A method for predicting roughness of tooth surface of internal meshing strong force gear hobbing considering multi-factor coupling

Abstract

This invention relates to the field of gear processing and manufacturing technology, and more specifically to a method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling. The method includes the following steps: S1, constructing the tooth surface equation and honing coordinate system, calculating the corresponding internal honing wheel tooth surface, and obtaining the position and velocity information of the meshing point; S2, employing an analytical-numerical hybrid solution strategy to obtain the geometric characteristics and induced curvature of the topology-modified workpiece tooth surface and the implicit envelope surface of the honing wheel at the instantaneous meshing point; S3, constructing a dual-stochastic statistical model integrating abrasive grain size and cutting edge height, and using a local abrasive grain modeling method based on the instantaneous meshing point to characterize the micro-topology of the honing wheel; S4, establishing a dynamic prediction model considering machine tool vibration, and obtaining the real-time displacement deviation caused by machine tool vibration through signal acquisition and frequency domain reconstruction; S5, coupling the micro-material removal mechanism to establish a single abrasive grain groove depth model, achieving quantitative prediction and evaluation of the overall tooth surface roughness characteristics.

Description

Technical Field

[0001] This invention relates to the field of gear processing and manufacturing technology, and more specifically to a method for predicting the surface roughness of internal meshing high-strength honing gears that considers the coupling of multiple factors. Background Technology

[0002] With the rapid development of electric drive systems for new energy vehicles towards speeds exceeding 30,000 r / min, the NVH and reliability of reducer gears under extreme service conditions have become bottlenecks restricting system performance improvement. Tooth surface roughness, as a core indicator of gear surface integrity, has a significant impact on dynamic excitation and transmission accuracy during high-speed meshing. Internal meshing high-strength honing, as a novel finishing process, can significantly reduce tooth surface roughness, making it widely used in high-performance transmission systems. However, the microstructure creation process of internal meshing high-strength honing is extremely complex. First, influenced by the honing wheel dressing process, the abrasive grain height distribution exhibits a significant asymmetric distribution, deviating from the ideal normal distribution. Second, honing often involves complex topological shaping, leading to dynamic changes in instantaneous induced curvature during meshing, altering the distribution law of micro-cutting depth. Finally, within the sub-micron level of finishing, machine tool vibration has become a dynamic factor that cannot be ignored in affecting surface quality.

[0003] Therefore, how to provide a method for predicting the surface roughness of internal meshing high-strength honing gears that considers the coupling of multiple factors is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the present invention provides a method for predicting the surface roughness of internal meshing high-strength honing gears that considers the coupling of multiple factors, aiming to solve the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling includes the following steps: S1. Construct the tooth surface equation and honing coordinate system, calculate the corresponding internal gear honing tooth surface, and obtain the position and velocity information of the meshing point; S2. An analytical-numerical hybrid solution strategy is adopted to obtain the geometric characteristics and induced curvature of the tooth surface of the topologically modified workpiece and the implicit envelope surface of the honing wheel at the instantaneous meshing point. S3. Construct a dual stochastic statistical model that integrates abrasive grain size and cutting edge height, and use a local abrasive grain modeling method based on instantaneous meshing point to characterize the micro-topology of the honing wheel; S4. Establish a dynamic prediction model that considers machine tool vibration, and obtain the real-time displacement deviation caused by machine tool vibration through signal acquisition and frequency domain reconstruction. S5. Couple the micro-material removal mechanism and establish a single abrasive groove depth model to achieve quantitative prediction and evaluation of the roughness characteristics of the entire tooth surface.

[0006] Furthermore, the equation for establishing the modified gear tooth surface in S1 is specifically as follows: The tooth profile bulging modification function is parabolically distributed along the involute arc length. During modeling, the maximum tooth profile bulging amount at the mid-section of the tooth width is used as the reference, and geometric offsets are superimposed along the radial direction to complete the calculation of the normal direction of the ideal involute tooth surface. The tooth profile bulging modification function is parabolically distributed along the theoretical helix, and the maximum tooth profile bulging amount at the midpoint of the tooth width is used as the control parameter. To ensure kinematic consistency, the tooth profile modification amount is converted into angular phase increments and incorporated into the model to realize the tooth profile modification calculation. The geometric offsets and angular phase increments are calculated from the pitch circle radius, involute development angle, and helix increment angle parameters. The topology modification function is superimposed onto the standard involute to obtain the position vector of the topology-modified gear. Combining the knowledge of differential geometry of the modified tooth surface, the normal vector is calculated through the partial derivative of the position vector to complete the tooth surface modeling.

