A method for rigidity field mapping and optimization processing of face gear tooth surface modification

Abstract

The application discloses a kind of face gear tooth surface modification rigidity field mapping and optimization processing integration method, belong to mechanical manufacturing field;The method comprises: establishing face gear wheel body three-dimensional finite element model, obtains wheel body rigidity distribution law;Boundary conditions are applied and displacement response is extracted, and normal comprehensive deformation of tooth surface is calculated;Second-order polynomial response surface model is used to establish the quantitative mapping relationship between wheel body rigidity distribution characteristic parameter and tooth surface modification amount;With the minimum contact stress standard deviation and transmission error peak-peak value as target, solve optimal modification scheme using sequential quadratic programming algorithm;Through five-axis numerical control gear milling machine, tooth surface modification processing is executed, and gear measuring center is used to verify modification effect, and closed loop iteration optimization is formed.The application can effectively balance the tooth surface contact stress distribution, significantly reduce transmission error, improve the stability and service life of face gear transmission by the above technical scheme.

Description

Technical Field

[0001] This invention relates to the field of mechanical manufacturing, specifically to an integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification. Background Technology

[0002] Face gear transmission is an important branch of mechanical transmission technology, widely used in high-precision transmission applications such as aero-engines, helicopter main reducers, and new energy vehicles. Compared with traditional cylindrical gear transmission, face gear transmission has significant advantages such as compact structure, large transmission ratio, high overlap ratio, strong load-bearing capacity, and low noise. It can realize power transmission between intersecting or staggered shafts and is a key component of high-end equipment transmission systems. With the increasing demands of modern mechanical equipment for transmission accuracy, reliability, and lightweighting, the design and manufacturing technology of face gears continues to be a research hotspot. Among them, tooth surface modification, as a core process for improving the meshing performance of face gears, plays a crucial role in improving transmission quality and extending service life.

[0003] Among them, the tooth surface modification method based on wheel stiffness distribution is a new generation of modification technology that combines the structural stiffness characteristics of the face gear with the geometric optimization of the tooth surface. This method analyzes the stiffness distribution characteristics of the wheel under stress to determine the inherent laws of tooth surface deformation, and then formulates targeted modification strategies to compensate for the impact of wheel deformation on tooth surface contact accuracy, thereby achieving the optimal design of face gear transmission performance. This modification method emphasizes understanding the intrinsic relationship between wheel stiffness and tooth surface morphology at the mechanistic level, and represents an important development direction for face gear precision manufacturing technology.

[0004] In existing technologies, face gear tooth surface modification mainly employs empirical formulas or standard curve methods. The determination of modification parameters is typically based on idealized assumptions or extensive trial cutting experiments, lacking a systematic consideration of the gear body stiffness distribution characteristics. During actual machining, the face gear body exhibits non-uniform stiffness characteristics due to differences in structural form, material properties, and thickness distribution. Under the influence of cutting forces, thermal deformation, and clamping forces, it undergoes complex elastic deformation. This deformation directly affects the tooth surface, causing deviations between the actual tooth surface and the theoretically designed tooth surface. Traditional modification methods fail to fully reveal the quantitative relationship between gear body stiffness distribution and tooth surface deformation. Modification schemes lack effective compensation for actual machining deformation. In high-precision transmission applications, this results in problems such as contact stress concentration, large transmission errors, and significant vibration and noise, hindering further improvements in face gear transmission performance and failing to meet the urgent needs of high-end equipment for high-precision, high-reliability face gear transmission systems. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an integrated method for stiffness field mapping and optimized machining of gear tooth surface modification, which can effectively solve the problems in the background art.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method integrating stiffness field mapping and optimized machining for face gear tooth surface modification includes the following specific steps:

[0008] Step 1, establish a three-dimensional finite element model of the face gear body: Based on the design parameters of the face gear, including the number of teeth, module, pressure angle, cone angle, inner diameter and rim thickness, establish a three-dimensional geometric model of the face gear body that includes a complete rim, hub and reinforcing rib structure;

[0009] Step 2, Mesh generation and material property setting: The three-dimensional geometric model is meshed using an adaptive mesh generation technique. In regions with drastic stiffness gradient changes, a local meshing strategy is adopted, with the mesh size set to 1 mm to 3 mm. In regions with gentle stiffness distribution, a sparse mesh strategy is adopted, with the mesh size set to 4 mm to 8 mm. The total number of mesh elements in the overall model is controlled within the range of 300,000 to 1,500,000.

[0010] Step 3, Apply boundary conditions and extract displacement response: Establish displacement constraints corresponding to the boundary conditions of the wheel finite element model, apply corresponding constraints and loads to the finite element model through the displacement constraints, and extract the displacement response of the wheel under cutting conditions; based on the displacement response, calculate the comprehensive deformation of different tooth surface regions;

[0011] Step 4: Establish a tooth surface modification prediction model: Based on the geometric parameters of different tooth surface regions and the corresponding comprehensive deformation, a polynomial response surface method is used to construct a tooth surface modification prediction model. The polynomial order is determined according to the goodness of fit to ensure that the prediction error is less than or equal to 0.005 mm. The wheel stiffness distribution characteristic parameters are used as the model input, and the tooth surface modification is used as the model output to obtain the mapping relationship between the tooth surface modification and the wheel stiffness distribution.

[0012] Step 5, determine the optimal modification scheme: Based on the tooth surface modification amount prediction model and the preset tooth surface contact quality target, the optimal modification amount of each tooth surface region is obtained by using a sequential quadratic programming algorithm to optimize the solution; combined with the tooth surface geometric constraints and machining process constraints of the face gear, the feasibility of the optimal modification amount is verified and adjusted to ensure that the modification scheme is feasible;

[0013] Step 6, perform tooth surface modification: Based on the optimal modification scheme, formulate CNC machining code; use a five-axis CNC gear milling machine to perform tooth surface modification, wherein the spindle speed is optimally set according to the tool material and workpiece material, the feed rate is adaptively adjusted according to the modification amount, the tool is a ball end mill, and the tool path is adaptively planned according to the modification amount distribution to ensure modification accuracy;

[0014] Step 7, verify the shaping effect: Use a gear measurement center to perform three-dimensional morphological measurement on the shaped tooth surface to obtain actual tooth surface data; compare the actual tooth surface data with the theoretically designed tooth surface, calculate the tooth surface deviation and contact spot distribution, and verify whether the shaping effect meets the preset quality requirements; if the deviation exceeds the allowable range, return to step 1 to readjust the parameters for iterative optimization.

