A reliability optimization design method of a spiral cooling jacket of an electric spindle

Abstract

The application provides a reliability optimization design method of a spiral cooling water jacket of an electric spindle, and relates to the technical field of parameter optimization of a machine tool spindle cooling structure. The method first establishes a thermal error model of the electric spindle to obtain the influence of the spiral cooling water jacket configuration on the thermal error of the electric spindle. Then, the influence of uncertain factors on the thermal error of the electric spindle is analyzed by combining a Kriging surrogate model and a Monte Carlo method, and a reliability-based optimization model is established to obtain the optimal cooling water jacket configuration. In the reliability optimization model, the volume of the cooling water jacket and the water flow are taken as the objective function, the sizing and positioning dimensions of the cooling water jacket are reasonably constrained, the inequality constraint set is normalized into a penalty function, and an intelligent optimization algorithm is used to solve the reliability optimization problem to obtain the optimal cooling water jacket configuration. The cooling water jacket configuration obtained by the method meets the machining reliability requirements of the electric spindle, the volume of the water jacket is greatly reduced, and the manufacturing cost of the cooling water jacket is reduced.

Description

Technical Field

[0001] This invention relates to the field of optimizing the cooling structure parameters of machine tool spindles, and in particular to a reliability optimization design method for a spiral cooling water jacket of an electric spindle. Background Technology

[0002] As a core component of precision machine tools, the electric spindle integrates a motor and a spindle to minimize transmission errors. However, its compact structure leads to a concentration of internal heat sources. To improve the heat dissipation capacity of the electric spindle, a spiral water jacket needs to be installed outside the stator for cooling. Therefore, while ensuring machining accuracy and reliability, the rational design of the spiral water jacket configuration is crucial to improving the machining capabilities of the electric spindle.

[0003] The optimization design of electric spindle cooling water jackets mainly focuses on improving their structural features. In recent years, scholars at home and abroad have proposed a variety of special spiral water jackets to improve the heat dissipation efficiency of the spindle. Fu Jianzhong et al. proposed a tree-shaped branching spiral water jacket, which can significantly improve the heat dissipation efficiency of the electric spindle. Fang et al. proposed a thermoelectric cooling system and performed finite element modeling and heat dissipation efficiency analysis on the proposed cooling system. Tang et al. adopted a water cooling channel with a convex structure and proved through numerical simulation that adding a convex structure can improve the cooling performance of the water jacket.

[0004] The aforementioned studies laid the foundation for the thermal analysis and structural optimization of electric spindle cooling water jackets, and their basic principles are quite mature. However, in these studies, the configuration of the electric spindle cooling water jacket was considered deterministic. From a practical engineering perspective, the dimensions of the water jacket, the water flow rate, etc., are all random. Therefore, the above studies have certain limitations. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a reliability optimization design method for the spiral cooling water jacket of an electric spindle, which addresses the shortcomings of the prior art.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] Step 1: Establish a parameterized model of the spiral water jacket based on the wall function and the k-ε turbulence model, and obtain the steady-state temperature field of the electric spindle by combining the heat generation and heat dissipation mechanism of the electric spindle;

[0008] Step 2: Using the obtained electric spindle temperature value as the initial condition, Hooke's law is used to obtain the axial thermal error at the front end of the shaft, and the relationship between the spiral water jacket configuration parameters and the thermal error is established. At the same time, an electric spindle thermal characteristic test bench is established and the accuracy of the electric spindle finite element model is verified.

[0009] Step 3: Establish the reliability limit state function of the electric spindle thermal error and analyze the reliability of the electric spindle thermal error;

[0010] Step 4: Optimize the cooling water jacket volume and input flow rate using the cooling water jacket configuration, including: radial positioning distance X, axial positioning distance Y, single-turn water jacket cross-sectional width W, single-turn water jacket cross-sectional length L, and cooling water input flow rate Q. i As a design variable, a reliability optimization design model for the electric spindle cooling water jacket is established.

[0011]

[0012] Where f(·) represents the objective function, and x represents the random design variable; G t (·) represents the limit state function under the t-th failure mode; R t G represents the given target reliability; i (·) denotes the inequality constraint matrix; M and N represent the number of reliability constraints and inequality constraints, respectively;

[0013] Step 5: Transform deterministic constraints and reliability constraints into penalty functions, and apply intelligent optimization methods to search for the optimal configuration of the cooling water jacket. When the objective function value remains stable and the reliability constraint reaches the given value, the iteration terminates, and the reliability optimization is completed.

[0014] Furthermore, step 1 includes:

[0015] Step 1.1: Determine the wall function of the spiral cooling water jacket:

[0016]

[0017] Among them, u + y represents the dimensionless velocity of the cooling water near the wall; + This represents the dimensionless distance from the cooling water to the wall.

[0018] A parameterized model of the cooling water jacket is established using wall functions and the standard k-ε turbulence model.