[0007] Furthermore, the specific steps for constructing the honing motion coordinate system in S1 are as follows: Reference frame S h and S g They are rigidly fixed to the honing wheel and gear, respectively. S 1 , S 2 and S 3 To provide an auxiliary coordinate system, based on spatial coordinate transformation, the honing wheel is positioned in the reference frame. S h Position vector in r h and normal vector n h Represented as: , , in L hg Represents the homogeneous transformation matrix M hg The top left submatrix, M hg The rotational component representing the spatial transformation relationship between the gear and the honing wheel can be expressed as: , in f h and f gLet represent the rotation angles of the honing wheel and the gear, respectively. Their kinematic relationship is determined by the following formula: A hg Indicates the center distance. L z Indicates the axial feed rate. ∑ hg This represents the angle between the axes.

[0008] , in i hd Indicates the transmission ratio. r hp and β h These represent the pitch circle radius and helix angle of the honing wheel, respectively.

[0009] Furthermore, the calculation of the internal gear tooth surface and the acquisition of position and velocity information based on the meshing principle in S1 specifically involves: According to the principle of gear meshing, the honing process is a two-degree-of-freedom motion, where the independent motion variable is the gear rotation angle. f g and axial feed L z The instantaneous contact point on the tooth surface must simultaneously satisfy the meshing equations consisting of these two independent variables, as shown below: , By solving this set of nonlinear equations, the parameters corresponding to each contact point can be obtained. Substituting these parameters into the tooth surface equation yields the corresponding meshing position information. Simultaneously, substituting them into the meshing equation yields the corresponding velocity information, along with the corresponding position and velocity information.

[0010] Furthermore, S2 specifically refers to: The topologically modified workpiece tooth surface with clearly defined parameterized equations is obtained by using differential geometry analytical method to obtain its unit normal vector and the coefficients of the first and second basic forms, and to determine the instantaneous principal curvature of meshing. For the implicit envelope surface of the honing wheel, a small perturbation step size is set in the neighborhood of the instantaneous contact point, and the meshing equation is solved by numerical difference method to obtain the spatial coordinates of the discrete point. The first, second, and mixed partial derivatives are calculated using the central difference operator to construct the first and second fundamental form coefficients of the honing wheel tooth surface, thereby obtaining the principal curvature.

[0011] Furthermore, S3 specifically includes: Based on the normal distribution model, the random discreteness of the equivalent diameter of abrasive grains is characterized, and the diameter of abrasive grains corresponding to discrete grid points is determined. The asymmetric right-skewed characteristics of the abrasive grain exit height are characterized by the Rayleigh distribution model, and the inverse cumulative distribution function transformation method is used for sampling to determine the abrasive grain exit height at each meshing point. The three-dimensional tooth surface is projected onto a two-dimensional parametric coordinate system based on the radius and tooth width, transforming the spatial topology into a regular height field numerical matrix.

[0012] Furthermore, S4 specifically includes: The time-domain vibration signal of the spindle during the machining process is collected by an accelerometer, and the acceleration amplitude is converted into the displacement amplitude using fast Fourier transform and frequency domain integral relationship. The top three dominant frequencies with the highest energy proportions are selected and reconstructed as a linear superposition of multi-frequency harmonic displacement terms. The time variable is mapped to the position function of the meshing point, and the reconstructed vibration displacement terms are superimposed.

[0013] Furthermore, S5 specifically includes: Based on the influence of radial feed rate and effective radius of curvature, and combined with the local effective spacing correction model of abrasive grains, the nominal groove depth is calculated; Based on the Rayleigh distribution, the nominal groove depth is mapped to the discrete abrasive scale to obtain the instantaneous groove depth with coupled dual random characteristics. The coupling of scratching, plowing and cutting mechanisms is used to calculate the additional height caused by plastic accumulation, and the single-point arithmetic mean deviation is obtained through the transformation relationship. Based on discrete mesh data of the entire tooth surface, the average roughness, range, and standard deviation are quantitatively evaluated.

[0014] Compared with existing technologies, the analytical-numerical hybrid solution strategy of this invention accurately obtains the instantaneous induced curvature of the topologically modified tooth surface and the implicit envelope surface of the honing wheel at the meshing point, constructs a "double random" statistical model that integrates abrasive grain size (normal distribution) and cutting edge height (Rayleigh distribution), superimposes multi-frequency harmonic vibration displacement into the static random groove depth model, and couples the micro-material removal mechanism (scraping, plowing, cutting) to achieve quantitative evaluation of the roughness of the entire tooth surface. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the honing coordinate system of the present invention.

[0017] Figure 2 This is a schematic diagram illustrating the normal distribution characteristics of abrasive grain geometry according to the present invention.

[0018] Figure 3 This is a schematic diagram illustrating the Rayleigh distribution characteristics of abrasive grain exit height according to the present invention.

[0019] Figure 4 This is a schematic diagram of tooth surface mesh division according to the present invention.

[0020] Figure 5 This is a schematic diagram of a tooth surface roughness simulation process according to the present invention.

