Method for constructing thermal error prediction model based on SRWNN and method for improving grinding accuracy of worm grinding wheel grinder with optimized thermal characteristics

Abstract

The present invention discloses a method for improving the grinding accuracy of a worm wheel grinding machine. On the one hand, a thermal characteristic simulation model is established, and it is found that the relative thermal deformation between the tool and the workpiece spindle increases linearly with the rotational speeds of the worm wheel grinding wheel and the workpiece spindle. By optimizing the thermal characteristics of the worm wheel grinding machine, thermal balance design is achieved and uniform distribution of the temperature field is ensured, thereby improving the ability to resist thermal deformation and enhancing thermal stability. On the other hand, a thermal error prediction model is created, and the parameters of the autoregressive wavelet neural network are optimized using the chaotic sparrow search algorithm. In the chaotic sparrow search algorithm of the present invention, Bernoulli chaotic sequences and perturbations, elite opposition-based learning, and sine-cosine search algorithm are combined. The created thermal error prediction model can effectively improve the prediction accuracy, and the predicted thermal error is used to compensate for the thermal error of the worm wheel grinding machine. Thus, by implementing thermal characteristic optimization and error compensation, the grinding accuracy of the worm wheel grinding machine can be effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical error control, and specifically relates to a method for constructing a thermal error prediction model based on SRWNN and a method for improving the grinding accuracy of a worm wheel grinding machine with optimized thermal characteristics. Background Art

[0002] Precision gears are mainly used in high-end manufacturing equipment in key technical fields such as aerospace, large ships, power generation equipment, petrochemicals, and high-end automobiles. The geometric accuracy of processed gears directly determines the performance of high-end equipment in the above key technical fields. The worm wheel gear grinding machine provides a reliable processing method, and the grinding accuracy is a key performance evaluation index of the worm wheel grinding machine. However, during the use of the worm wheel grinding machine, it is affected by static loads, thermal loads, as well as impact and vibration loads, resulting in a significant decrease in its grinding accuracy. In particular, the grinding accuracy of the worm wheel grinding machine is very sensitive to thermal errors. Therefore, the grinding errors caused by thermal errors should be effectively reduced.

[0003] Heat sources (including servo motors, bearings, rolling guide pairs, and nut pairs) generate a large amount of frictional and electrical heat, and result in uneven temperature distribution, making the thermal errors exhibit complex non-linearity. Common methods for reducing thermal errors mainly include thermal characteristic optimization (thermal characteristic optimization) and thermal error compensation methods (thermal error compensation). Thermal error compensation is used to control the processing accuracy during the machine usage stage, but the thermal characteristics are extremely complex, and the thermal errors have time-varying, non-linear, and unstable effects. The error compensation method is a passive post-compensation method and cannot completely eliminate thermal errors. Therefore, during the machine tool design stage, thermal errors should be eliminated as much as possible. The thermal characteristic optimization method used in the design stage can improve the ability to resist thermal deformation and improve thermal stability. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for constructing a thermal error prediction model based on SRWNN and a method for improving the grinding accuracy of a worm wheel grinding machine with optimized thermal characteristics. The constructed thermal error prediction model can improve the thermal error prediction accuracy and be used to achieve error control during the processing of the worm wheel grinding machine. At the same time, thermal characteristics are optimized during the design of the worm wheel grinding machine to improve the ability of the worm wheel grinding machine to resist thermal deformation and improve thermal stability, ultimately improving the grinding accuracy of the worm wheel grinding machine.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] The present invention first proposes a method for constructing a thermal error prediction model based on SRWNN, including the following steps:

[0007] S1: Preprocess the thermal error data and construct a training set;

[0008] S2: Determine the basic parameters of the chaotic sparrow search algorithm and the initial parameters of the SRWNN neural network;

[0009] S3: Use the chaotic sparrow search algorithm to randomly generate a vector such that each dimension of the vector is within the range of [1 / 2, 1 / 2]; use this vector as the first sparrow individual, and generate a chaotic sequence through Bernoulli transformation to obtain the remaining M - 1 chaotic individuals to initialize the sparrow population;

[0010] S4: Calculate the fitness of each sparrow individual, and map the position of the sparrow individual with the best fitness to the best initial parameters of the SRWNN neural network;

[0011] S5: Use the training set to train the SRWNN neural network with the best initial parameters, and determine whether the loss function of the SRWNN neural network is less than a preset threshold:

[0012] If so, the training is completed, and execute S9;

[0013] If not, determine whether the current iteration number t is less than the set maximum iteration number T max : If so, let t = t + 1 and execute S6; if not, stop the iteration and execute S9;

[0014] S6: Select the first M / 2 sparrow individuals with larger fitness to form an elite group, use the elite opposition learning strategy to calculate the reverse individuals of the elite individuals, and combine the elite individuals and the reverse individuals to obtain new sparrow individuals;

[0015] S7: Determine the position of the sparrow individual with the best fitness and the position of the sparrow individual with the worst fitness, and use the sine-cosine search algorithm to update the positions of the scouting sparrows and the warning sparrows;

[0016] S8: Perform boundary constraints, map the chaotic variables to each sparrow individual to obtain a new sparrow population, and loop to execute step four;

[0017] S9: Take the best initial parameters as the optimal hyperparameters of the SRWNN neural network, and construct a thermal error prediction model.

[0018] Furthermore, in the step S1, use the lifting wavelet transform decomposition to preprocess the thermal error data, and the method is:

[0019]

[0020] Among them, d' j-1 represents the high-frequency part after threshold processing; d j-1 represents the wavelet coefficient; thr represents the threshold; k represents the number of signal decomposition levels; and:

[0021]

[0022] σ = median|d j-1 | / 0.6745

[0023] Where N represents the length of the high-frequency coefficient sequence of each wavelet layer; median represents the median function; σ represents the standard deviation of noise estimation.

[0024] Furthermore, in the step S3, the Bernoulli map is used in the chaotic sparrow search algorithm:

[0025]

[0026] Generate a chaotic sequence through the Bernoulli transformation:

[0027] x k+1 =(2x k ) mod 1 + rand(0,1) / M

[0028] Where x k+1 represents the position of the (k + 1)-th sparrow individual; x k represents the position of the k-th sparrow individual; B represents the mapping element range; z k represents the range of the randomly generated vector of the chaotic sparrow search algorithm; rand(0,1) / M represents a random variable; M represents the number of particles in the chaotic sequence.

[0029] Furthermore, in the step S6, the elite opposition-based learning strategy is:

[0030] Let the ordinary particle be X t =(x i1 , x i2 ,..., x iD ), and the elite particle be Then the elite reverse solution is:

[0031]

[0032] After obtaining the elite reverse solution, perform boundary constraints:

[0033]

[0034] Where represents the j-th dimensional vector of the elite solution ; represents the j-th dimensional vector of the elite reverse solution ; both represent the boundaries of the j-th dimensional search space; δ ∈ [0,1]; rand(lb j, ub j ) ∈ [lb j , ub j .

[0035] Further, in the step S7, the sine-cosine search algorithm is as follows:

[0036] For the known unconstrained n-dimensional minimum optimization problem:

[0037] min f(x) = min f(x1, x2, …, x n )

[0038] s.t lb j ≤ X i ≤ ub j , i = 1, 2…, n

[0039] where X i represents the i-th variable to be optimized;

[0040] The individual with the best fitness is recorded as the best individual X * , then the position update method of the scouting sparrow is:

[0041]

[0042] r1 = a × (1 - t / T max )

[0043] where, represents the position of the i-th individual in the t-th generation population; represents the position of the current best individual; a is a constant; t represents the current iteration number; T max represents the maximum iteration number; r2 ∈ (0, 360°); r3 ∈ (0, 2) and r4 ∈ (0, 1);

[0044] The position update method of the warning sparrow is:

[0045]

[0046] where, represents the position of the i-th individual in the (t + 1)-th generation population; represents the position of the i-th individual in the t-th generation population; represents the position of the best individual in the t-th generation population; represents the position of the worst individual in the t-th generation population; β represents the step size control parameter, which is a random number obeying the normal distribution with a mean of 0 and a variance of 1; K represents a random number between [-1, 1]; ε represents the smallest constant, intended to avoid a zero denominator; f i represents the fitness value of the i-th individual; f gRepresents the current global best fitness value; f w Represents the current global worst fitness value.