[0019] Step 1.2: Obtain the analytical formula for heat generation of the internal heat source using the heat generation mechanism of the electric spindle:

[0020] Based on the operating mode of the electric spindle's internal motor driving the shaft rotation, the internal heat sources of the electric spindle include the heat generated by the double-row angular contact ball bearings during rotation and the power loss due to heat loss from the motor stator and rotor. According to the motor efficiency calculation method, the power loss generated by the motor during operation is expressed as:

[0021] Q m =P i (1-η)+Pw

[0022] Among them, Q m P represents the heat generated by the motor. i P represents the input power of the motor; η represents the motor efficiency; w The power loss represents air resistance; the heat generation of the stator and rotor are expressed as follows:

[0023]

[0024] Among them, Q r and Q s These represent the heat generated by the rotor and stator, respectively; f p and f s These represent the motor's slip and synchronous frequency, respectively.

[0025] The heat generated by the bearing is expressed as:

[0026] Q b =1.047×10 -4 n(M f +M R )

[0027] Among them, Q b This represents the heat generated by the bearing's rotation; n represents the shaft speed; M f The rolling friction torque acting on the bearing is expressed as:

[0028] M f =f1P1d m

[0029] Where, d m The bearing's pitch diameter is represented by f1; the bearing load condition coefficient is represented by f1; and the calculated load is represented by P1.

[0030] M R The viscous frictional torque of the lubricating oil received by the bearing is expressed as:

[0031]

[0032] Where μ represents the kinematic viscosity of the lubricant; n represents the rotational speed of the shaft; and f0 represents a coefficient related to the bearing and lubrication type.

[0033] Step 1.3: Obtain the analytical expression for the convective heat transfer coefficient at the heat transfer location of the electric spindle using the theories of forced convection and natural convection;

[0034] According to the dimensionless convective heat transfer calculation method, the forced convective heat transfer coefficient between the bearing and the oil-gas mixture is expressed as:

[0035]

[0036] Among them, a c1 d represents the forced convection heat transfer coefficient between the bearing and the oil-air mixture; o and d i V represents the average diameter of the outer raceway and the inner raceway, respectively; air Indicates airflow rate; f shaft The frequency of shaft rotation is indicated; the free convection heat transfer coefficient between the air and the electric spindle housing is expressed as:

[0037]

[0038] Among them, a c2 G represents the free convection heat transfer coefficient between the air and the electric spindle housing. r P represents the Grashof number; r The Prandtl number represents the air mass; d represents the characteristic length; λ represents the air mass number. air The thermal conductivity of air is expressed as: The forced convection heat transfer coefficient between air and the motor air gap is expressed as:

[0039]

[0040] Among them, a c3 The forced convection heat transfer coefficient between air and the motor air gap is represented by: Re represents the Reynolds number of air; the forced convection heat transfer coefficient between the shaft and air is expressed as:

[0041]

[0042] Among them, a c4 This represents the forced convection heat transfer coefficient between the rotating shaft and the air;

[0043] Step 1.4: Solve the finite element model of the electric spindle to obtain the steady-state temperature field of the electric spindle.

[0044] Furthermore, step 2 includes:

[0045] Step 2.1: Use the steady-state temperature field of the electric spindle obtained in Step 1 as the initial condition, and at the same time, introduce the thermal expansion coefficient of each component of the electric spindle as the material parameter for calculating the thermal expansion.

[0046] Step 2.2: Using Hooke's Law, the overall axial thermal expansion of the electric spindle is expressed as:

[0047]

[0048] Where, ε x Indicates the thermal error of the electric spindle; α i T represents the axial linear expansion coefficient of the electric spindle material; i T represents the temperature value of the i-th unit node;a =25℃ indicates the temperature of the working environment;

[0049] The coupling effect of cooling water jacket configuration on the thermal error of electric spindle was obtained by changing the configuration parameters of the spiral water jacket;

[0050] Step 2.3: Construct an experimental platform for the thermal characteristics of the electric spindle. First, set a predetermined cooling water input flow rate. Embed two PT100 magnetic temperature sensors on the outer side of the front and rear bearings of the electric spindle. Collect the temperatures of the front and rear bearings when the electric spindle reaches thermal equilibrium at different speeds using a digital-to-analog converter. After obtaining the temperature data, stop the electric spindle, place the dial indicator at the front end of the spindle and zero the dial, and wait for all components of the electric spindle to return to room temperature. Utilize the cooling contraction of the spindle to indirectly measure the thermal error value of the electric spindle at that speed, verifying the accuracy of the established finite element model of the electric spindle.

[0051] Furthermore, step 3 includes:

[0052] Step 3.1: The proposed reliability limit state function for the thermal error of the electric spindle:

[0053] G(x)=ε lim -ε x (X,Y,L,W,Q i )

[0054] Where, ε lim Indicates the limiting thermal error; ε x (·) represents the thermal error function of the electric spindle; G(x)<0 indicates that the electric spindle has failed in machining; G(x)>0 indicates that the electric spindle has passed machining; G(x)=0 indicates that the electric spindle is in the limit state of machining accuracy.

