Intelligent regulation and control method for tooth surface contact imprint based on small sample actual measurement data

Abstract

The invention discloses a small sample actual measurement data-based tooth surface contact mark intelligent regulation and control method, which comprises the following steps of: obtaining a pair of installation error measurement values of a gear through a test to carry out boundary expansion, and obtaining an installation error variation range; after the tooth surface measurement is accurately positioned, the point-by-point measurement of tooth surface grid points is completed by using a measurement program of the CMM, and the deviation between a real tooth surface and a theoretical tooth surface is obtained; establishing an ETCA sensitivity model based on installation error probability distribution, and constructing an installation error-contact impression sample data pair according to an ETCA analysis result; a multi-head self-attention mechanism model based on Transform position coding is established to intelligently predict tooth surface contact impressions, assembly parameters are intelligently regulated and controlled in combination with a reinforcement learning algorithm, automatic traceability, positioning and optimization of errors are achieved, and finally rapid assembly of the hypoid gear is achieved.

Description

Technical Field

[0001] This invention relates to the field of precision mechanical transmission technology, specifically a method for intelligent control of tooth surface contact imprints based on small sample measured data. Background Technology

[0002] Hypoid gears are widely used in key areas such as automotive drive axles and industrial reducers due to their spatially interlaced shaft transmission capabilities. Their meshing performance is extremely sensitive to installation errors; even minute assembly deviations can lead to misalignment and distortion of the tooth surface contact imprint (contact area), resulting in serious problems such as increased noise and vibration, and shortened lifespan.

[0003] In the traditional assembly process of hypoid gears, assemblers mainly rely on experience, observing the contact marks after loading tests and repeatedly adjusting the shim thickness to regulate installation parameters such as gear axial position (P, G), offset distance (E), and shaft angle (A). This method has significant drawbacks: 1) Long trial-and-error cycle: Each adjustment requires reloading and testing, which is time-consuming and labor-intensive; 2) Reliance on expert experience: The adjustment direction and values ​​lack precise data support, resulting in low efficiency; 3) Limited sample size: Due to actual assembly conditions, only a small number of measured installation error points can be obtained, making it difficult to fully cover the possible error combinations; 4) Difficulty in achieving optimality: Finding the optimal solution under complex multidimensional error coupling is difficult.

[0004] Therefore, there is an urgent need for a method that can overcome the limitations of small samples, accurately predict the state of contact marks under different installation errors, and intelligently guide the rapid optimization and adjustment of assembly parameters in order to achieve high-precision and high-efficiency assembly of quasi-hypoid gears. Summary of the Invention

[0005] The purpose of this invention is to provide an intelligent control method for tooth surface contact imprints based on small sample measured data. This method involves obtaining installation error measurements of a pair of gears through experiments, expanding the boundary to obtain the range of installation error variation, measuring tooth surface errors using a CMM (Continuous Modeling) system, constructing a realistic tooth surface simulation model, establishing an ETCA (Electronic Technology and Compatibility) sensitivity model based on the probability distribution of installation errors, and constructing installation error-contact imprint sample data pairs based on ETCA analysis results. Furthermore, it establishes a multi-head self-attention mechanism model based on Transformer position encoding to achieve efficient and accurate prediction of tooth surface imprints, and combines reinforcement learning algorithms to intelligently control assembly parameters, enabling automatic source tracing, localization, and optimization of errors, thereby solving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for intelligent control of tooth surface contact imprints based on small sample measured data, the method steps are as follows:

[0008] Step 1: Measurement of Installation Error Parameters: For a pair of hyperboloid gears, in its actual assembly environment, the large and small gears are installed on a test bench. The key installation error parameters are measured multiple times using a coordinate measuring machine (CMM), and the error value of each measurement is recorded. Among the key installation error parameters, the axial position error of the small gear is denoted as P, the axial position error of the large gear is denoted as G, the offset distance error is denoted as E, and the shaft intersection angle error is denoted as A, forming an initial discrete installation error dataset containing a finite number of sample points. The initial discrete installation error dataset is denoted as D_init. Using engineering experience and statistical methods, the boundary of the initial discrete installation error dataset D_init is expanded to obtain a continuous, engineering-reasonable, and multi-dimensional installation error variation range Ω that covers the expected range of actual assembly tolerances.

[0009] Step Two: Precise Positioning of Tooth Surface Measurement: Based on the gear sample after cutting and heat treatment, the CMM's built-in measurement program is used to complete point-by-point measurement of the tooth surface grid points, obtaining a normal deviation detection file between the actual tooth surface and the theoretical tooth surface. In the detection file, the normal deviation corresponding to each point is expressed in the form of a difference surface, and the error tooth surfaces of the large gear and the small gear are stored in matrix form respectively, thus building a digital model of the actual tooth surface.

[0010]

[0011] Where E Pcave E is the tooth profile error matrix of the concave surface of the small gear. Pvex Let E be the tooth profile error matrix of the small wheel convex surface; where E Gcave E is the error matrix of the concave tooth profile of the large wheel. Gvex The error matrix for the convex tooth profile of the large wheel;

[0012] Step 3: Calculate the coordinates of the actual tooth surface: The normal deviation of the theoretical tooth surface is recorded as the tooth surface error. Based on the obtained tooth surface errors at each point, and according to the positions of the tooth surface grid points in the inspection file, the theoretical point vector in the cutting coordinate system is calculated. Using the theoretical coordinate values ​​corresponding to each tooth surface grid point, and combining the normal error, the coordinates of the actual tooth surface are calculated.