[0047] Further, in the step S8, map the chaotic variable to the solution space:

[0048] newX d = min d +(ub j - lb j )·x d

[0049] where newX d represents the generated chaotic perturbation; min d represents the minimum value of the d - dimensional variable newX d ; and are the boundaries of the j - dimensional search space; X d represents the individual position in the solution space; x d represents the chaotic variable position;

[0050] Add the chaotic perturbation to the sparrow individual:

[0051] newX d '=(X d '+ newX d ) / 2

[0052] where X d ' represents the individual that needs chaotic perturbation; newX d ' represents the individual with chaotic perturbation.

[0053] The present invention also proposes a method for improving the grinding accuracy of a worm - wheel grinding machine based on thermal characteristics optimization, including the following steps:

[0054] Step 1: Optimize the thermal characteristics of the worm - wheel grinding machine;

[0055] 11) Create a three - dimensional model of the worm - wheel grinding machine;

[0056] 12) Conduct a thermal characteristics analysis of the worm - wheel grinding machine;

[0057] 13) Optimize the thermal characteristics of the worm - wheel grinding machine, optimize the layout of the rib plates of the worm - wheel grinding machine bed, and realize the regulation of the static and dynamic characteristics of the worm - wheel grinding machine; add a cooling oil pool to the bed to realize the regulation of the thermal characteristics of the worm - wheel grinding machine;

[0058] Step 2: Perform thermal error compensation on the worm - wheel grinding machine

[0059] 21) Use the method described above to construct a thermal error prediction model;

[0060] 22) During the operation of the worm wheel grinding machine, the thermal error is predicted in real time using the thermal error prediction model;

[0061] 23) The worm wheel grinding machine is compensated for thermal error according to the predicted thermal error.

[0062] Furthermore, in the step 21), the method for analyzing the thermal characteristics of the worm wheel grinding machine is as follows:

[0063] (1) Set the initial temperature to the ambient temperature T ∞ ;

[0064] (2) Input the working conditions of the bearing, including the initial preload, rotational speed, and assembly conditions; calculate the temperature-related variables, including the bearing size, bearing preload, and lubricant viscosity;

[0065] (3) Calculate the initial thermal load intensity, convection coefficient, and initial contact thermal conductance;

[0066] (4) Establish a thermal characteristics simulation model;

[0067] (5) Calculate the temperature field and thermal deformation;

[0068] (6) Compare the temperatures of all nodes in two adjacent iterative sub-steps: If T i n -T i-1 n <1×10 -6 , then terminate the algorithm, and then save the temperatures of the key points to calculate the thermal deformation; if the condition of T i n -T i-1 n <1×10 -6 is not satisfied, then update the lubricant viscosity, bearing size, convection coefficient, and bearing preload according to the calculated temperature field; update the bearing preload, contact thermal conductance, and bearing size according to the calculated thermal deformation; loop and execute step (2) until the convergence condition of T i n -T i-1 n <1×10 -6 is satisfied.

[0069] The beneficial effects of the present invention are as follows:

[0070] Method for improving grinding accuracy of worm wheel grinding machine of the present invention. On the one hand, a thermal characteristic simulation model is established, and it is found that the relative thermal deformation between the tool and the workpiece spindle increases linearly with the rotational speeds of the worm wheel grinding wheel and the workpiece spindle. By optimizing the thermal characteristics of the worm wheel grinding machine, thermal balance design is realized and uniform distribution of the temperature field is ensured, so as to improve the ability to resist thermal deformation and improve thermal stability. On the other hand, a thermal error prediction model is created, and the parameters of the autoregressive wavelet neural network (SRWNN) are optimized by using the chaotic sparrow search algorithm. In the chaotic sparrow search algorithm of the present invention, Bernoulli chaotic sequence and perturbation, learning based on elite opposition and sine-cosine search algorithm are combined. The created thermal error prediction model based on ILWT-ICSSA-SRWNN can effectively improve the prediction accuracy, and the predicted thermal error is used to realize thermal error compensation for the worm wheel grinding machine. Thus, by implementing thermal characteristic optimization and error compensation, the grinding accuracy of the worm wheel grinding machine can be effectively improved. Description of the Drawings

[0071] In order to make the objectives, technical solutions and beneficial effects of the present invention clearer, the following drawings are provided for illustration of the present invention:

[0072] Figure 1 It is a model diagram of the original bed of the worm wheel grinding machine; (a) Top view; (b) Bottom view with the flow direction of the cooling oil; (c) 3D structure;

[0073] Figure 2 It is a 3D model diagram of the worm wheel grinding machine;

[0074] Figure 3 It is a flow chart for thermal characteristic analysis of the worm wheel grinding machine;

[0075] Figure 4 It is a mesh division diagram of the 3D solid structure of the worm wheel grinding machine;

[0076] Figure 5 It is for thermal characteristic measurement; (a) Test site; (b) Arrangement of displacement sensors;

[0077] Figure 6 It is the thermal characteristics of the original worm wheel grinding machine; (a)-(c) are thermal deformations in the X, Y and Z directions respectively:

[0078] Figure 7 It is the temperature of the outer ring of the bearing of the worm wheel grinding wheel spindle; (a) Rear bearing; (b) Front bearing;

[0079] Figure 8 It is the relative thermal deformation in the X direction;

[0080] Figure 9 It is for optimizing the bed structure; (a) Top view; (b) Bottom view with the flow direction of the cooling oil; (c) 3D structure;

[0081] Figure 10 For the optimized thermal characteristics of the worm wheel grinding machine; (a) Temperature distribution; (b) Total thermal deformation; (c)-(e) Thermal deformation in the XYZ directions

[0082] Figure 11 For relative thermal deformation

[0083] Figure 12 Flow chart of the method for constructing the thermal error prediction model based on SRWNN of the present invention

[0084] Figure 13 Thermal characteristics under Condition #1; (a) Temperature; (b) Thermal deformation

[0085] Figure 14 Thermal characteristics under Condition #2; (a) Temperature; (b) Thermal deformation

[0086] Figure 15 Prediction results under Condition #1; (a) Training results; (b) Residuals of training results

[0087] Figure 16 Prediction results under Condition #2; (a) Training results; (b) Residuals of training results

[0088] Figure 17 Physical diagram of the optimized bed; (a) Manufactured optimized bed; (b) Cooling oil tank

[0089] Figure 18 Peripheral cooling system; (a) Monitoring and control of Sp1 axis; (b) Monitoring and control of C1 axis; (c) Monitoring and control of B1 axis; (d) Monitoring of Z1 axis; (e) Monitoring of cooling oil; (f) Pump and cooler

[0090] Figure 19 Optimized worm wheel grinding machine; (a) 3D model of the worm wheel grinding machine with an optimized bed (b) Actual worm wheel grinding machine with an optimized bed

[0091] Figure 20 Measurement results; (a) Without thermal characteristic optimization and thermal error compensation; (b) With thermal characteristic optimization; (c) With thermal error compensation; (d) With thermal characteristic optimization and thermal error compensation Specific implementation manners

[0092] The following further illustrates the present invention in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments cited do not limit the present invention.

[0093] The method for improving the grinding accuracy of the worm wheel grinding machine in this embodiment includes the following steps.

[0094] Step 1: Optimize the thermal characteristics of the worm wheel grinding machine.

[0095] 11) Create a 3D model of the worm wheel grinding machine.

[0096] As Figure 1 shown, the original bed structure of the worm wheel grinding machine uses a thermally symmetric structure. Figure 1 (a) shows the cross-vertical rib plates used in the original bed. Figure 2 shows that the oil injection nozzles are set on one side close to the worm wheel shaft. The cooling oil is sprayed from the worm wheel spindle to the cutting area. The cooling oil mainly falls on the left side of the worktable. A small amount of cooling oil splashes to the left side of the bed, far from the small column. Finally, all the cooling oil flows back to the cooling system along the cooling channels, as Figure 1 (b) shown. In addition, the cooling channels are symmetrically arranged along the entire length of the surface of the worm wheel grinding machine bed. However, it is difficult for the cooling oil to reach the right side of the worktable. The heat of the worktable enters the worm wheel grinding machine bed in the form of heat conduction, resulting in the temperature on the left side of the worm wheel grinding machine bed being lower than that on the right side.