[0015] Preferably, when establishing the three-dimensional model of the face gear body in step 1, the structural features such as the rim, hub, and reinforcing ribs are accurately modeled. The rim thickness is set to 15 mm to 25 mm, and the ratio of the hub outer diameter to the bore diameter is set to 3 to 5 to ensure the accuracy of the finite element model.

[0016] Preferably, the material properties in step 2 include elastic modulus, Poisson's ratio, and density, wherein the elastic modulus is set to 210 gigapascals, the Poisson's ratio is set to 0.3, and the density is set to 7850 kg per cubic meter. An isotropic linear elastic constitutive model is used to describe the material behavior. The mesh generation adopts a hexahedral dominant mesh, and the element type adopts an eight-node linear reduced integral element to ensure a balance between computational accuracy and efficiency.

[0017] Preferably, in step 2, the mesh size is set to 2 mm in areas with drastic stiffness changes and 5 mm in areas with moderate stiffness, and the total number of mesh elements in the overall model is controlled within the range of 500,000 to 2 million.

[0018] Preferably, in step 3, the boundary conditions are simulated by applying radial and axial constraints to simulate the clamping state in actual machining. The radial constraint is applied to the inner surface of the hub, and the axial constraint is applied to the end face of the hub. The displacement response extraction includes extracting the nodal displacements of three typical regions: tooth root, tooth middle, and tooth tip. The sampling point density is not less than 20 points per square centimeter to ensure the sufficiency of deformation data.

[0019] Preferably, the displacement response extraction in step 3 adopts a multi-condition combined loading method, including considering the coupling effect of cutting force, thermal deformation and clamping force. The cutting force is calculated and determined based on the tool parameters and cutting parameters, the thermal deformation is calculated and determined based on the temperature field distribution, and the clamping force is determined based on the fixture layout and clamping method.

[0020] Preferably, in step 4, the tooth surface modification prediction model adopts the second-order polynomial response surface method, which considers the nonlinear relationship between stiffness distribution characteristics and deformation; the model training samples are generated by the Latin hypercube sampling method, with no less than 200 sets of samples to ensure the model's generalization ability.

[0021] Preferably, in step 5, the shaping scheme optimization takes the uniformity of contact stress and the minimization of transmission error as the objective functions, and solves them through a sequential quadratic programming algorithm to ensure that the standard deviation of contact stress is less than 0.1 MPa and the peak-to-peak value of transmission error is less than 10 micrometers.

[0022] Preferably, in step 6, the five-axis CNC gear milling machine has a precision level of not less than the precision level, a spindle runout of less than 0.005 mm, and a positioning accuracy of better than 0.01 mm, to ensure the accuracy and stability of the shaping process.

[0023] Preferably, in step 7, the tooth surface measurement is performed using a gear measuring center with a measurement accuracy of ±0.002 mm; the contact spot distribution is obtained through a loading meshing test, with the loading load set to 1.2 times the rated load, and the contact spot area ratio being greater than or equal to 85% indicates that the shaping effect is qualified.

[0024] Preferably, it also includes: establishing a modification amount distribution mapping model using a backpropagation neural network, wherein the input layer contains wheel stiffness distribution feature parameters, the hidden layer contains a 3-layer structure with 20 neurons in each layer, and the output layer contains the tooth surface modification amount. After training with a large amount of sample data, the model's determination coefficient is greater than or equal to 0.95, thereby achieving fast and accurate prediction of the modification amount.

[0025] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0026] 1. The stiffness distribution characteristics of the face gear body under machining conditions are obtained through finite element analysis. Displacement response data are extracted by multi-condition coupling analysis. Then, the polynomial response surface method is used to establish a quantitative mapping relationship between the stiffness distribution of the gear body and the deformation of the tooth surface, so as to realize the accurate prediction of the modification amount. This solves the problem that empirical formulas and standard curves in traditional modification methods cannot accurately reflect the actual machining deformation, and provides a scientific and reliable basis for the modification of face gear tooth surfaces.

[0027] 2. Based on the established modification amount prediction model, the sequential quadratic programming algorithm is used to globally optimize the modification scheme. The solution is based on the objective functions of minimizing the uniformity of contact stress and the transmission error. This significantly improves the uniformity of contact stress distribution and controls the peak-to-peak value of transmission error to below 10 micrometers. This effectively avoids the stress concentration and fatigue failure problems caused by contact stress concentration in traditional modification methods, and greatly improves the accuracy and load-bearing capacity of face gear transmission.

[0028] 3. By establishing a mapping model between wheel stiffness distribution and machining deformation, precise control of deformation compensation can be achieved, avoiding under- or over-modification problems caused by estimation errors in compensation in traditional modification methods. The deviation between the modified tooth surface and the theoretically designed tooth surface is controlled within ±0.005 mm, and the consistency of repeated modification is good, meeting the stringent requirements of high-precision surface gear transmission for high-end equipment such as aero-engines and helicopter main reducers.

[0029] 4. Establish a closed-loop iterative optimization mechanism for the modification process and effect verification. The gear measurement center performs three-dimensional morphology measurement and loading meshing test on the modified tooth surface to quantitatively evaluate the modification effect. When the deviation exceeds the allowable range, the parameter adjustment and re-optimization process is automatically triggered until the preset quality requirements are met. This ensures that the modification quality of each product is stable and reliable, eliminates the adverse effects of human experience on the modification effect, and improves product consistency and pass rate. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the overall technical solution architecture of the integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification proposed in this invention.

[0031] Figure 2 This is a schematic diagram of the core principle framework of the present invention, which is based on the characteristics of wheel stiffness distribution to drive tooth surface modification.

[0032] Figure 3 This is a flowchart illustrating the modeling and analysis process for the stiffness distribution of the surface gear body in this invention.

[0033] Figure 4 This is a logical flowchart illustrating the coupling mapping relationship between tooth surface modification amount and stiffness distribution in this invention.

[0034] Figure 5 This is a schematic diagram illustrating the synergistic control relationship between the shaping processing parameters and the stiffness optimization results in this invention;

[0035] Figure 6 This is a schematic diagram comparing the overall process flow and stiffness compensation principle of the gear tooth surface modification machining in this invention. Detailed Implementation

[0036] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0037] Example 1: To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments.