[0013] R or =R ot +E Cave *N ot (1)

[0014] R tr =R tt +E Vex *N tt (2)

[0015] Where R or R tr R is the matrix of actual coordinate values ​​of the grid points on the concave and convex surfaces of the gear.ot R tt N is the theoretical coordinate matrix of concave and convex mesh points. ot N tt For concave and convex mesh points, the theoretical normal vector matrix is ​​used.

[0016] Step 4: Establish the quasi-hypoid gear model: Using the coordinates of the actual tooth surface, establish the CAD model of the quasi-hypoid gear, and complete the assembly model of the quasi-hypoid gear pair based on the relative positional relationships such as the shaft intersection angle, offset distance, and distance from the pitch cone point to the intersection point of the large and small gears.

[0017] Step 5: Obtain installation error samples: Use Latin hypercube sampling to uniformly extract N installation error sample points e_i, e_i=[P_i,G_i,E_i,A_i] in the multidimensional installation error variation range Ω, and establish an ETCA sensitivity model based on the installation error probability distribution.

[0018] Step Six: Constructing Installation Error-Contact Imprint Sample Data Pairs: Based on the ETCA analysis results, construct installation error-contact imprint sample data pairs. Perform contact imprint simulation based on e_i. Perform hexahedral meshing on the large and small wheels in the assembly coordinate system to complete the preprocessing part of the contact analysis. Add the installation error to the corresponding assembly constraints. Define the elastic modulus and Poisson's ratio for the large and small wheels respectively. Couple the tooth roots of the large and small wheels and constrain the load and displacement through control points to achieve slight interference between the tooth surfaces of the large and small wheels, enabling normal meshing. Calculate and assemble the stiffness matrices of the large and small wheels, and balance and solve for force and deformation using partial differential equations. Extract the contact imprint features of the tooth surfaces under the corresponding installation error conditions. Extract the positional features of the contact imprints, define the center point of the contact imprints and discrete points on the instantaneous imprint boundary, and process the above features into a fixed-dimensional numerical vector f_contact_i.

[0019] f_contact_i=[(x1,y1), (x2,y2),...(xk,yk)]

[0020] x1, y1 represent the two-dimensional coordinates of discrete points on the contact imprint boundary, and f_contact_i represents the set of two-dimensional coordinates of discrete points on the contact imprint boundary obtained under the installation error of the i-th sample.

[0021] Calculate the distances of the contact imprint relative to the four boundaries of the tooth surface to determine whether edge contact has occurred. Obtain sample pairs and store them as (e_i, f_contact_i). After accumulation, form dataset D.

[0022] D={(e_1,f_contact_1),(e_2,f_contact_2),...,(e_N,f_contact_N)};

[0023] Data preprocessing is performed by standardizing the installation error vector e_i and the contact imprint feature vector f_contact_i in dataset D using StandardScaler to obtain dataset D_scaled.

[0024] Step 7: Construct a contact imprint prediction model. Design a Transformer encoder and a multi-head self-attention mechanism. Construct a contact imprint prediction model based on the Transformer architecture and multi-head self-attention mechanism. Normalize the sample data pairs and train the model using a multi-head self-attention mechanism based on Transformer position encoding. Define the loss function: criterion = nn.MSELoss() and the optimizer: optimizer = torch.optim.Adam(model.parameters()). The input sequence of the model consists of multi-dimensional installation error parameters sampled within the multi-dimensional installation error variation range Ω, and the output sequence is the corresponding contact imprint feature vector. Extract the spatial correlation of the input installation error through a multi-layer encoder, and use the attention weight matrix to learn the deep nonlinear mapping relationship between the installation error parameters and the position and shape features of the contact imprint, thus constructing an intelligent prediction model for tooth surface contact imprints.

[0025] Step 8: Establish a reinforcement learning agent to train the contact imprint prediction model. Based on the installation error-contact imprint sample data, supervise the training of the Transformer model. The training loop iterates through the training set, calculates the loss between the model's predicted normalized contact imprint feature f_pred and the actual f_contact, and updates the model parameters through backpropagation and optimization algorithms until convergence. The trained model can efficiently and accurately predict the corresponding contact imprint features under a given installation error vector. Save the best model weight file for subsequent prediction.

[0026] Step Nine: Interactive Trial and Error in Simulation Environment: Define the elements of the reinforcement learning agent: state space, action space, and reward function. Based on the trained Transformer prediction model as the simulation environment, reinforcement learning algorithm (RL) is used for reinforcement learning. The reinforcement learning agent is iteratively trained through the simulation environment that interacts with the intelligent prediction model, exploring the state space-action space mapping strategy. This allows the reinforcement learning agent to interactively try and fail in the simulation environment, obtain environmental feedback, update the strategy and value, and finally learn an optimal mapping strategy π from the state space to the action space.

[0027] Step 10: Final Assembly: When the imprint prediction or physical assembly verification shows that the contact imprint meets the requirements, lock the installation parameters and complete the assembly.

