A multi-scale topology optimization method for machine tool spindle box considering temperature constraints

Abstract

The present invention discloses a multi-scale topology optimization method for a machine tool spindle box that considers temperature constraints. The machine tool spindle box is initialized equivalently; the plane structure of the spindle box is processed to obtain an overall thermal stress load matrix; the overall stiffness matrix and the overall displacement matrix are obtained based on the overall thermal stress load matrix; sensitivity analysis and filtering are performed to obtain the sensitivity of the flexibility to macro-design variables and micro-design variables respectively; the macro-design variables and micro-design variables are optimized based on the sensitivity to achieve multi-scale optimization of the machine tool spindle box. The method of the present invention can better optimize the topology of the machine tool spindle box, effectively reduce the thermal deformation of the spindle box and lighten the spindle box mass, and is green, economical, and energy-saving.

Description

Technical Field

[0001] The present invention relates to a machine tool spindle box optimization method in the field of machine tool spindle box design, and in particular to a multi-scale topology optimization method for a machine tool spindle box considering temperature constraints. Background Art

[0002] The spindle box is a critical precision moving component in a CNC machining center. The quality of its structural performance directly determines the overall machining accuracy and quality of the CNC machining center. Therefore, the spindle box must possess sufficient rigidity. Furthermore, numerous studies have shown that thermal error is the single largest factor affecting machine tool accuracy, accounting for 40% to 70% of manufacturing error. When the machine tool is operating, the heat generated by the high-speed rotation of the spindle is transferred to the spindle box through heat conduction, causing the spindle box temperature to rise. Therefore, it is necessary to limit the maximum spindle box temperature while maintaining sufficient rigidity.

[0003] Since the 21st century, green machine tool manufacturing has become a development trend in the manufacturing industry, and lightweight machine tool design has become a research focus and hotspot. Lightweight design of machine tool spindle boxes embodies the requirements of modern manufacturing technologies that are green, economical, and energy-efficient. Lightweight design has important economic significance for the machine tool manufacturing industry, guiding production. However, the traditional single-scale topology optimization methods currently used have limited effectiveness in reducing spindle box weight and do not limit spindle box temperature. Multi-scale topology optimization methods, which simultaneously optimize parts at both the macro and micro scales, can effectively achieve lightweight spindle boxes. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing methods and provide a multi-scale topology optimization method for machine tool spindle boxes that considers temperature constraints. This method can effectively reduce thermal deformation and lighten the spindle box mass, and is environmentally friendly, economical, and energy-saving.

[0005] like Figure 1 As shown, the method of the present invention comprises the following steps:

[0006] The present invention optimizes the position of the main spindle box.

[0007] (1) Initialization of the machine tool spindle box is equivalent

[0008] Since the cross sections of the spindle box are similar, the cross section of the machine tool spindle box is equivalent to a plane structure, and the cross section of the spindle box is extracted as the plane structure; the machine tool is placed in a constant temperature workshop, and the spindle box exchanges heat with the constant temperature air, and the ambient temperature is 20°C;

[0009] The spindle box contains the spindle, spindle bearings, motor, motor shaft bearings and other parts. In the method, the location of the spindle, spindle bearings and motor is set as the non-design domain, and the non-design domain remains unchanged in the method.

[0010] (2) Process the plane structure of the spindle box to obtain the overall thermal stress load matrix F th :

[0011] The plane structure of the spindle box is discretized into macro unit i and micro unit j. The heat conduction matrix K of the plane structure is obtained according to the processing of macro unit i and micro unit j. T And the structural temperature matrix T, and then according to the structural temperature matrix T to obtain the overall thermal stress load matrix F th ;

[0012] The macro unit i refers to the planar structure of the spindle box obtained by discrete means, and the micro unit j refers to the discretization obtained by each macro unit i.

[0013] (3) According to the overall thermal stress load matrix F th Processing to obtain the overall stiffness matrix K and overall displacement matrix U;

[0014] (4) The pseudo-density of all macro units i Composition of macro design variables ρ M , which is occupied by the density of the part material of all micro units j Composition of micro-design variables ρ m , sensitivity analysis and filtering are performed based on the overall stiffness matrix K and the overall displacement matrix U, and the flexibility C is obtained to determine the macro design variable ρ M and micro-design variables ρ m sensitivity;

[0015] The flexibility C mentioned refers to the design properties of the machine tool spindle box.

