An optimization design method for high-rigidity precision cylindrical grinding electric spindle

Abstract

The present invention relates to a method for optimizing the design of a high-rigidity precision cylindrical grinding electric spindle, the steps of which are as follows: S1: establishing a spindle finite element model and determining initial values; S2: preselecting several suitable spindle pairing combinations; S3: establishing a spindle optimization model based on the NSGA-Ⅱ algorithm; S4: obtaining two Pareto solution sets through the algorithm model, taking the intersection of the two solution sets as the optimal solution set of the algorithm model, and judging whether there is an optimal solution set that meets the conditions; S5: performing simulation fine-tuning on a three-dimensional model established by inputting parameter values ​​from the optimal solution set. The present invention not only considers the influence of preload on the optimization of electric spindle stiffness on the basis of the electric spindle bearing span and the spindle overhang, but also expands the constraint conditions such as temperature rise and maximum speed in the algorithm, and also fine-tunes the optimization parameters through experimental verification of the parameter adjustment module to improve the accuracy and convenience of the electric spindle optimization system.

Description

Technical Field

[0001] The invention relates to a design method of a precision cylindrical grinding electric spindle, in particular to an optimization design method of a high-rigidity precision cylindrical grinding electric spindle. Background Art

[0002] An electric spindle is a device that integrates a motor and a spindle, characterized by its small size, compact structure, and excellent static and dynamic performance. With the continued development of electric spindles for grinding in recent years, the demand for their rigidity has also increased. Designing electric spindle structural parameters to meet the required rigidity is becoming increasingly important.

[0003] Patent application number 2015106585719 discloses a method for optimizing the structure of an electric spindle based on a parametric finite element model. This method takes into account multiple design variables, including the spindle overhang a, the front bearing span L1, the rear bearing span L2, and the electric spindle outer diameter D. It utilizes an algorithmic model to achieve the dual-objective optimization of high rigidity and lightweighting for the electric spindle. However, this method only optimizes bearing structural parameters and does not consider the effects of factors such as preload and bearing configuration on spindle stiffness. Furthermore, this method lacks experimental verification and cannot guarantee that the electric spindle parameters optimized using the algorithmic model will achieve the desired results.

[0004] Looking at the existing technologies, most of the high-rigidity optimization design models for electric spindles are too simple, or only optimize and adjust a single variable. However, in fact, the design of electric spindles requires the simultaneous coordination of multiple parameters for adjustment, and the results obtained only through algorithm optimization cannot ensure the optimal solution for the electric spindle, and may deviate from the experimental results. It is necessary to consider the influence of preload and bearing configuration on the optimization of electric spindle stiffness on the basis of considering the electric spindle bearing span and spindle overhang, and at the same time expand the temperature rise, maximum speed and other constraints in the algorithm, and fine-tune the optimization parameters through experimental verification of the parameter adjustment module to improve the accuracy and convenience of the electric spindle design optimization system. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the prior art and to propose a simpler, more effective and more accurate optimization design method for a high-rigidity precision cylindrical grinding electric spindle.

[0006] In order to achieve the above objectives, the present invention is implemented by adopting the following technical solutions:

[0007] A method for optimizing the design of a high-rigidity precision cylindrical grinding electric spindle comprises the following steps:

[0008] S1: Establish a parametric finite element model of the spindle and determine the initial values ​​of the electric spindle parameters;

[0009] S2: Pre-design stage: Based on the actual working conditions, such as the maximum speed and load requirements, several suitable spindle configuration combinations are pre-selected;

[0010] S3: Parameter optimization stage: Select a configuration combination, set the spindle overhang, bearing span, and bearing preload as design variables, use the spindle axial and radial deformation displacement limits, maximum speed limit, and temperature rise range as constraints, and use the minimum axial and radial displacement and minimum temperature rise as objective functions to establish a spindle optimization model based on the NSGA-II algorithm;

[0011] S4: Condition judgment stage: Two Pareto solution sets are obtained through the algorithm model. The intersection of the two solution sets is taken as the optimal solution set of the algorithm model to determine whether there is an optimal solution set that meets the conditions. If there is no optimal solution set that meets the conditions, the configuration combination is changed and the S3-S4 process is repeated.