[0028] As a further aspect of the present invention: in step one, P is the deviation of the axial position of the small wheel along its axis direction from the reference position, G is the deviation of the axial position of the large wheel along its axis direction from the reference position, E is the offset distance deviation between the axes of the large and small wheels, and A is the deviation between the actual axis angle and the theoretical axis angle of the large and small wheels; D_init={[P1、G1、E1、A1]、[P2、G2、E2、A2],···,[Pk、Gk、Ek、Ak]}.

[0029] As a further aspect of the present invention: in step four, e_i represents the value composed of the four installation errors extracted from the i-th sample.

[0030] As a further aspect of the present invention: the positional characteristics of the contact imprint in step six are represented by the minimum spatial distance between the contact imprint and the edge of the tooth surface. Taking the contact imprint position data under error-free conditions as a reference, the corresponding contact imprint position data under installation error conditions are subtracted and denoted as ΔL1~ΔL4 and Δl1~Δl4, which represent the distance the contact imprint moves. A positive value indicates that it is away from the corresponding contact imprint edge, and a negative value indicates that it is close to the corresponding contact imprint edge. L1~L4 represent the minimum spatial distances of the convex contact imprint of the large wheel from the edge of the large end, the edge of the tooth tip, the edge of the small end, and the edge of the tooth root, respectively. l1~l4 represent the minimum spatial distances of the concave contact imprint of the large wheel from the edge of the large end, the edge of the tooth tip, the edge of the small end, and the edge of the tooth root, respectively.

[0031] As a further aspect of the present invention: in step seven, criterion = nn.MSELoss() is Python code, indicating that the loss function is MSE; optimizer = torch.optim.Adam(model.parameters() is Python code, indicating that the model parameters are optimized.

[0032] As a further aspect of the present invention: in step eight, f_pred represents the predicted coordinates of the contact imprint boundary points, and f_contact represents the actual coordinates of the contact imprint boundary points calculated by the mechanism. When updating the model parameters, the loss is monitored on the validation set to prevent overfitting, and the final prediction accuracy is evaluated on the test set.

[0033] As a further aspect of the present invention: the reinforcement learning algorithm (RL) in step nine includes the following algorithmic steps:

[0034] 1) The state space s_t is defined as the normalized contact imprint feature vector f_pred output by the trained contact imprint prediction model;

[0035] 2) The action space a_t refers to the continuous adjustment amount of P, G, E, A, denoted as ΔP, ΔG, ΔE, ΔA. The action space is defined as Box(low=-max_step,high=max_step,shape=(4,));

[0036] 3) Based on the given current contact imprint state s_t and the action space a_t selected by the agent, perform state transition and calculate the new installation error vector: e_new, e_new=e_t+a_t. Input the normalized e_new into the contact imprint model to predict the new normalized contact imprint feature vector f_pred_new, f_pred_new represents the new contact imprint feature value calculated under the new installation error value. Store the new imprint in s_(t+1) to represent the state, s_(t+1=f_pred_new;

[0037] 4) The reward function r_t = pos_penalty + shape_penalty is constructed based on the position deviation, shape irregularity and size deviation of the contact imprint feature vector, and a composite optimization objective is constructed by combining the control amount constraint.

[0038] The predicted imprint center point deviates from the actual imprint point by the position deviation penalty pos_penalty, and the predicted imprint boundary discrete point deviates from the actual imprint boundary discrete point by the shape deviation penalty shape_penalty.

[0039] 5) Select and train the RL algorithm, and save the trained RL agent mapping policy π(s);

[0040] 6) After training is completed, deploy the strategy to perform closed-loop dynamic control on the assembly parameters P, G, E, and A of the actual gear pair in order to minimize the position and shape deviation of the contact imprint, and finally achieve high-precision and rapid assembly optimization of the quasi-hypoid gear.

[0041] As a further aspect of the present invention, the closed-loop dynamic control steps are as follows:

[0042] ① Initial installation: Install the gear pair at the assembly site for initial installation;

[0043] ② Initial measurement: Measure the current installation error e_current using a CMM or simple tooling;

[0044] ③ Initial prediction: Input the normalized e_current into the contact imprint prediction model to obtain the initial imprint prediction state s_current;

[0045] ④ Agent decision-making: Load the trained RL agent policy π(s), input the current state s_current, and the policy output action a_t=[ΔP_rec,ΔG_rec];

[0046] ⑤ State update and iteration: After adjustment, the new e_current is normalized and input into the contact imprint prediction model to predict the new state s_new;

[0047] ⑥ Evaluation: If s_new reaches a satisfactory state, the adjustment ends and the assembly is completed; otherwise, s_new is used as the new s_current for the next round of intelligent decision-making and adjustment.

[0048] As a further aspect of the present invention: ΔP_rec and ΔG_rec represent the adjustment amounts of installation errors P and G, s_new represents the new state, and the basic parameters of the model.

[0049] Compared with the prior art, the beneficial effects of the present invention are:

[0050] This invention obtains the installation error measurement values ​​of a pair of gears through experiments and expands the boundary to obtain the range of installation error variation. After precise positioning of the tooth surface, the CMM's built-in measurement program completes point-by-point measurement of the tooth surface grid points to obtain the deviation between the actual tooth surface and the theoretical tooth surface. An ETCA sensitivity model based on the probability distribution of installation error is established, and installation error-contact imprint sample data pairs are constructed based on the ETCA analysis results. A multi-head self-attention mechanism model based on Transformer position encoding is established to intelligently predict tooth surface contact imprints, and reinforcement learning algorithms are combined to intelligently adjust assembly parameters to achieve optimization, ultimately realizing the rapid assembly of quasi-hypoid gears. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the installation error of a quasi-hyperboloid gear, based on an intelligent control method for tooth surface contact imprints using small sample measured data.

