A method for modeling the tooth surface waviness of an internal meshing strong force gear honing process

Abstract

The application provides a kind of internal meshing strong force gear honing process tooth surface waviness modeling method, comprising the following steps: first, analyze internal meshing strong force gear honing processing principle and material removal mechanism, reveal the formation mechanism of workpiece tooth surface waviness.Second, based on the principle of internal meshing strong force gear honing processing, establish the theoretical model of internal meshing strong force gear honing workpiece tooth surface, and establish the actual model of workpiece tooth surface by considering machine tool vibration and honing wheel wear based on the theoretical model of workpiece tooth surface.Finally, extract the waviness of workpiece tooth surface on the actual model of workpiece tooth surface, analyze the spectrum of tooth surface waviness, identify the spectrum characteristics of tooth surface waviness and find possible gear transmission noise problems, improve the NVH performance of new energy vehicle gear transmission system.

Description

Technical Field

[0001] This invention relates to a method for modeling and evaluating gear tooth surface machining, specifically a method for modeling and evaluating the waviness of gear tooth surfaces in internal meshing high-strength honing processes. Background Technology

[0002] As a core component of new energy vehicles, the gear transmission system's machining quality directly impacts the vehicle's NVH (Noise, Vibration, Harshness) performance. With the increasing power density of electric drive transmission systems in new energy vehicles through higher motor speeds, current motor speeds have reached 25,000 r / min and are trending towards 30,000 r / min. Under these transmission conditions, the gears in the gear transmission system of new energy vehicles endure higher speeds, placing more stringent demands on the machining quality of the gear tooth surfaces. Simply improving the gear shape accuracy is no longer sufficient to solve the NVH problems of new energy vehicle transmission systems. Under high-speed gear operation, the surface morphology of the gear tooth surface has a significantly amplified impact on gear transmission performance, becoming a major factor in the deterioration of NVH performance in high-speed gear transmissions.

[0003] Tooth surface waviness is a surface geometric structure in gear tooth morphology that lies between microscopic tooth surface roughness and macroscopic tooth profile error, exhibiting periodic surface irregularities. Tooth surface waviness affects the correct meshing position of meshing gear pairs, generating irregular transmission deviations, leading to vibration and noise in the gear transmission system. This effect becomes particularly significant under high-speed transmission conditions, and existing research has shown that tooth surface waviness is a major cause of transmission noise in gears.

[0004] Internal meshing high-strength honing is an important machining process for gears in the transmission system of new energy vehicles. It is usually used in the final finishing process after gear heat treatment and has a significant impact on gear machining quality. Therefore, this paper proposes a modeling method for the waviness of the tooth surface in the internal meshing high-strength honing process to improve the NVH performance of gear transmissions at the theoretical level. Summary of the Invention

[0005] This invention provides a method for modeling the waviness of tooth surfaces in internal meshing high-strength honing processes, in order to optimize the waviness of workpiece tooth surfaces and thus improve the NVH performance of gear transmission.

[0006] The technical solution adopted to achieve the purpose of this invention is as follows: a method for modeling the waviness of internal meshing high-strength honed tooth surfaces, comprising the following steps:

[0007] Step 1: Analyze the machining principle and material removal mechanism of internal meshing high-strength honing, and reveal the formation mechanism of workpiece tooth surface waviness.

[0008] Step 2: Establish a theoretical model of the tooth surface of the internal meshing high-strength honing workpiece, and establish an actual model of the workpiece based on the material removal mechanism of the tooth surface.

[0009] Step 3: Extract the waviness of the workpiece tooth surface, and identify potential NVH performance problems by performing spectral analysis on the waviness.

[0010] Preferably, the specific analysis process of the internal meshing high-strength honing machining principle and material removal mechanism described in step 1 is as follows:

[0011] (1) Processing principle of internal meshing high-strength honing:

[0012] Internal meshing high-force gear honing is one of the high-precision gear machining processes, and its typical process machine tool mechanism is as follows: Figure 2 As shown in the figure. C1 axis is the honing wheel rotation axis, C2 axis is the workpiece rotation axis, A axis is the axis angle adjustment axis, X axis is the workpiece radial feed axis, Z axis is the workpiece axial feed axis, and B axis is the honing wheel oscillation axis. The machining principle of the internal meshing high-strength honing process is to precisely control the meshing motion of the honing wheel and the workpiece gear to achieve micro-removal of material from the workpiece gear tooth surface, completing high-precision machining of the workpiece gear tooth surface. Specifically, the meshing motion of the tool honing wheel and the workpiece gear is equivalent to the meshing transmission of a pair of internal and external cylindrical helical gears. The difference is that in the internal meshing high-strength honing process, to ensure uniform wear of the honing wheel, the honing wheel will move axially along the workpiece gear axis. Its meshing transmission is as follows: Figure 3 As shown. The rotational speeds of the honing wheel and the workpiece are set as follows:

[0013]

[0014] Where, n c1 It is the rotational speed of the honing wheel's rotating shaft, n c2 It is the rotational speed of the workpiece's rotary axis, z c1 It is the number of teeth on the honing wheel, z c2 It is the number of teeth on the workpiece gear, v z It is the axial feed speed of the honing wheel, β c2 It is the helix angle of the workpiece gear.

[0015] (2) Material removal mechanism of internal meshing high-strength honing process:

[0016] To remove material from the tooth surface of the workpiece, the internal meshing high-power honing machine tool adjusts the radial feed shaft of the workpiece gear to change the relative position of the honing wheel and the workpiece gear, so that the abrasive grains on the honing wheel tooth surface penetrate the workpiece tooth surface material during the relative movement between the honing wheel and the workpiece gear, and remove the workpiece tooth surface material under the action of the abrasive grains on the honing wheel.

[0017] Theoretically, without considering the machining allowance of the gear tooth surface material, the honing wheel and the workpiece gear are in line contact; considering the machining allowance of the gear tooth surface material, the honing wheel and the workpiece gear are in a band-shaped contact area that is approximately line contact, such as... Figure 4 .

[0018] During the honing process, both the honing wheel and the workpiece gear vibrate. This vibration causes the actual contact line between the honing wheel and the workpiece gear to deviate from the theoretical contact line, thereby altering the amount of material removed from the workpiece by the abrasive grains along the contact line of the honing wheel. This results in periodic surface unevenness on the tooth surface of the workpiece gear, such as... Figure 5 .

[0019] Furthermore, as the number of workpieces processed increases, the honing wheel teeth gradually wear. Due to the different honing conditions at the tooth tip and root, and the randomness of the honing wheel surface material, the honing wheel teeth also exhibit surface roughness. This surface roughness is reflected onto the workpiece tooth surface during processing, forming surface roughness on the workpiece tooth surface, such as... Figure 6 .

[0020] Among them, tooth surface waviness is a surface unevenness characteristic between tooth surface roughness and tooth profile error. The tooth surface waviness curve is obtained after processing by a filtering algorithm.

[0021] Preferably, the modeling process of the theoretical model and the actual model of the workpiece tooth surface in step 2 is as follows:

[0022] (1) Establishment of the theoretical model of the tooth surface of the workpiece.

[0023] In internal meshing high-strength honing, the surface of the honing wheel is the envelope surface of the dressing wheel, that is, the honing wheel is formed by the envelope motion of the dressing wheel. The dressing wheel usually has the same shape parameters as the workpiece gear.

[0024]

[0025] θ and u are the parameters of the dressing gear tooth surface.

[0026] According to the gear meshing principle, the velocity of the dressing gear tooth surface and the honing gear tooth surface in the common normal direction at the meshing point is 0, i.e., the gear meshing equation is:

[0027]

[0028] In the formula, n is the common normal at the meshing point between the dressing wheel tooth surface and the honing wheel tooth surface, and v is the relative velocity at the meshing point between the dressing wheel tooth surface and the honing wheel tooth surface. The calculation of n and v needs to be performed in the same coordinate system.

[0029] In the coordinate system of the dressed gear tooth surface, the normal vector n of the dressed gear tooth surface... d for:

[0030]

[0031] The relative velocity v between the honing wheel tooth surface and the dressing wheel tooth surface hd for:

[0032]

[0033] By utilizing homogeneous coordinate transformation, the above variables are unified into a single coordinate system, and a gear meshing equation is constructed. By solving the meshing equation, the unknowns are obtained, and the meshing point on the tooth surface can be obtained. This meshing point is then represented using homogeneous coordinates in the honing wheel coordinate system, yielding the corresponding point on the honing wheel tooth surface.

[0034]

[0035]

[0036] r h These are the coordinates of the honing wheel tooth surface, n h The tooth surface coordinate r h The normal vector at point M hd L is the homogeneous coordinate transformation matrix between the dressing wheel and the honing wheel. hd It is M hd The first 3 rows and 3 columns.

[0037] Based on the above method, the coordinates of the workpiece tooth surface can be solved by using the envelope motion of the honing wheel and the workpiece gear, that is, a theoretical model of the workpiece tooth surface can be established.