[0097] 12) Conduct a thermal characteristics analysis of the worm wheel grinding machine.

[0098] As Figure 3 shown, the method for conducting a thermal characteristics analysis of the worm wheel grinding machine is as follows:

[0099] (1) Set the initial temperature to the ambient temperature T ∞ ;

[0100] (2) Input the working conditions of the bearings, including the initial preload, rotational speed, and assembly conditions; calculate the temperature-related variables, including bearing size, bearing preload, and lubricant viscosity;

[0101] (3) Calculate the initial heat load intensity, convection coefficient, and initial contact thermal conductance;

[0102] (4) Establish a thermal characteristics simulation model of the worm wheel grinding machine;

[0103] (5) Calculate the temperature field and thermal deformation of the worm wheel grinding machine;

[0104] (6) Compare the temperatures of all nodes in two adjacent iterative sub-steps: If T i n -T i-1 n <1×10 -6 , then terminate the algorithm, and then save the temperatures of the key points to calculate the thermal deformation; if T i n -T i-1 n <1×10-6 Under the conditions, update the lubricant viscosity, bearing size, convection coefficient, and bearing preload according to the calculated temperature field; update the bearing preload, contact thermal conductance, and bearing size according to the calculated thermal deformation; loop through step (2) until the condition of T i n -T i-1 n <1×10 -6 is met for convergence.

[0105] Import the simplified three-dimensional model of the entire worm grinding wheel machine into ANSYS and perform meshing as Figure 4 shown. The material properties are listed in Table 1. For the worm grinding wheel spindle, the two front bearings are B7008 and are positioned and preloaded. The two rear bearings are both B7007 and are spring constant pressure preloaded. The lubrication method is oil mist lubrication. The compressed air flow rate is 10 L / s and the pressure is 0.32 Pa. The thermal boundary conditions of the worm grinding wheel spindle are calculated. The heat generation rates of the rolling elements, inner rings, and outer rings of B7008 are 86700 W / m 3 、133000 W / m 3 and 191000 W / m 3 respectively. The heat generation rates of the rolling elements, inner rings, and outer rings of B7007 are 71200 W / m 3 、99900 W / m3 and 149000 W / m3 respectively. The heat generation rates of the rotor and stator are 4.53×105 W / m3 and 9.90×105 W / m3 respectively. The convection coefficients of the static outer surface / air, structure / coolant, front end surface / air, air gap between stator / rotor, rear end surface / air, and rolling elements / oil mist lubrication are 9.7 W / (m 2 ·℃), 34355 W / (m 2 ·℃), 96 W / (m 2 ·℃), 105 W / (m 2 ·℃) respectively. For the workpiece spindle, the models of the ball bearings are S7020ACD / P4ADBC and S7024ACD / P4AQBCC. The rotational speed of the workpiece spindle is 500 r / min. The heat generation rates of the rolling elements, inner rings, and outer rings of S7024 are 157000 W / m 3 、859000 W / m 3 and 8590000 W / m 3 respectively. The heat generation rates of the rolling elements, inner rings, and outer rings of S7020 are 109000 W / m 3 , 162000 W / m 3 and 162000 W / m 3 respectively. The heat generation rates of the rotor and stator are 22200 W / m 3 and 38047 W / m3 The convective coefficients of the static outer surface / air, the outer rotating surface of the workbench / air, the stator / cooling water jacket, the rotor end / air, the air gap between the stator / rotor, and the coolant / structure are 9.7 W / (m 2 ·°C), 15.5 W / (m 2 ·°C), 29, 418 W / (m 2 ·°C), 38 W / (m 2 ·°C), 14.3 W / (m 2 ·°C), and 296 W / (m 2 ·°C), respectively.

[0106] Table 1 Material properties of the worm wheel grinding machine

[0107]

[0108] In this embodiment, a thermal characteristics experiment was conducted. The test location of the thermal characteristics experiment is as shown in Figure 5 (a). The measured thermal-induced error is the relative displacement between the workpiece and the worm wheel grinding spindle in the X direction. Figure 5 (b) shows the layout of the displacement sensors. The temperature nodes are as follows: T1 (front bearing seat of the worm wheel grinding spindle), T2 (rear bearing seat of the worm wheel grinding spindle), T3 (ambient temperature), T4 (outside the torque motor), T5 (base), T6 (rear bearing ring of the workpiece spindle), T7 (contact area between the workbench and the base), T8 (front bearing ring of the workpiece spindle), T9 (outside the workbench), and T10 (upper surface of the workbench).

[0109] The rotational speeds of the worm wheel grinding and the workpiece spindle are 8300 r / min and 500 r / min, respectively. Figure 6 (a) shows that the highest temperature reaches 52.084 °C, that is, the temperature at the upper bearing of the worm wheel grinding spindle is 1 °C. Figure 6 (b) shows the total deformation. The maximum total thermal deformation of the worm wheel grinding spindle is greater than that of the workpiece spindle. The relative thermal deformation between the worm wheel grinding and the workpiece spindle generates tooth surface errors.

[0110] Figure 7Shows the measured temperature of the bearing rings in the worm grinding wheel spindle. The measured temperature increases with the running time and then starts to decrease when the worm grinding wheel spindle device is shut down. In addition, at 4000 seconds of the first start-up, the temperature rises significantly, and when the heat source intensity is equal to the heat dissipated by the air, the temperature stabilizes. Moreover, due to the influence of compressed air, the measured temperature fluctuates significantly. More importantly, the predicted temperature is consistent with the experimental data, which verifies the thermal characteristic modeling method. The average deviations between the measured data of the two bearings and the experimental temperature are 4.36% and 3.15% respectively. The maximum deviations between the predicted temperature and the measured data of the two bearings are 6.5% and 5.8% respectively. When the worm grinding wheel spindle device is shut down, the temperature drops sharply.

[0111] According to Figure 8 , the relative thermal deformation between the tool and the workpiece spindle increases linearly with the rotational speeds of the worm grinding wheel and the workpiece spindle. When the rotational speed of the workpiece spindle is 900 r / min, when the rotational speed of the worm grinding wheel spindle increases from 2300 r / min to 8300 r / min, the relative thermal deformation increases from 70.4 μm to 169.0 μm. When the rotational speed of the workpiece spindle is 700 r / min, when the rotational speed of the worm grinding wheel spindle increases from 2300 r / min to 8300 r / min, the relative thermal deformation increases from 56.7 μm to 135.7 μm. When the rotational speed of the workpiece spindle is 500 r / min, when the rotational speed of the worm grinding wheel spindle increases from 2300 r / min to 8300 r / min, the relative thermal deformation increases from 30.8 μm to 95.1 μm. When the rotational speed of the workpiece spindle is 300 r / min, when the rotational speed of the worm grinding wheel spindle increases from 2300 r / min to 8300 r / min, the relative thermal deformation increases from 12.3 μm to 70.3 μm.

[0112] When the spindle speed of the worm wheel grinding wheel is 8300 r / min, when the spindle speed of the workpiece increases from 300 r / min to 9000 r / min, the relative thermal deformation increases from 70.3 μm to 169.0 μm. When the spindle speed of the worm wheel grinding wheel is 6300 r / min, when the spindle speed of the workpiece increases from 300 r / min to 900 r / min, the relative thermal deformation increases from 52.6 μm to 149.6 μm. When the spindle speed of the worm wheel grinding wheel is 4300 r / min, when the spindle speed of the workpiece increases from 300 r / min to 9000 r / min, the relative thermal deformation increases from 31.1 μm to 121.6 μm. When the spindle speed of the worm wheel grinding wheel is 2300 r / min, when the spindle speed of the workpiece increases from 300 r / min to 9000 r / min, the relative thermal deformation increases from 12.3 μm to 70.4 μm. More importantly, the simulated relative thermal deformation is in good agreement with the collected data. Then the effectiveness of the thermal characteristic simulation model is verified. In actual machining, the rotation of the worm wheel grinding wheel and the workpiece spindle cannot be avoided. Therefore, the relative thermal deformation between the worm wheel grinding wheel and the workpiece spindle is significant.