[0038] like Figures 1 to 6As shown, this invention provides an integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification. This method follows a systematic technical approach, obtaining the stiffness distribution characteristics of the gear body through finite element analysis, establishing a quantitative mapping relationship between stiffness distribution and tooth surface deformation, determining the optimal modification scheme using an optimization algorithm, and finally achieving tooth surface modification through precision CNC machining. This method covers a complete technical loop from model establishment to effect verification, including seven core steps: Step 1: Establishing a three-dimensional finite element model of the face gear body; Step 2: Meshing and setting material properties; Step 3: Applying boundary conditions and extracting displacement response; Step 4: Establishing a tooth surface modification amount prediction model; Step 5: Determining the optimal modification scheme; Step 6: Performing tooth surface modification machining; Step 7: Verifying the modification effect. The technical details of each step are elaborated below.

[0039] In step 1, the process of establishing a three-dimensional finite element model of the face gear body first requires constructing a complete three-dimensional geometric model based on the design parameters of the face gear. These design parameters include, but are not limited to, key geometric features such as the number of teeth, module, pressure angle, cone angle, inner diameter, and rim thickness. As a special type of bevel gear, the face gear's tooth surface has a parabolic or exponential curve shape; accurate acquisition of the tooth surface geometric parameters is fundamental to establishing an accurate finite element model. During the modeling process, structural features such as the rim, hub, and reinforcing ribs are precisely modeled to ensure that the finite element model can fully reflect the actual structural morphology of the face gear body. Specifically, the rim thickness is set within the range of 15 mm to 25 mm, which directly affects the overall stiffness distribution characteristics of the gear body; the ratio of the hub outer diameter to the bore diameter is set between 3 and 5, which determines the load-bearing capacity and stress transmission characteristics of the hub; the arrangement of the reinforcing ribs is determined based on the gear body diameter and thickness, and the layout principle is to ensure a uniform stiffness distribution of the gear body under machining conditions.

[0040] The 3D geometric model was established using a parametric modeling method. With the central axis of the face gear as the origin of the reference coordinate system, the geometric features of the hub, transition, and rim sections were constructed sequentially along the axial direction. The hub section adopted a hollow cylindrical structure, with its inner diameter determined according to the fit requirements of the drive shaft, and its outer diameter calculated using a ratio. The transition section adopted a conical transition structure to achieve a smooth transition from the hub to the rim. As the main load-bearing part of the gear ring, the rim section required precise control of its thickness-direction geometric dimensions. The geometry of the tooth surface was defined using a theoretical tooth surface equation, which comprehensively considered the variation of parameters such as end face module, pressure angle, and helix angle along the tooth height and length directions. After geometric modeling, the model underwent smoothness and topology checks to ensure the absence of geometric singularities, overlapping surfaces, or free edges, providing a high-quality geometric foundation for subsequent mesh generation.

[0041] In step 2, during mesh generation and material property setting, an adaptive meshing technique was used to perform finite element meshing on the 3D geometric model. The core principle of the meshing strategy is to employ a localized meshing strategy in regions with drastic stiffness gradient changes and a sparse meshing strategy in regions with gentle stiffness distribution, thereby achieving an optimal balance between computational accuracy and efficiency. Regions with drastic stiffness gradient changes mainly include the transition region between the wheel rim and hub, the connection region between the stiffener and the wheel rim, and stress concentration areas such as the tooth root. The mesh size for these regions was set to 1 mm to 3 mm. Regions with gentle stiffness distribution mainly include the hub body and the middle of the wheel rim, with the mesh size set to 4 mm to 8 mm. The overall model mesh element count was controlled within the range of 300,000 to 1,500,000, a range that ensures computational accuracy while keeping computation time within a reasonable range.

[0042] In a preferred embodiment, the mesh size is set to 2 mm in areas with drastic stiffness changes and 5 mm in areas with moderate stiffness during mesh generation, with the overall model mesh element count controlled within the range of 500,000 to 2 million.

[0043] This parameter configuration further improves computational accuracy, particularly in transition and stress concentration regions, yielding more detailed displacement response data. Meshing employs a hexahedral-dominant strategy, prioritizing hexahedral elements and using pentahedral or tetrahedral elements for transitions in geometrically complex regions. The element type used is an eight-node linear reduced integral element, which offers high computational efficiency, low memory footprint, and sufficient accuracy. During mesh quality checks, aspects such as aspect ratio, skewness, and Jacobian ratio are evaluated to ensure all elements meet computational requirements.

[0044] The material properties are set using an isotropic linear elastic constitutive model to describe the material behavior. The material properties include three core parameters: elastic modulus, Poisson's ratio, and density. The elastic modulus is set to 210 gigapascals, corresponding to commonly used carburized alloy steel; the Poisson's ratio is set to 0.3, a typical Poisson's ratio for steel; and the density is set to 7850 kg / m³, corresponding to the density of ordinary carbon steel. After defining the material properties, verification is required. This involves verifying the correctness of the material parameter settings through single-point tensile or compressive simulations to ensure that the stress-strain relationship conforms to Hooke's Law.

[0045] In step 3, when applying boundary conditions and extracting displacement response, it is first necessary to establish displacement constraints corresponding to the boundary conditions of the wheel finite element model. Boundary conditions are applied through displacement constraints: radial constraints are applied to the inner surface of the hub, limiting the radial displacement of nodes on the inner surface, simulating the clamping action of the mandrel in actual machining; axial constraints are applied to the end face of the hub, limiting the axial displacement of nodes on the end face, simulating the positioning effect of the end face in actual machining. By applying corresponding constraints and loads to the finite element model using these displacement constraints, the actual loading state of the face gear under cutting conditions is simulated.

[0046] Displacement response extraction employs a multi-condition combined loading method, comprehensively considering the coupling effects of cutting force, thermal deformation, and clamping force. Cutting force is calculated based on tool parameters and cutting parameters. Tool parameters include geometric parameters such as tool diameter, number of cutting edges, rake angle, and clearance angle. Cutting parameters include process parameters such as cutting speed, feed rate, and depth of cut. The magnitude and direction of the cutting force are obtained through empirical formulas for cutting force or finite element simulation of cutting mechanics. Thermal deformation is calculated based on the temperature field distribution. The temperature distribution of each region of the wheel body is obtained through finite element analysis of heat conduction, and the amount of thermal deformation is calculated based on the coefficient of thermal expansion. Clamping force is calculated based on the fixture layout and clamping method. The fixture layout includes the number, location, and distribution of clamping points, while the clamping method includes the direction and magnitude of the clamping force. The influence of the clamping force on wheel deformation is determined through static analysis.

