirectly changed, thereby affecting the texture morphology of the workpiece gear tooth surface.

[0041] The technical solutions are further defined as follows:

[0042] In step (1), the workpiece tooth surface contact line model is not only applicable to standard gears, but also to modified gears. The values ​​of the root circle and the addendum circle are calculated according to the modification coefficient, thereby changing the value range of the involute incremental angle in the workpiece tooth surface contact line equation. The formula for the value range of the involute incremental angle is as follows:

[0043]

[0044] In formula (7), r f1 is the root diameter of the gear being processed, r a1is the tooth top circle diameter of the gear being machined.

[0045] In step (5), under the premise of discretization of the abrasive particle motion trajectory, the length of the semicircular pit straight trajectory generated by the abrasive particle motion on the workpiece tooth surface reflects the size of the abrasive particle cutting speed value, which is always on the curved surface of the gear; by proportionally reducing the cutting speed value, many discrete straight line trajectory segments are finally approximated to several complete curves, and through mathematical calculation, each grid center point is used as the starting point of the abrasive particle movement, and it moves a small distance along the cutting speed direction, and finally the three-dimensional arc texture of the honing tooth surface is approximately simulated.

[0046] The beneficial technical effects of the present invention are embodied in the following aspects:

[0047] 1. The present invention's three-dimensional modeling and control method predicts and controls the directional distribution of tooth surface texture before and after honing by adjusting the axis angle. Furthermore, the discretized abrasive particle motion trajectory is used to establish the texture of the workpiece tooth surface after honing. This simple and computationally efficient modeling method reduces the time required for modeling and prediction by two-thirds compared to conventional microscopic measurement methods, and achieves a prediction accuracy of 90%. This method provides a simple and efficient prediction solution for controlling tooth surface texture during actual honing operations.

[0048] 2. The three-dimensional modeling and control method of the present invention can realize arbitrary control of the texture direction of the tooth surface after honing within the direction of 0° to 90° by adjusting the axis angle, which can provide theoretical and technical support for honing.

[0049] 3. The three-dimensional modeling and control method of the present invention is aimed at the needs of gear vibration and noise reduction, and can optimize the design of tooth surface texture and gear modification amount, and find the optimal topological modification amount and optimal texture structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is an operation flow chart of the present invention;

[0051] Figure 2 This is a spatial coordinate system diagram of the internal gear honing wheel power honing machine tool of the present invention;

[0052] Figure 3 Schematic diagram of the motion trajectory of abrasive particles during the honing wheel processing process of the present invention;

[0053] Figure 4 Schematic diagram of the geometric shape of the abrasive grains of the honing wheel of the present invention;

[0054] Figure 5 A three-dimensional modeling diagram of the local texture of the tooth surface of the workpiece gear of the present invention;

[0055] Figure 6 This is the tooth surface modification result diagram of the present invention;

[0056] Figure 7 A comparison diagram of the texture modeling before and after tooth surface modification in the present invention;

[0057] Figure 8 The prediction of the modified tooth surface texture when the axis intersection angle is 7° in the present invention;

[0058] Figure 9 This is the prediction of the modified tooth surface texture when the axis intersection angle is 9° in the present invention. DETAILED DESCRIPTION

[0059] The present invention will be further described below through embodiments with reference to the accompanying drawings.

[0060] Example 1

[0061] The processing equipment used in this embodiment 1 is a powerful gear honing machine; the module m of the diamond dressing wheel is n1 =2mm, number of teeth z1 = 39, helix angle β1 = 20°, normal pressure angle α n1 =20°, tooth width b1=20mm. Module m of honing wheel n2 =2mm, number of teeth z2 = 123, helix angle β2 = 25°, normal pressure angle α n2＝ 20°, tooth width b2 = 30mm. The module m of the workpiece gear to be processed n3 =2mm, number of teeth z3 = 39, helix angle β3 = 20°, normal pressure angle α n3＝ 20°, tooth width b3=20mm.