[0055] Step 3.2: Obtain the initial sample set of the limit state function using the Latin hypercube sampling method;

[0056] Step 3.3: Divide the sample set into a training set and a validation set, and simultaneously construct a Kriging surrogate model on the training set. The surrogate model g k (X) is represented as:

[0057]

[0058] Where f(X)=[f1(X),f2(X)...f p (X)] T Let X be a polynomial function vector; β = [β1, β2...β] p ] T Let z(X) be a vector of regression coefficients; z(X) is a Gaussian process with zero mean.

[0059] When the relative error between the response of the validation set and the response of the surrogate model is within 10%, the accuracy of the surrogate model is considered to meet the requirements; otherwise, the accuracy of the surrogate model is considered to be low, and validation points with a relative error greater than 10% need to be added to the training set and the surrogate model needs to be retrained until the convergence condition is met.

[0060] Step 3.4: Obtain the reliability estimate using the Monte Carlo method based on the trained agent model:

[0061]

[0062] Among them, I R (·) represents the security domain indication function; f X (x) represents the joint probability density function of the design variable x.

[0063] Furthermore, step 4 includes:

[0064] Step 4.1: Use the configuration of the cooling water jacket as the design variable, assuming that the design variables are independent and follow a normal distribution;

[0065] Step 4.2: The spiral water jacket volume and the input water flow rate are used as two optimization objectives, and the objective function is expressed as follows:

[0066]

[0067] Where V represents the volume of the spiral water jacket; T represents the number of turns of the spiral water channel; d1 represents the length between adjacent water channels; c i k represents the weighting coefficient. c Indicates the cost contribution coefficient;

[0068] Step 4.3: Establish deterministic and reliability constraints. Based on the shell structure, the outer wall of the spiral water jacket must be smaller than the outer radius of the shell; the constraint function G1(x) is expressed as:

[0069] G1 = W + XR o

[0070] Among them, R o Let G represent the outer radius of the shell; the spiral water jacket is installed in conjunction with the shell, and the spiral water jacket is located behind the shell flange. The constraint function G2(x) is expressed as:

[0071] G2=(L+d1)·T+YL s

[0072] Among them, L s The axial length between the spiral water jacket and the rear end face of the outer shell is represented by G3(x); the constraint function for machining accuracy is expressed as:

[0073] G3=ε x(x)-ε lim

[0074] Where, ε x (·) indicates that the thermal error function of the electric spindle can be obtained from steps 1 and 2; ε lim This represents the maximum permissible machining error; and the target reliability is set as R. t =0.94;

[0075] Step 4.4: Establish design variable boundary constraints:

[0076]

[0077] Furthermore, step 5 includes:

[0078] Step 5.1: Normalize all constraint functions from Step 4 into penalty functions.

[0079]

[0080] Where Rt(x) represents the reliability constraint function; p i and p t These represent the penalty factors for deterministic and reliability constraints, respectively.

[0081] Step 5.2: Given the distribution law of random design variables, use the global chaotic game optimization algorithm to search for the optimal configuration of the cooling water jacket, and perform structural optimization and reliability analysis simultaneously. When the objective function value remains stable and the reliability constraint reaches the given value, the iteration terminates, and the reliability optimization is completed.

[0082] The beneficial effects of adopting the above technical solution are as follows: This invention proposes a reliability optimization design method for an electric spindle spiral cooling water jacket considering uncertain parameters. This method first establishes a thermal error model for the electric spindle to obtain the influence of the spiral cooling water jacket configuration on the thermal error of the electric spindle. Then, combining a surrogate model and the Monte Carlo method, the influence of uncertain factors on the thermal error of the electric spindle is analyzed, and a reliability-based optimization model is established to obtain the optimal cooling water jacket configuration. In the reliability optimization model, the volume of the cooling water jacket and the inflow rate of the water are used as objective functions. The fixed dimensions of the cooling water jacket are reasonably constrained, the inequality constraint set is normalized into a penalty function, and an intelligent optimization algorithm is used to solve the reliability optimization problem to obtain the optimal cooling water jacket configuration. Compared with the traditional cooling water jacket structure, this invention improves upon the original spiral water jacket structure, retaining the original spiral water jacket structure to reduce processing economic losses, while considering the influence of uncertain parameters, making it more valuable for practical application. Attached Figure Description

[0083] Figure 1 This is a flowchart of the reliability optimization method for the electric spindle cooling system in this invention;

[0084] Figure 2 The present invention defines the structure and dimensional parameters of the electric spindle and cooling water jacket.

[0085] Figure 3 The diagrams show the coupling relationship between the configuration parameters of the spiral cooling water jacket and the thermal error in this invention: (a) Coupling relationship between cooling water input flow rate and single-turn water jacket cross-sectional width on the thermal error of the electric spindle; (b) Coupling relationship between cooling water input flow rate and single-turn water jacket cross-sectional length on the thermal error of the electric spindle; (c) Coupling relationship between cooling water input flow rate and water jacket axial positioning distance on the thermal error of the electric spindle; (d) Coupling relationship between cooling water input flow rate and water jacket radial positioning distance on the thermal error of the electric spindle.