[0047] In the specific operation of displacement response extraction, the nodal displacements of three typical regions—tooth root, tooth middle, and tooth tip—are extracted as the basic data for deformation analysis. The sampling point density is no less than 20 points per square centimeter to ensure the sufficiency and completeness of the deformation data. The output format of the displacement response includes three translational displacement components and one rotational displacement component for each node in the global coordinate system. The displacement data is stored in a sparse matrix format to save storage space. Based on the extracted displacement response data, according to the displacement components of each node in the global coordinate system and the unit normal vector of the tooth surface at that point, the comprehensive normal deformation of each sampling point on the tooth surface is calculated using the following formula: ;in, , , Let X, Y, and Z be the elastic displacement components of the i-th sampling point in the X, Y, and Z directions, respectively. , , These represent the components of the unit normal vector of the tooth surface at that point in three directions. The total deformation along this normal direction... The positive and negative signs indicate whether the tooth surface is raised (positive value) or recessed (negative value) along the external normal direction, respectively, and are used to determine the direction of material removal or addition at that point. The comprehensive deformation is defined as the displacement component along the tooth surface normal direction, reflecting the degree of elastic deformation of the wheel body under machining conditions, and is the core physical quantity connecting stiffness analysis and deformation prediction.

[0048] In step 4, during the establishment of the tooth surface modification prediction model, a polynomial response surface methodology is used to construct the model based on the geometric parameters and corresponding comprehensive deformation of different tooth surface regions. The core function of this prediction model is to establish a quantitative mapping relationship between the wheel stiffness distribution characteristic parameters and the tooth surface modification amount, achieving rapid and accurate prediction from stiffness distribution characteristics to modification amount. The basic principle of the polynomial response surface methodology is to approximate the nonlinear mapping relationship between input and output variables using a polynomial function. The polynomial order is determined based on the goodness of fit, and the goodness of fit is optimized by continuously adjusting the polynomial order while avoiding overfitting.

[0049] The input variables of the tooth surface modification prediction model are the characteristic parameters of wheel stiffness distribution. These parameters include, but are not limited to, parameters reflecting stiffness distribution characteristics such as rim thickness, hub outer diameter to bore diameter ratio, stiffener distribution density, and mesh size in key areas. The output variable is the tooth surface modification amount, defined as the normal distance between the theoretical tooth surface and the actual tooth surface after considering machining deformation. Positive and negative modification amounts correspond to the positive and negative modification directions along the tooth surface normal, respectively. The mapping relationship is expressed using a second-order polynomial model as follows:

[0050] ;

[0051] Where Y represents the tooth surface modification amount. , Here, k represents the characteristic parameter of the wheel stiffness distribution, and k is the total number of stiffness distribution characteristic parameters. The coefficient of the constant term, The coefficients of the first-order term (reflecting the degree of linear influence of each parameter on the amount of shaping). The coefficients of the quadratic term (reflect the degree of nonlinear influence of each parameter on the shaping amount, and embody the coupling effect of stiffness distribution). The cross term coefficient (reflects the influence of the interaction between parameters i and j on the shaping amount). The fitting error (representing the random error that the model fails to explain; its standard deviation is used to assess model accuracy) is used. During model construction, input variables need to be normalized to eliminate differences in units and orders of magnitude between different variables. Model coefficients are estimated using the least squares method, minimizing the sum of squared residuals to obtain optimal model parameter estimates.

[0052] The training samples for the model are generated using the Latin hypercube sampling method, which enables uniform sampling in a high-dimensional parameter space, ensuring the uniformity and representativeness of the sample distribution. The number of samples is no less than 200 sets, sufficient to guarantee the model's generalization ability. After model training, the prediction accuracy needs to be validated using metrics including prediction error and coefficient of determination, ensuring the prediction error is less than or equal to 0.005 mm and the coefficient of determination is greater than or equal to 0.95. If the model's prediction accuracy does not meet the requirements, the number of training samples needs to be increased or the polynomial order adjusted for model reconstruction.

[0053] This second-order polynomial model includes constant terms, linear terms, quadratic terms, and cross terms, comprehensively describing the nonlinear mapping relationship between input and output variables. In a preferred embodiment, a backpropagation neural network is also used to establish a modification amount distribution mapping model. The input layer of this neural network contains wheel stiffness distribution feature parameters, the number of which is consistent with the number of input parameters in the aforementioned prediction model; the hidden layer contains a three-layer structure, each layer containing 20 neurons, with the hyperbolic tangent function as the activation function; the output layer contains the tooth surface modification amount, the number of output nodes being consistent with the number of regions divided on the tooth surface. The hidden layer output of the backpropagation neural network is:

[0054] ;

[0055] The output layer outputs:

[0056] ;

[0057] in, Let be the i-th stiffness feature parameter of the input layer, and n be the number of neurons in the input layer. These are the connection weights from the input layer to the hidden layer. For hidden layer bias terms, The output of the l-th hidden layer neuron. The hyperbolic tangent activation function (introducing nonlinearity, the formula is as follows) L represents the total number of neurons in the hidden layer. These are the connection weights from the hidden layer to the output layer. For output layer bias terms, Let be the predicted modification amount for the j-th tooth surface region. After training with a large amount of sample data, the model's coefficient of determination is greater than or equal to 0.95, achieving fast and accurate prediction of the modification amount. The backpropagation neural network is trained using gradient descent, with a learning rate set to 0.001, a momentum factor set to 0.9, and the number of training iterations set to 1000 to 5000. An early stopping strategy is used during training to prevent overfitting. This neural network model complements the multinomial response surface model, and in engineering applications, one or a combination of the two models can be selected according to actual needs.

[0058] In step 5, during the determination of the optimal profile modification scheme, based on the tooth surface modification amount prediction model and the preset tooth surface contact quality target, a sequential quadratic programming algorithm is used to optimize and solve the problem, obtaining the optimal modification amount for each tooth surface region. The objective function for optimizing the profile modification scheme focuses on minimizing contact stress uniformity and transmission error. Mathematical optimization methods are used to seek the optimal solution while satisfying various constraints. Contact stress uniformity is quantified using the contact stress standard deviation, and transmission error is quantified using the transmission error peak-to-peak value. The goal of the optimization solution is to minimize both the contact stress standard deviation and the transmission error peak-to-peak value.

[0059] The objective function of the sequential quadratic programming algorithm is:

[0060] ;

[0061] Where q is the shape modification scheme vector to be optimized, i.e. m is the number of tooth surface regions to be divided; The standard deviation (MPa) of the tooth surface contact stress under the current modification scheme is obtained through tooth surface contact analysis or finite element calculation to measure the uniformity of stress distribution. The peak-to-peak value of the transmission error under the current modification scheme ( m), obtained through tooth surface contact analysis, is used to measure transmission smoothness; , The weighting coefficients for each optimization objective are... Adjustments can be made according to design requirements (e.g., for aircraft gears, settings can be configured). , The optimization constraints include upper and lower limits on the shaping amount for each region. ) and the smoothness constraint of the rate of change of the shaping amount in adjacent regions ( ).