[0062] See also Figure 1 The predictive control operation steps of the tooth surface texture of an internal meshing power honing helical gear are as follows:

[0063] Step (1) Establish the workpiece tooth surface contact line equation

[0064] According to the spatial coordinate system of the internal gear honing wheel power honing machine, the contact line equation on the workpiece tooth surface is established;

[0065] The tooth surface of the gear being processed is the workpiece tooth surface. The workpiece tooth surface is a standard involute helical surface. The contact line equation of the workpiece tooth surface is as follows:

[0066]

[0067] In formula (1), r w is the position vector of the workpiece gear, r b1 is the base circle radius, σ0 is the involute starting angle, θ is the helix incremental angle, λ is the involute incremental angle, v whis the cutting velocity vector of the tooth contact point, w ow is the workpiece gear angular velocity vector in the workpiece gear coordinate system, w ow is the angular velocity vector of the honing wheel in the workpiece gear coordinate system, n w is the normal vector of the workpiece gear, r ow is the workpiece gear position coordinate vector in the workpiece gear coordinate system, r oh is the position coordinate vector of the honing wheel in the workpiece gear coordinate system, and p is the lead.

[0068] See also Figure 2 When the axial intersection angle between the honing wheel and the workpiece gear is 5°, the specific calculation data for establishing the workpiece tooth surface contact line equation is as follows based on the spatial coordinate system of the internal gear honing wheel power honing machine tool:

[0069]

[0070] In formula (1), (x w ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece, is the rotation angle of the workpiece gear.

[0071] This workpiece tooth surface contact line model can also be applied to modified gears. The values ​​of the root circle and the addendum circle are calculated based on the modification coefficient, thereby changing the value range of the involute incremental angle and re-updating the contact line equation. The calculation data of the involute incremental angle are as follows:

[0072]

[0073] In formula (7), r f1 、r a1 They are the root circle diameter and tooth root diameter of the working gear respectively.

[0074] Step (2) Calculate the cutting speed direction of the abrasive at each contact point

[0075] According to the conjugate meshing relationship between the honing wheel and the processed gear, the rotation angle of the gear pair when meshing in and out is determined By dividing the rotation angle equally, multiple contact lines on the workpiece tooth surface are obtained according to the workpiece tooth surface contact line equation (1). Grid points are formed by taking points at equal intervals along the tooth width direction, that is, each grid point is the contact point between the abrasive and the workpiece gear; the cutting speed direction at each grid point represents the cutting movement direction of the abrasive on the honing wheel surface on the workpiece tooth surface, that is, the cutting speed formula of the abrasive at each contact point on the workpiece tooth surface is as follows:

[0076]

[0077] In formula (2), (x w ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece, ν wh is the cutting speed value of the abrasive at any position on the tooth surface of the workpiece, ω w is the angular velocity of the gear being processed, ω h is the angular velocity of the honing wheel, Σ wh is the axial angle between the honing wheel and the workpiece gear, E wh is the center distance between the honing wheel and the workpiece gear.

[0078] Based on the condition that the honing wheel and the workpiece gear maintain co-meshing, and taking the workpiece gear fixed coordinate system as a reference, the specific calculation data of the relative cutting speed value of the honing wheel abrasive at different contact points on the workpiece tooth surface are as follows:

[0079]

[0080] In formula (2), (x w ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece.

[0081] The calculation formula for the direction of the cutting speed of the abrasive at any position on the workpiece tooth surface is:

[0082]

[0083] In formula (3), α is the cutting speed direction of the abrasive at any contact point on the workpiece tooth surface, v l It is the cutting speed of the contact point on the pitch circle of the machined gear. This is because the cutting speed and direction of the abrasive at any contact point on the tooth surface of the machined gear are different. On the pitch circle of the machined gear, the cutting speed direction of the contact point is 0 degrees.

[0084] For example, if the cutting speed at one position of the workpiece is 1701 mm / s, the cutting speed at the pitch circle is 1229 mm / s. Therefore, the specific calculation data for the direction of the cutting speed at any position of the abrasive on the workpiece tooth surface is as follows:

[0085]

[0086] Step (3) simulates the two-dimensional texture trajectory generated by the movement of abrasive particles

[0087] By further dividing the tooth surface grid finely, and according to the cutting speed direction of each contact point, the two-dimensional texture trajectory generated by the abrasive particles moving along the cutting speed direction is simulated; the specific operation is as follows:

[0088] By finely dividing the grid, the workpiece rotation angle is divided into 50 equal parts in the tooth profile direction, that is, 50 contact lines are formed on the tooth surface, and the gear width is divided into 55 equal parts along the tooth direction. According to the movement direction of the abrasive grains of the honing wheel when meshing with the workpiece tooth surface, the direction of the cutting speed at many contact points is used to simulate the two-dimensional texture trajectory generated by the movement of the abrasive grains.