[0086] Figure 4 The following are experimental and theoretical comparison diagrams of bearing temperature and spindle thermal error in this invention: (a) Comparison diagram of theoretical and experimental bearing temperatures at different spindle speeds; (b) Comparison diagram of theoretical and experimental spindle thermal error at different speeds.

[0087] Figure 5 This is a robustness diagram of the reliability optimization design in this invention;

[0088] Figure 6 This is a comparison chart showing the thermal error reliability before and after optimization in this invention. Detailed Implementation

[0089] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0090] like Figure 1 The diagram shown is a flowchart of the reliability optimization method for the electric spindle cooling system in this invention. The specific steps of the reliability optimization design method for an electric spindle spiral cooling water jacket in this embodiment are as follows:

[0091] like Figure 2 As shown, a thermal characteristic model of the electric spindle is constructed. A parameterized model of the spiral water jacket is established based on the wall function and the k-ε turbulence model. The heat generation of each component of the electric spindle is obtained according to the heat generation mechanism of the heat source. The convective heat transfer coefficient of the main heat transfer location of the electric spindle is calculated according to the principle of convective heat transfer, and the overall steady-state temperature field of the electric spindle is obtained.

[0092] Step 1: Establish a parameterized model of the helical water jacket based on the wall function and the k-ε turbulence model. Combine this with the heat generation and dissipation mechanism of the electric spindle to obtain the steady-state temperature field of the electric spindle, including:

[0093] Step 1.1: Determine the wall function of the spiral cooling water jacket:

[0094]

[0095] Among them, u + y represents the dimensionless velocity of the cooling water near the wall; + This represents the dimensionless distance from the cooling water to the wall.

[0096] A parameterized model of the cooling water jacket is established using wall functions and the standard k-ε turbulence model.

[0097] Step 1.2: Obtain the analytical formula for heat generation of the internal heat source using the heat generation mechanism of the electric spindle:

[0098] Based on the operating mode of the electric spindle's internal motor driving the shaft rotation, it can be known that the heat sources include the heat generated by the double-row angular contact ball bearing during high-speed rotation and the power loss due to heat loss from the motor stator and rotor. According to the motor efficiency calculation method, the power loss generated by the motor during operation is:

[0099] Q m =P i (1-η)+P w

[0100] Among them, Q m P represents the heat generated by the motor. i P represents the input power of the motor; η represents the motor efficiency; w The power loss represents air resistance; the heat generation of the stator and rotor are expressed as follows:

[0101]

[0102] Among them, Q r and Q s These represent the heat generated by the rotor and stator, respectively; f p and f s These represent the motor's slip and synchronous frequency, respectively.

[0103] The heat generated by the bearing can be expressed as:

[0104] Q b =1.047×10 -4 n(M f +M R )

[0105] Among them, Q b This represents the heat generated by the bearing's rotation; n represents the shaft speed; M f The rolling friction torque acting on the bearing is expressed as:

[0106] M f =f1P1d m

[0107] Where, d m The bearing's pitch diameter is represented by f1; the bearing load condition coefficient is represented by f1; and the calculated load is represented by P1.

[0108] M R The viscous frictional torque of the lubricating oil received by the bearing is expressed as:

[0109]

[0110] Where μ represents the kinematic viscosity of the lubricant; n represents the rotational speed of the shaft; and f0 represents a coefficient related to the bearing and lubrication type.

[0111] Step 1.3: Convective heat transfer is divided into forced convection heat transfer and natural convection heat transfer. The heat transfer capacity at the heat transfer location of the electric spindle can be described using the convective heat transfer coefficient. According to the dimensionless convective heat transfer calculation method, the forced convection heat transfer coefficient between the bearing and the oil-air mixture is expressed as:

[0112]

[0113] Among them, a c1 d represents the forced convection heat transfer coefficient between the bearing and the oil-air mixture; o and d i V represents the average diameter of the outer raceway and the inner raceway, respectively; air Indicates airflow rate; f shaft The frequency of shaft rotation is indicated by the free convection heat transfer coefficient between the air and the electric spindle housing.

[0114]

[0115] Among them, a c2 G represents the free convection heat transfer coefficient between the air and the electric spindle housing. r P represents the Grashof number; r The Prandtl number represents air; d represents the characteristic length; λ represents the characteristic length. air The thermal conductivity of air is expressed as: The forced convection heat transfer coefficient between air and the motor air gap is expressed as:

[0116]

[0117] Among them, a c3 The forced convection heat transfer coefficient between air and the motor air gap is represented by: Re represents the Reynolds number of air; the forced convection heat transfer coefficient between the shaft and air is expressed as:

[0118]

[0119] Among them, a c4 This represents the forced convection heat transfer coefficient between the rotating shaft and the air;

[0120] Step 1.4: Use the numerical results obtained above as the boundary conditions of the electric spindle finite element model. Assume that the fluid wall boundary is no slip. Use a simplified algorithm to couple the velocity field and pressure field to establish the electric spindle finite element model. Solve the electric spindle finite element model to obtain the steady-state temperature field of the electric spindle.