[0038]

[0039]

[0040] r g M is the coordinate of the workpiece tooth surface. gh It is the coordinate transformation matrix between the honing wheel and the workpiece gear, which is determined based on the positional relationship between the honing wheel and the workpiece gear.

[0041] (2) Establishment of the actual model of the workpiece.

[0042] The formation of the workpiece tooth surface is the result of multiple grinding operations by a large number of abrasive grains on the honing wheel, which removes material. This can be expressed as the sum of the depth of material removal per abrasive grain and the number of grinding passes. For example... Figure 7 As shown.

[0043] The depth of material removal per abrasive grain is represented by a matrix, and the distribution of the material removal depth is adjusted by considering the grinding direction of the abrasive grain.

[0044]

[0045] D is the material removal depth within the abrasive grain's influence range, which can represent the material removal height along the abrasive grain velocity direction and its perpendicular direction.

[0046] Based on necessary data such as material removal allowance and feed rate in the process parameters, the theoretical number of material removal cycles is determined. Considering the vibration of the honing wheel and the machine tool, only a portion of the abrasive grains participate in material removal within each material removal cycle. According to the actual proportion of abrasive grains participating in grinding, the positions of the abrasive grains participating in grinding are randomly assigned. At this position, the material removal depth of the abrasive grains is considered and the residual height data of the tooth surface is updated. After multiple iterations, the morphology of the workpiece tooth surface can be obtained.

[0047]

[0048] Preferably, the method for waviness extraction and tooth surface waviness spectrum analysis in step 3 is as follows:

[0049] (1) Calculate the deviation between the actual model of the workpiece tooth surface and the theoretical model of the workpiece tooth surface:

[0050] To fully measure the deviation characteristics of the workpiece tooth surface, the deviation of the workpiece tooth surface is extracted along the tooth profile direction and the tooth direction, such as... Figure 8 As shown.

[0051] Tooth surface waviness is one of the main components of tooth surface deviation. Its wavelength lies between tooth surface roughness and tooth profile error. By setting filter parameters based on waviness characteristics to filter the acquired tooth surface deviation data, it is ensured that the acquired data reflects the tooth surface waviness characteristics. Figure 9 .

[0052] (2) By extracting the tooth surface waviness, the tooth surface waviness curves in the tooth profile direction and tooth direction of the workpiece are obtained. By performing a fast Fourier transform on the tooth surface waviness curve, the spectrum analysis diagram of the tooth surface waviness is obtained. The spectrum diagram shows the amplitude corresponding to the frequency. By analyzing the spectrum diagram, potential gear transmission noise problems can be identified, and the gear machining morphology quality and the rationality of the process parameter settings can be predicted in advance. Attached Figure Description

[0053] Figure 1 Modeling process for waviness of internal meshing high-strength honing tooth surface

[0054] Figure 2 Internal meshing high-strength honing machine structure

[0055] Figure 3 Honing wheel meshes with workpiece gear for transmission

[0056] Figure 4 Theoretical line contact between the honing wheel and the workpiece gear

[0057] Figure 5The honing wheel and the workpiece gear are in near-line contact.

[0058] Figure 6 Workpiece tooth surface morphology

[0059] Figure 7 Tooth surface material removal process

[0060] Figure 8 Tooth surface deviation extraction direction

[0061] Figure 9 ripple transmission characteristics

[0062] Figure 10 Position and movement relationship of dressing wheel and honing wheel

[0063] Figure 11 Tooth deviation - signal decomposition

[0064] Figure 12 Tooth Profile Deviation-Signal Decomposition

[0065] Figure 13 Tooth-Wave Spectrum

[0066] Figure 14 Tooth profile-wrinkle spectrum Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings and embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practice in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0068] This invention provides a method for modeling the waviness of internal meshing high-strength honing gear tooth surfaces. By considering the machining principle of internal meshing high-strength honing machine tools and the motion characteristics of each axis of the machine tool, a theoretical model of the workpiece gear is established based on the gear meshing principle. Taking into account honing wheel wear and machine tool vibration, an actual model of the workpiece tooth surface that closely reflects actual machining is established. By extracting and analyzing the waviness of the obtained actual workpiece tooth surface model, a waviness spectrum is obtained. Based on the characteristics of the waviness spectrum, potential gear transmission noise problems are identified. This modeling method specifically includes the following steps:

[0069] S1: Determine the basic gear parameters and process parameters for internal meshing high-strength honing.