[0089] See also Figure 3 By finely dividing the grid, the workpiece rotation angle is divided into 50 equal parts in the tooth profile direction, that is, 50 contact lines are formed on the tooth surface, and the gear width is divided into 55 equal parts along the tooth direction. According to the movement direction of the abrasive grains of the honing wheel when they engage with the tooth surface of the workpiece, the direction of the cutting speed at many contact points is used to simulate the movement trajectory of the abrasive grains (simple diagram).

[0090] Step (4) Calculate the texture cross-sectional features of the abrasive particles on the workpiece tooth surface

[0091] Assuming that the center points of the spherical abrasive particles are all on the grid points, the texture cross-sectional features of the abrasive particles on the workpiece tooth surface, the interference depth associated with any grid point within the spherical particle area, and the trajectory of a small distance moving in the direction of the cutting speed are calculated;

[0092] To simplify the calculation model of the honing tooth surface texture, the factors affecting machining chatter, assembly and motion deviation of the machining axis, and thermal deformation of the honing wheel and the machined gear are ignored. All abrasive particles are assumed to be rigid bodies, all of which are spherical particles with equal diameters and firmly fixed on the honing wheel with a diameter of 0.3 mm. The center of the abrasive particle is used as the location of the contact line grid point on the machined gear. The fracture and wear of the abrasive particles during the honing process are ignored. The formula for the interference depth of the abrasive particles on the workpiece tooth surface is as follows:

[0093]

[0094] In formula (4), h i is the interference depth, d gr is the diameter of the spherical abrasive particles, r i It is any position on the interference area between the abrasive and the workpiece tooth surface.

[0095] The abrasive particles make cutting motion on the workpiece tooth surface along the direction of the relative cutting speed. The specific calculation data of the depth of the interference area (i.e., cutting depth) are as follows:

[0096]

[0097] Figure 4 (a) is the shape feature of the abrasive particles, Figure 4 (b) in the figure is the cutting motion state of the abrasive.

[0098] Step (5) Use the method of discrete abrasive motion trajectory to approximately simulate the three-dimensional arc texture of the tooth surface

[0099] The semicircular pit trajectory of the abrasive moving a small distance along the cutting speed direction at the contact point position of each grid point is calculated. By using the method of discrete abrasive motion trajectory, countless discrete semicircular pit straight line trajectories are approximated to countless complete arc-shaped semicircular pit curves, thereby approximately simulating the three-dimensional arc texture of the honing tooth surface.

[0100] See also Figure 5 , the three-dimensional texture of the tooth surface is approximately simulated by using the method of discrete abrasive motion trajectory.

[0101] The specific operation is as follows: under the premise of discretization of the abrasive motion trajectory, the length of the straight trajectory of the semicircular pit generated by the abrasive motion on the workpiece tooth surface reflects the size of the abrasive cutting speed value, which is always on the curved surface of the gear; by proportionally reducing the cutting speed value, many discrete straight line trajectory segments are eventually approximated to several complete curves. In the mathematical software Matrix Laboratory (MATLAB) program (not limited to MATLAB software, other mathematical calculation software can also be implemented), each grid center point is used as the starting point of the abrasive movement, and it moves a small distance along the cutting speed direction, and finally the three-dimensional arc texture of the honing tooth surface is approximately simulated.

[0102] Step (6) realizes flexible topology modification and predicts the tooth surface texture after modification

[0103] According to the parameters of the standard diamond dressing wheel and the standard workpiece gear, that is, in formula (1), r d =r w Based on the coordinate transformation, the tooth surface equation of the honing wheel is derived, and then the tooth surface equation of the modified workpiece is derived. The formula is as follows:

[0104]

[0105] in,

[0106]

[0107]

[0108] In formula (5), r h is the position coordinate vector of the honing wheel, n h is the normal vector of the honing wheel, r w1 and is the position coordinate vector of the workpiece gear after modification, n w1 is the normal vector of the workpiece gear after modification, To adjust the wheel rotation angle, is the honing wheel rotation angle, Σ hd is the axis angle between the dressing wheel and the honing wheel, the M matrix is ​​the coordinate transformation matrix, and Ehd is the center distance between the dressing wheel and the honing wheel, is the swing axis of the honing wheel frame, Σ wh is the axial angle between the honing wheel and the workpiece gear, Lz is the oscillation distance of the honing wheel;