[0016] (5) Optimize design variables:

[0017] Optimize macro design variables ρ according to sensitivity M and micro-design variables ρ m , to achieve multi-scale optimization of the machine tool spindle box.

[0018] Said (2) is specifically:

[0019] After drawing the plane structure of the spindle box, a grid division process is established. A grid of the plane structure is regarded as a macro unit i. A grid subdivision process is established for each macro unit i. A grid in the macro unit i is regarded as a micro unit j. Then:

[0020] (2.1) The equivalent heat conduction matrix of macro unit i is obtained by the homogenization method:

[0021]

[0022] Among them, |Ω E | is the area of macro unit i, is the density of the part material in micro unit j. When micro unit j has part material, Otherwise, it is 0, k0 is the equivalent heat conduction matrix under normal conditions, that is, the equivalent heat conduction matrix when multi-scale optimization is not used, χ a is the induced temperature parameter, y b Represents the thermal conductivity temperature coefficient, Ω E represents the spatial representation of macro unit i, The pseudo density of macro unit i is calculated by the material density of each micro unit j in the macro unit i. m represents micro, M represents macro, and Ω represents e represents the spatial representation of micro-unit j, ne represents the total number of micro-units j in a single macro-unit i, I represents the identity matrix, represents the equivalent heat conduction matrix of macro unit i; f( ) represents the interpolation function;

[0023] (2.2) The equivalent heat conduction matrix of each macro unit is summed to obtain the heat conduction matrix K of the planar structure T :

[0024]

[0025] Where NE represents the total number of macro units;

[0026] (2.3) According to the structural heat conduction finite element equation K T T=P to obtain the structural temperature matrix T, where P is the temperature load matrix;

[0027] (2.4) The temperature change ΔT of each macro unit i is obtained according to the structural temperature matrix T, and then the thermal stress load matrix of the macro unit i caused by the temperature field is obtained according to the following formula

[0028]

[0029] Among them, B is the macro unit strain displacement matrix, D H is the homogenized constitutive matrix, ε T is the thermal strain of macro unit i, T' represents the matrix transpose; α represents the thermal expansion coefficient; ΔT represents the temperature change of macro unit i;

[0030] (2.6) The thermal stress load matrix of each macro unit i Add together to obtain the overall thermal stress load matrix F of the plane structure th :

[0031]

[0032] Where NE represents the total number of macro units.

[0033] The interpolation function in (2.1) and Correlation, interpolation function and Related, the interpolation function in (2.1) and interpolation functions Calculated as:

[0034]

[0035]

[0036] Where c is a parameter to avoid singularity of heat conduction matrix, which is a constant, and p represents the penalty parameter;

[0037] The homogenized constitutive matrix D in (2.4) is H Calculated as:

[0038]

[0039] Among them, D0 is the constitutive matrix under normal conditions, that is, the constitutive matrix when multi-scale optimization is not used, B j and u j are the strain-displacement matrix and displacement matrix of microelement j, respectively.

[0040] The temperature change ΔT of the macro unit i in (2.4) is calculated as:

[0041]

[0042] in, and are the temperatures of the four nodes of macro unit i, is the ambient temperature of the workshop where the machine tool is located; the nodes refer to the four corners of the macro unit i, and the temperatures of the four nodes of each macro unit i are obtained by extracting the structural temperature matrix T;

[0043] Said (3) is specifically:

[0044] First calculate the element stiffness matrix K of the macro element i i for:

[0045]

[0046] The unit stiffness matrix K of each macro unit i is i Add together to obtain the overall stiffness matrix K:

[0047]

[0048] Then substitute the overall stiffness matrix K into the following formula to obtain the overall displacement matrix U composed of the displacements of each node in the plane structure:

[0049] KU=F m +F th

[0050] Among them, F m is the mechanical load matrix of the planar structure.

[0051] Said (4) is specifically:

[0052] (4.1) First, calculate the flexibility C with respect to the macro design variable ρ M Sensitivity for:

[0053]

[0054] in, Represents the effect of the overall thermal stress load on the macro design variable ρ M Sensitivity, The macro design variable ρ represents the overall stiffness matrix for element i M sensitivity;

[0055] The above overall thermal stress load has an impact on the macro design variable ρ M Sensitivity Calculated as:

[0056]

[0057] (4.2) Calculate the flexibility C for the microscopic design variable ρ m Sensitivity for:

[0058]

[0059] in, Represents the effect of the overall thermal stress load on the micro-design variable ρ m Sensitivity, represents the microscopic design variable ρ of the overall stiffness matrix for element i m sensitivity;

[0060] The above overall thermal stress load has an impact on the micro-design variable ρ m Sensitivity Calculated as:

[0061]

[0062] in, Denotes the homogenized constitutive matrix D H For micro-design variables ρ msensitivity;

[0063] The above homogenized constitutive matrix D H For micro-design variables ρ m Sensitivity Calculated as:

[0064]

[0065] Among them, B j and u j are the strain-displacement matrix and displacement matrix of microelement j, respectively.