[0113] 13) Optimize the thermal characteristics of the worm wheel grinding machine.

[0114] (1) Optimization of the bed structure and cooling performance of the worm wheel grinding machine

[0115] The static stiffness of the bed of the worm wheel grinding machine directly affects the grinding accuracy and is an important index of physical performance. The average deformation in the horizontal direction is selected as the index to evaluate the static behavior. In addition, the total strain energy of the bed of the worm wheel grinding machine and the quality index related to the manufacturing cost of the bed of the worm wheel grinding machine are also considered. The performance of the rib plate shown in layout scheme #1 is used as a benchmark. According to Table 2, the layout schemes of #2 and #3 are arranged on the basis of the layout scheme of #1, which are unidirectional oblique vertical rib plates and bidirectional oblique vertical rib plates respectively. Compared with the bed of the worm wheel grinding machine in layout scheme #1, the average deformation of the beds of the worm wheel grinding machines in layout schemes #2 and #3 is reduced by 46% and 59% respectively. That is, the inclined vertical rib plates significantly improve the stiffness of the bed of the worm wheel grinding machine and slightly improve the overall stiffness. In addition, the influence of the bidirectional oblique rib plates on the stiffness is better than that of the unidirectional oblique rib plates. Compared with the bed of the worm wheel grinding machine with unidirectional oblique vertical rib plates, there are more transverse rib plates in the bed of the worm wheel grinding machine with bidirectional oblique vertical rib plates, which can greatly improve the torsional stiffness of the bed of the worm wheel grinding machine. However, the bidirectional oblique rib plates increase the mass of the bed of the worm wheel grinding machine.

[0116] The No. 4 layout is to arrange herringbone diagonal ribs on the basis of the No. 1 layout. Compared with the double-direction diagonal ribs shown in the No. 3 layout, its mass is reduced by 1%, and the overall stiffness of the bed body of the worm grinding wheel grinder is slightly lower than that of the worm grinding wheel grinder with the No. 3 layout. The average deformation of the No. 4 layout is 7% lower than that of the No. 3 layout. The No. 4 to No. 7 layouts adopt herringbone ribs. For the 1℃al stiffness, layout scheme #6 is the best combination of longitudinal and diagonal ribbed plates, while layout scheme #7 has poor 1℃al rigidity when there are transverse and diagonal ribbed plates, because the transverse ribbed plates have poor bending stiffness and excellent torsional stiffness. In addition, there are longitudinal ribbed plates on the center line, which can improve the bending stiffness of the bed body of the worm grinding wheel grinder. The bending and torsional properties of the ribbed plates are relatively excellent. Therefore, in layout scheme 7, the 1℃al stiffness of the bed body structure of the worm grinding wheel grinder with herringbone diagonal ribbed plates is also very high. There is almost no difference in the overall stiffness of the above four layout schemes. For the above four layout schemes, layout scheme #7 has the lightest weight, followed by layout scheme #6.

[0117] The machining accuracy depends not only on elastic deformation but also on vibration. The dynamic mechanical properties of the bed body of the worm grinding wheel grinder are another key factor affecting the machining accuracy and stability of the worm grinding wheel grinder. The low-order modal characteristics usually determine the dynamic mechanical properties of the bed body of the worm grinding wheel grinder. The structural dynamic analysis is used to study the first natural frequency, as shown in Table 2. The first natural vibration frequency of the No. 5 layout is 18% higher than that of the traditional No. 1 layout because its overall and local bending and torsional stiffness are relatively large. Layout scheme 4 is a combination of longitudinal, transverse and herringbone diagonal ribbed plates. Compared with layout scheme #5, layout scheme #4 has multiple longitudinal ribbed plates, so its natural frequency is the second among all layout schemes. Layout scheme #6 is a combination of longitudinal and herringbone diagonal ribbed plates. Its first natural frequency is slightly lower than that of other herringbone ribbed plates and higher than that of the longitudinal and transverse ribbed plates of layout scheme #1. Layout scheme #7 uses herringbone ribbed plates and has excellent first natural frequency. The first frequency of the bed body of the worm grinding wheel grinder in layout scheme #3 is about 13% higher than that of the worm grinding wheel grinder in layout scheme #1 because layout scheme #3 adds diagonally placed double-direction diagonal ribbed plates to the combined vertical and horizontal ribbed plates, making the overall structure of the bed body of the worm grinding wheel grinder have strong bending and torsional stiffness.

[0118] Table 2 Static, dynamic and thermal characteristics

[0119]

[0120]

[0121] According to Table 2, the original cross-vertical rib plate is changed to a cross-shaped rib plate, and the thermal deformation is decomposed into the diagonal direction. Then the ability to resist dynamic cutting force and thermal deformation is improved. The top view and front view of the optimized bed structure of the worm wheel grinding machine are shown in Figs. 9(a) and (b). The bottom of the worm wheel grinding machine bed with the original circular and hollow cross-section is changed to a closed bottom, and the lower part of each rib plate is strengthened to ensure that all rib plates are integrated to improve the overall rigidity of the worm wheel grinding machine bed. In addition, the fixed position from the workbench to the surface of the worm wheel grinding machine bed is changed to an arc transition and extends to the entire surface of the worm wheel grinding machine bed, as Figure 9 shown by the green area in (b). Then, compared with the right-angle transition in the original worm wheel grinding machine bed, stress concentration is avoided.

[0122] To ensure the ability to resist thermal deformation, for the original worm wheel grinding machine bed, the cooling channels are symmetrically arranged from left to right on the surface of the worm wheel grinding machine bed, as Figure 1 shown in (b). The cooling oil flows out from the outlet. However, for the original worm wheel grinding machine bed, it is difficult for the cooling oil to reach the right side of the workbench. That is, the temperature gradient of the original worm wheel grinding machine bed is significant. For the optimized worm wheel grinding machine bed, a new cooling oil pool is added on the right side of the workbench on the original structure of the worm wheel grinding machine bed to remove the heat generated by the workbench and reduce the temperature gradient, as Figure 9 shown by the red area in (c). Under the same thermal effect, due to the influence of the cooling oil pool, the temperature rise of the optimized worm wheel grinding machine bed will be less than that of the original worm wheel grinding machine bed. Similarly, the cooling channels are symmetrically arranged in the entire length direction of the surface of the worm wheel grinding machine bed. Then, the cooling oil flows out from the outlet and flows back to the cooling system. Then the temperature field distribution of the worm wheel grinding machine bed is uniform. Finally, the thermal equilibrium design of the worm wheel grinding machine bed is achieved.

[0123] (2) Verification of optimization results

[0124] The ambient temperature is set to 18 °C. As Figure 10 shown in (a), the highest temperature at the angular contact bearing of the worm wheel spindle is about 47.919 °C. Figure 10 (b) shows the total deformation of the entire worm wheel grinding machine, and the maximum thermal deformation reaches 29.853 μm. Table 3 shows that the highest temperature and thermal deformation are significantly reduced. Using thermal characteristic optimization, the highest temperature is reduced from 52.084 °C to 47.919 °C. The highest temperature is reduced by 4.081 °C, and the reduction rate is about 8.00%. The maximum total thermal deformation is reduced from 62.100 μm to 29.853 μm, and the reduction rate is 51.93%.