[0109] The feed rate of the honing wheel radial feed axis, the rotation angle of the cross axis between the honing wheel and the workpiece gear, and the rotation angle of the honing wheel tool holder swing axis are defined as fifth-order polynomials about the axial motion of the honing wheel axial feed axis. The numerical method of the least squares estimation algorithm based on the sensitivity matrix is ​​adopted to solve the polynomial coefficients of these additional motions through multiple closed-loop iterations. The polynomial coefficients are substituted into formula (5), and the obtained r w1 With n w1 This is the tooth surface equation of the workpiece after modification, which is replaced by r in step (1) w With n w , recalculate the contact line equation after modification, repeat steps (2) to (5), obtain the new modified texture, and compare it with the tooth surface texture before modification to verify the influence of the minor modification on the tooth surface texture; the formula is as follows:

[0110]

[0111] In formula (6), the polynomial coefficients a0~a5, b0~b5 and c0~c5 are the dynamic parameters used to modify the topological structure during the honing process, a total of 18; Lz is the axial feed of the honing wheel, φ B is the swing axis angle of the honing wheel tool holder.

[0112] The target modified tooth surface is as follows: the maximum deviation is 24.2μm, the modification amount in the middle of the tooth surface is the smallest, and the normal deviation of the tooth surface is 5.57μm. The additional motion relationship calculation data of each motion axis of the gear honing machine are as follows:

[0113]

[0114] The topological data of the normal deviation of the target modified tooth surface are shown in the following table:

[0115]

[0116] Step (7) Change the size of the axis angle to obtain different modified tooth surface textures

[0117] By changing the helix angle of the honing wheel, the axial angle between the honing wheel and the gear being processed is changed, thereby achieving texture control on the tooth surface of the workpiece gear.

[0118] The specific operation is as follows: During the dressing process of the honing wheel using the dressing wheel, the angle of the honing wheel inclination swing axis is adjusted, that is, the axial angle of the honing wheel is adjusted by the dressing wheel; the helix angle of the honing wheel is directly changed by the dressing of the dressing wheel, and in the gear honing project, the axial angle between the workpiece gear and the honing wheel is indirectly changed, thereby affecting the texture morphology of the workpiece gear tooth surface.

[0119] See also Figure 6 a and Figure 6 b in the figure represent the target modified tooth surface morphology and the actual modified tooth surface morphology, respectively. The maximum modification error does not exceed 5 μm. Figure 6 The c in the figure satisfies the requirements of the modification accuracy. The modified tooth surface equation under the influence of the polynomial coefficient is calculated as r w1 , n w1 Then r w1 ,n w1 The value of replace r in formula (1) w , n w The value of is used to recalculate the new workpiece tooth surface contact line equation.

[0120] See also Figure 7 In a, select the tooth surface texture morphology for reference, repeat the steps (2) to (5), see Figure 7 b in the figure is used to obtain the three-dimensional morphology of the tooth surface texture before modification; see Figure 7 c in the figure is used to obtain the tooth surface texture after modification. By comparing the tooth surface texture before and after modification, it is found that a small modification amount has no effect on the tooth surface texture.

[0121] Example 2 (Changing the Axis Angle Prediction Process 1)

[0122] The processing equipment, diamond dressing wheel, honing wheel and workpiece gear to be processed used in this embodiment 2 are the same as those in embodiment 1.

[0123] The steps for predicting and controlling the tooth surface texture of an internal meshing power honing helical gear are as follows:

[0124] Step (1) Establish the workpiece tooth surface contact line equation

[0125] See also Figure 2 When the axial intersection angle between the honing wheel and the workpiece gear is 7°, the specific calculation results of the workpiece tooth surface contact line equation are established according to the spatial coordinate system of the internal gear honing wheel power honing machine tool as follows:

[0126]

[0127] In formula (1), θ is the helix increment angle, and λ is the involute increment angle. w is the position vector of the workpiece gear, (xw ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece. n w is the normal vector of the workpiece gear, v wh is the cutting velocity vector of the tooth contact point, w ow With w ow are the workpiece gear angular velocity vector and the honing wheel angular velocity vector in the workpiece gear coordinate system, r ow With r oh They are the workpiece gear position coordinate vector and the honing wheel position coordinate vector in the workpiece gear coordinate system respectively.

[0128] This workpiece tooth surface contact line model can also be applied to gears with modified positions. The values ​​of the root circle and the addendum circle are calculated based on the modification coefficient, thereby changing the value range of the involute incremental angle and re-updating the contact line equation. The calculation area of ​​the involute incremental angle is as follows:

[0129]

[0130] In formula (7), r f1 、r a1 They are the root circle diameter and the root circle diameter of the working gear after displacement.