[0066] Said (5) is specifically:

[0067] The flexibility C is respectively related to the macro design variable ρ M and micro-design variables ρ m sensitivity to the current macro design variables ρ M and micro-design variables ρ m The two design variables are used as input parameters and are input into the MMA algorithm optimization process to obtain the two optimized design variables. The optimized macro design variable ρ M and micro-design variables ρ m Determine whether the optimization results meet the convergence conditions;

[0068] If the convergence condition is met, the macro design variable ρ obtained in the last iteration is M and micro-design variables ρ m Characterization is performed as the optimal machine tool spindle box structure;

[0069] If the convergence condition is not met, return to step (2) and execute each step repeatedly until the convergence condition is met.

[0070] Whether the optimization result meets the convergence condition is determined, specifically, when the number of iterations reaches a preset number threshold, the difference between the results of two iterations is less than a preset difference threshold.

[0071] In the sensitivity and sensitivity The two sensitivities are input into the MMA algorithm after being filtered.

[0072] The beneficial effects of the present invention are:

[0073] The method of the present invention can perform better topological optimization on the machine tool spindle box, effectively reduce the thermal deformation of the spindle box and lighten the weight of the spindle box, and is green, economical and energy-saving. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1It is the flow chart of machine tool spindle box optimization;

[0075] Figure 2 It is the initial macro structure of the machine tool spindle box;

[0076] Figure 3 It is the initial microstructure of the machine tool spindle box;

[0077] Figure 4 This is the result diagram of the macro structure optimization of the machine tool spindle box;

[0078] Figure 5 This is the result diagram of the microstructure optimization of the machine tool spindle box. DETAILED DESCRIPTION

[0079] The specific implementation of the present invention is described in detail below. It is necessary to point out that the following implementation is only used to further illustrate the present invention and cannot be understood as limiting the scope of protection of the present invention. Some non-essential improvements and adjustments made by technical personnel in this field based on the above-mentioned present invention still fall within the scope of protection of the present invention.

[0080] The specific embodiments and implementation process of the method of the present invention are as follows: Figure 1 As shown;

[0081] (1) Initialization

[0082] The cross section of the machine tool spindle box is equivalent to a plane structure and the cross section of the spindle box is extracted as a plane structure; the spindle box is 600 mm long and 400 mm wide, and it is discretized into 120X80 macro cells, where each macro cell is composed of 50X50 micro cells; Figure 2 and Figure 3 They are the initial macro and micro structures of the machine tool spindle box.

[0083] The spindle box material is made of resin mineral composite material, which has an elastic modulus of 40GPa, a Poisson's ratio of 0.22, and a thermal expansion coefficient of 1.5X10 -6 / ℃, thermal conductivity is 1.8W / m·℃; the machine tool is placed in a constant temperature workshop, the spindle box exchanges heat with the constant temperature air, the ambient temperature around it is always 20℃, and its maximum temperature cannot exceed 80 degrees Celsius.

[0084] (2) Process the plane structure of the spindle box to obtain the overall thermal stress load matrix F th : The plane structure of the spindle box is discretized into macro units i and micro units j, and the heat conduction matrix K of the plane structure is obtained according to the macro units i and micro units j. T And the structural temperature matrix T, and then according to the structural temperature matrix T to obtain the overall thermal stress load matrix F th .