[0021] Figure 6 This is a schematic diagram illustrating the effect of vibration on roughness according to the present invention.

[0022] Figure 7 This is a schematic diagram illustrating the effect of cutting depth on radius of curvature according to the present invention.

[0023] Figure 8 This is a schematic diagram of the structure of the abrasive groove depth according to the present invention.

[0024] Figure 9 This is a schematic diagram of an internal meshing high-strength honing machine tool according to the present invention.

[0025] Figure 10 This is a schematic diagram of the tooth surface roughness result according to the present invention. Detailed Implementation

[0026] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] The process of constructing the tooth surface equation and obtaining position and velocity information in step 1 is as follows: (1) Establish the equation for the tooth surface of the modified gear, as detailed below: For complex topologically modified tooth surfaces, the mid-section of the tooth width exhibits only profile bulging modification, while the mid-section of the tooth profile exhibits only tooth-direction bulging modification. The profile bulging modification function follows a parabolic distribution along the involute arc length; in the numerical modeling process, the maximum profile bulging amount at the mid-section of the tooth width is used. C p Based on the radial vector direction, a geometric offset is superimposed. P This allows for the calculation of the ideal involute tooth surface in the normal direction. Simultaneously, the tooth profile shaping function exhibits a parabolic distribution along the theoretical helix, with the maximum tooth profile bulge at the midpoint of the tooth width. C lTo control parameters; to ensure kinematic consistency, the tooth profile modification is converted into angular phase increments. DF The model is then incorporated to perform profile modification calculations along the tooth direction. The calculations for geometric offset and angular phase increment are shown below: in, r b The radius of the pitch circle, m For the involute development angle, i The spiral increment angle, p The helical lead of a standard gear is defined as follows: p = r b / tan β g , β g It is the helix angle. L The total length of a standard involute; m 0 The development angle at the starting point of the involute; b This refers to the tooth width.

[0028] By superimposing the topology modification function onto the standard involute, the position vector of the topology-modified gear can be obtained, as shown in the following equation.

[0029] in g = m + i + m 0 + DF This indicates the combined phase angle.

[0030] Based on the differential geometry of the modified tooth surface, the normal vector is calculated using the partial derivative of the position vector. n g_tm As shown in the following formula: (2) Construct the honing motion coordinate system, as detailed below: Figure 1 A spatial coordinate system established for the honing process. Reference frame. S h and S g They are rigidly fixed to the honing wheel and gear, respectively. S 1 , S 2 and S 3As an auxiliary coordinate system. Based on spatial coordinate transformation, the honing wheel is in the reference frame. S h Position vector in r h and normal vector n h It can be represented as: in L hg Represents the homogeneous transformation matrix M hg The top left submatrix. M hg The rotational component representing the spatial transformation relationship between the gear and the honing wheel can be expressed as: in f h and f g These represent the rotation angles of the honing wheel and the gear, respectively, and their kinematic relationship is determined by the following formula. A hg Indicates the center distance. L z Indicates the axial feed rate. ∑ hg This represents the angle between the axes.

[0031] in i hd Indicates the transmission ratio. r hp and β h These represent the pitch circle radius and helix angle of the honing wheel, respectively.

[0032] (3) Calculate the tooth surface of the internal gear honing machine based on the meshing principle and obtain its position and velocity information, as follows: According to the principle of gear meshing, the honing process is a two-degree-of-freedom motion, where the independent motion variable is the gear rotation angle. f g and axial feed L z The instantaneous contact point on the tooth surface must simultaneously satisfy the meshing equations consisting of these two independent variables, as shown below: By solving this set of nonlinear equations, the parameters corresponding to each contact point can be obtained. Substituting these parameters into the tooth surface equation yields the corresponding meshing position information. Simultaneously, substituting them into the meshing equation yields the corresponding velocity information, as well as the corresponding position and velocity information.