[0131] Step (2) Calculate the cutting speed direction of the abrasive at each contact point

[0132] Based on the condition that the honing wheel and the workpiece gear maintain co-engagement, and with the workpiece gear fixed coordinate system as a reference, the specific calculation method for the relative cutting speed value of the honing wheel abrasive grains at different contact points on the workpiece tooth surface is as follows:

[0133]

[0134] In formula (2), (x w ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece.

[0135] For example, if the cutting speed at one position of the workpiece is 1701 mm / s, the cutting speed at the pitch circle is 1229 mm / s. Therefore, the calculation formula for the direction of the cutting speed at any position of the abrasive on the workpiece tooth surface is:

[0136]

[0137] In formula (3), α is the cutting velocity direction of the abrasive at any contact point on the workpiece tooth surface.

[0138] Step (3) simulates the two-dimensional texture trajectory generated by the movement of abrasive particles

[0139] See also Figure 3 By finely dividing the grid, the workpiece rotation angle is divided into 50 equal parts in the tooth profile direction, that is, 50 contact lines are formed on the tooth surface, and the gear width is divided into 55 equal parts along the tooth direction. According to the movement direction of the abrasive grains of the honing wheel when they engage with the workpiece tooth surface, the cutting speed direction at many contact points is used to simulate the movement trajectory of the abrasive grains.

[0140] Step (4) Calculate the texture cross-sectional features of the abrasive particles on the workpiece tooth surface

[0141] See also Figure 4 , the abrasive particles make cutting motion on the workpiece tooth surface along the direction of the relative cutting speed. The calculation results of the depth of the interference area (i.e., cutting depth) are as follows:

[0142]

[0143] In formula (4), r i It is any position in the interference area between the abrasive and the workpiece.

[0144] Figure 4 (a) is the shape feature of the abrasive particles, Figure 4 (b) in the figure is the cutting motion state of the abrasive.

[0145] Step (5) Use the method of discrete abrasive motion trajectory to approximately simulate the three-dimensional arc texture of the tooth surface

[0146] The three-dimensional texture of the tooth surface is approximately simulated by using the method of discrete abrasive particle motion trajectory. Since the texture remains unchanged before and after honing, it can be ignored here.

[0147] Step (6) realizes flexible topology modification and predicts the tooth surface texture after modification

[0148] The target modified tooth surface is as follows: the maximum deviation is 24.2 μm, the modification amount in the middle of the tooth surface is the smallest, and the normal deviation of the tooth surface is 5.57 μm. The calculation results of the additional motion relationship of each motion axis of the gear honing machine are as follows:

[0149]

[0150] The topological data of the normal deviation of the target modified tooth surface are shown in the following table:

[0151]

[0152] Step (7) Change the size of the axis angle to obtain different modified tooth surface textures

[0153] By changing the helix angle of the honing wheel, the axial angle between the honing wheel and the gear being processed is changed, thereby achieving texture control on the workpiece tooth surface.

[0154] See also Figure 8 , the tooth surface equation after modification under the influence of polynomial coefficients, that is, calculate r w1 ,n w1 Then r w1 ,n w1 The value of replace r in formula (1) w ,n w The value of is used to recalculate the new workpiece tooth surface contact line equation. Repeat steps (2) to (5) to obtain the three-dimensional morphology of the modified tooth surface texture.

[0155] Example 3 (Changing the Axis Angle Prediction Process 2)

[0156] The processing equipment, diamond dressing wheel, honing wheel and workpiece gear to be processed used in this embodiment 3 are the same as those in embodiment 1.

[0157] The steps for predicting and controlling the tooth surface texture of an internal meshing power honing helical gear are as follows:

[0158] Step (1) Establish the workpiece tooth surface contact line equation

[0159] See also Figure 2 When the axial intersection angle between the honing wheel and the workpiece gear is 9°, the specific calculation results of the workpiece tooth surface contact line equation are established according to the spatial coordinate system of the internal gear honing wheel power honing machine tool as follows:

[0160]

[0161] In formula (1), θ is the helix increment angle, and λ is the involute increment angle. w is the position vector of the workpiece gear, (x w ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece. n w is the normal vector of the workpiece gear, v wh is the cutting velocity vector of the tooth contact point, w ow With w ow are the workpiece gear angular velocity vector and the honing wheel angular velocity vector in the workpiece gear coordinate system, r ow With r oh They are the workpiece gear position coordinate vector and the honing wheel position coordinate vector in the workpiece gear coordinate system respectively.