[0125] Table 3 Comparison of simulation results

[0126]

[0127] The uneven temperature distribution leads to inconsistent thermal deformations of various components, resulting in a relative position deviation of the spindle with respect to the workpiece. By reasonably designing the number and layout of the rib plates of the worm grinding wheel grinder bed, the static and dynamic stiffness of the worm grinding wheel grinder is ensured. In addition, a new cooling oil sump is added to the worm grinding wheel grinder bed to dissipate the heat generated by internal heat sources such as motors and bearings. Then, the relative thermal deformation between the worm grinding wheel spindle and the workpiece spindle is effectively reduced, thereby improving the grinding accuracy of the worm grinding wheel grinder. According to Figure 11 , the relative thermal deformation increases with the rotational speeds of the worm grinding wheel and the workpiece spindle. When the rotational speed of the workpiece spindle is 900 r / min, the maximum simulated relative thermal deformation is reduced from 169.0 μm to 56.3 μm, and the reduction rate is 66.69%. When the rotational speed of the workpiece spindle is 700 r / min, the relative thermal deformation is reduced from 149.6 μm to 50.0 μm, and the reduction rate is 66.58%. When the rotational speed of the workpiece spindle is 500 r / min, the relative thermal deformation is reduced from 121.6 μm to 41.0 μm, and the reduction rate is 66.28%. More importantly, the measured and simulated relative thermal deformations are in good agreement. Then, the effectiveness of the thermal characteristic optimization is verified.

[0128] Step 2: Perform thermal error compensation on the worm grinding wheel grinder

[0129] 21) Construct a thermal error prediction model;

[0130] 22) During the operation of the worm grinding wheel grinder, use the thermal error prediction model to predict the thermal error in real time;

[0131] 23) Perform thermal error compensation on the worm grinding wheel grinder according to the predicted thermal error.

[0132] Specifically, the method for constructing the thermal error prediction model based on SRWNN in this embodiment includes the following steps.

[0133] S1: Preprocess the thermal error data and construct a training set.

[0134] In this embodiment, the lifting wavelet transform decomposition is used to preprocess the thermal error data. It is found that the effective signal and high-frequency noise have different characteristics, and the core content of wavelet denoising is to filter the high-frequency part to achieve the purpose of signal-to-noise ratio separation. The specific steps of the lifting wavelet threshold denoising are to perform the lifting wavelet transform decomposition, and then obtain the high-frequency and low-frequency parts. By setting the threshold, non-linear threshold processing is performed on the high-frequency part.

[0135]

[0136] σ = median|d j-1 | / 0.6745

[0137] Among them, thr represents the threshold; N represents the length of the high-frequency coefficient sequence of each wavelet layer; median represents the median function; d j-1 represents the wavelet coefficient; σ represents the standard deviation of noise estimation. The existing functions are as follows:

[0138] Function expression one:

[0139]

[0140] Function expression two:

[0141]

[0142] Among them, d' j-1 represents the high-frequency part after threshold processing. For function expression one, discontinuous temperatures appear within the (±thr) threshold range, which leads to pseudo-Gibbs artifacts. Although function expression two has better continuity than function expression one, there is always a deviation, that is, some high-frequency coefficients are lost, and then certain errors are generated in the reconstructed signal. Based on function expression two, in this embodiment, a smooth transition region is established within the ±thr threshold range to reduce the loss of high-frequency coefficients, and then the natural continuity of the threshold-processed signal is consistent with that of the original signal.

[0143]

[0144] Among them, d' j-1 represents the high-frequency part after threshold processing; d j-1 represents the wavelet coefficient; thr represents the threshold; k represents the number of signal decomposition levels.

[0145] The wavelet transform is adaptive to the signal and can process any details of the signal f℃us. Therefore, it has excellent l℃al characteristics. The Morlet wavelet with strong robustness is used.

[0146]

[0147] Among them, h(u) represents the Morlet wavelet function; u represents the signal.

[0148] S2: Determine the basic parameters of the chaotic sparrow search algorithm and the initial parameters of the SRWNN neural network.

[0149] Specifically, the basic parameters of the chaotic sparrow search algorithm include the population size N, the number of discoverers pNum, the number of sparrows sNum for reconnaissance and early warning, the dimension d of the objective function, the initial lower and upper limits of lb and ub, and the maximum number of iterations T maxOr the solution accuracy ε, etc. The initial parameters of the SRWNN neural network include the learning rate, the maximum number of training times, etc.

[0150] S3: Use the chaotic sparrow search algorithm to randomly generate a vector so that each dimension of the vector is within the range of [1 / 2, 1 / 2]; use this vector as the first sparrow individual, and generate a chaotic sequence through Bernoulli transformation to obtain the remaining M - 1 chaotic individuals to initialize the sparrow population.

[0151] Specifically, the parameters and settings of the SRWNN directly affect the prediction results. In this embodiment, an improved chaotic sparrow search algorithm (ICSSA) is proposed. For the sparrow search algorithm (SSA), the population diversity decreases in subsequent iterations. To avoid the decrease in population diversity, this embodiment uses a chaotic operator to initialize the population of SSA because the randomness and regularity of the chaotic operator can traverse all states within a certain range without repetition. Specifically, the Bernoulli map is used:

[0152]

[0153] When 1 ≤ B ≤ 1.4, the Bernoulli map has multiple periodic points. When 1.4 < B ≤ 2, the Bernoulli map enters the chaotic state, and all trajectory points are connected together. The mapping sequence exhibits random characteristics, and the range of the sequence is [-1 / 2, 1 / 2]. The Bernoulli map follows a uniform distribution and has a uniform probability density distribution function. The time probability density distribution is close to the statistical probability density distribution, indicating that the Bernoulli map has good ergodicity. The initial sparrow population consists of M-dimensional individuals. The value of B is set to 2. After introducing the random variable rand(0, 1) / M, we get:

[0154]

[0155] Generate a chaotic sequence through Bernoulli transformation:

[0156] x k+1 =(2x k ) mod 1 + rand(0, 1) / M

[0157] where, x k+1 represents the position of the (k + 1)-th sparrow individual; x k represents the position of the k-th sparrow individual; B represents the mapping element range; z k represents the range of the vector randomly generated by the chaotic sparrow search algorithm; rand(0, 1) / M represents the random variable; M represents the number of particles in the chaotic sequence.

[0158] S4: Calculate the fitness of each sparrow individual, and map the position of the sparrow individual with the best fitness as the best initial parameters of the SRWNN neural network.

[0159] Specifically, the fitness function of a sparrow individual is as follows:

[0160]

[0161] Among them, y n and represent the predicted data and the expected data respectively.

[0162] S5: Train the SRWNN neural network with the best initial parameters using the training set, and determine whether the loss function of the SRWNN neural network is less than a preset threshold. Specifically, the loss function is as follows:

[0163]

[0164] Among them, y n and represent the predicted data and the expected data respectively.

[0165] If so, the training is completed, and S9 is executed;

[0166] If not, determine whether the current iteration number t is less than the set maximum iteration number T max : If so, let t = t + 1 and execute S6; if not, stop the iteration and execute S9.

[0167] S6: Select the top M / 2 sparrow individuals with larger fitness to form an elite group, use the elite opposition learning strategy to calculate the reverse individuals of the elite individuals, and combine the elite individuals and the reverse individuals to obtain new sparrow individuals.

[0168] The elite opposition learning strategy uses dominant individuals to construct a reverse population to increase population diversity. Let the ordinary particle be X t =(x i1 ,x i2 ,...,x iD ), and the elite particle be Then the elite reverse solution is:

[0169]

[0170] After obtaining the elite reverse solution, perform boundary constraints:

[0171]

[0172] Among them, represents the j-dimensional vector of the elite solution ; represents the j-dimensional vector of the elite reverse solution ; Both represent the boundaries of the j-dimensional search space; δ ∈ [0, 1]; rand(lb j , ub j ) ∈ [lb j , ub j .

[0173] S7: Determine the positions of the sparrow individuals with the best fitness and the sparrow individuals with the worst fitness, and use the sine-cosine search algorithm to update the positions of the scouting sparrows and the warning sparrows. The sine-cosine search algorithm is as follows:

[0174] For the known unconstrained n-dimensional minimum optimization problem:

[0175] minf(x) = minf(x1, x2,…, x n )

[0176] s.t lb j ≤ X i ≤ ub j , i = 1, 2…, n

[0177] where X i represents the i-th variable to be optimized;

[0178] The individual with the best fitness is recorded as the best individual X * , then the position update method of the scouting sparrow is:

[0179]

[0180] r1 = a × (1 - t / T max )

[0181] where represents the position of the i-th individual in the t-th generation population; represents the position of the current best individual; a is a constant; t represents the current iteration number; T max represents the maximum iteration number; r2 ∈ (0, 360°); r3 ∈ (0, 2) and r4 ∈ (0, 1);

[0182] The position update method of the warning sparrow is:

[0183]

[0184] where represents the position of the i-th individual in the (t + 1)-th generation population; represents the position of the i-th individual in the t-th generation population; represents the position of the best individual in the t-th generation population; represents the position of the worst individual in the t-th generation population; β represents the step size control parameter, which is a random number following a normal distribution with a mean of 0 and a variance of 1; K represents a random number between [-1, 1]; ε represents the smallest constant, intended to avoid a zero denominator; f i represents the fitness value of the i-th individual; f g represents the current global best fitness value; f w represents the current global worst fitness value.