[0033] Step 2 employs a hybrid analytical-numerical solution strategy to obtain the geometric characteristics and induced curvature process of the topologically modified workpiece tooth surface and the implicit envelope surface of the honing wheel at the instantaneous meshing point, as follows: (1) For the tooth surface of a topologically modified workpiece with a clear parameterized equation, the unit normal vector and the coefficients of the first and second basic forms are obtained by using the differential geometry analytical method, and then the instantaneous principal curvature of meshing is determined. The tooth surface of a topologically modified workpiece has a well-defined parametric equation, and its local curvature can be determined using the fundamental form of differential geometry. First, calculate the unit normal vector of the topologically modified tooth surface: Then, construct the first basic form coefficients ( E g , F g , G g This characterizes the length relationships within the tangential plane of the modified tooth surface: To describe the bending properties of the topologically modified tooth surface at the instantaneous contact point, its second fundamental form coefficients are determined using the dot product of the second-order partial derivative and the normal vector. L g , M g , N g ): Finally, based on the first and second fundamental form coefficients, the characteristic equation is solved to obtain the instantaneous principal curvature of the topologically modified tooth surface during meshing. K g : Instantaneous principal curvature K g With radius of curvature r g The relationship is shown in the following formula: (2) For the implicit envelope surface of the honing wheel, a small perturbation step size is set in the neighborhood of the instantaneous contact point, and the meshing equation is solved by numerical difference method to obtain the spatial coordinates of the discrete point. Since the honing wheel tooth surface is an implicit envelope surface constrained by a nonlinear meshing equation, its second-order geometric characteristics are determined using numerical differentiation. First, at the instantaneous contact point M ( m , i Within the neighborhood of ), set a small perturbation step size. Dm and Dth The spatial coordinates of discrete points within the neighborhood are obtained by solving the meshing equation. Then, the first, second, and mixed partial derivatives of the topologically modified tooth surface at the instantaneous contact point are calculated using the central difference operator. In the formula f g (i+1) , f g (i) , f g (i-1) , L z (i+1) , L z (i) , L z (i-1) These are the numerical solutions of the instantaneous rotation angle and feed rate at the corresponding neighborhood points that satisfy the meshing equation.

[0034] The mixed partial derivatives are calculated using the cross-difference scheme: In the formula f g (i+1,j+1) and L z (i+1,j+1) It is a parameter ( m + Dm , i + Dth Numerical solutions for the instantaneous rotation angle and feed rate at the corresponding points that satisfy the meshing equation. f g (i+1,j-1) , f g (i-1,j+1) , f g (i-1,j-1) , L z (i+1,j-1) , L z (i-1,j+1) , L z (i-1,j-1) similar.

[0035] (3) Calculate the first, second and mixed partial derivatives using the central difference operator, construct the first and second basic form coefficients of the honing wheel tooth surface, and obtain its principal curvature; Using the numerical derivatives described above, the unit normal vector at the instant of contact between the honing wheel and the honing wheel is first determined: Then, reconstruct the first and second basic form coefficients of the honing wheel according to step 2 (1). Finally, obtain the principal curvature of the honing wheel by solving the characteristic equation that is consistent with the form of the workpiece gear.

[0036] The process of constructing a "double-random" statistical model that integrates abrasive grain size and cutting edge height in step 3, and characterizing the micro-topology of the honing wheel using a local abrasive grain modeling method based on instantaneous meshing points, is as follows: (1) Introduce a normal distribution model to characterize the random discreteness of the equivalent diameter of the abrasive grains and determine the abrasive grain diameter corresponding to the discrete grid point; The abrasive geometry model is based on the following assumptions: (a) The abrasive grain shape is simplified to a cone; (b) The abrasive geometry is determined by the equivalent base diameter. d g and half cone angle α The only certainty.

[0037] The geometric dimensions of the abrasive grains in honing wheels are constrained by the sieving process. According to abrasive grading standards, the equivalent diameters corresponding to abrasive grains of the same grit size are not identical, exhibiting significant random dispersion. Considering the statistical characteristics of abrasive grain size fluctuations in large-scale production, a normal distribution model is introduced to characterize this randomness, such as... Figure 2 As shown. The probability density function of the equivalent diameter of the abrasive grains is as follows: In the formula, m d This represents the nominal diameter, and its value is determined by the grit size of the honing wheel. s d Representing the standard deviation, this value reflects the dispersion of the abrasive grain geometry. Based on the actual precision range being selected, it is used in this paper as... s d =0.1 m d .

[0038] To map this continuous probability model to discrete abrasive grains on the honing wheel, a Monte Carlo sampling method was used. The total number of effective abrasive grains is... N total This value is determined by the number of discrete points on the tooth profile. i and number of discrete points in the tooth direction j Joint decision, Ntotal = i × j Then the engagement point ( i , j The abrasive grain diameter at () d g ( i , j As shown below.

[0039] in x ( i , j ) is an independent random variable that follows a standard normal distribution N(0,1).

[0040] (2) The Rayleigh distribution model is introduced to characterize the asymmetric right-skewed characteristics of the abrasive grain exit height, and the inverse cumulative distribution function transformation method is used for sampling to determine the exit height of the abrasive grain at each meshing point; The randomness of the tooth surface morphology of honing wheels mainly stems from their manufacturing and dressing processes. When a dressing wheel dresses a honing wheel, most of the prominent abrasive grains are flattened or randomly broken, while those within the bond and at greater depths are retained. This process determines that the abrasive grain protrusion height is not a symmetrical normal distribution, but rather exhibits a significant right-skewed characteristic, such as... Figure 3 As shown. Therefore, a Rayleigh distribution is used to stochastically model the blade exit height. Its probability density function is shown below: In the formula s h The scale parameter representing the Rayleigh distribution is taken in this paper as... s h =0.05 m d .