[0121] Step 2: Using the obtained steady-state temperature field of the electric spindle as initial conditions, Hooke's law is applied to obtain the axial thermal error at the front end of the shaft, and the relationship between the configuration parameters of the spiral water jacket and the thermal error is established. Simultaneously, an experimental rig for the thermal characteristics of the electric spindle is established to obtain experimental data on bearing temperature and spindle axial thermal error, and to verify the accuracy of the established finite element model of the electric spindle, including:

[0122] Step 2.1: Use the steady-state temperature field of the electric spindle obtained in Step 1.4 as the initial condition, and at the same time, introduce the thermal expansion coefficient of each component of the electric spindle as the material parameter for calculating the thermal expansion.

[0123] Step 2.2: According to Hooke's Law, the overall axial thermal expansion of the electric spindle is expressed as:

[0124]

[0125] Where, ε x Indicates the thermal error of the electric spindle; α i T represents the axial linear expansion coefficient of the electric spindle material; i T represents the temperature value of the i-th unit node; a =25℃ indicates the temperature of the working environment;

[0126] Changing the configuration parameters of the spiral water jacket reveals the coupled effect of the cooling water jacket configuration on the thermal error of the electric spindle, such as... Figure 3 As shown;

[0127] Step 2.3: As Figure 4 As shown, in this embodiment, an experimental platform for the thermal characteristics of an electric spindle is constructed. First, the predetermined cooling water input flow rate is set to 12L / min. Two PT100 magnetic temperature sensors are embedded on the outer side of the front and rear bearings of the electric spindle. The temperature of the front and rear bearings is collected by a digital-to-analog converter when the electric spindle reaches thermal equilibrium at different speeds. After obtaining the temperature data, the electric spindle is stopped, the dial indicator is placed at the front end of the shaft and the dial is zeroed. The components of the electric spindle are allowed to return to room temperature. The thermal error value of the electric spindle at that speed is indirectly measured by the cooling contraction of the shaft to verify the accuracy of the established finite element model of the electric spindle.

[0128] Step 3: Establish the reliability limit state function for the thermal error of the electric spindle, and analyze the reliability of the thermal error of the electric spindle, including:

[0129] Step 3.1: The proposed reliability limit state function for the thermal error of the electric spindle:

[0130] G(x)=ε lim -ε x (X,Y,L,W,Q i )

[0131] Where X represents the radial positioning distance of the spiral water jacket; Y represents the axial positioning distance of the spiral water jacket; W represents the width of a single-turn water jacket section; L represents the length of a single-turn water jacket section; Q i Indicates the cooling water input flow rate; ε lim This represents the limit of thermal error. G(x) < 0 indicates that the electric spindle machining has failed; G(x) > 0 indicates that the electric spindle machining is qualified; G(x) = 0 indicates that the electric spindle machining accuracy is at its limit.

[0132] Step 3.2: Obtain the initial sample set of the limit state function using the Latin hypercube sampling method;

[0133] Step 3.3: Divide the sample set into a training set and a validation set. Use the Kriging method to construct a surrogate model on the training set. The surrogate model g k (X) is represented as:

[0134]

[0135] Where f(X)=[f1(X),f2(X)...f p (X)] T Represents a polynomial function vector of X; β = [β1, β2...β] p ] T The vector represents the regression coefficients; z(X) represents a Gaussian process with zero mean.

[0136] Using the surrogate model g k (X) Predict the hot error value in the validation set. If the relative error between the response of the validation set and the response of the surrogate model is within 10%, the accuracy of the Kriging surrogate model is considered to meet the requirements. Otherwise, the accuracy of the surrogate model is considered to be low. The validation points with larger relative errors need to be added to the training set and the surrogate model needs to be retrained until the convergence condition is met.

[0137] Step 3.4: Obtain the reliability estimate using the Monte Carlo method based on the trained agent model:

[0138]

[0139] Among them, I R (·) represents the security domain indication function; f X (x) represents the joint probability density function of the design variable x.

[0140] Step 4: Optimize the cooling water jacket volume and input flow rate using the cooling water jacket configuration, including: radial positioning distance X, axial positioning distance Y, single-turn water jacket cross-sectional width W, single-turn water jacket cross-sectional length L, and cooling water input flow rate Q. i As a design variable, establish a reliability optimization design model for the electric spindle cooling water jacket:

[0141]

[0142] Where f(·) represents the objective function, and x represents the random design variable; G t (·) represents the limit state function under the t-th failure mode; R t G represents the given target reliability; i (·) denotes the inequality constraint matrix; M and N represent the number of reliability constraints and inequality constraints, respectively;

[0143] Step 4.1: Use the configuration of the cooling water jacket as the design variable, assuming that the design variables are independent and follow a normal distribution;

[0144] Step 4.2: Using the spiral water jacket volume and the input water flow rate as two optimization objectives, the objective function is expressed as:

[0145]