[0012] S5: Simulation adjustment stage: Input the parameter values ​​in the optimal solution set into the established three-dimensional model for simulation to determine whether the simulation results meet the actual requirements; if so, directly output the parameter results; if not, adjust the selected parameters according to the simulation results, and reselect the appropriate parameter solution in the optimal solution set for simulation;

[0013] S6: Output the optimal solution parameter combination.

[0014] Furthermore, in step S2, based on the spindle working conditions: limiting speed and load, a simulation experiment is performed on the spindle model using initial parameters to obtain simulation data of several configuration modes. The data are compared and the configuration mode with the highest limiting speed in the data is selected.

[0015] Furthermore, in step S3, the design variables, constraints, and objective function of the main shaft optimization model based on the NSGA-II algorithm are determined by the following expressions:

[0016] Design variables:

[0017] x=(x1,x2,x3,x4) T =(a,L,F1,F2) T

[0018] x min ≤x≤x max

[0019] Where: a is the spindle overhang; L is the bearing span; F1 is the front bearing preload; F2 is the rear bearing preload; x min is the lower limit of the design variable; x max is the upper limit of the design variable;

[0020] Constraints:

[0021] δ 轴向 ≤δ1;

[0022] δ 径向 ≤δ2;

[0023] T≤20℃;

[0024] W≥W0;

[0025] Where: 轴向 is the actual axial deformation displacement of the main shaft; δ1 is the maximum axial displacement of the main shaft required for the main shaft design; δ 径向 is the actual radial deformation displacement of the spindle; δ2 is the maximum radial displacement of the spindle required for the spindle design; T is the actual temperature rise of the spindle; W is the actual limit speed of the spindle; W0 is the minimum limit speed required for the spindle design;

[0026] Objective function:

[0027] ①The axial stiffness is the largest, the corresponding axial displacement is the smallest, and the temperature rise is the smallest: minf1=minδ 轴向 ;minf3=minT;

[0028] ②The radial stiffness is the largest, the corresponding radial displacement is the smallest, and the temperature rise is the smallest: minf2=minδ 径向 ;minf3=minT.

[0029] Furthermore, in step S5, the simulation parameters that do not meet the requirements are analyzed and adjusted. The specific method is as follows:

[0030] 1) Select the boundary points in the optimal solution set as the initial values ​​and input them into the established three-dimensional simulation model;

[0031] 2) Determine whether the simulation results meet the design requirements; if so, output the design parameters and model; if not, adjust the parameters according to step 3);

[0032] 3) Parameter adjustment: Analyze simulation results that do not meet design requirements:

[0033] ① When the stiffness does not meet the conditions, the optimal solution set is discretized with the spindle overhang as the first adjustment variable, and the minimum spindle overhang adjustment amount is taken as one step, that is, the optimal solution set is (a i , L i , F 1i , F 2i ), a0 i n , i=0, 1, 2...n, where i is the number of spindle overhang adjustment steps; if the stiffness obtained by the experiment is less than the actual requirement, the parameter value of step i+1 is selected from the optimal solution set and iteratively input into the three-dimensional simulation model; ​​

[0034] ② When the temperature rise does not meet the conditions, the optimal solution set is discretized with the preload force as the first adjustment variable, and the minimum front bearing preload force adjustment amount is taken as one step, that is, the optimal solution set is (a j , L j , F 1j , F 2j ), F 10 <F 1j <F 1n ,j=0,1,2...n, where j is the number of steps for preload adjustment; if the temperature rise obtained from the experiment is greater than the actual requirement, the parameter value of step j-1 is selected from the optimal solution set and iteratively input into the three-dimensional simulation model;

[0035] ③When neither stiffness nor temperature rise meets the requirements, give priority to adjusting stiffness.

[0036] Furthermore, during the parameter discretization iteration process, if none of the parameter solutions in the optimal solution set can make the simulation results meet the design requirements, a new configuration method is used and steps S3 to S5 are repeated.