[0041] To assign specific geometric properties to discrete abrasive grains in numerical simulation, the inverse cumulative distribution function transformation method is used for sampling. Then the meshing point ( i , j The corresponding abrasive grain exit height h ( i , j This can be represented as: In the formula U ( i , j ) represents a uniform random number in the interval [0,1].

[0042] (3) Project the three-dimensional tooth surface onto a two-dimensional parametric coordinate system based on the radius and tooth width, and transform the spatial topology into a regular height field numerical matrix. like Figure 4 As shown, presets are made in both the tooth profile direction and the tooth direction. i Individual and j Equally spaced sampling points divide the continuous tooth surface into i × j Discrete grid lattice.

[0043] The three-dimensional tooth surface is mapped to a two-dimensional parametric coordinate system using a parametric projection method. The position of any discrete point B on the tooth surface is determined by its coordinates (…). x , y , z ) uniquely determined. Among them, x and y The tooth profile position at that point has been determined. z The tooth orientation at this point has been determined. This mapping strategy transforms the complex spatial topology into a regular height field numerical matrix. Specifically, it is shown below: Figure 5 Numerical simulation procedures for tooth surface roughness are presented. After determining the workpiece gear parameters, honing wheel parameters, and process parameters such as honing wheel speed, radial feed rate, and shaft angle, the discrete honing process of the tooth surface is simulated. For each discrete point, the tooth surface morphology change caused by a single abrasive grain is calculated based on its instantaneous position, relative velocity, and induced curvature, among other geometric kinematic parameters. When all discrete points ( i = i 0, j = j After the numerical update of 0) is completed, the height matrix reflecting the tooth surface roughness is obtained. Finally, based on the discrete point cloud data, the quantitative calculation of tooth surface roughness is completed.

[0044] Step 4 establishes a dynamic prediction model considering machine tool vibration. The process of obtaining the real-time displacement deviation caused by machine tool vibration through signal acquisition and frequency domain reconstruction is as follows: (1) The time-domain vibration signal of the spindle during the machining process is collected by an accelerometer, and the acceleration amplitude is converted into the displacement amplitude by fast Fourier transform and frequency domain integral relationship. For internal meshing high-strength honing machine tools, both the workpiece spindle and the tool spindle vibrate during machining. Therefore, accelerometers are installed on both the workpiece spindle and the tool spindle to collect the time-domain vibration signals during the machining process. Then, fast Fourier transform spectral analysis is performed on these signals. Since tooth surface roughness is mainly affected by displacement fluctuations (such as...),... Figure 6 (As shown), therefore, the acceleration amplitude is converted into the displacement amplitude using the frequency domain integral relationship, as shown below: in A acc,n It is the nth-order acceleration amplitude measured by the sensor and extracted by FFT. f It is the sampling frequency.

[0045] (2) Select the top three dominant frequencies in terms of energy proportion and reconstruct them as a linear superposition of multiple harmonic displacement terms. Since tooth surface roughness is typically at the micrometer level, the impact of small vibrations on roughness is negligible. Considering that machine tool vibration energy is mainly concentrated in the low-frequency range (meshing frequency and its harmonics), the top three dominant frequencies with the highest energy proportion are selected for reconstruction. This not only significantly improves computational efficiency but also effectively filters out high-frequency random noise interference during signal acquisition, ensuring the stability of numerical calculations. Based on this, the displacement vibration term is reconstructed as a linear superposition of multiple harmonics, as shown below: In the formula, A n , f n , The first n The displacement amplitude, frequency, and phase of the first-order vibration.

[0046] (3) Map the time variable to the position function of the meshing point to obtain the reconstructed vibration displacement term. To achieve coupled solution in the spatiotemporal domains, the time variable also needs to be considered. t This is mapped to the position function of the meshing point (i,j). When solving for the meshing point, its corresponding rotation angle can be obtained. The angle corresponding to the first meshing point on the tooth surface is denoted as... f 1 Let the workpiece rotation speed be... n g Then the abrasive grain m The moment corresponding to the contact line t for: In the formula f ( i , j ) is the meshing point ( i , j The corresponding corner.

[0047] Step 5 involves coupling the microscopic material removal mechanism, establishing a single abrasive groove depth model, and achieving quantitative prediction and evaluation of the roughness characteristics of the entire tooth surface, as follows: (1) Considering the influence of radial feed rate and effective radius of curvature, and combining the local effective spacing correction model of abrasive grains, calculate the nominal groove depth; Ignoring grinding wheel wear, machine tool thermal deformation, and tool elastic yielding, and assuming uniform abrasive grain shape and distribution, the maximum height of the tooth profile (i.e., nominal groove depth) perpendicular to the cutting speed direction is as follows. H nom ( i , j It is determined not only by the kinematic envelope, but also by the radial feed.