[0162] This workpiece tooth surface contact line model can also be applied to gears with modified positions. The values ​​of the root circle and the addendum circle are calculated based on the modification coefficient, thereby changing the value range of the involute incremental angle and re-updating the contact line equation. The calculation area of ​​the involute incremental angle is as follows:

[0163]

[0164] In formula (7), r f1 、r a1 They are the root circle diameter and tooth root diameter of the working gear respectively.

[0165] Step (2) Calculate the cutting speed direction of the abrasive at each contact point

[0166] Based on the condition that the honing wheel and the workpiece gear maintain co-engagement, and with the workpiece gear fixed coordinate system as a reference, the specific calculation method for the relative cutting speed value of the honing wheel abrasive grains at different contact points on the workpiece tooth surface is as follows:

[0167]

[0168] In formula (2), (x w ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece.

[0169] For example, if the cutting speed at one position of the workpiece is 2196 mm / s, the cutting speed at the pitch circle is 1951 mm / s. Therefore, the calculation formula for the direction of the cutting speed at any position of the abrasive on the workpiece tooth surface is:

[0170]

[0171] In formula (3), α is the cutting velocity direction of the abrasive at any contact point on the workpiece tooth surface.

[0172] Step (3) simulates the two-dimensional texture trajectory generated by the movement of abrasive particles

[0173] See also Figure 3 By finely dividing the grid, the workpiece rotation angle is divided into 50 equal parts in the tooth profile direction, that is, 50 contact lines are formed on the tooth surface, and the gear width is divided into 55 equal parts along the tooth direction. According to the movement direction of the abrasive grains of the honing wheel when they engage with the workpiece tooth surface, the cutting speed direction at many contact points is used to simulate the movement trajectory of the abrasive grains.

[0174] Step (4) Calculate the texture cross-sectional features of the abrasive particles on the workpiece tooth surface

[0175] See also Figure 4 , the abrasive particles make cutting motion on the workpiece tooth surface along the direction of the relative cutting speed. The calculation results of the depth of the interference area (i.e., cutting depth) are as follows:

[0176]

[0177] In formula (4), r iIt is any position in the interference area between the abrasive and the workpiece.

[0178] Figure 4 (a) is the shape feature of the abrasive particles, Figure 4 (b) in the figure is the cutting motion state of the abrasive.

[0179] Step (5) Use the method of discrete abrasive motion trajectory to approximately simulate the three-dimensional arc texture of the tooth surface

[0180] The three-dimensional texture of the tooth surface is approximately simulated by using the method of discrete abrasive particle motion trajectory. Since the texture remains unchanged before and after honing, it can be ignored here.

[0181] Step (6) realizes flexible topology modification and predicts the tooth surface texture after modification

[0182] The target modified tooth surface is as follows: the maximum deviation is 24.2 μm, the modification amount in the middle of the tooth surface is the smallest, and the normal deviation of the tooth surface is 5.57 μm. The calculation results of the additional motion relationship of each motion axis of the gear honing machine are as follows:

[0183]

[0184] The topological data of the normal deviation of the target modified tooth surface are shown in the following table:

[0185]

[0186] Step (7) Change the size of the axis angle to obtain different modified tooth surface textures

[0187] By changing the helix angle of the honing wheel, the axial angle between the honing wheel and the gear being processed is changed, thereby achieving texture control on the workpiece tooth surface.

[0188] See also Figure 9 , the tooth surface equation after modification under the influence of polynomial coefficients, that is, calculate r w1 ,n w1 Then r w1 , n w1 The value of replace r in formula (1) w , n w The value of is used to recalculate the new workpiece tooth surface contact line equation. Repeat steps (2) to (5) to obtain the three-dimensional morphology of the modified tooth surface texture.