[0052] Figure 2 This is a schematic diagram of the quasi-hyperboloid normal deviation, which is a method for intelligent control of tooth surface contact imprints based on small sample measured data.

[0053] Figure 3 This diagram illustrates the deviation in the shape of the contact imprint in a smart control method for tooth surface contact imprints based on small sample measured data. Figure 1 .

[0054] Figure 4 This diagram illustrates the deviation in the shape of the contact imprint in a smart control method for tooth surface contact imprints based on small sample measured data. Figure 2 .

[0055] Figure 5 This is a schematic diagram of the minimum spatial distance of the contact imprint on the convex surface of a large wheel in an intelligent control method for tooth surface contact imprints based on small sample measured data.

[0056] Figure 6 This is a schematic diagram of the minimum spatial distance of the concave contact imprint on a large wheel in an intelligent control method for tooth surface contact imprints based on small sample measured data.

[0057] Figure 7 This refers to the quasi-hypoid gear tooth surface contact imprint obtained from a vehicle test in an intelligent control method for tooth surface contact imprints based on small sample measured data.

[0058] Figure 8 This is a simulation model of the contact imprint under error-free conditions in an intelligent control method for tooth surface contact imprints based on small sample measured data.

[0059] Figure 9 This is a simulated model of contact imprints for tooth surfaces, based on a small sample of measured data, where the contact imprints include installation errors. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.

[0061] Please see Figures 1-9 In this embodiment of the invention, a method for intelligent control of tooth surface contact imprints based on small sample measured data is described, and the method steps are as follows:

[0062] Step 1: Measurement of Installation Error Parameters: For a pair of hyperboloid gears, in its actual assembly environment, the large and small gears are installed on a test bench. The key installation error parameters are measured multiple times using a coordinate measuring machine (CMM), and the error value of each measurement is recorded. Among the key installation error parameters, the axial position error of the small gear is denoted as P, the axial position error of the large gear is denoted as G, the offset distance error is denoted as E, and the shaft intersection angle error is denoted as A, forming an initial discrete installation error dataset containing a finite number of sample points (i.e., a small sample). The initial discrete installation error dataset is denoted as D_init. Using engineering experience and statistical methods, the boundary of the initial discrete installation error dataset D_init is expanded to obtain a continuous, engineering-reasonable, and multi-dimensional installation error variation range Ω that covers the expected range of actual assembly tolerances.

[0063] P is the deviation of the small wheel's axial position along its axis from the reference position; G is the deviation of the large wheel's axial position along its axis from the reference position; E is the offset distance deviation between the axes of the small and large wheels; and A is the deviation between the actual axis angle and the theoretical axis angle of the small and large wheels.

[0064] D_init={[P1, G1, E1, A1], [P2, G2, E2, A2],···,[Pk,Gk,Ek,Ak]};

[0065] Step Two: Precise Positioning of Tooth Surface Measurement: Based on the gear sample after cutting and heat treatment, the CMM's built-in measurement program is used to complete point-by-point measurement of the tooth surface grid points, obtaining a normal deviation detection file between the actual tooth surface and the theoretical tooth surface. In the detection file, the normal deviation corresponding to each point is expressed in the form of a difference surface, and the error tooth surfaces of the large gear and the small gear are stored in matrix form respectively, thus building a digital model of the actual tooth surface.

[0066]

[0067] Where E Pcave E is the tooth profile error matrix of the concave surface of the small gear. Pvex Let E be the tooth profile error matrix of the small wheel convex surface; where E Gcave E is the error matrix of the concave tooth profile of the large wheel. Gvex The error matrix for the convex tooth profile of the large wheel;

[0068] Step 3: Calculate the coordinates of the actual tooth surface: The normal deviation of the theoretical tooth surface is recorded as the tooth surface error. Based on the obtained tooth surface errors at each point, and according to the positions of the tooth surface grid points in the inspection file, the theoretical point vector in the cutting coordinate system is calculated. Using the theoretical coordinate values ​​corresponding to each tooth surface grid point, and combining the normal error, the coordinates of the actual tooth surface are calculated.

[0069] R or =R ot +E Cave *N ot (3)

[0070] R tr =R tt +E Vex *N tt (4)

[0071] Where R or R tr R is the matrix of actual coordinate values ​​of the grid points on the concave and convex surfaces of the gear. ot R tt N is the theoretical coordinate matrix of concave and convex mesh points. ot N tt For concave and convex mesh points, the theoretical normal vector matrix is...

[0072] Taking a small wheel as an example, the calculation process is as follows:

[0073] Based on the blank parameters, machine tool parameters, and cutting tool parameters, the point vector and normal vector of the theoretical tooth surface are obtained according to the meshing equation and discrete equation, where the concave point vector and normal vector are R. Pot N Pot The point vector and normal vector of the convex surface are R. Ptt N Ptt The coordinates of the actual tooth surface are calculated by taking into account the tooth surface mesh error.