[0185] S8: Perform boundary constraints, map the chaotic variables to each sparrow individual to obtain a new sparrow population, and loop to execute Step Four.

[0186] Specifically, the boundary constraint method is:

[0187]

[0188] Among them, represents the elite solution of the j-dimensional vector; represents the elite reverse solution of the j-dimensional vector; both represent the boundaries of the j-dimensional search space; δ ∈ [0, 1]; rand(lb j , ub j ) ∈ [lb j , ub j .

[0189] The method of adding chaotic perturbations to sparrow individuals is:

[0190] (1) Map the chaotic variables to the solution space:

[0191] newX d = min d + (ub j - lb j ) · x d

[0192] Among them, newX d represents the generated chaotic perturbation; min d represents the minimum value of the d-dimensional variable newX d ; and are the boundaries of the j-dimensional search space; X d represents the individual position in the solution space; x d represents the position of the chaotic variable;

[0193] (2) Add the chaotic perturbation to the sparrow individual:

[0194] newX d' = (X d ' + newX d )2

[0195] where X d ' represents the individual that needs chaotic perturbation; newX d ' represents the individual with chaotic perturbation.

[0196] S9: Take the best initial parameters as the optimal hyperparameters of the SRWNN neural network to construct a thermal error prediction model (hereinafter referred to as: ILWT - ICSSA - SRWNN model).

[0197] 1. Thermal Error Model Verification

[0198] The rotational speed of the workpiece spindle is 600 r / min, and the thermal characteristics without bed flushing and cooling are tested. The temperature rise curve is as Figure 13 (a) shown. During the heating process, the initial temperature pr℃ess is the ambient temperature, about 19 °C, and the highest temperature rises to about 44.1 °C. The thermal deformation changes are as Figure 13 (b) shown. The minimum difference between the measured thermal deformation values of X1 and X2 is about 21 μm, and the maximum thermal inclination angle is about 82”. When the rotational speed of the workpiece spindle is 600 r / min, the thermal characteristics with bed flushing and cooling are as Figure 14 shown. The initial ambient temperature is about 20 °C, and the highest temperature is about 32.0 °C, which is about 12.1 °C lower than the highest temperature without bed cooling. The added cooling oil pool can reduce the temperature of the bed. The maximum difference between the measured thermal deformation values of S1 and S2 is about 24 μm, and the maximum thermal inclination angle during flushing and cooling is about 68”. The maximum thermal inclination angle during flushing and cooling is less than that without flushing and cooling. The added cooling oil pool can reduce the thermal error in the X direction. The regular fluctuation of thermal deformation is related to the regular change of coolant temperature.

[0199] 1.1 Parameter Setting and Model Fitting

[0200] The fuzzy clustering method is used to select typical temperatures from the collected data. The temperatures of T1, T3, T6, and T10 are used as the model inputs, and the thermal inclination angle is the model output. The drastic change of thermal error poses high requirements on the following capabilities. The error model is trained ten times with the training data set, and the average value of the fitting results in the ten - time training is as Figure 15 (a) shown. The following ability of ILWT - ICSSA - SRWNN is better than that of ILWT - SRWNN, followed by ILWT - ICSSA - WNN and ILWT - WNN. The following ability of ILWT - MLR is the worst, verifying the effectiveness of ILWT and ICSSA. The residual is the difference between the fitting result and the measured data, as Figure 15(as shown in (b)). The residual fluctuations of ILWT-MLR and ILWT-WNN are greater than those of the other four models. The residual fluctuation of ILWT-ICSSA-WNN is greater than that of ILWT-SRWNN and ILWT-ICSSA-SRWNN because the fitting accuracy of SRWNN is higher than that of WNN. The high fitting accuracy of ILWT-SRWNN and ILWT-ICSSA-SRWNN is attributed to the strong memory behavior and parameter optimization of ICSSA. The results show that SRWNN can describe the error mechanism. ILWT-WNN, ILWT-ICSSA-WNN, and ILWT-MLR have no memory behavior and cannot remember long-term historical thermal information. Therefore, the memory behavior is very important for accurate error prediction.

[0201] The F value is used as a significance test method, called the F test. If the F value follows the F distribution, that is, F ∼ F(m, n - m - 1). At the significance level of α, when F > F αWhen (m, n - m - 1), assume it is rejected and the proposed model is significant. Otherwise, the proposed model is considered insignificant and the critical value can be obtained by checking the F-distribution table. The calculated F-values of ILWT-MLR, ILWT-WNN, ILWT-ICSSA-WNN, ILWT-SRWNN, and ILWT-ICSSA-SRWNN are 1326.3, 2424.5, 2833.6, 3027.8, and 3696.7 respectively. The results are consistent with the F-tests of the above models. That is, the above proposed models are important. Table 4 lists the evaluation parameters demonstrating the effectiveness of the above models. The fitting accuracies of the ILWT-WNN, ILWT-ICSSA-WNN, ILWT-SRWNN, ILWT-ICSSA-SRWNN, and ILWT-MLR models are 97.20%, 97.94%, 97.96%, 98.00%, and 92.50% respectively. The fitting accuracy of ILWT-ICSSA-SRWNN is higher than the other four models. The fitting accuracy of ILWT-SRWNN is higher than that of ILWT-WNN and ILWT-ICSSA-WNN. Using ICSSA for parameter optimization can effectively improve the prediction accuracy. ICSSA can ensure that the parameters of SRWNN and WNN match well with the characteristics of the data, thus improving the fitting performance. More importantly, ILWT-SRWNN has a higher accuracy than ILWT-ICSSA-WNN, indicating that the memory performance is more important than parameter optimization. Through the above analysis, the model that can reflect the error mechanism has strong prediction ability. The calculation times of ILWT-WNN, ILWT-ICSSA-WNN, ILWT-SRWNN, ILWT-ICSSA-SRWNN, and ILWT-LSTM are 3.8s, 7.3s, 4.5s, 8.1s, and 1.2s respectively. The parameter optimization of ICSSA increases the calculation time. In addition, the calculation time of ILWT-MLR is much shorter than that of other models because the number of parameters of the ILWT-MLR-error model is the smallest among the above models.

[0202] 1.2 Model Prediction

[0203] Use the thermal data under Condition 2# as the validation set. Figure 16The predicted results obtained through the above model are shown. Compared with the fitting performance, the prediction performance of the above five models has decreased. More importantly, the prediction performances of ILWT-ICSSA-SRWNN, ILWT-LSTM, and ILWT-SRWNN are better than those of ILWT-WNN and ILWT-ICSSA-WNN. The residual fluctuation ranges of ILWT-MLR, ILWT-WNN, and ILWT-ICSSA-WNN are larger than those of ILWT-ICSSA-SRWNN and ILWT-SRWNN. Then, it is important to achieve thermal information in the past state. SRWNN can reflect long-term memory behavior, thus improving the robustness of the error models of ILWT-ICSSA-SRWNN and ILWT-SRWNN. For error prediction, a similar conclusion is found, that is, memory performance is more important than parameter optimization.