[0146] Where V represents the volume of the spiral water jacket; T represents the number of turns of the spiral water channel; d1 represents the length between adjacent water channels; c i k represents the weighting coefficient. c Indicates the cost contribution coefficient;

[0147] Step 4.3: Establish deterministic and reliability constraints. Based on the shell structure, the outer wall of the spiral water jacket must be smaller than the outer radius of the shell; therefore, the constraint function G1(x) is expressed as:

[0148] G1 = W + XR o

[0149] Among them, R o Let G represent the outer radius of the shell; the spiral water jacket is installed in conjunction with the shell, therefore, the spiral water jacket is located behind the shell flange; therefore, the constraint function G2(x) is expressed as:

[0150] G2=(L+d1)·T+YL s

[0151] Among them, L sThis represents the axial length between the spiral water jacket and the rear end face of the outer shell. During the search for optimized cooling configuration, unreasonable design variables can lead to excessive thermal errors in the electric spindle, reducing machining accuracy. Therefore, the machining accuracy constraint function G3(x) is expressed as:

[0152] G3=ε x (x)-ε lim

[0153] Where, ε x (·) indicates that the thermal error function of the electric spindle can be obtained from steps 1 and 2; ε lim This represents the maximum permissible machining error; and the target reliability is set as R. t =0.94;

[0154] Step 4.4: Establish design variable boundary constraints:

[0155]

[0156] Step 5: Transform deterministic constraints and reliability constraints into penalty functions, and apply intelligent optimization methods to search for the optimal configuration of the cooling water jacket. The iteration terminates when the objective function value remains stable and the reliability constraint reaches a given value, completing the reliability optimization, including:

[0157] Step 5.1: Normalize all constraint functions from Step 4 into penalty functions:

[0158]

[0159] Where Rt(x) represents the reliability constraint function; p i and p t These represent the penalty factors for deterministic and reliability constraints, respectively.

[0160] Step 5.2: Describe the distribution pattern of the random design variables:

[0161] Table 1. Probability distribution characteristics of basic parameters

[0162]

[0163] A chaotic game optimization algorithm is used to search for the optimal configuration of the cooling water jacket, simultaneously performing structural optimization and reliability analysis. When the objective function value remains stable and the reliability constraint reaches a given value, such as... Figure 5 As shown, the iteration terminates, and the reliability optimization is completed. It can be seen that the optimized objective function value is stable, proving that the present invention has good robustness.

[0164] The chaotic game optimization in step 5 is applied to solve the reliability optimization problem; the objective function of this example is nonlinear. In the programming optimization, MATLAB programming language is used in this paper. The comparison before and after optimization is shown in Table 2.

[0165] Table 2 Comparison of Optimization Results

[0166]

[0167] The cumulative distribution of the limit state function before and after optimization is as follows: Figure 6 As shown, the results indicate that the machining reliability of the electric spindle before optimization and after deterministic optimization are 15.25% and 49.47%, respectively, while the reliability optimization method proposed in this invention yields the highest reliability of 92.01%. Furthermore, compared to the deterministic optimization method, the reliability optimization method can further reduce the volume of the spiral water jacket from 4.94 × 10⁻⁶. 5 mm 3 Reduced to 4.54 × 10 5 mm 3 .

[0168] To minimize the manufacturing cost of cooling water jackets while ensuring machining accuracy and reliability, this invention proposes a design method for spiral cooling water jackets of electric spindles considering uncertain parameters. First, a thermal error model of the electric spindle is established to obtain the influence of the spiral cooling water jacket configuration on the thermal error of the electric spindle. Then, the influence of uncertain factors on the thermal error of the electric spindle is analyzed by combining a surrogate model and the Monte Carlo method, and a reliability-based optimization model is established to obtain the optimal cooling water jacket configuration. In the reliability optimization model, the volume of the cooling water jacket and the inflow rate of the water are used as objective functions. The fixed dimensions of the cooling water jacket are reasonably constrained, and the inequality constraint set is normalized into a penalty function. An intelligent optimization algorithm is used to solve the reliability optimization problem to obtain the optimal cooling water jacket configuration. Practical application proves that the cooling water jacket configuration obtained by this method meets the machining reliability requirements of the electric spindle, and the volume of the water jacket is significantly reduced. Compared with existing optimization strategies, the proposed reliability optimization design of the spiral cooling water jacket for electric spindles improves the machining reliability of the electric spindle and reduces the manufacturing cost of the water jacket without changing the cooling structure.