[0074] R Por =R Pot +E Pcave *N Pot

[0075] R Ptr =R Ptt +E Pvex *N Ptt

[0076] Where R Por R Ptr The matrix of actual coordinate values ​​for the concave and convex grid points on the small wheel is given by the same method. Gor R Gtr ;

[0077] Step 4: Establish the quasi-hypoid gear model: Using the coordinates of the actual tooth surface, establish the CAD model of the quasi-hypoid gear, and complete the assembly model of the quasi-hypoid gear pair based on the relative positional relationships such as the shaft intersection angle, offset distance, and distance from the pitch cone point to the intersection point of the large and small gears.

[0078] Step 5: Obtain installation error samples: Use Latin hypercube sampling in the multidimensional installation error variation range Ω to uniformly extract N installation error sample points e_i, where e_i represents the value of the four installation errors extracted in the i-th sample, e_i=[P_i,G_i,E_i,A_i], and establish an ETCA sensitivity model based on the installation error probability distribution.

[0079] Step Six: Constructing Installation Error-Contact Imprint Sample Data Pairs: Based on the ETCA analysis results, construct installation error-contact imprint sample data pairs. Perform contact imprint simulation based on e_i. Perform hexahedral meshing on the large and small wheels in the assembly coordinate system to complete the preprocessing part of the contact analysis. Add the installation error to the corresponding assembly constraints. Define the elastic modulus and Poisson's ratio for the large and small wheels respectively. Couple the tooth roots of the large and small wheels and constrain the load and displacement through control points to achieve slight interference between the tooth surfaces of the large and small wheels, enabling normal meshing. Calculate and assemble the stiffness matrices of the large and small wheels, and balance and solve for force and deformation using partial differential equations. Extract the contact imprint features of the tooth surfaces under the corresponding installation error conditions. Extract the positional features of the contact imprints, define the center point of the contact imprints and discrete points on the instantaneous imprint boundary, and process the above features into a fixed-dimensional numerical vector f_contact_i.

[0080] f_contact_i=[(x1,y1), (x2,y2),...(xk,yk)]

[0081] x1, y1 represent the two-dimensional coordinates of discrete points on the contact imprint boundary, and f_contact_i represents the set of two-dimensional coordinates of discrete points on the contact imprint boundary obtained under the installation error of the i-th sample.

[0082] Calculate the distances of the contact imprint relative to the four boundaries of the tooth surface to determine whether edge contact has occurred. Obtain sample pairs and store them as (e_i, f_contact_i). After accumulation, form dataset D.

[0083] D={(e_1,f_contact_1),(e_2,f_contact_2),...,(e_N,f_contact_N)};

[0084] Data preprocessing is performed by standardizing the installation error vector e_i and contact imprint feature vector f_contact_i in dataset D using StandardScaler, resulting in dataset D_scaled.

[0085] The positional characteristics of the contact imprint are represented by the minimum spatial distance between the contact imprint and the edge of the tooth surface. Using the contact imprint position data under error-free conditions as a benchmark, the corresponding contact imprint position data under installation error conditions are subtracted, denoted as ΔL1~ΔL4 and Δl1~Δl4, representing the distance the contact imprint has moved. A positive value indicates movement away from the corresponding contact imprint edge, while a negative value indicates movement towards the corresponding contact imprint edge. L1~L4 represent the minimum spatial distances of the convex contact imprint of the large wheel from the large end edge, tooth tip edge, small end edge, and tooth root edge, respectively. l1~l4 represent the minimum spatial distances of the concave contact imprint of the large wheel from the large end edge, tooth tip edge, small end edge, and tooth root edge, respectively.

[0086]

[0087] Step 7: Construct a contact imprint prediction model. Design a Transformer encoder and a multi-head self-attention mechanism. Construct a contact imprint prediction model based on the Transformer architecture and multi-head self-attention mechanism. Normalize the sample data pairs and train the model using a multi-head self-attention mechanism based on Transformer position encoding. Define the loss function: criterion = nn.MSELoss() and the optimizer: optimizer = torch.optim.Adam(model.parameters()). The input sequence of the model consists of multi-dimensional installation error parameters sampled within the multi-dimensional installation error variation range Ω, and the output sequence is the corresponding contact imprint feature vector. Extract the spatial correlation of the input installation error through a multi-layer encoder, and use the attention weight matrix to learn the deep nonlinear mapping relationship between the installation error parameters and the position and shape features of the contact imprint, thus constructing an intelligent prediction model for tooth surface contact imprints.

[0088] The criterion = nn.MSELoss() is Python code indicating that the loss function is MSE;

[0089] `optimizer = torch.optim.Adam(model.parameters())` is Python code that indicates the optimization of model parameters.

[0090] Step 8: Train a reinforcement learning agent to predict contact imprints. Supervise the Transformer model using installation error-contact imprint sample data. Repeat the training loop, iterating through the training set and calculating the loss between the model's predicted normalized contact imprint feature f_pred and the actual contact imprint feature f_contact. Update the model parameters using backpropagation and an optimization algorithm (such as Adam) until convergence. The trained model should be able to efficiently and accurately predict the contact imprint features corresponding to a given installation error vector. Save the best-fit model weight file for subsequent predictions.

[0091] f_pred represents the predicted coordinates of the contact imprint boundary points. f_contact represents the actual coordinates of the contact imprint boundary points calculated from the mechanism.

[0092] Monitor the loss on the validation set when updating model parameters to prevent overfitting. Evaluate the final prediction accuracy (e.g., MSE) on the test set.