[0062] The basic principle of the Sequential Quadratic Programming (SQP) algorithm is to transform a nonlinear constrained optimization problem into a series of quadratic programming subproblems for iterative solution. In each iteration, a quadratic approximation model for the current iteration point is first constructed, then the quadratic programming subproblem is solved to obtain the search direction and step size, and finally a line search is performed along the search direction to update the iteration point. In each iteration, the SQP algorithm constructs a Lagrange quadratic approximation of the objective function F(q), solves the quadratic programming subproblems to obtain a new search direction, and gradually approximates the optimal solution that satisfies the constraints. The convergence criteria of the algorithm include the relative change in the objective function value, the change in the constraint violation, and the change in the gradient norm. When all these indicators are less than the preset convergence threshold, the algorithm stops iterating and outputs the optimal solution.

[0063] Combining the geometric constraints and machining constraints of the gear tooth surface, the feasibility of the optimal modification amount is verified and adjusted. The geometric constraints include minimum tooth surface thickness constraints, root transition surface curvature constraints, and tip thickness constraints. These constraints ensure that the modified tooth surface geometry meets strength and assembly requirements. Machining constraints include maximum modification amount constraints, minimum modification step constraints, and tool accessibility constraints. These constraints ensure that the modification scheme can be implemented under existing machining conditions. When the optimal modification amount exceeds the constraint range, the excess portion needs to be trimmed or adjusted to ensure the overall feasibility of the modification scheme.

[0064] In a preferred embodiment, the profile modification scheme optimization ensures that the standard deviation of contact stress is less than 0.1 MPa and the peak-to-peak value of transmission error is less than 10 micrometers. This optimization objective guarantees that the face gear transmission has a uniform contact stress distribution and low-noise transmission characteristics. The constraints in the optimization process include upper and lower limits on the tooth surface modification amount, smoothness constraints on the rate of change of modification amount, and continuity constraints on tooth surface curvature. Through the global search capability of the sequential quadratic programming algorithm, the optimal profile modification scheme that satisfies all constraints can be found in the vast solution space.

[0065] During the tooth surface shaping process in step 6, CNC machining code is generated based on the optimal shaping scheme. A five-axis CNC gear milling machine is used for tooth surface shaping. This machining method features high rigidity, high precision, and high flexibility, and can meet the machining requirements of complex tooth surface geometries. The spindle speed is optimally set according to the tool material and workpiece material. When the tool material is cemented carbide, the spindle speed is set to 3000 to 8000 rpm; when the tool material is cubic boron nitride, the spindle speed is set to 5000 to 12000 rpm. The feed rate is adaptively adjusted according to the shaping amount. A smaller feed rate is used in areas with larger shaping amounts to ensure machining accuracy, and a larger feed rate is used in areas with smaller shaping amounts to improve machining efficiency.

[0066] Ball end mills are selected as the cutting tools. The ball end radius is determined based on the tooth surface curvature and the required profile correction accuracy, generally chosen to be 0.8 to 1.2 times the minimum radius of curvature of the tooth surface to be machined. The advantage of ball end mills is that they ensure a constant contact angle between the tool and the tooth surface, avoiding the impact of tool rake angle variations on machining quality. In terms of toolpath planning, the toolpath is adaptively planned based on the profile correction amount distribution. Areas with larger profile correction amounts use smaller line spacing and step distances, while areas with smaller profile correction amounts use larger line spacing and step distances, achieving an optimal balance between machining accuracy and efficiency. The toolpath travel strategy employs a helical or reciprocating machining method to ensure stable tool load and uniform machined surface finish.

[0067] The five-axis CNC gear milling machine has a precision level no lower than precision grade, with spindle runout less than 0.005 mm and positioning accuracy better than 0.01 mm. These precision indicators ensure the accuracy and stability of the profile machining process, meeting the stringent requirements of high-end equipment for gear machining precision. During machining, the machining allowance is monitored in real time through an online measurement system, and machining parameters are dynamically adjusted based on the measurement results to achieve closed-loop control machining. After machining, the tooth surface undergoes deburring and cleaning to eliminate the impact of residual chips and contaminants on the tooth surface quality.

[0068] In step 7, during the verification of the face gear modification effect, a gear measuring center was used to perform three-dimensional morphological measurements on the modified tooth surface to obtain actual tooth surface data. The measurement accuracy of the gear measuring center is ±0.002 mm, which meets the measurement requirements of precision gears. During the measurement process, the modified face gear was mounted on the measuring spindle, and the probe was used to scan and measure along the tooth surface to obtain three-dimensional coordinate data of a large number of sampling points on the tooth surface. The processing of the measurement data included noise reduction filtering, coordinate alignment, and error separation, ultimately yielding tooth surface deviation data.

[0069] The actual tooth surface data is compared with the theoretically designed tooth surface to calculate the tooth surface deviation and contact spot distribution. The tooth surface deviation is defined as the distance along the normal direction between each sampling point on the actual tooth surface and the theoretical tooth surface, reflecting the level of modification accuracy. The contact spot distribution is obtained through a loaded meshing test. During the test, the modified face gear is meshed with the mating gear, and the distribution of contact marks on the tooth surface is observed under a load of 1.2 times the rated load. A contact spot area ratio greater than or equal to 85% indicates that the modification effect is qualified; this indicator reflects the uniformity of the tooth surface contact stress distribution.

[0070] If the deviation exceeds the allowable range, the process returns to step 1 to readjust the parameters and perform iterative optimization. Parameter adjustments during iterative optimization include correcting the boundary conditions of the finite element model, recalibrating material properties, updating the parameters of the prediction model, and re-optimizing the shaping scheme. This process continues through multiple iterations until the shaping effect meets the preset quality requirements. The convergence criteria for iterative optimization include the maximum value and standard deviation of the tooth surface deviation; the iteration process ends when both indicators are less than preset thresholds. This iterative optimization mechanism ensures stable and reliable shaping quality for each product, eliminates the adverse effects of human experience on the shaping effect, and improves product consistency and pass rate.