[0169] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A reliability optimization design method for an electric spindle spiral cooling water jacket, characterized in that: Includes the following steps: Step 1: Establish a parameterized model of the spiral water jacket based on the wall function and the standard k-ε turbulence model, and obtain the steady-state temperature field of the electric spindle by combining the heat generation and heat dissipation mechanism of the electric spindle; Step 2: Using the steady-state temperature field of the electric spindle as the initial condition, Hooke's law is used to obtain the axial thermal error at the front end of the shaft, the relationship between the spiral water jacket configuration parameters and the thermal error is established, an experimental platform for the thermal characteristics of the electric spindle is established, and the accuracy of the finite element model of the electric spindle is verified. Step 3: Establish the reliability limit state function of the electric spindle thermal error and analyze the reliability of the electric spindle thermal error; Step 4: Using the cooling water jacket volume and input flow rate as optimization objectives, and the configuration of the cooling water jacket as design variables, establish the electric spindle cooling water jacket reliability optimization design model as follows: ； where f(•) denotes the objective function, x denotes the random design variable; G t (•) denotes the limit state function under the tth failure mode; R t denotes the given target reliability; G i (•) denotes the inequality constraint matrix; M and N denote the number of reliability constraints and inequality constraints, respectively; Step 4.1: Using the configuration of the cooling water jacket as a design variable, assume that the design variables are independent and follow a normal distribution; the configuration of the cooling water jacket includes: radial positioning distance X, axial positioning distance Y, single-turn water jacket cross-sectional width W, single-turn water jacket cross-sectional length L, and cooling water input flow rate Q. i ; Step 4.2: The spiral water jacket volume and the input water flow rate are used as two optimization objectives. The objective function is: ； Where V represents the volume of the spiral water jacket; T represents the number of turns of the spiral water jacket; d1 represents the length between adjacent water channels; c i k represents the weighting coefficient. c Indicates the cost contribution coefficient; Step 4.3: Establish deterministic and reliability constraints, considering deterministic and reliability constraints from the perspectives of the qualitative positioning dimensions of the cooling water jacket and the flow rate of the incoming water, and set the target reliability. Step 4.4: Establish design variable boundary constraints: ； Step 5: Transform the deterministic constraints and reliability constraints into penalty functions, and apply intelligent optimization methods to search for the optimal configuration of the cooling water jacket. When the objective function value remains stable and the reliability constraint reaches the given value, the iteration terminates, and the reliability optimization is completed.

2. The reliability optimization design method for an electric spindle spiral cooling water jacket according to claim 1, characterized in that: Step 1 specifically also includes: Step 1.1: Determine the wall function of the spiral cooling water jacket: ； Among them, u + y represents the dimensionless velocity of the cooling water near the wall; + This represents the dimensionless distance from the cooling water to the wall. A parameterized model of the cooling water jacket is established using wall functions and the standard k-ε turbulence model. Step 1.2: Obtain the analytical formula for the internal heat source's heat generation by utilizing the heat generation mechanism of the internal heat source of the electric spindle; The internal heat sources of the electric spindle include the heat generated by the double-row angular contact ball bearings during rotation and the power loss due to heat loss from the motor stator and rotor; according to the motor efficiency calculation method, the power loss generated by the motor during operation is expressed as: ； Among them, Q m P represents the heat generated by the motor. i P represents the input power of the motor; η represents the motor efficiency; w The power loss represents air resistance; the heat generation of the stator and rotor are expressed as follows: ； Among them, Q r and Q s These represent the heat generated by the rotor and stator, respectively; f p and f s These represent the motor's slip and synchronous frequency, respectively. The heat generated by the bearing is expressed as: ； Among them, Q b This represents the heat generated by the bearing's rotation; n represents the shaft speed; M f The rolling friction torque acting on the bearing is expressed as: ； Where, d m The bearing's pitch diameter is represented by f1; the bearing load condition coefficient is represented by f1; and the calculated load is represented by P1. M R The viscous frictional torque of the lubricating oil received by the bearing is expressed as: ； Where μ represents the kinematic viscosity of the lubricant; n represents the rotational speed of the shaft; and f0 represents a coefficient related to the bearing and lubrication type. Step 1.3: Obtain the analytical expression for the convective heat transfer coefficient at the heat transfer location of the electric spindle using the theories of forced convection and natural convection; According to the dimensionless convective heat transfer calculation method, the forced convective heat transfer coefficient between the bearing and the oil-gas mixture is expressed as: ； Among them, a c1 d represents the forced convection heat transfer coefficient between the bearing and the oil-air mixture; o and d i V represents the average diameter of the outer raceway and the inner raceway, respectively; air Indicates airflow rate; f shaft The frequency of shaft rotation is indicated; the free convection heat transfer coefficient between the air and the electric spindle housing is expressed as: ； Among them, a c2 G represents the free convection heat transfer coefficient between the air and the electric spindle housing. r P represents the Grashof number; r The Prandtl number represents the air mass; d represents the characteristic length; λ represents the air mass number. air The thermal conductivity of air is expressed as: The forced convection heat transfer coefficient between air and the motor air gap is expressed as: ； Among them, a c3 The forced convection heat transfer coefficient between air and the motor air gap is represented by: Re represents the Reynolds number of air; the forced convection heat transfer coefficient between the shaft and air is expressed as: ； Among them, a c4 This represents the forced convection heat transfer coefficient between the rotating shaft and the air; Step 1.4: Use the numerical results of the analytical expression as the boundary conditions of the electric spindle finite element model. Assume that the fluid wall boundary is no slip. Use a simplified algorithm to couple the velocity field and pressure field to establish the electric spindle finite element model. Solve the electric spindle finite element model to obtain the steady-state temperature field of the electric spindle.