[0093] Step Nine: Interactive Trial and Error in Simulation Environment. Define the elements of the reinforcement learning agent: state space, action space, and reward function. Based on the trained Transformer prediction model as the simulation environment, reinforcement learning algorithm (RL) is used for reinforcement learning. The reinforcement learning agent is iteratively trained through the simulation environment that interacts with the intelligent prediction model, exploring the state space-action space mapping strategy. This allows the reinforcement learning agent to interactively try and fail in the simulation environment, obtain environmental feedback, update the strategy and value, and finally learn an optimal mapping strategy π from the state space to the action space.

[0094] The reinforcement learning (RL) algorithm includes the following steps:

[0095] 1) The state space s_t is defined as the normalized contact imprint feature vector f_pred output by the trained contact imprint prediction model;

[0096] 2) The motion space a_t refers to the continuous adjustment amount of P, G, E, A. The continuous adjustment amount is denoted as ΔP, ΔG, ΔE, ΔA. The motion space is defined as Box(low=-max_step,high=max_step,shape=(4,)), where max_step is the maximum allowable single adjustment amplitude (e.g., 0.001mm / deg).

[0097] 3) Based on the given current contact imprint state s_t (corresponding to the imprint prediction under the installation error state e_t) and the action space a_t selected by the agent, perform state transition and calculate the new installation error vector: e_new, e_new=e_t+a_t, e_new represents the new installation error value obtained through iteration. Input the normalized e_new into the contact imprint model to predict the new normalized contact imprint feature vector f_pred_new, f_pred_new represents the new contact imprint feature value calculated under the new installation error value. Store the new imprint in s_(t+1) to represent the state, s_(t+1=f_pred_new;

[0098] 4) The reward function r_t = pos_penalty + shape_penalty is constructed based on the position deviation, shape irregularity and size deviation of the contact imprint feature vector, and a composite optimization objective is constructed by combining the control amount constraint.

[0099] The predicted imprint center point deviates from the actual imprint point by the position deviation penalty pos_penalty, and the predicted imprint boundary discrete point deviates from the actual imprint boundary discrete point by the shape deviation penalty shape_penalty.

[0100] 5) Select and train an RL algorithm (such as PPO), and save the trained RL agent mapping policy π(s);

[0101] 6) After training is completed, deploy the strategy to perform closed-loop dynamic control on the assembly parameters P, G, E, and A of the actual gear pair in order to minimize the position and shape deviation of the contact imprint, and finally achieve high-precision and rapid assembly optimization of the quasi-hypoid gear.

[0102] The closed-loop dynamic control steps are as follows:

[0103] ① Initial installation: Install the gear pair at the assembly site for initial installation;

[0104] ② Initial measurement: Measure the current installation error e_current using CMM or simple tooling (if it cannot be measured accurately, it can be set to 0 or a point within Ω can be randomly selected as the starting point);

[0105] ③ Initial prediction: Input the normalized e_current into the contact imprint prediction model to obtain the initial imprint prediction state s_current;

[0106] ④ Agent decision-making: Load the trained RL agent policy π(s), input the current state s_current, and output the action (suggested adjustment amount) a_t=[ΔP_rec,ΔG_rec];

[0107] ⑤ State update and iteration: After adjustment, the new e_current is normalized and input into the contact imprint prediction model to predict the new state s_new;

[0108] ⑥ Evaluation: If s_new reaches a satisfactory state (e.g., the imprint does not make edge contact or the imprint is in the middle of the tooth surface), then the adjustment ends and the assembly is completed. Otherwise: s_new is used as the new s_current for the next round of intelligent decision-making and adjustment.

[0109] ΔP_rec and ΔG_rec represent the adjustment amounts for installation errors P and G, and s_new represents the new state, which are the basic parameters of the model.

[0110] Step 10: Final assembly. When the contact imprint prediction or physical assembly verification (which can be performed once after multiple rounds) shows that the contact imprint meets the requirements, lock the installation parameters and complete the assembly.