[0071] The technical solution of this invention demonstrates significant advantages in practical applications. Finite element analysis is used to obtain the stiffness distribution characteristics of the face gear body under machining conditions. Combined with multi-condition coupling analysis, displacement response data is extracted. Then, a polynomial response surface methodology is employed to establish a quantitative mapping relationship between the wheel body stiffness distribution and tooth surface deformation, enabling accurate prediction of the modification amount and providing a scientific and reliable basis for face gear tooth surface modification. Based on the established modification amount prediction model, a sequential quadratic programming algorithm is used to globally optimize the modification scheme, significantly improving the uniformity of contact stress distribution and controlling the peak-to-peak transmission error below 10 micrometers, greatly enhancing the accuracy and load-bearing capacity of the face gear transmission. By establishing a mapping model between wheel body stiffness distribution and machining deformation, precise control of deformation compensation is achieved. The deviation between the modified tooth surface and the theoretically designed tooth surface is controlled within ±0.005 mm, with good consistency in repeated modification, meeting the stringent requirements of high-precision face gear transmissions for high-end equipment such as aero-engines and helicopter main reducers. A closed-loop iterative optimization mechanism for modification processing and effect verification is established to quantitatively evaluate the modification effect, ensuring stable and reliable modification quality for each product.

[0072] In a preferred embodiment, the normal composite deformation amount mentioned in step 3 The calculation also considers the superposition effect of the displacement components of each node under multi-condition coupled loading, that is:

[0073] ;

[0074] ;

[0075]

[0076] In this analysis, the superscripts (F), (T), (C), and (V) represent the displacement components caused by cutting force, thermal deformation, clamping force, and vibration deformation, respectively. Each component is solved independently through its respective finite element sub-analysis, and then combined using the principle of linear superposition to obtain the comprehensive displacement response. This multiphysics coupling analysis method can more accurately simulate the wheel deformation state under actual machining conditions, improving the calculation accuracy of the comprehensive normal deformation.

[0077] In a preferred embodiment, the goodness of fit of the second-order polynomial response surface model in step 4 is determined by the coefficient of determination. Conduct an assessment:

[0078] ;

[0079] Where N is the number of validation samples. Let be the actual reshaping amount of the i-th validation sample. To predict the amount of reshaping for the model, This represents the average amount of actual reshaping. (Determination coefficient) The closer the value is to 1, the better the model fits the data. In a preferred embodiment, it is required that... This ensures that the prediction model has sufficient accuracy.

[0080] In a preferred embodiment, the weighting coefficients in step 5 and The adjustment is adaptive based on the operating conditions of the face gear. This is particularly relevant for applications such as aero-engines where high transmission precision is a primary requirement. Value greater than This means prioritizing minimizing transmission errors; for applications such as heavy-duty transmissions where load-bearing capacity is the primary requirement. Value greater than This prioritizes ensuring the uniformity of contact stress. The adjustment range of the weighting coefficients is... , ,and By adaptively adjusting the weighting coefficients, the reshaping scheme can adapt to the performance requirements of different application scenarios.

[0081] Example 2: Based on Example 1, this example provides a method for modifying the profile of large face gears. Due to their large size and mass, large face gears exhibit more significant non-uniformity in stiffness distribution, resulting in more prominent machining deformation problems. Therefore, more refined stiffness distribution analysis and modification strategies are required.

[0082] In step 1, during the creation of the three-dimensional finite element model of the large face gear, the geometric model is first constructed based on the design parameters of the large face gear. These parameters include a tooth count of 80 to 120, a module of 8 to 15 mm, a cone angle of 15 to 45 degrees, an inner diameter of 100 to 300 mm, and a rim thickness of 25 to 50 mm. The geometric model is created using a partitioned modeling strategy, dividing the gear body into four parts: the rim area, the transition area, the hub area, and the reinforcing rib area. These parts are then modeled separately and assembled using Boolean operations. For the reinforcing rib design, a hybrid layout combining radial and annular reinforcing ribs is used. The number of radial reinforcing ribs is set to 8 to 16, and the number of annular reinforcing ribs is set to 2 to 4 layers. This layout effectively improves the overall stiffness of the gear body and makes the stiffness distribution more uniform.

[0083] In step 2, during mesh generation, a hierarchical meshing strategy was adopted to address the geometric characteristics of the large face gear. The first-level mesh, with a mesh size of 10-20 mm, was used for overall structural analysis to quickly obtain the overall stiffness characteristics of the gear body. The second-level mesh, with a mesh size of 3-5 mm, was used for local region analysis to analyze the stiffness distribution in transition and stress concentration areas in detail. The third-level mesh, with a mesh size of 1-2 mm, was used for finer analysis of critical areas to analyze the stress-strain state of the tooth root region and the stiffener connection region. The total number of mesh elements in the overall model was controlled within the range of 2 million to 5 million.

[0084] In step 3, during the displacement response extraction process, a partitioned loading strategy was adopted to address the machining characteristics of large face gears. The cutting area was divided into multiple sub-regions, and the corresponding cutting force was calculated for each sub-region based on its location and cutting depth. Thermal deformation analysis employed the transient heat conduction finite element method, considering the influence of cutting heat on the gear body temperature field, and calculating the temperature field distribution and thermal deformation. Clamping force analysis used a multi-point clamping model, with the number of clamping points set to 6 to 12, and the clamping force determined based on the gear body mass and machining stability requirements.

[0085] In step 4, a hierarchical prediction strategy is adopted during the prediction model construction. First, a prediction model for the overall stiffness distribution and average profile modification amount of the wheel body is established; this model is used to determine the baseline value of the profile modification amount. Then, a prediction model for the local stiffness distribution and local profile modification amount is established; this model is used to determine the distribution pattern of the profile modification amount on the tooth surface. The two models are fused through a weighted combination, with the weighting coefficients determined based on the stiffness characteristics and deformation features of each region. The model training samples are generated using a hierarchical Latin hypercube sampling method, with a sample size of no less than 500 sets.

[0086] In step 5, a multi-objective optimization method is used to optimize the profile modification scheme. The optimization objectives include four aspects: contact stress uniformity, minimization of transmission error, uniformity of tooth surface machining allowance, and maximization of profile modification efficiency. A Pareto front-based multi-objective optimization algorithm is used to generate a Pareto optimal solution set for decision-makers to choose from. Optimization constraints include tooth surface geometry constraints, machining process constraints, tool path constraints, and machine tool travel constraints.

[0087] During the execution of step 6, a dual-spindle synchronous machining strategy is adopted in view of the machining characteristics of large face gears. The five-axis CNC gear milling machine is equipped with two synchronously moving spindles, on which a roughing tool and a finishing tool are respectively mounted, so that both the roughing and finishing processes can be completed in a single clamping. Roughing uses a large feed rate to quickly remove the allowance, while finishing uses a small feed rate to accurately complete the modification. For on-machine measurement during the machining process, a scheme combining a contact probe and a non-contact probe is adopted, where the contact probe is used for accurate measurement of critical dimensions, and the non-contact probe is used for rapid scanning of the overall topography.