[0189] It will be easily understood by those skilled in the art that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A predictive control method for the tooth surface texture of an internal meshing power honing helical gear, the predictive control method being applicable to a power honing machine tool, characterized in that: The steps are as follows: (1) Establish the workpiece tooth surface contact line equation According to the spatial coordinate system of the internal gear honing wheel power honing machine, the contact line equation on the workpiece tooth surface is established; The tooth surface of the gear being processed is the workpiece tooth surface. The workpiece tooth surface is a standard involute helical surface. The contact line equation of the workpiece tooth surface is as follows: In formula (1), r w is the position vector of the workpiece gear, r b1 is the base circle radius, σ0 is the involute starting angle, θ is the helix incremental angle, λ is the involute incremental angle, v wh is the cutting velocity vector of the tooth contact point, w ow is the workpiece gear angular velocity vector in the workpiece gear coordinate system, w oh is the angular velocity vector of the honing wheel in the workpiece gear coordinate system, n w is the normal vector of the workpiece gear, r ow is the workpiece gear position coordinate vector in the workpiece gear coordinate system, r oh is the position coordinate vector of the honing wheel in the workpiece gear coordinate system, and p is the lead; (2) Calculate the cutting speed direction of the abrasive at each contact point According to the conjugate meshing relationship between the honing wheel and the processed gear, the rotation angle of the gear pair when meshing in and out is determined By dividing the rotation angle into equal parts, multiple contact lines on the workpiece tooth surface are obtained according to the workpiece tooth surface contact line equation (1). Grid points are formed by taking points at equal intervals along the tooth width direction. That is, each grid point is the contact point between the abrasive and the workpiece gear. The cutting speed direction at each grid point represents the cutting motion direction of the abrasive grains on the surface of the honing wheel on the workpiece tooth surface. That is, the cutting speed formula at each contact point of the abrasive grains on the workpiece tooth surface is as follows: In formula (2), (x w ,y w ,z w ) is the coordinate of any position on the tooth surface of the workpiece, ν wh is the cutting speed value of the abrasive at any position on the workpiece tooth surface, ω w is the angular velocity of the gear being processed, ω h is the angular velocity of the honing wheel, Σ wh is the axial angle between the honing wheel and the workpiece gear, E wh is the center distance between the honing wheel and the workpiece gear; the calculation formula for the direction of the cutting speed of the abrasive at any position on the workpiece tooth surface is: In formula (3), α is the cutting speed direction of the abrasive at any contact point on the workpiece tooth surface, v l The cutting speed of the contact point on the pitch circle of the gear being processed is different because the cutting speed and direction of the abrasive at any contact point on the tooth surface of the gear being processed are different. On the pitch circle of the gear being processed, the cutting speed direction of the contact point is 0 degrees. (3) Simulating the two-dimensional texture trajectory generated by abrasive motion By further dividing the tooth surface grid finely, and according to the cutting speed direction of each contact point, the two-dimensional texture trajectory generated by the abrasive particles moving along the cutting speed direction is simulated; the specific operation is as follows: By finely dividing the grid, the workpiece rotation angle is divided into 50 equal parts in the tooth profile direction, that is, 50 contact lines are formed on the tooth surface, and the gear width is divided into 55 equal parts along the tooth direction. According to the movement direction of the abrasive grains of the honing wheel when meshing with the workpiece tooth surface, the direction of the cutting speed at many contact points is used to simulate the two-dimensional texture trajectory generated by the movement of the abrasive grains; (4) Calculate the texture cross-sectional characteristics of the abrasive particles on the workpiece tooth surface Assuming that the center points of the spherical abrasive particles are all on the grid points, the texture cross-sectional features of the abrasive particles on the workpiece tooth surface, the interference depth associated with any grid point within the spherical particle area, and the trajectory of a small distance moving in the direction of the cutting speed are calculated; To simplify the calculation model of the honing tooth surface texture, the factors affecting machining chatter, assembly and motion deviation of the machining axis, and thermal deformation of the honing wheel and the machined gear are ignored. All abrasive particles are assumed to be rigid bodies, all of which are spherical particles with equal diameters and firmly fixed on the honing wheel with a diameter of 0.3 mm. The center of the abrasive particle is used as the location of the contact line grid point on the machined gear. The fracture and wear of the abrasive particles during the honing process are ignored. The formula for the interference depth of the abrasive particles on the workpiece tooth surface is as follows: In formula (4), h i is the interference depth, d gr is the diameter of the spherical abrasive particles, r i Any position in the interference area between the abrasive and the workpiece tooth surface; (5) Using the method of discrete abrasive particle motion trajectory to approximate the three-dimensional arc texture of the tooth surface The semicircular pit