[0204] Table 5 lists the evaluation parameters demonstrating the effectiveness of the above model. The values of the ILWT-WNN, ILWT-ICSSA-WNN, ILWT-SRWNN, ILWT-ICSSA-SRWNN, and ILWT-MLR models are 85.41%, 87.84%, 89.99%, 91.70%, and 69.93% respectively. Using ICSSA, the prediction performance of the ILWT-WNN model is improved from 85.41% to 87.84%, and the expected performance of the ILWT-SRWNN model is improved from 89.99% to 91.70%. The improvement in prediction performance is significant, then verifying the effectiveness of ICSSA. The prediction accuracy of ILWT-MLR is 69.93%, which is lower than that of ILWT-ICSSA-SRWNN. Comparing Table 4 and Table 5, the precision degradation of ILWT-ICSSA-SRWNN and ILWT-SRWNN under different working conditions is not obvious, while the precision degradation of ILWT-ICSSA-WNN, ILWT-WNN, and ILWT-MLR is obvious. That is, the robustness of the ILWT-ICSSA-SRWNN and ILWT-SRWNN models is stronger than that of the ILWT-ICSSA-WNN and ILWT-WNN models. The prediction accuracy of ILWT-ICSSA-SRWNN is much higher than that of ILWT-MLR. Then, the prediction performance and robustness of the proposed ILWT-ICSSA-SRWNN error model are fully verified.

[0205] Table 5 Prediction Result Evaluation

[0206]

[0207] 2. Experimental Verification

[0208] 2.1 Implementation of Thermal Characteristic Optimization

[0209] The optimized worm wheel grinding machine bed is designed and manufactured according to thermal characteristics, as shown in Figure 17 (a). The material of the optimized worm wheel grinding machine bed is HT300, and the original cross-shaped vertical rib plate is changed to a double-cross pattern rib plate. In addition, Figure 17 (b) shows that a cooling oil sump is added to the optimized worm wheel grinding machine bed. In addition, Figure 18 The peripheral cooling system is shown. The cooling oil outlet temperatures of the SP1-, C1-, B1-, and Z1-axes are very close, which is beneficial to high-precision grinding. By using the peripheral cooling system and the optimized worm wheel grinding machine bed, the thermal balance design and optimization of the worm wheel grinding machine are achieved.

[0210] The maximum outer diameter of the ground gear is Φ300mm. The minimum root diameter of the ground gear is Φ20mm. The gear module is from 1mm to 6mm. The number of teeth of the ground gear is from 8mm to 300mm. The tooth width is 300mm. The maximum helix angle is ±45°. The maximum rotational speed of the worm wheel is 8500r / min. Four improvement strategies are adopted during gear grinding. (1) Thermal characteristic optimization and thermal error compensation are not implemented. (2) Only thermal characteristic optimization is performed. (3) Only thermal error compensation is performed. (4) Thermal characteristic optimization and thermal error compensation are implemented. The worm wheel grinding machine adopts thermal characteristic optimization, and the original worm wheel grinding machine bed is replaced with the optimized worm wheel grinding machine bed. Then the optimized bed is configured to the worm wheel grinding machine, as shown in Figure 19 . In addition, the worm wheel grinding machine with the optimized bed is used to grind gears.

[0211] 2.2 Thermal Error Compensation

[0212] Using homogeneous coordinate transformation, the deviations of each moving axis during the motion process are decoupled and calculated to obtain the error components finally reflected on the machined surface. Assume that the absolute coordinate system (ACS) is fixed to the machine tool. The directions of XA, YA, and AA are the same as the XM, YM, and ZM axes of the machine coordinate system (MCS) respectively. The coordinate transformation is as follows:

[0213]

[0214] where, B P(X M ,Y M ,Z M ) is the position of a point in the MCS; A P(X A ,Y A ,Z A ) is the position of a point in the ACS; and A P B represent the rotation matrix and the translation matrix respectively.

[0215] The gear is ground by a worm wheel grinding machine, with or without thermal characteristic optimization and thermal error compensation. The geometric accuracy of the ground gear is as Figure 20 shown. Through the implementation of thermal characteristic optimization and thermal error compensation, it is found that the maximum errors of the left and right tooth surfaces are reduced from 18.5 μm to 6.3 μm and from 16.7 μm to 5.4 μm respectively. With the implementation of thermal characteristic optimization, it is found that the maximum errors of the left and right tooth surfaces are reduced from 18.5 μm to 8.7 μm and from 16.7 μm to 7.6 μm respectively. With the implementation of thermal error compensation, it is found that the maximum errors of the left and right tooth surfaces are reduced from 18.5 μm to 13.1 μm and from 16.7 μm to 12.6 μm respectively. Using thermal characteristic optimization and thermal error compensation, the grinding accuracy of the worm wheel grinding machine is improved by more than 65%. Using thermal characteristic optimization, the grinding accuracy of the worm wheel grinding machine is improved by about 53%. After adopting thermal error compensation, the grinding accuracy of the worm wheel grinding machine is improved by about 24%. Thermal characteristic optimization is much more effective than thermal error compensation in improving grinding accuracy. The maximum errors of the left and right tooth surfaces are both less than the tolerance requirements in ISO1328-1:2013

[41] .

[0216] 3. Conclusions

[0217] To improve the grinding accuracy, the gear grinding accuracy of a worm wheel grinding machine with thermal characteristic optimization and thermal error compensation is proposed. On the one hand, the rib plate layout scheme of the worm wheel grinding machine bed is determined by considering the ability to resist static load, dynamic cutting force and thermal deformation. In addition, the thermal balance design of the worm wheel grinding machine bed is carried out by adding a new cooling oil tank. On the other hand, ICSSA is proposed to optimize the parameters of SRWNN, and the proposed ILWT-ICSSA-SRWNN is used to realize thermal error compensation. With the implementation of thermal characteristic optimization, the grinding accuracy is significantly improved. The following conclusions are drawn:

[0218] (1) In this embodiment, the static stiffness and dynamic stiffness of the worm wheel grinding machine bed with different rib plate layout methods are compared, and the optimal rib plate layout scheme is determined. Through the analysis of the static stiffness and dynamic stiffness of different layout schemes of stiffening plates, the stiffening plates of the worm wheel grinding machine bed structure are changed from the original cross vertical stiffening plates to double cross pattern stiffening plates. By reasonably designing the structure, quantity and layout of the rib plates, the static and dynamic stiffness are improved. The first natural frequency increases from 241.8 Hz to 277.4 Hz. In the optimized worm wheel grinding machine bed, the bottom of the original worm wheel grinding machine bed with a hollow circular cross section is changed to a closed bottom. The physical volume of the worm wheel grinding machine bed for installing the workbench is increased, and the shape of the fixed position of the worm wheel grinding machine bed and the workbench is modified to an arc transition to avoid stress concentration.

[0219] (2) A thermal characteristic optimization method is proposed for worm wheel grinding machines, which can effectively improve the grinding accuracy of worm wheel grinding machines. Using thermal characteristic optimization, the grinding accuracy is improved by about 53%. The thermal characteristics of the worm wheel grinding machine are optimized from two aspects: the mechanical structure of the worm wheel grinding machine bed layer and the cooling scheme. For the cooling scheme, a cooling oil pool is added to the worm wheel grinding machine bed. Thus, the heat dissipation capacity of the worm wheel grinding machine bed is improved, and the temperature gradient is reduced. The cooling channels are arranged along the entire length of the surface of the worm wheel grinding machine bed, and a peripheral cooling system is used. Finally, the thermal balance design of the worm wheel grinding machine bed is achieved.

[0220] (3) Thermal error compensation is used for worm wheel grinding machines through the proposed ILWT-ICSSA-SRWNN. Using thermal error compensation, the grinding accuracy is improved by about 24%. The ILWT-ICSSA-SRWNN model is proposed, which has the highest prediction accuracy, with a value of 91.70%. Followed by the ILWT-SRWNN error model, with a value of 89.99%. The prediction accuracies of ILWT-WNN and ILWT-ICSSA-WNN are 85.41% and 87.84% respectively. The parameter optimization of SRWNN and WNN is crucial for improving the prediction accuracy. ICSSA can effectively optimize the parameters of SRWNN and WNN. The ILWT-ICSSA-SRWNN model is more robust than ILWT-SRWNN, ILWT-ICSSA-WNN, ILWT-WNN, and ILWT-MLR. Memory performance is more important than parameter optimization.

[0221] (4) The proposed method for improving grinding accuracy based on thermal characteristic optimization and thermal error compensation is effective in improving grinding accuracy. Using TOE and thermal error compensation, the grinding accuracy is improved by more than 65%. Thermal characteristic optimization is much more effective than thermal error compensation in improving grinding accuracy. The maximum errors of the left and right tooth surfaces are both less than the tolerance requirements in ISO1328-1:2013.