[0088] During the effect verification process in step 7, the applied load for contact pattern distribution is set to 1.5 times the rated load, so as to assess the contact performance of the large face gear under high load. The evaluation indicators for the modification effect include four aspects: tooth surface deviation, contact pattern distribution, transmission error and noise characteristics. The modification effect is judged as qualified only when all four indicators meet the preset requirements. This evaluation system can comprehensively assess the comprehensive performance of large face gears.

[0089] Embodiment 3: On the basis of Embodiment 1 and Embodiment 2, this embodiment provides a modification and machining method for high-precision aviation face gears. Aviation face gears have extremely high requirements for transmission accuracy and reliability, which require the most rigorous stiffness distribution analysis and the strictest modification strategy.

[0090] During the modeling process in step 1, high-performance carburizing alloy steel with the material grade 18CrNiMo7-6 or a material of the same grade is selected as the material of the aviation face gear. Sub-grid subdivision technology is adopted to establish the finite element model, and the sub-grid model is used for encryption analysis in the area near the tooth surface, with the sub-grid size set to 0.5 mm to 1 mm. The wheel body structure adopts an integral structure, avoiding a split structure to eliminate the problem of sudden stiffness change caused by the connection interface. The rim thickness is optimized to 30 mm to 40 mm, and the ratio of the hub outer diameter to the aperture is optimized to 4 to 5, so as to ensure that the wheel body has sufficient overall stiffness.

[0091] During the meshing process in step 2, a feature-sensitive meshing method is adopted to determine the mesh density according to the sensitivity of geometric features. The tooth surface area, as the highest-sensitivity area, adopts a mesh size of 0.5 mm to 1 mm; the transition area, as a high-sensitivity area, adopts a mesh size of 1 mm to 2 mm; the main body area, as a medium-sensitivity area, adopts a mesh size of 3 mm to 5 mm. The ten-node quadratic reduced integration element is selected as the mesh element type, which has higher interpolation accuracy and can better capture the nonlinear characteristics of the stress concentration area. The total number of mesh elements of the overall model is controlled in the range of 3 million to 8 million.

[0092] In step 3, during the displacement response extraction, a multiphysics coupling analysis method was employed. Cutting force analysis used finite element cutting simulation to obtain the actual cutting force distribution; thermal deformation analysis used a thermo-mechanical coupled finite element method, considering the influence of cutting heat and temperature field distribution on deformation; clamping deformation analysis used a nonlinear contact finite element method, considering the nonlinear contact between the fixture and the workpiece; and vibration deformation analysis used a dynamic finite element method, considering the influence of vibration during machining on deformation. These four deformation mechanisms were combined using the superposition principle to obtain the comprehensive displacement response.

[0093] In step 4, during the prediction model construction, an ensemble learning method was used to build a shape modification prediction model. The ensemble model comprises three sub-models: a multinomial response surface model, a backpropagation neural network model, and a Gaussian process regression model. The prediction results of the three sub-models were fused using a weighted average, with the weights determined through cross-validation. Model training employed a bootstrap resampling method to generate multiple training subsets, with each sub-model trained on its corresponding subset. The ensemble model demonstrated superior prediction accuracy and robustness compared to a single model.

[0094] In step 5, a hybrid optimization strategy combining sequential quadratic programming and global search algorithms is employed. Sequential quadratic programming is used for local search, quickly converging to a local optimum; the global search algorithm is used to escape local optima and find the global optimum. The optimization objective for the contact stress standard deviation is set to 0.05 MPa, and the optimization objective for the transmission error peak-to-peak value is set to 5 micrometers. The constraint conditions are handled using the penalty function method, transforming the constrained optimization problem into an unconstrained optimization problem for solution.

[0095] During step 6 of the machining process, the shaping of the aerospace-grade gears is carried out in a constant temperature and humidity precision machining workshop. Temperature fluctuations are controlled within ±0.5 degrees Celsius, and humidity fluctuations within ±5%. The precision level of the five-axis CNC gear milling machine is upgraded to ultra-precision, with spindle runout less than 0.002 mm and positioning accuracy better than 0.005 mm. Diamond-coated ball end mills are used, with the tool radius precisely selected based on the tooth surface curvature. Cooling during machining employs a low-temperature micro-cooling method, with the coolant temperature set between 15 and 20 degrees Celsius, effectively suppressing the impact of cutting heat on machining accuracy.

[0096] In step 7, during the effect verification process, a sub-micron gear measurement center was used for tooth surface measurement, improving the measurement accuracy to ±0.001 mm. The loading load for the contact spot distribution was set to 1.0 to 2.0 times the rated load, and multi-point loading tests were conducted to obtain complete contact characteristic data. The evaluation of the modification effect adopted a comprehensive scoring method, which normalized four indicators—tooth surface deviation, contact spot distribution, transmission error, and surface roughness—and then weighted the sum. A comprehensive score of 95 or higher was considered a qualified modification effect. This evaluation system can comprehensively and objectively evaluate the modification effect of aerospace surface gears.

[0097] In a preferred embodiment, the normal composite deformation amount mentioned in step 3 The calculation considers the impact of the distribution density of sampling points on the tooth surface on the computational accuracy. An adaptive density strategy is adopted for the distribution of sampling points. In areas with drastic changes in tooth surface curvature (such as the transition area between the tooth root and tooth tip), the sampling point density is increased to no less than 30 points per square centimeter; in areas with gentle changes in tooth surface curvature (such as the central area of ​​the tooth surface), a standard sampling density of 20 points per square centimeter is used. This adaptive density strategy can improve the deformation calculation accuracy in key areas without significantly increasing the computational load, thereby improving the overall accuracy of the modification amount prediction model.

[0098] In a preferred embodiment, the cross-term coefficients of the second-order polynomial response surface model in step 4 The significance was assessed using a t-test. For the significance level... Insignificant interaction terms are removed from the model to simplify its structure and avoid overfitting. The simplified model is then optimized by adjusting the coefficient of determination. Conduct an assessment:

[0099] ;

[0100] Where N is the number of training samples, and p is the number of terms in the model (excluding constant terms). Adjusting the coefficient of determination. It can effectively reflect the model's true predictive ability after removing insignificant terms, when At that time, it was believed that the simplified model still had sufficient prediction accuracy.