3. The reliability optimization design method for an electric spindle spiral cooling water jacket according to claim 1, characterized in that: Step 2 specifically also includes: Step 2.1: Take the steady-state temperature field of the electric spindle as the initial condition, and at the same time, introduce the thermal expansion coefficient of each component of the electric spindle as the material parameter for calculating the thermal expansion. Step 2.2: According to Hooke's Law, the overall axial thermal expansion of the electric spindle is expressed as: ； Where, ε x For the thermal error of the electric spindle; α i T represents the axial linear expansion coefficient of the electric spindle material; i T represents the temperature value of the i-th unit node; a =25℃ indicates the temperature of the working environment; The coupling effect of changing the configuration parameters of the spiral water jacket on the thermal error of the electric spindle was obtained. Step 2.3: Construct an experimental platform for the thermal characteristics of the electric spindle. First, set a predetermined cooling water input flow rate. Embed two PT100 magnetic temperature sensors on the outer side of the front and rear bearings of the electric spindle. Collect the temperatures of the front and rear bearings when the electric spindle reaches thermal equilibrium at different speeds using a digital-to-analog converter. After obtaining the temperature data, stop the electric spindle, place the dial indicator at the front end of the spindle and zero the dial, and wait for all components of the electric spindle to return to room temperature. Utilize the cooling contraction of the spindle to indirectly measure the thermal error value of the electric spindle at that speed, verifying the accuracy of the established finite element model of the electric spindle.

4. The reliability optimization design method for an electric spindle spiral cooling water jacket according to claim 1, characterized in that: Step 3 specifically also includes: Step 3.1: The reliability limit state function for the thermal error of the electric spindle is expressed as follows: ； Where X represents the radial positioning distance of the spiral water jacket; Y represents the axial positioning distance of the spiral water jacket; L represents the cross-sectional length of a single turn of the water jacket; W represents the cross-sectional width of a single turn of the water jacket; Q i Indicates the cooling water input flow rate; ε lim Indicates the limiting thermal error; ε x (·) represents the thermal error function of the electric spindle; G(x) < 0 indicates that the electric spindle machining has failed; G(x) > 0 indicates that the electric spindle machining is qualified; G(x) = 0 indicates that the electric spindle machining accuracy is at its limit. Step 3.2: Obtain the initial sample set of the limit state function using the Latin hypercube sampling method; Step 3.3: Divide the sample set into a training set and a validation set, and simultaneously construct a Kriging surrogate model on the training set. The surrogate model g k (X) is represented as: ； Where f(X) = [f1(X), f2(X) ... f p (X)] T Let X be a vector of polynomial functions; β = [β1, β2...β] p ] T The vector represents the regression coefficients; z(X) is a Gaussian process with zero mean. When the relative error between the response of the validation set and the response of the surrogate model is within 10%, the accuracy of the surrogate model is considered to meet the requirements; otherwise, the accuracy of the surrogate model is considered to be low, and validation points with larger relative errors need to be added to the training set and the surrogate model needs to be retrained until the convergence condition is met. Step 3.4: Based on the trained surrogate model, obtain a reliability estimate using the Monte Carlo method. This estimate characterizes the reliability of the electric spindle's thermal error. Represented as: ； Among them, I R (·) denotes the security domain indicator function; f X (x) represents the joint probability density function of the design variable x.

5. The reliability optimization design method for an electric spindle spiral cooling water jacket according to claim 1, characterized in that: In step 4.3, the deterministic and reliability constraints are established. Based on the shell structure, the outer wall of the spiral water jacket must be smaller than the outer radius of the shell, resulting in the constraint function G1(x) expressed as: ； Among them, R o Indicates the outer radius of the shell; Based on the installation of the spiral water jacket and the housing, with the spiral water jacket positioned behind the housing flange, the constraint function G2(x) is expressed as: ； Among them, L s This indicates the axial length between the spiral water jacket and the rear end face of the outer casing; During the search process to optimize the cooling configuration, the constraint function G3(x) for machining accuracy is obtained as follows: ； Where, ε x (·) represents the thermal error function of the electric spindle; ε lim This represents the maximum permissible machining error; the target reliability is set as R. t =0.

94.

6. The reliability optimization design method for an electric spindle spiral cooling water jacket according to claim 1, characterized in that: Step 5 specifically also includes: Step 5.1: Normalize all constraint functions from Step 4 into penalty functions: ； Among them, R t (x) represents the reliability constraint function; p i and p t These represent the penalty factors for deterministic and reliability constraints, respectively. Step 5.2: Given the distribution law of random design variables, use the chaotic game optimization algorithm to search for the optimal configuration of the cooling water jacket, and perform structural optimization and reliability analysis simultaneously. When the objective function value remains stable and the reliability constraint reaches the given value, the iteration terminates, and the reliability optimization is completed.

Images