[0222] The above-described embodiments are only preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims

1. A method for improving the grinding accuracy of a worm wheel grinding machine based on thermal characteristic optimization, characterized in that: It includes the following steps: Step 1: Optimize the thermal characteristics of the worm wheel grinding machine; 11) Create a three-dimensional model of the worm wheel grinding machine; 12) Conduct a thermal characteristics analysis of the worm wheel grinding machine. The method is as follows: (1) Set the initial temperature to the ambient temperature T ∞ ; (2) Input the working conditions of the bearings, including the initial preload, rotational speed, and assembly conditions; Calculate temperature-related variables, including bearing size, bearing preload, and lubricant viscosity; (3) Calculate the initial heat load intensity, convection coefficient, and initial contact thermal conductance; (4) Establish a thermal characteristics simulation model of the worm wheel grinding machine; (5) Calculate the temperature field and thermal deformation of the worm wheel grinding machine; (6) Compare the temperatures of all nodes in two adjacent iterative sub-steps: If it satisfies T i n -T i-1 n <1×10 -6 , then terminate the algorithm, and then save the temperatures of the key points to calculate the thermal deformation; if it does not satisfy T i n -T i-1 n <1×10 -6 , then update the lubricant viscosity, bearing size, convection coefficient, and bearing preload according to the calculated temperature field; update the bearing preload, contact thermal conductance, and bearing size according to the calculated thermal deformation; loop and execute step (2) until the convergence condition of T i n -T i-1 n <1×10 -6 is satisfied; 13) Optimize the thermal characteristics of the worm wheel grinding machine, optimize the layout of the rib plates on the bed of the worm wheel grinding machine. The rib plates on the bed adopt double-cross pattern rib plates to achieve the regulation of the static and dynamic characteristics of the worm wheel grinding machine; the bottom of the bed of the worm wheel grinding machine is closed, and a cooling oil pool is added to the bed of the worm wheel grinding machine to achieve the regulation of the thermal characteristics of the worm wheel grinding machine; Step 2: Perform thermal error compensation on the worm wheel grinding machine 21) Construct a thermal error prediction model; the thermal error prediction model is constructed based on the construction method of the thermal error prediction model of SRWNN, and includes the following steps: S1: Preprocess the thermal error data and construct a training set; S2: Determine the basic parameters of the chaotic sparrow search algorithm and the initial parameters of the SRWNN neural network; S3: Use the chaotic sparrow search algorithm to randomly generate a vector, and make each dimension of the vector within the range of [-1 / 2, 1 / 2]; use this vector as the first sparrow individual, and generate a chaotic sequence through Bernoulli transformation to obtain the remaining M - 1 chaotic individuals to initialize the sparrow population; S4: Calculate the fitness of each sparrow individual, and map the position of the sparrow individual with the best fitness to the best initial parameters of the SRWNN neural network; S5: Use the training set to train the SRWNN neural network with the best initial parameters, and judge whether the loss function of the SRWNN neural network is less than the preset threshold: If so, the training is completed, and execute S9; If not, determine whether the current iteration number t is less than the set maximum iteration number T max : If so, let t = t + 1 and execute S6; if not, stop the iteration and execute S9; S6: Select the first M / 2 sparrow individuals with larger fitness to form an elite group, use the elite confrontation learning strategy to calculate the reverse individuals of the elite individuals, and combine the elite individuals and the reverse individuals to obtain new sparrow individuals; S7: Determine the position of the sparrow individual with the best fitness and the position of the sparrow individual with the worst fitness, and use the sine-cosine search algorithm to update the positions of the scouting sparrows and the warning sparrows; S8: Perform boundary constraints, map the chaotic variables to each sparrow individual to obtain a new sparrow population, and loop to execute step four; S9: Use the best initial parameters as the optimal hyperparameters of the SRWNN neural network to construct a thermal error prediction model; 22) During the operation of the worm wheel grinding machine, use the thermal error prediction model to predict the thermal error in real time; 23) Perform thermal error compensation on the worm wheel grinding machine according to the predicted thermal error.

2. The method for improving the grinding accuracy of a worm wheel grinding machine optimized based on thermal characteristics according to claim 1, wherein: In the above step S1, the lifting wavelet transform decomposition is used to preprocess the thermal error data. The method is as follows: Among them, d' j-1 represents the high-frequency part after threshold processing; d j-1 represents the wavelet coefficient; thr represents the threshold; k represents the number of signal decomposition levels; and: σ = median|d j-1 | / 0.6745 Where, N represents the length of the high-frequency coefficient sequence of each wavelet layer; median represents the median function; σ represents the standard deviation of noise estimation.

3. The method for improving the grinding accuracy of a worm wheel grinding machine optimized based on thermal characteristics according to claim 1, wherein: In the step S3, the Bernoulli map is used in the chaotic sparrow search algorithm: Generate a chaotic sequence through Bernoulli transformation: x k+1 =(2x k ) mod 1 + rand(0,1) / M Among them, x k+1 represents the position of the (k + 1)-th sparrow individual; x k represents the position of the k-th sparrow individual; B represents the mapping element range; z k represents the range of the randomly generated vector of the chaotic sparrow search algorithm; rand(0, 1) / M represents a random variable; M represents the number of particles in the chaotic sequence.

4. The method for improving the grinding accuracy of a worm wheel grinding machine optimized based on thermal characteristics according to claim 1, characterized in that: In the step S6, the elite adversarial learning strategy is: Let the ordinary particle be X t =(x i1 ,x i2 ,…,x iD ), and the elite particle be Then the elite reverse solution is: After obtaining the elite reverse solution, perform boundary constraints: Among them, represents the j-dimensional vector of the elite solution ; represents the j-dimensional vector of the elite reverse solution ; both represent the boundaries of the j-dimensional search space; δ ∈ [0, 1]; rand(lb j , ub j ) ∈ [lb j , ub j .

5. The method for improving the grinding accuracy of a worm wheel grinding machine optimized based on thermal characteristics according to claim 1, characterized in that: In the step S7, the sine-cosine search algorithm is: For the known unconstrained n-dimensional minimum optimization problem: minf(x) = minf(x1, x2, …, x n ) s.t lb j ≤ X i ≤ ub j , i = 1, 2…, n Among them, X i represents the i-th variable to be optimized; The individual with the best fitness is recorded as the best individual X * , then the position update method of the scouting sparrow is as follows: r1 = a×(1 - t / T max ) Among them, represents the position of the $i$-th individual in the $t$-th generation population; represents the position of the current best individual; $a$ is a constant; $t$ represents the current iteration number; $T$ max represents the maximum iteration number; $r2 \in (0, 360^{\circ})$; $r3 \in (0, 2)$ and $r4 \in (0, 1)$; The position update method of the early warning sparrow is: Among them, represents the position of the $i$-th individual in the $(t + 1)$-th generation population; represents the position of the $i$-th individual in the $t$-th generation population; represents the position of the best individual in the $t$-th generation population; represents the position of the worst individual in the $t$-th generation population; $\beta$ represents the step size control parameter, which is a random number following a normal distribution with a mean of 0 and a variance of 1; $K$ represents a random number between $[-1, 1]$; $\varepsilon$ represents the smallest constant, which is intended to avoid a zero denominator; $f$ i represents the fitness value of the $i$-th individual; $f$ g represents the current global best fitness value; $f$ w represents the current global worst fitness value.

6. The method for improving the grinding accuracy of a worm wheel grinding machine optimized based on thermal characteristics according to claim 1, characterized in that: In the step S8, map the chaotic variable to the solution space: newX d = min d + (ub j - lb j ) · x d Among them, newX d represents the generated chaotic perturbation; min d represents the minimum value of the d-dimensional variable newX d ; and are the boundaries of the j-dimensional search space; X d represents the individual position in the solution space; x d represents the chaotic variable position; Add chaotic perturbation to the sparrow individual: newX d ' = (X d ' + newX d ) / 2 Among them, X d ' represents the individual that needs chaotic perturbation; newX d ' represents the individual with chaotic perturbation.

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