[0085] After drawing the plane structure of the spindle box, a grid division process is established. A grid of the plane structure is regarded as a macro unit i. A grid subdivision process is established for each macro unit i. A grid in the macro unit i is regarded as a micro unit j. Then:

[0086] (2.1) The equivalent heat conduction matrix of macro unit i is obtained by the homogenization method:

[0087]

[0088] Among them, |Ω E | is the area of macro unit i, is the density of the part material in micro unit j. When micro unit j has part material, Otherwise, it is 0, k0 is the equivalent heat conduction matrix under normal conditions, that is, the equivalent heat conduction matrix when multi-scale optimization is not used, χ a is the induced temperature parameter, y b Represents the thermal conductivity temperature coefficient, Ω E represents the spatial representation of macro unit i, The pseudo density of macro unit i is calculated by the material density of each micro unit j in the macro unit i. m represents micro, M represents macro, and Ω represents e represents the spatial representation of micro-unit j, ne represents the total number of micro-units j in a single macro-unit i, I represents the identity matrix, represents the equivalent heat conduction matrix of macro unit i; f( ) represents the interpolation function;

[0089] The interpolation function and Correlation, interpolation function and Correlation, interpolation function and interpolation functions Calculated as:

[0090]

[0091]

[0092] Where c is a parameter to avoid singularity of heat conduction matrix, which is a constant, and p represents the penalty parameter;

[0093] (2.2) The equivalent heat conduction matrix of each macro unit is summed to obtain the heat conduction matrix K of the planar structure T :

[0094]

[0095] Where NE represents the total number of macro units;

[0096] (2.3) According to the structural heat conduction finite element equation K T The structural temperature matrix T is obtained by T=P, where P is the temperature load matrix; P is the heat generated by the bearing and motor, both of which are 800W.

[0097] (2.4) The temperature change ΔT of each macro unit i is obtained according to the structural temperature matrix T, and then the thermal stress load matrix of the macro unit i caused by the temperature field is obtained according to the following formula

[0098]

[0099] Among them, B is the macro unit strain displacement matrix, D H is the homogenized constitutive matrix, ε T is the thermal strain of macro unit i, T' represents the matrix transpose; α represents the thermal expansion coefficient; ΔT represents the temperature change of macro unit i;

[0100] Homogenized constitutive matrix D H Calculated as:

[0101]

[0102] Among them, D0 is the constitutive matrix under normal conditions, that is, the constitutive matrix when multi-scale optimization is not used, B j and u j are the strain-displacement matrix and displacement matrix of microelement j, respectively;

[0103] The temperature change ΔT of macro unit i is calculated as:

[0104]

[0105] in, and are the temperatures of the four nodes of macro unit i, is the ambient temperature of the workshop where the machine tool is located; the nodes refer to the four corners of the macro unit i, and the temperatures of the four nodes of each macro unit i are obtained by extracting the structural temperature matrix T;

[0106] (2.6) The thermal stress load matrix of each macro unit i Add together to obtain the overall thermal stress load matrix F of the plane structure th :

[0107]

[0108] Where NE represents the total number of macro units.

[0109] (3) According to the overall thermal stress load matrix Fth Processing to obtain the overall stiffness matrix K and overall displacement matrix U;

[0110] First calculate the element stiffness matrix K of the macro element i i for:

[0111]

[0112] The unit stiffness matrix K of each macro unit i is i Add together to obtain the overall stiffness matrix K:

[0113]

[0114] Then substitute the overall stiffness matrix K into the following formula to obtain the overall displacement matrix U composed of the displacements of each node in the plane structure:

[0115] KU=F m +F th

[0116] Among them, F m is the mechanical load matrix of the planar structure.

[0117] Calculation shows that the bearing has a mechanical load of 1000N on the spindle box.

[0118] (4) The pseudo-density of all macro units i Composition of macro design variables ρ M , which is occupied by the density of the part material of all micro units j Composition of micro-design variables ρ m , sensitivity analysis and filtering are performed based on the overall stiffness matrix K and the overall displacement matrix U, and the flexibility C is obtained to determine the macro design variable ρ M and micro-design variables ρ m sensitivity.

[0119] (4.1) First, calculate the flexibility C with respect to the macro design variable ρ M Sensitivity for:

[0120]

[0121] in, Represents the effect of the overall thermal stress load on the macro design variable ρ M Sensitivity, The macro design variable ρ represents the overall stiffness matrix for element i M sensitivity;

[0122] The above overall thermal stress load has an impact on the macro design variable ρ M Sensitivity Calculated as:

[0123]

[0124] (4.2) Calculate the flexibility C for the microscopic design variable ρ m Sensitivity for:

[0125]

[0126] in, Represents the effect of the overall thermal stress load on the micro-design variable ρ m Sensitivity, represents the microscopic design variable ρ of the overall stiffness matrix for element i m sensitivity;

[0127] The above overall thermal stress load has an impact on the micro-design variable ρ m Sensitivity Calculated as:

[0128]

[0129] in, Denotes the homogenized constitutive matrix D H For micro-design variables ρ m sensitivity;

[0130] The above homogenized constitutive matrix D H For micro-design variables ρ m Sensitivity Calculated as:

[0131]

[0132] Among them, B j and u j are the strain-displacement matrix and displacement matrix of microelement j, respectively.