[0048] During the honing process, the honing wheel moves radially at a speed of v fr Feed, and generate instantaneous depth of cut on the tooth surface. a p , a p = v fr / n h ,in n h The honing wheel speed. According to the equivalent gear cutting model, the presence of the cutting depth will cause a slight shift in the radius of curvature at the contact point. For example... Figure 7 As shown, when the cutting depth is a p At that time, the effective radius of curvature of the workpiece at the instantaneous contact point P r g for: Therefore, the nominal groove depth considering the feed can be calculated by the following formula: In the formula D It is the average spacing between adjacent abrasive grains; α It is the semi-cone angle of the abrasive grain; q For abrasive grains, take the abrasive grain shape factor (for conical abrasive grains, take...). q =0.4); v hg g and v hg h These are the velocity vector components of the gear and the honing wheel in the direction of their relative motion velocity.

[0049] Average spacing between abrasive grains D The theoretical value is determined by the abrasive characteristics of the honing wheel, and is calculated using the following formula: in M This refers to the abrasive grain size of the grinding wheel. S This is the honing wheel organization number.

[0050] Because of abrasive grain sizeM Its actual bottom diameter d g There exists an approximately inverse physical constraint relationship, and the macroscopic spacing formula cannot reflect the local density fluctuations at the microscopic scale. Therefore, the random diameter is... d g ( i , j Substituting into the spacing formula, we establish the local effective spacing based on discrete grid points. Δ(i,j) The model is modified as shown in the following equation: Through the above modifications, the random distribution characteristics of abrasive grain size are coupled into the geometric boundary conditions of single-particle cutting, realizing a numerical mapping from a macroscopic average field to a microscopic discrete field.

[0051] (2) Using the cutting edge height modulation factor based on Rayleigh distribution, the nominal groove depth is mapped to the discrete abrasive scale to obtain the instantaneous groove depth with coupled dual random characteristics; Besides being related to the abrasive grain geometry, the groove depth of a single abrasive grain is also affected by the cutting edge height. h ( i , j The influence of ) is discussed. To characterize this microscopic individual difference, an edge height modulation factor is introduced, which modulates the nominal furrow depth. H nom (i,j) is mapped to the discrete abrasive grain scale. The meshing point ( i , j Instantaneous random groove depth generated by abrasive grains at ) H s ( i , j The definition is as follows: In the formula, n(i,j) This is a randomized modulation weight based on a Rayleigh distribution. This weight characterizes the random blade extension height. h ( i , j The degree of deviation from the average height. Its expression is shown in the following formula: Combined local effective spacing Δ(i,j) Modulation factor with blade height n(i,j) The groove depth prediction model that couples the dual random characteristics of abrasive particles can be obtained, as shown in the following equation: Finally, the vibration displacement term is superimposed on the static random trench depth. H s The dynamic single abrasive groove depth is obtained above: (3) Couple the scratching, plowing and cutting mechanisms, calculate the extra height caused by plastic accumulation, and obtain the single-point arithmetic mean deviation through the conversion relationship; In the high-power honing process, the interaction between abrasive grains and the workpiece typically involves three stages: scratching, ploughing, and cutting. Among these, ploughing and cutting determine the maximum height of the normal profile and are the main factors affecting the workpiece surface roughness. The formula for calculating the maximum height considering the effects of ploughing and cutting can be expressed as: If the cross-sectional shape is simplified to similar triangles, then H p It can be represented as (e.g.) Figure 8 (as shown) The surface roughness of the internal meshing high-strength honing tooth can be expressed as: (4) Based on the discrete mesh data of the entire tooth surface, the average roughness, range and standard deviation are quantitatively evaluated; The simulated tooth surface morphology was reconstructed in i 0 × j 0 In the grid. Ra ( i , j ) represents a grid node ( i , j The roughness value at point () is calculated. Subsequently, based on these discrete mesh data, the tooth surface roughness is quantitatively evaluated.

[0052] Three parameters are selected to characterize tooth surface roughness. (1) Average roughness Defined as the arithmetic mean of the roughness of all grid nodes within the selected area, used to characterize the overall roughness level of the tooth surface.

[0053] (2) Range Ra range Defined as the difference between the maximum and minimum roughness values ​​of all grid nodes within the selected region, it is used to characterize the extreme deviation of tooth surface roughness.

[0054] (3) Standard deviation s Ra This is used to calculate the dispersion of the roughness of each node relative to the average value, and is used to characterize the uniformity of the tooth surface quality. As shown in the following formula: In the formula istart and i end These represent the start and end row indices of the corresponding experimental measurement region in the grid, respectively; j start and j end These are the start and end column indices for the corresponding regions; Ra max and Ra min These represent the maximum and minimum roughness values ​​of the grid nodes within the selected feature region, respectively.