[0070] Table 1. Basic and process parameters of gears

[0071] Honing wheel / workpiece normal module, honing wheel teeth, workpiece teeth, honing wheel helix angle, workpiece helix angle, axial feed rate, axial oscillation distance, radial feed. 2.5471234521.833.8135 mm--°°mm / rmmμm

[0072] S2: Establish the equation for the tooth surface of the dressing wheel as the modeling basis for the internal meshing high-strength honing;

[0073]

[0074] S3: Based on the position and motion relationship between the dressing wheel and the honing wheel, establish the spatial coordinate transformation relationship M. dh ;

[0075] The position and movement relationship between the dressing wheel and the honing wheel are as follows: Figure 10 As shown.

[0076]

[0077]

[0078] S4: Based on the equation of the dressing wheel tooth surface and the spatial motion coordinate relationship between the dressing wheel and the honing wheel, establish the gear meshing equation, and solve the meshing equation to obtain the honing wheel tooth surface.

[0079] The basic equation of gear meshing principle is:

[0080]

[0081] Calculate the normal vector n and relative velocity v at the meshing point of the dressing wheel and honing wheel.

[0082] The normal vector of the dressed gear tooth surface can be obtained from the equation of the dressed gear tooth surface:

[0083]

[0084] During the meshing motion of the honing wheel and the dressing wheel, the relative linear velocity v between the honing wheel and the gear tooth surface of the workpiece is... hd The solution process is as follows:

[0085]

[0086] The dressing wheel speed is w d The honing wheel rotates at a speed of w. h .

[0087] Using a coordinate transformation matrix, the above variables are unified to the same coordinate system for calculation, and the meshing equation is determined as follows:

[0088]

[0089] Solve for the unknowns in the equation by calculating f = 0.

[0090] u and θ are parameters of the dressed gear tooth surface, used to determine discrete points on the dressed gear tooth surface. By combining the unknowns obtained from solving the meshing equation for each discrete point, the coordinate transformation matrix M of that point when it is in mesh can be determined. hd And obtain the coordinate representation of the meshing point in the honing wheel coordinate system:

[0091]

[0092] S5: After obtaining the honing wheel tooth surface, the theoretical model of the workpiece tooth surface is established by using the relative motion relationship between the honing wheel tooth surface and the workpiece gear and the gear meshing equation.

[0093] The method for establishing the theoretical model of the workpiece tooth surface is the same as the method for establishing the honing wheel tooth surface model. That is, by establishing a coordinate transformation matrix, calculating the tooth surface normal vector n and the relative motion velocity v, and constructing the meshing equation; solving the meshing equation, and using the obtained parameters to calculate the tooth surface coordinate points, the theoretical model of the workpiece tooth surface is obtained.

[0094]

[0095] S6: Considering process parameters, combined with honing wheel wear and machine tool vibration, determine the cutting marks of the abrasive grains and the number of grinding cycles to construct an actual model of the workpiece tooth surface.

[0096] First, determine the initial height matrix H of the workpiece tooth surface based on the initial condition of the workpiece tooth surface.

[0097] Based on the kinematic relationship between the honing wheel and the workpiece gear, the velocity of the abrasive grain at any point on the workpiece tooth surface relative to the workpiece is calculated.

[0098]

[0099] The grinding marks of abrasive grains are determined based on their velocity. The marks left by abrasive grains on the tooth surface of the workpiece are represented as a double parabolic surface, that is, the direction of abrasive grain velocity and the perpendicular direction are considered as parabolic functions.

[0100]

[0101] The matrix Z is rotated and adjusted according to the velocity direction to obtain the grinding marks D of the abrasive grains.

[0102] Based on the processing parameters, the number of material removal cycles is calculated, and this data is used as the number of tooth surface iterations. In each iteration, the wear of the honing wheel and the vibration of the machine tool are considered to determine the grinding ratio of the abrasive parameters, and the position of the abrasive is randomly assigned. Near the position where the abrasive contacts the workpiece tooth surface, the abrasive grinding mark D is considered, and the tooth surface height matrix H is updated.

[0103] S8: The tooth surface height matrix H is the result of multiple abrasive processing of the tooth surface, representing the tooth surface morphology. Tooth surface deviation values ​​are extracted along the tooth direction and tooth profile direction of the workpiece tooth surface to obtain the tooth direction deviation curve and tooth profile deviation curve.