[0111] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for intelligent control of tooth surface contact imprints based on small sample measured data, characterized in that: The method steps are as follows: Step 1: Measurement of Installation Error Parameters: For a pair of hyperboloid gears, in its actual assembly environment, the large and small gears are installed on a test bench. The key installation error parameters are measured multiple times using a coordinate measuring machine (CMM), and the error value of each measurement is recorded. Among the key installation error parameters, the axial position error of the small gear is denoted as P, the axial position error of the large gear is denoted as G, the offset distance error is denoted as E, and the shaft intersection angle error is denoted as A, forming an initial discrete installation error dataset containing a finite number of sample points. The initial discrete installation error dataset is denoted as D_init. Using engineering experience and statistical methods, the boundary of the initial discrete installation error dataset D_init is expanded to obtain a continuous, engineering-reasonable, and multi-dimensional installation error variation range Ω that covers the expected range of actual assembly tolerances. Step Two: Precise Positioning of Tooth Surface Measurement: Based on the gear sample after cutting and heat treatment, the CMM's built-in measurement program is used to complete point-by-point measurement of the tooth surface grid points, obtaining a normal deviation detection file between the actual tooth surface and the theoretical tooth surface. In the detection file, the normal deviation corresponding to each point is expressed in the form of a difference surface, and the error tooth surfaces of the large gear and the small gear are stored in matrix form respectively, thus building a digital model of the actual tooth surface. Where E Pcave E is the tooth profile error matrix of the concave surface of the small wheel. Pvex Let E be the tooth profile error matrix of the small wheel convex surface; where E Gcave E is the error matrix of the concave tooth profile of the large wheel. Gvex The error matrix for the convex tooth profile of the large wheel; Step 3: Calculate the coordinates of the actual tooth surface: The normal deviation of the theoretical tooth surface is recorded as the tooth surface error. Based on the obtained tooth surface errors at each point, and according to the positions of the tooth surface grid points in the inspection file, the theoretical point vector in the cutting coordinate system is calculated. Using the theoretical coordinate values ​​corresponding to each tooth surface grid point, and combining the normal error, the coordinates of the actual tooth surface are calculated. R or =R ot +E Cave *N ot (1) R tr =R tt +E Vex *N tt (2) Where R or R tr R is the matrix of actual coordinate values ​​of the grid points on the concave and convex surfaces of the gear. ot R tt N is the theoretical coordinate matrix of concave and convex mesh points. ot N tt For concave and convex mesh points, the theoretical normal vector matrix is ​​used. Step 4: Establish the quasi-hypoid gear model: Using the coordinates of the actual tooth surface, establish the CAD model of the quasi-hypoid gear, and complete the assembly model of the quasi-hypoid gear pair based on the relative positional relationships such as the shaft intersection angle, offset distance, and distance from the pitch cone point to the intersection point of the large and small gears. Step 5: Obtain installation error samples: Use Latin hypercube sampling to uniformly extract N installation error sample points e_i, e_i=[P_i,G_i,E_i,A_i] in the multidimensional installation error variation range Ω, and establish an ETCA sensitivity model based on the installation error probability distribution. Step Six: Constructing Installation Error-Contact Imprint Sample Data Pairs: Based on the ETCA analysis results, construct installation error-contact imprint sample data pairs. Perform contact imprint simulation based on e_i. Perform hexahedral meshing on the large and small wheels in the assembly coordinate system to complete the preprocessing part of the contact analysis. Add the installation error to the corresponding assembly constraints. Define the elastic modulus and Poisson's ratio for the large and small wheels respectively. Couple the tooth roots of the large and small wheels and constrain the load and displacement through control points to achieve slight interference between the tooth surfaces of the large and small wheels, enabling normal meshing. Calculate and assemble the stiffness matrices of the large and small wheels, and balance and solve for force and deformation using partial differential equations. Extract the contact imprint features of the tooth surfaces under the corresponding installation error conditions. Extract the positional features of the contact imprints, define the center point of the contact imprints and discrete points on the instantaneous imprint boundary, and process the above features into a fixed-dimensional numerical vector f_contact_i. f_contact_i=[(x1,y1), (x2,y2),...(xk,yk)] x1, y1 represent the two-dimensional coordinates of discrete points on the contact imprint boundary, and f_contact_i represents the set of two-dimensional coordinates of discrete points on the contact imprint boundary obtained under the installation error of the i-th sample. Calculate the distances of the contact imprint relative to the four boundaries of the tooth surface to determine whether edge contact has occurred. Obtain sample pairs and store them as (e_i, f_contact_i). After accumulation, form dataset D. D={(e_1,f_contact_1),(e_2,f_contact_2),...,(e_N,f_contact_N)}; Data preprocessing is performed by standardizing the installation error vector e_i and the contact imprint feature vector f_contact_i in dataset D using StandardScaler to obtain dataset D_scaled. Step 7: Construct a contact imprint prediction model. Design a Transformer encoder and a multi-head self-attention mechanism. Construct a contact imprint prediction model based on the Transformer architecture and multi-head self-attention mechanism. Normalize the sample data pairs and train the model using a multi-head self-attention mechanism based on Transformer position encoding. Define the loss function: criterion = nn.MSELoss() and the optimizer: optimizer = torch.optim.Adam(model.parameters()). The input sequence of the model consists of multi-dimensional installation error parameters sampled within the multi-dimensional installation error variation range Ω, and the output sequence is the corresponding contact imprint feature vector. Extract the spatial correlation of the input installation error through a multi-layer encoder, and use the attention weight matrix to learn the deep nonlinear mapping relationship between the installation error parameters and the position and shape features of the contact imprint, thus constructing an intelligent prediction model for tooth surface contact imprints. Step 8: Establish a reinforcement learning agent to train the contact imprint prediction model. Based on the installation error-contact imprint sample data, supervise the training of the Transformer model. The training loop iterates through the training set, calculates the loss between the model's predicted normalized contact imprint feature f_pred and the actual f_contact, and updates the model parameters through backpropagation and optimization algorithms until convergence. The trained model can efficiently and accurately predict the corresponding contact imprint features under a given installation error vector. Save the best model weight file for subsequent prediction. Step Nine: Interactive Trial and Error in Simulation Environment: Define the elements of the reinforcement learning agent: state space, action space, and reward function. Based on the trained Transformer prediction model as the simulation environment, reinforcement learning algorithm (RL) is used for reinforcement learning. The reinforcement learning agent is iteratively trained through the simulation environment that interacts with the intelligent prediction model, exploring the state space-action space mapping strategy. This allows the reinforcement learning agent to interactively try and fail in the simulation environment, obtain environmental feedback, update the strategy and value, and finally learn an optimal mapping strategy π from the state space to the action space. Step 10: Final Assembly: When the imprint prediction or physical assembly verification shows that the contact imprint meets the requirements, lock the installation parameters and complete the assembly.