[0037] The beneficial effects of the present invention compared with the prior art are:

[0038] 1. The design method adopted by the present invention uses the NSGA-Ⅱ algorithm to collaboratively consider multiple design variables such as spindle overhang, bearing span, and preload force, and takes into account conditions such as temperature rise and maximum speed. The optimized external cylindrical grinding electric spindle stiffness value obtained under these constraints is closer to the stiffness under actual working conditions, and the optimization effect is more accurate.

[0039] 2. The design method adopted by the present invention is verified by experiments on the basis of algorithm optimization, and the results that deviate from the experimental results are excluded from the optimization parameter set, and the design variables that are most suitable for the actual working conditions are selected. The design method of the present invention is simpler and has better optimization effect.

[0040] 3. The design method adopted by the present invention also takes into account different bearing configurations. Compared with the existing technology that optimizes on the basis of a confirmed configuration, the design method of the present invention is more comprehensive and can optimize the performance of the cylindrical grinding electric spindle. In addition, the design method of the present invention realizes a closed-loop design, making the method more stable and the optimization process more accurate and powerful. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is the overall flow chart of the method of the present invention;

[0042] Figure 2 This is a simplified geometric structure of the cylindrical grinding electric spindle according to an embodiment of the present invention;

[0043] Figure 3 Design variables for optimizing the structure of the cylindrical grinding electric spindle according to an embodiment of the present invention;

[0044] Figure 4 This is the bearing configuration finally selected for the cylindrical grinding electric spindle according to the embodiment of the present invention;

[0045] Explanation of the accompanying symbols: spindle overhang a, bearing span L, front end bearing preload force F1, rear end bearing preload force F2. DETAILED DESCRIPTION

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] like Figure 1 As shown, the present invention is aimed at optimizing the design of the cylindrical grinding electric spindle, and the electric spindle is optimized according to the following steps:

[0048] First, according to Figure 2 The geometric model of Figure 3 The established design variables are variable parameters, and the parametric geometric model of the electric spindle is established. The stiffness of each supporting bearing is calculated in advance using the pseudo-static model of the angular contact ball bearing, and then the spring is used to replace the Figure 3 The corresponding bearings are then meshed with tetrahedral elements, and the mesh is refined at the contact point between the spring and the main shaft. The outer ring of the bearing is constrained as a fixed support to constrain the rotational freedom of the rotor and limit its circumferential rotation. A radial force of 350N is applied at 111mm from the main shaft end to simulate the radial load. A parametric finite element model of the electric spindle is established, and the structural dimensions of the electric spindle are preliminarily determined based on the actual working conditions.

[0049] Table 1 Initial values ​​of electric spindle parameters

[0050]

[0051] Secondly, according to the requirements of actual working conditions (limit speed, actual load), several suitable matching methods are preliminarily screened out, and bearing matching methods with little possibility of meeting the working conditions are eliminated.

[0052] Table 2 Bearing configuration selected

[0053]

[0054] Next, a configuration combination is selected, and the spindle overhang a, bearing span L, front bearing preload F1, and rear bearing preload F2 are set as design variables. The spindle axial and radial deformation displacement limits (the radial deformation displacement of the spindle is taken at 111 mm from the spindle end), maximum speed limit, and temperature rise range are used as constraints. The minimum axial and radial displacements and minimum temperature rise are used as objective functions to establish a spindle optimization model based on the NSGA-11 algorithm.

[0055] Design variables:

[0056] x=(x1,x2,x3,x4) T =(a,L,F1,F2) T

[0057] x min ≤x≤x max

[0058] x min =(144, 160, 100, 100) T ;

[0059] x max =(160, 220, 2000, 2000) T ;

[0060] Where: a is the spindle overhang; L is the bearing span; F1 is the front bearing preload; F2 is the rear bearing preload; x min is the lower limit of the design variable; x max is the upper limit of the design variable;

[0061] Constraints:

[0062] δ 轴向 ≤δ1=1.75μm;

[0063] δ 径向 ≤δ2=1.5μm;

[0064] T≤20℃;

[0065] W≥W0=18000 / (r / min);

[0066] Where: 轴向 is the actual axial deformation displacement of the main shaft; δ1 is the maximum axial displacement of the main shaft required for the main shaft design; δ 径向 is the actual radial deformation displacement of the spindle; δ2 is the maximum radial displacement of the spindle required for the spindle design; T is the actual temperature rise of the spindle; W is the actual limit speed of the spindle; W0 is the minimum limit speed required for the spindle design;

[0067] Objective function:

[0068] ①The axial stiffness is the largest, the corresponding axial displacement is the smallest, and the temperature rise is the smallest: minf1=minδ 轴向 ;minf3=minT.