[0055] The machine tools used in the process are shown in Figure 9 This embodiment employs a six-axis linkage internal meshing high-power honing machine for machining. This machine integrates the X-axis for radial feed of the workpiece, the Z-axis for axial feed, the C2-axis for workpiece rotation, the C1-axis for honing wheel rotation, the A-axis for adjusting the spatial axis angle, and the U-axis for workpiece positioning to achieve complex spatial motion coordination. In terms of specific hardware configuration, the core parameters of the selected workpiece gear are: 18 teeth, helix angle 21.8° (right-hand), tooth width 40mm, normal pressure angle 19°, and normal module 2.615. The specific parameters of the matching honing wheel are: 79 teeth, helix angle 15° (right-hand), tooth width 60mm, normal pressure angle 19°, and normal module 2.615.

[0056] (1) Construct the tooth surface equation and the honing coordinate system, calculate the corresponding internal gear honing tooth surface, and obtain the position and velocity information of the meshing point. In this embodiment of the invention, when predicting roughness, a parametric geometric equation for the workpiece tooth surface is first established to accurately describe the microscopic morphological features of the tooth surface to be machined. Then, based on the kinematic constraints of the aforementioned six-axis linkage machine tool, a honing coordinate system encompassing the spatial positional transformation relationship between the honing wheel and the workpiece is constructed. Finally, the tooth surface equation is coupled with the machining coordinate system through kinematic mapping to calculate the relative velocity and coordinates of the abrasive grains at each instantaneous meshing point during the honing process. The specific calculation results are shown in the table below: Table 1 Calculation results of relative motion velocity

[0057] Table 2. Location Information Calculation Results (RL Plane)

[0058] (2) Based on the analytical-numerical hybrid solution strategy, the geometric characteristics and induced curvature of the tooth surface of the topology-modified workpiece and the implicit envelope surface of the honing wheel at the instantaneous meshing point are obtained. The results are shown in the table below: Table 3 Instantaneous induced curvature at the meshing point

[0059] (3) Based on the formulas in steps 3 and 4, the dynamic single abrasive coupling depth considering machine tool vibration is calculated, and the results are as follows: Table 4 Dynamic single abrasive groove depth considering machine tool vibration

[0060] (4) Calculate the tooth surface roughness according to the quantification criteria proposed in step 5. The results are as follows: Figure 10 As shown.

[0061] Table 4 Dynamic single abrasive groove depth considering machine tool vibration

[0062] As can be seen from the table, the average roughness value of region 9 is 0.3097, the experimentally measured value is 0.32, and the error is 3.22%. It can be seen that the calculation results of this method are within the acceptable range, so the tooth surface roughness prediction method proposed in this invention is feasible.

[0063] This invention proposes a method for predicting the surface roughness of internal meshing high-strength honing gears, considering the coupling of multiple factors. This method adopts an analytical-numerical hybrid solution strategy to accurately obtain the instantaneous induced curvature of the topologically modified tooth surface and the implicit envelope surface of the honing wheel at the meshing point. It constructs a "double random" statistical model that integrates abrasive grain size (normal distribution) and cutting edge height (Rayleigh distribution), and superimposes the multi-frequency harmonic vibration displacement into the static random groove depth model, coupling the micro-material removal mechanism (scraping, plowing, cutting), thereby realizing a quantitative evaluation of the surface roughness of the entire tooth.

[0064] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0065] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling, characterized in that, Includes the following steps: S1. Construct the tooth surface equation and honing coordinate system, calculate the corresponding internal gear honing tooth surface, and obtain the position and velocity information of the meshing point; S2. An analytical-numerical hybrid solution strategy is adopted to obtain the geometric characteristics and induced curvature of the tooth surface of the topologically modified workpiece and the implicit envelope surface of the honing wheel at the instantaneous meshing point. S3. Construct a dual stochastic statistical model that integrates abrasive grain size and cutting edge height, and use a local abrasive grain modeling method based on instantaneous meshing point to characterize the micro-topology of the honing wheel; S4. Establish a dynamic prediction model that considers machine tool vibration, and obtain the real-time displacement deviation caused by machine tool vibration through signal acquisition and frequency domain reconstruction. S5. Couple the micro-material removal mechanism and establish a single abrasive groove depth model to achieve quantitative prediction and evaluation of the roughness characteristics of the entire tooth surface.