[0104] Apply filtering algorithms to the tooth profile deviation curve and the tooth profile deviation curve respectively to obtain the corresponding tooth profile waviness curve and tooth profile waviness curve, such as... Figure 11 and Figure 12 These are the tooth profile deviation curve and its filtering result, and the tooth profile deviation curve and its filtering result, respectively.

[0105] S9: Perform Fourier transforms on the obtained tooth waviness curves and tooth profile waviness curves respectively to obtain the corresponding tooth waviness spectrum and tooth profile waviness spectrum, such as... Figure 13 and Figure 14 As shown, in the tooth waviness spectrum, the fundamental frequency is 1.5 cycles / mm, corresponding to an amplitude of 1.99 μm, which is the main frequency component. The 3.5th harmonic (1.01 μm), 8th harmonic (1.49 μm), and 28th harmonic (0.70 μm) decrease sequentially, with the amplitude of the high-frequency components significantly lower than that of the fundamental frequency. In the tooth profile waviness spectrum, the fundamental frequency is 0.6 cycles / mm, corresponding to an amplitude of approximately 1.45 μm, with the 3.8th harmonic (approximately 0.88 μm) and 13th harmonic (approximately 0.72 μm) decreasing progressively. Based on the relationship between frequency and amplitude in the spectrum, combined with the operating frequency of the workpiece gear transmission system, it can be determined whether the workpiece tooth surface waviness can induce resonance in the gear transmission system, causing transmission noise. This allows for the early identification of the potential transmission noise characteristics of the gear.

Claims

1. A method for modeling the waviness of tooth surfaces in an internal meshing high-strength honing process, characterized in that, Includes the following steps: Step 1: Analyze the machining principle and material removal mechanism of internal meshing high-strength honing, and reveal the formation mechanism of workpiece tooth surface waviness. (1) The internal meshing high-strength honing process changes the relative position of the honing wheel and the workpiece gear by adjusting the radial feed shaft of the workpiece gear, so that the abrasive grains on the honing wheel tooth surface penetrate the workpiece tooth surface material and remove the workpiece tooth surface material; wherein, there is vibration during the relative movement of the honing wheel and the workpiece gear, and the vibration causes periodic surface unevenness on the workpiece gear tooth surface; as the number of workpieces processed increases, the surface unevenness caused by the wear of the honing wheel tooth surface is mapped onto the workpiece tooth surface, forming the surface unevenness of the workpiece tooth surface. (2) The surface roughness of the workpiece tooth surface is filtered to obtain the tooth surface waviness curve; Step 2: Establish a theoretical model of the tooth surface of the internal meshing high-strength honing workpiece, and establish an actual model of the workpiece based on the material removal mechanism of the tooth surface; (1) The theoretical model of the tooth surface of the internal meshing high-strength honing workpiece described in this invention is based on the internal meshing high-strength honing processing principle, the motion characteristics of each axis and the relative positional relationship between the honing wheel and the workpiece gear. The meshing equation between the honing wheel and the workpiece gear is established, and the formation process of the workpiece tooth surface is modeled. The theoretical tooth surface of the workpiece gear is obtained by solving the meshing equation. (2) The actual internal meshing high-strength honing process is affected by the wear of the honing wheel and the vibration of the machine tool, resulting in a deviation between the actual machined workpiece tooth surface and the theoretical tooth surface of the workpiece gear. In order to establish an actual model of the workpiece tooth surface, this modeling method considers the wear of the honing wheel and the vibration of the machine tool based on the theoretical model of the workpiece tooth surface, constructs the material removal behavior of the honing wheel tooth surface abrasive particles on the workpiece tooth surface, so that the model is close to the actual gear machining state, and obtains the actual model of the workpiece tooth surface; Step 3: Extract the waviness of the workpiece tooth surface, and identify potential NVH performance problems by performing spectral analysis on the waviness of the tooth surface. (1) Tooth surface waviness is a surface irregularity feature in gear surface morphology that lies between tooth surface roughness and tooth profile error. The tooth surface waviness is obtained by setting a wavelength extraction threshold for the tooth surface morphology. Due to the tooth surface machining characteristics of internal meshing high-strength honing, the material removal state varies at different locations on the workpiece tooth surface. To fully characterize the waviness feature of the workpiece tooth surface, waviness values ​​are extracted along the tooth profile direction and the tooth direction of the workpiece tooth surface, respectively. (2) Perform Fourier transform on the extracted tooth surface waviness to obtain the tooth surface waviness spectrum features; the tooth surface waviness spectrum features are related to gear transmission error, which is an important factor causing gear transmission noise; based on the tooth surface waviness spectrum features, determine the potential transmission noise problem of the gear.

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