[0069] ②The radial stiffness is the largest, the corresponding radial displacement is the smallest, and the temperature rise is the smallest: minf2=minδ 径向 ;minf3=minT.

[0070] After the algorithm model is optimized, two Pareto solution sets are obtained. The intersection of the two solution sets is taken as the optimal solution set of the algorithm optimization model. If the optimal solution set does not exist, a different coordination method is used and then input into the algorithm model for parameter optimization.

[0071] If there is an optimal solution set, fine-tune the selected parameter combination based on the experimental results.

[0072] 1) Select the boundary points in the optimal solution set as the initial values ​​and input them into the established three-dimensional simulation model;

[0073] 2) Determine whether the simulation results meet the design requirements; if so, output the design parameters and model; if not, adjust the parameters according to step 3);

[0074] 3) Parameter adjustment: Analyze simulation results that do not meet design requirements:

[0075] ① When the stiffness does not meet the conditions, the optimal solution set is discretized with the spindle overhang as the first adjustment variable, and the minimum spindle overhang adjustment amount is taken as one step, that is, the optimal solution set is (a i , L i , F 1i , F 2i ), a0 i n , i = 0, 1, 2...n, where i is the number of spindle overhang adjustment steps. If the stiffness obtained from the experiment is less than the actual requirement, the parameter value with i+1 steps greater than the initial value is selected from the optimal solution set and iteratively input into the 3D simulation model;

[0076] ② When the temperature rise does not meet the conditions, the optimal solution set is discretized with the preload force as the first adjustment variable, and the minimum front bearing preload force adjustment amount is taken as one step, that is, the optimal solution set is (a j , L j , F 1j , F 2j ), F 10 <F 1j <F 1n ,j=0,1,2...n, where j is the number of steps for preload adjustment. If the temperature rise obtained from the experiment is greater than the actual requirement, the parameter value with j-1 steps greater than the initial value is selected from the optimal solution set and iteratively input into the 3D simulation model;

[0077] ③When neither stiffness nor temperature rise meets the requirements, give priority to adjusting stiffness.

[0078] The comparison of the optimized target amount after experimental verification and fine-tuning is as follows:

[0079] Table 3 Target values ​​after optimization

[0080] ​​

[0081] The optimized parameters after fine-tuning after experimental verification are:

[0082] Table 4 Optimized spindle parameters

[0083]

[0084] After the method of the present invention is optimized, the Figure 4 The final bearing configuration selected for the cylindrical grinding electric spindle shown in the figure increases the spindle's axial stiffness by 18%, the spindle's radial stiffness by 19%, reduces the spindle's front-end bearing temperature rise by 34%, and reduces the rear-end bearing temperature rise by 46%, achieving significant optimization effects and greatly improving the spindle's stiffness and overall performance.