2. The intelligent control method for tooth surface contact imprints based on small sample measured data according to claim 1, characterized in that: In step one, P is the deviation of the small wheel's axial position along its axis from the reference position, G is the deviation of the large wheel's axial position along its axis from the reference position, E is the offset distance deviation of the large and small wheel axes, and A is the deviation between the actual and theoretical axis angles of the large and small wheels; D_init={[P1、G1、E1、A1]、[P2、G2、E2、A2],···,[Pk、Gk、Ek、Ak]}.

3. The intelligent control method for tooth surface contact imprints based on small sample measured data according to claim 1, characterized in that: In step four, e_i represents the value composed of the four installation errors extracted from the i-th sample.

4. The intelligent control method for tooth surface contact imprints based on small sample measured data according to claim 1, characterized in that: In step six, the positional characteristics of the contact imprint are represented by the minimum spatial distance between the contact imprint and the edge of the tooth surface. Taking the contact imprint position data under error-free conditions as a benchmark, the corresponding contact imprint position data under installation error conditions are subtracted and denoted as ΔL1~ΔL4 and Δl1~Δl4, which represent the distance the contact imprint has moved. A positive value indicates that it is away from the corresponding contact imprint edge, and a negative value indicates that it is close to the corresponding contact imprint edge. L1~L4 represent the minimum spatial distances of the convex contact imprint of the large wheel from the large end edge line, tooth tip edge line, small end edge line, and tooth root edge line, respectively. l1~l4 represent the minimum spatial distances of the concave contact imprint of the large wheel from the large end edge line, tooth tip edge line, small end edge line, and tooth root edge line, respectively.

5. The intelligent control method for tooth surface contact imprints based on small sample measured data according to claim 1, characterized in that: In step seven, criterion = nn.MSELoss() is Python code, indicating that the loss function is MSE; optimizer = torch.optim.Adam(model.parameters() is Python code, indicating that the model parameters are optimized.

6. The intelligent control method for tooth surface contact imprints based on small sample measured data according to claim 1, characterized in that: In step eight, f_pred represents the predicted coordinates of the contact imprint boundary points, and f_contact represents the actual coordinates of the contact imprint boundary points calculated by the mechanism. When updating the model parameters, the loss is monitored on the validation set to prevent overfitting, and the final prediction accuracy is evaluated on the test set.

7. The intelligent control method for tooth surface contact imprints based on small sample measured data according to claim 1, characterized in that: The reinforcement learning algorithm (RL) in step nine includes the following steps: 1) The state space s_t is defined as the normalized contact imprint feature vector f_pred output by the trained contact imprint prediction model; 2) The action space a_t refers to the continuous adjustment amount of P, G, E, A, denoted as ΔP, ΔG, ΔE, ΔA. The action space is defined as Box(low=-max_step,high=max_step,shape=(4,)); 3) Based on the given current contact imprint state s_t and the action space a_t selected by the agent, perform state transition and calculate the new installation error vector: e_new, e_new=e_t+a_t. Input the normalized e_new into the contact imprint model to predict the new normalized contact imprint feature vector f_pred_new, f_pred_new represents the new contact imprint feature value calculated under the new installation error value. Store the new imprint in s_(t+1) to represent the state, s_(t+1=f_pred_new; 4) The reward function r_t = pos_penalty + shape_penalty is constructed based on the position deviation, shape irregularity and size deviation of the contact imprint feature vector, and a composite optimization objective is constructed by combining the control amount constraint. The predicted imprint center point deviates from the actual imprint point by the position deviation penalty pos_penalty, and the predicted imprint boundary discrete point deviates from the actual imprint boundary discrete point by the shape deviation penalty shape_penalty. 5) Select and train the RL algorithm, and save the trained RL agent mapping policy π(s); 6) After training is completed, deploy the strategy to perform closed-loop dynamic control on the assembly parameters P, G, E, and A of the actual gear pair in order to minimize the position and shape deviation of the contact imprint, and finally achieve high-precision and rapid assembly optimization of the quasi-hypoid gear.

8. The intelligent control method for tooth surface contact imprints based on small sample measured data according to claim 7, characterized in that: The closed-loop dynamic control steps are as follows: ① Initial installation: Install the gear pair at the assembly site for initial installation; ② Initial measurement: Measure the current installation error e_current using a CMM or simple tooling; ③ Initial prediction: Input the normalized e_current into the contact imprint prediction model to obtain the initial imprint prediction state s_current; ④ Agent decision-making: Load the trained RL agent policy π(s), input the current state s_current, and the policy output action a_t=[ΔP_rec,ΔG_rec]; ⑤ State update and iteration: After adjustment, the new e_current is normalized and input into the contact imprint prediction model to predict the new state s_new; ⑥ Evaluation: If s_new reaches a satisfactory state, the adjustment ends and the assembly is completed; otherwise, s_new is used as the new s_current for the next round of intelligent decision-making and adjustment.

9. The intelligent control method for tooth surface contact imprints based on small sample measured data according to claim 8, characterized in that: ΔP_rec and ΔG_rec represent the adjustment amounts for installation errors P and G, respectively, and s_new represents the new state, which are the basic parameters of the model.

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