trajectory of the abrasive particles moving a small distance in the direction of the cutting speed at the contact point position at each grid point is calculated. By using the method of discretizing the abrasive particle motion trajectory, countless discrete semicircular pit straight line trajectories are approximated to countless complete arc-shaped semicircular pit curves, thereby approximately simulating the three-dimensional arc texture of the honing tooth surface. (6) Realize flexible topological modification and predict the tooth surface texture after modification According to the parameters of the standard diamond dressing wheel and the standard workpiece gear, that is, in formula (5), r d =r w , based on the coordinate transformation, the tooth surface equation of the honing wheel workpiece is derived, and then the tooth surface equation of the modified workpiece is derived. The formula is as follows: in, In formula (5), r h is the position coordinate vector of the honing wheel, n h is the normal vector of the honing wheel, r w1 and is the position coordinate vector of the workpiece gear after modification, n w1 is the normal vector of the workpiece gear after modification, To adjust the wheel rotation angle, is the honing wheel rotation angle, Σ hd is the axis angle between the dressing wheel and the honing wheel, the M matrix is ​​the coordinate transformation matrix, and E hd is the center distance between the dressing wheel and the honing wheel, is the swing axis of the honing wheel frame, Σ wh is the axial angle between the honing wheel and the workpiece gear, Lz is the oscillation distance of the honing wheel; To achieve flexible topological modification of the workpiece gear tooth surface, the multi-axis linkage relationship during the honing machine operation is expressed as a polynomial. By optimizing the polynomial coefficients, the standard honing wheel can be used to modify the working gear surface in any topological manner, thus achieving arbitrary topological modification of the workpiece tooth surface without the need for a customized diamond dressing wheel. The feed rate of the honing wheel radial feed axis, the rotation angle of the cross axis between the honing wheel and the workpiece gear, and the rotation angle of the honing wheel tool holder swing axis are defined as fifth-order polynomials about the axial motion of the honing wheel axial feed axis. The numerical method of the least squares estimation algorithm based on the sensitivity matrix is ​​adopted to solve the polynomial coefficients of these additional motions through multiple closed-loop iterations. The polynomial coefficients are substituted into formula (5), and the obtained r w1 With n w1 This is the tooth surface equation of the workpiece after modification, which is replaced by r in step (1) w With n w , recalculate the contact line equation after modification, repeat steps (2), (3), and (5) to obtain the new modified texture, and compare it with the tooth surface texture before modification to verify the degree of influence of the minor modification on the tooth surface texture; the formula is as follows: In formula (6), the polynomial coefficients a0~a5, b0~b5 and c0~c5 are the dynamic parameters used to modify the topological structure during the honing process, a total of 18; Lz is the axial feed of the honing wheel, is the swing axis angle of the honing wheel tool holder; (7) Changing the size of the axis angle to obtain different modified tooth surface textures By changing the helix angle of the honing wheel, the axial angle between the honing wheel and the gear being processed is changed, and the texture of the workpiece gear tooth surface can be controlled; The specific operation is as follows: During the dressing process of the honing wheel using the dressing wheel, the angle of the honing wheel inclination swing axis is adjusted, that is, the axial angle of the honing wheel is adjusted by the dressing wheel; the helix angle of the honing wheel is directly changed by the dressing of the dressing wheel, and in the gear honing project, the axial angle between the workpiece gear and the honing wheel is indirectly changed, thereby affecting the texture morphology of the workpiece gear tooth surface.

2. The method for predicting and controlling the tooth surface texture of an internal meshing power honing helical gear according to claim 1, characterized in that: In step (1), the workpiece tooth surface contact line model is not only applicable to standard gears, but also to modified gears. The values ​​of the root circle and the addendum circle are calculated according to the modification coefficient, thereby changing the value range of the involute incremental angle in the workpiece tooth surface contact line equation. The formula for the value range of the involute incremental angle is as follows: In formula (7), r f1 is the root diameter of the gear being processed, r a1 is the tooth top circle diameter of the gear being machined.

3. The method for predicting and controlling the tooth surface texture of an internal meshing power honing helical gear according to claim 1, characterized in that: In step (5), under the premise of discretization of the abrasive particle motion trajectory, the length of the semicircular pit straight trajectory generated by the abrasive particle motion on the workpiece tooth surface reflects the size of the abrasive particle cutting speed value, which is always on the curved surface of the gear; by proportionally reducing the cutting speed value, many discrete straight line trajectory segments are finally approximated to several complete curves, and through mathematical calculation, each grid center point is used as the starting point of the abrasive particle movement, and it moves a small distance along the cutting speed direction, and finally the three-dimensional arc texture of the honing tooth surface is approximately simulated.

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