2. The method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling as described in claim 1, characterized in that, The specific steps for establishing the gear tooth surface equation in S1 are as follows: The tooth profile bulging modification function is parabolically distributed along the involute arc length. During modeling, the maximum tooth profile bulging amount at the mid-section of the tooth width is used as the reference, and geometric offsets are superimposed along the radial direction to complete the calculation of the normal direction of the ideal involute tooth surface. The tooth profile bulging modification function is parabolically distributed along the theoretical helix, and the maximum tooth profile bulging amount at the midpoint of the tooth width is used as the control parameter. To ensure kinematic consistency, the tooth profile modification amount is converted into angular phase increments and incorporated into the model to realize the tooth profile modification calculation. The geometric offsets and angular phase increments are calculated from the pitch circle radius, involute development angle, and helix increment angle parameters. The topology modification function is superimposed onto the standard involute to obtain the position vector of the topology-modified gear. Combining the knowledge of differential geometry of the modified tooth surface, the normal vector is calculated through the partial derivative of the position vector to complete the tooth surface modeling.

3. The method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling as described in claim 1, characterized in that, The specific steps for constructing the honing motion coordinate system in S1 are as follows: Reference frame S h and S g They are rigidly fixed to the honing wheel and gear, respectively. S 1 , S 2 and S 3 To provide an auxiliary coordinate system, based on spatial coordinate transformation, the honing wheel is positioned in the reference frame. S h Position vector in r h and normal vector n h Represented as: ， ， in L hg Represents the homogeneous transformation matrix M hg The top left submatrix, M hg The rotational component representing the spatial transformation relationship between the gear and the honing wheel can be expressed as: ， in φ h and φ g Let represent the rotation angles of the honing wheel and the gear, respectively. Their kinematic relationship is determined by the following formula: A hg Indicates the center distance. L z Indicates the axial feed rate. ∑ hg Indicates the angle between axes. ， in i hd Indicates the transmission ratio. r hp and β h These represent the pitch circle radius and helix angle of the honing wheel, respectively.

4. The method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling as described in claim 1, characterized in that, The calculation of the internal gear tooth surface and the acquisition of position and velocity information based on the meshing principle in S1 are specifically as follows: According to the principle of gear meshing, the honing process is a two-degree-of-freedom motion, where the independent motion variable is the gear rotation angle. φ g and axial feed L z The instantaneous contact point on the tooth surface must simultaneously satisfy the meshing equations consisting of these two independent variables, as shown below: ， By solving this set of nonlinear equations, the parameters corresponding to each contact point can be obtained. Substituting these parameters into the tooth surface equation yields the corresponding meshing position information. Simultaneously, substituting them into the meshing equation yields the corresponding velocity information, along with the corresponding position and velocity information.

5. The method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling as described in claim 1, characterized in that, Specifically, S2 is: The topologically modified workpiece tooth surface with clearly defined parameterized equations is obtained by using differential geometry analytical method to obtain its unit normal vector and the coefficients of the first and second basic forms, and to determine the instantaneous principal curvature of meshing. For the implicit envelope surface of the honing wheel, a small perturbation step size is set in the neighborhood of the instantaneous contact point, and the meshing equation is solved by numerical difference method to obtain the spatial coordinates of the discrete point. The first, second, and mixed partial derivatives are calculated using the central difference operator to construct the first and second fundamental form coefficients of the honing wheel tooth surface, thereby obtaining the principal curvature.

6. The method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling as described in claim 1, characterized in that, Specifically, S3 is: Based on the normal distribution model, the random discreteness of the equivalent diameter of abrasive grains is characterized, and the diameter of abrasive grains corresponding to discrete grid points is determined. The asymmetric right-skewed characteristics of the abrasive grain exit height are characterized by the Rayleigh distribution model, and the inverse cumulative distribution function transformation method is used for sampling to determine the exit height of the abrasive grain at each meshing point. The three-dimensional tooth surface is projected onto a two-dimensional parametric coordinate system based on the radius and tooth width, transforming the spatial topology into a regular height field numerical matrix.

7. The method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling as described in claim 1, characterized in that, Specifically, S4 is: The time-domain vibration signal of the spindle during the machining process is collected by an accelerometer, and the acceleration amplitude is converted into the displacement amplitude using fast Fourier transform and frequency domain integral relationship. The top three dominant frequencies with the highest energy proportions are selected and reconstructed as a linear superposition of multi-frequency harmonic displacement terms. The time variable is mapped to the position function of the meshing point, and the reconstructed vibration displacement terms are superimposed.

8. The method for predicting the surface roughness of internal meshing high-strength honing gears considering multi-factor coupling as described in claim 1, characterized in that, Specifically, S5 is: Based on the influence of radial feed rate and effective radius of curvature, and combined with the local effective spacing correction model of abrasive grains, the nominal groove depth is calculated; Based on the Rayleigh distribution, the nominal groove depth is mapped to the discrete abrasive particle scale to obtain the instantaneous groove depth with coupled dual random characteristics. The coupling of scratching, plowing and cutting mechanisms is used to calculate the additional height caused by plastic accumulation, and the single-point arithmetic mean deviation is obtained through the transformation relationship. Based on discrete mesh data of the entire tooth surface, the average roughness, range, and standard deviation are quantitatively evaluated.

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