Claims

1. A method for optimizing the design of a high-rigidity precision cylindrical grinding electric spindle, characterized in that: The following steps are involved: S1: Establish a parametric finite element model of the spindle and determine the initial values ​​of the electric spindle parameters; S2: Pre-design stage: Based on the actual working conditions, such as the maximum speed and load requirements, several suitable spindle configuration combinations are pre-selected; S3: Parameter optimization stage: Select a configuration combination, set the spindle overhang, bearing span, and bearing preload as design variables, use the spindle axial and radial deformation displacement limits, maximum speed limit, and temperature rise range as constraints, and use the minimum axial and radial displacement and minimum temperature rise as objective functions to establish a spindle optimization model based on the NSGA-II algorithm; S4: Condition judgment stage: Two Pareto solution sets are obtained through the algorithm model. The intersection of the two solution sets is taken as the optimal solution set of the algorithm model to determine whether there is an optimal solution set that meets the conditions. If there is no optimal solution set that meets the conditions, the configuration combination is changed and the S3-S4 process is repeated. S5: Simulation adjustment stage: Input the parameter values ​​in the optimal solution set into the established three-dimensional model for simulation to determine whether the simulation results meet the actual requirements; if they do, directly output the parameter results; if the simulation results do not meet the requirements, adjust the selected parameters according to the simulation results, and reselect appropriate parameter solutions from the optimal solution set for simulation; analyze and adjust the simulation parameters that do not meet the requirements. The specific methods are as follows: 1) Select the boundary points in the optimal solution set as the initial values ​​and input them into the established three-dimensional simulation model; 2) Determine whether the simulation results meet the design requirements; if so, output the design parameters and model; if not, adjust the parameters according to step 3); 3) Parameter adjustment: Analyze simulation results that do not meet design requirements: ① When the stiffness does not meet the conditions, the optimal solution set is discretized with the spindle overhang as the first adjustment variable, and the minimum spindle overhang adjustment amount is taken as one step, that is, the optimal solution set is (a i , L i , F 1i , F 2i ), a0 i n ,i=0,1,2……n, where i is the number of spindle overhang adjustment steps;​​ If the stiffness obtained from the experiment is less than the actual requirement, the parameter value of step i+1 is selected from the optimal solution set and iteratively input into the three-dimensional simulation model; ② When the temperature rise does not meet the conditions, the optimal solution set is discretized with the preload force as the first adjustment variable, and the minimum front bearing preload force adjustment amount is taken as one step, that is, the optimal solution set is (a j , L j , F 1j , F 2j ), F 10 <F 1j <F 1n ,j=0,1,2...n, where j is the number of steps for preload adjustment; if the temperature rise obtained from the experiment is greater than the actual requirement, the parameter value of step j-1 is selected from the optimal solution set and iteratively input into the three-dimensional simulation model; ③When neither stiffness nor temperature rise meets the requirements, give priority to adjusting stiffness; S6: Output the optimal solution parameter combination.

2. The method for optimizing the design of a high-rigidity precision cylindrical grinding electric spindle according to claim 1, characterized in that: In step S2, based on the spindle working conditions: limit speed and load, a simulation experiment is performed on the spindle model using initial parameters to obtain simulation data of several configuration modes. The data are compared and the configuration mode with the highest limit speed is selected.

3. The method for optimizing the design of a high-rigidity precision cylindrical grinding electric spindle according to claim 1, characterized in that: In step S3, the design variables, constraints, and objective function of the spindle optimization model based on the NSGA-II algorithm are determined by the following expressions: Design variables: x=(x1,x2,x3,x4) T =(a,L,F1,F2) T x min ≤x≤x max Where: a is the spindle overhang; L is the bearing span; F1 is the front bearing preload; F2 is the rear bearing preload; x min is the lower limit of the design variable; x max is the upper limit of the design variable; Constraints: d 轴向 ≤δ1; d 径向 ≤δ2; T≤20℃； W≥W0; Where: 轴向 is the actual axial deformation displacement of the main shaft; δ1 is the maximum axial displacement of the main shaft required for the main shaft design; δ 径向 is the actual radial deformation displacement of the spindle; δ2 is the maximum radial displacement of the spindle required for the spindle design; T is the actual temperature rise of the spindle; W is the actual limit speed of the spindle; W0 is the minimum limit speed required for the spindle design; Objective function: ①The axial stiffness is the largest, the corresponding axial displacement is the smallest, and the temperature rise is the smallest: minf1=minδ 轴向 ;minf3=minT; ②The radial stiffness is the largest, the corresponding radial displacement is the smallest, and the temperature rise is the smallest: minf2=minδ 径向 ;minf3=minT.

4. The method for optimizing the design of a high-rigidity precision cylindrical grinding electric spindle according to claim 1, characterized in that: During the parameter discretization iteration process, if none of the parameter solutions in the optimal solution set can make the simulation results meet the design requirements, then a new configuration method is used and steps S3 to S5 are repeated.

Images