[0101] In a preferred embodiment, the initial value of the modification scheme vector q in step 5 is quickly predicted by the tooth surface modification amount prediction model and used as the initial iteration point of the sequential quadratic programming algorithm. This initial point selection strategy can effectively reduce the number of iterations of the SQP algorithm and improve the efficiency of optimization. Specifically, the measured values ​​of the wheel stiffness distribution characteristic parameters are input into the trained prediction model, and the initial modification amount of each tooth surface region is directly output. Since the initial value is close to the optimal solution, the SQP algorithm only needs a few iterations to converge to the optimal solution that meets the accuracy requirements.

[0102] In a preferred embodiment, the convergence condition for the iterative optimization in step 7 adopts a comprehensive convergence criterion. The comprehensive convergence criterion requires that the iterative process terminate only when all three of the following conditions are met simultaneously: (1) the iterative change in the maximum value of the tooth surface deviation is less than 0.001 mm; (2) the iterative change in the standard deviation of the tooth surface deviation is less than 0.0005 mm; and (3) the iterative change in the proportion of the contact spot area is less than 1%. Only when all three conditions are met is it determined that the shaping effect has converged to a stable state, and the iterative optimization process is terminated. This comprehensive convergence criterion can comprehensively measure the convergence degree of the shaping effect, ensuring the reliability and effectiveness of the iterative optimization.

[0103] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method integrating stiffness field mapping and optimized machining for surface gear tooth surface modification, characterized in that, Includes the following steps: Step 1: Establish a three-dimensional finite element model of the face gear body. Construct a complete three-dimensional geometric model based on the design parameters of the face gear, including the number of teeth, module, pressure angle, cone angle, inner diameter, and rim thickness. Accurately model the rim, hub, and reinforcing rib structure. Step 2: Mesh the grid and set material properties. Adaptive mesh generation technology is used. Local meshing strategy is used in regions with drastic stiffness gradient changes, and sparse meshing strategy is used in regions with gentle stiffness distribution. The material properties adopt an isotropic linear elastic constitutive model. Step 3: Apply boundary conditions and extract displacement responses. Apply radial and axial constraints using displacement constraints. Extract nodal displacement data for three typical regions: tooth root, tooth middle, and tooth tip, using a multi-condition combined loading method. Based on the displacement components of each node in the global coordinate system and the unit normal vector of the tooth surface at that point... According to the formula Calculate the combined normal deformation at each sampling point on the tooth surface. ; in, , , The first The elastic displacement components of each sampling point in the X, Y, and Z directions. , , These are the components of the unit normal vector of the tooth surface at that point in three directions. Step 4: Establish a tooth surface modification prediction model. Based on the geometric parameters of different tooth surface regions and the corresponding comprehensive deformation, a multinomial response surface method is used to construct a tooth surface modification prediction model. The prediction model establishes a quantitative mapping relationship between the wheel stiffness distribution characteristic parameters and the tooth surface modification amount. The mapping relationship is expressed using a second-order polynomial model. ; in, For tooth surface shaping, , These are the characteristic parameters of wheel stiffness distribution. , , , The coefficients to be fitted are... The model coefficients are determined using the least squares method based on no fewer than 200 training samples, ensuring a prediction error ≤ 0.005 mm. Step 5: Determine the optimal modification scheme. Based on the tooth surface modification amount prediction model and the preset tooth surface contact quality target, the sequential quadratic programming algorithm is used to optimize the solution and obtain the optimal modification amount for each tooth surface region. The objective function of the sequential quadratic programming algorithm is: ,in Let be the vector of the reshaping scheme to be optimized. The standard deviation of tooth surface contact stress under the current modification scheme is given. This represents the peak-to-peak value of the transmission error under the current modification scheme. , The weighting coefficients and The optimization constraints include upper and lower limits for the shaping amount in each region and the smoothness constraint of the rate of change of the shaping amount in adjacent regions; Step 6: Perform tooth surface modification machining. Based on the optimal modification scheme, formulate CNC machining code and use a five-axis CNC gear milling machine to perform tooth surface modification machining. Step 7: Verify the shaping effect. Use a gear measurement center to perform three-dimensional morphological measurement on the shaped tooth surface to obtain actual tooth surface data. Compare the actual tooth surface data with the theoretically designed tooth surface, calculate the tooth surface deviation and contact spot distribution. If the deviation exceeds the allowable range, return to step 1 to readjust the parameters and perform iterative optimization.

2. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 1, the design parameters also include a rim thickness setting range of 15 mm to 25 mm and a hub outer diameter to bore diameter setting range of 3 to 5.

3. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 2, the mesh size in regions with drastic stiffness gradient changes is set to 1 mm to 3 mm, and the mesh size in regions with gentle stiffness distribution is set to 4 mm to 8 mm. The total number of mesh elements in the overall model is controlled within the range of 300,000 to 1,500,000.

4. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 2, the mesh generation adopts a hexahedral dominant meshing strategy, and the element type adopts an eight-node linear reduced integral element.

5. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 3, radial constraints are applied to the inner surface of the hub and axial constraints are applied to the end face of the hub. The multi-condition combined loading comprehensively considers the coupling effect of cutting force, thermal deformation and clamping force.

6. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 4, a prediction model for tooth surface modification is constructed using the second-order polynomial response surface method. The training samples for the model are generated using the Latin hypercube sampling method, with a sample size of no less than 200 sets.

7. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 4, a backpropagation neural network is used to establish a shaping amount distribution mapping model. The input layer of the neural network contains wheel stiffness distribution characteristic parameters, and the hidden layer contains a three-layer structure, with 20 neurons in each layer. The activation function is the hyperbolic tangent function. The output of the hidden layer of the backpropagation neural network is... The output layer output is ,in For the input layer One stiffness characteristic parameter, These are the connection weights from the input layer to the hidden layer. For hidden layer bias terms, For the first The output of each hidden layer neuron These are the connection weights from the hidden layer to the output layer. For output layer bias terms, For the first Predicted profile modification amount for each tooth surface region. The coefficient of determination after network training is ≥0.

95.

8. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 5, the optimization objectives include minimizing contact stress uniformity and transmission error, ensuring that the standard deviation of contact stress is less than 0.1 MPa and the peak-to-peak value of transmission error is less than 10 micrometers.

9. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 6, a ball end mill is selected as the cutting tool, and the ball end radius is selected to be 0.8 to 1.2 times the minimum radius of curvature of the tooth surface to be machined. The tool path is adaptively planned according to the shape modification amount distribution.

10. The integrated method for stiffness field mapping and optimized machining of face gear tooth surface modification according to claim 1, characterized in that, In step 7, the contact spot distribution is obtained through a loading engagement test. The distribution of tooth surface contact marks is observed under a loading load of 1.2 times the rated load. If the contact spot area ratio is greater than or equal to 85%, the shaping effect is qualified.

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