[0133] (5) Optimize design variables: Optimize macro design variables ρ based on sensitivity M and micro-design variables ρ m , to achieve multi-scale optimization of the machine tool spindle box.

[0134] The flexibility C is respectively related to the macro design variable ρ M and micro-design variables ρ M sensitivity to the current macro design variables ρ M and micro-design variables ρ M The two design variables are used as input parameters and are input into the MMA algorithm optimization process to obtain the two optimized design variables. The optimized macro design variable ρ M and micro-design variables ρm Determine whether the optimization results meet the convergence conditions;

[0135] If the convergence condition is met, the macro design variable ρ obtained in the last iteration is M and micro-design variables ρ m Characterization is performed as the optimal machine tool spindle box structure;

[0136] If the convergence condition is not met, return to step (2) and execute each step repeatedly until the convergence condition is met.

[0137] Whether the optimization result meets the convergence condition is determined, specifically, when the number of iterations reaches a preset number threshold, the difference between the results of two iterations is less than a preset difference threshold.

[0138] In the specific implementation, the sensitivity and sensitivity Before the two sensitivities are input into the MMA algorithm, they are filtered and then input to avoid the checkerboard phenomenon.

[0139] In this embodiment, the convergence condition is set as the change of the design variable is not greater than 0.01 and the number of cycles is not less than 300 times. The MMA algorithm is used to calculate the macro design variable ρ M and micro-design variables ρ m Optimize and determine whether the optimization result meets the convergence conditions; if it meets the convergence conditions, the optimal machine tool spindle box structure is obtained; if it does not meet the convergence conditions, return to step 2 and execute each step repeatedly until the convergence conditions are met; the optimal machine tool spindle box macro and micro structures obtained after optimization are as follows Figure 4 and Figure 5 shown.

Claims

1. A multi-scale topology optimization method for a machine tool spindle box considering temperature constraints, characterized by: The method comprises the following steps: (1) Initialization equivalence of the machine tool spindle box: the cross section of the machine tool spindle box is equivalent to a plane structure, and the cross section of the spindle box is extracted as a plane structure; the machine tool is placed in a constant temperature workshop, and the spindle box exchanges heat with the constant temperature air; (2) Process the plane structure of the spindle box to obtain the overall thermal stress load matrix F th : The plane structure of the spindle box is discretized into macro units i and micro units j, and the heat conduction matrix K of the plane structure is obtained according to the macro units i and micro units j. T And the structural temperature matrix T, and then according to the structural temperature matrix T to obtain the overall thermal stress load matrix F th ; (3) According to the overall thermal stress load matrix F th Processing to obtain the overall stiffness matrix K and overall displacement matrix U; (4) The pseudo-density of all macro units i Composition of macro design variables ρ M , which is occupied by the density of the part material of all micro units j Composition of micro-design variables ρ m , sensitivity analysis and filtering are performed based on the overall stiffness matrix K and the overall displacement matrix U, and the flexibility C is obtained to determine the macro design variable ρ M and micro-design variables ρ m sensitivity; (5) Optimize design variables: Optimize macro design variables ρ based on sensitivity M and micro-design variables ρ m , to achieve multi-scale optimization of the machine tool spindle box.

2. The multi-scale topology optimization method for a machine tool spindle box considering temperature constraints according to claim 1, characterized in that: Said (2) is specifically: After drawing the plane structure of the spindle box, a grid division process is established. A grid of the plane structure is regarded as a macro unit i. A grid subdivision process is established from each macro unit i. A grid in the macro unit i is regarded as a micro unit j. Then: (2.1) The equivalent heat conduction matrix of macro unit i is obtained by the homogenization method: Among them, |Ω E | is the area of macro unit i, is the material density of the micro unit j, k0 is the equivalent heat conduction matrix under normal conditions, χ a is the induced temperature parameter, y b Represents the thermal conductivity temperature coefficient, Ω E represents the spatial representation of macro unit i, represents the pseudo-density of macro unit i, m represents micro, M represents macro, Ω e represents the spatial representation of micro-unit j, ne represents the total number of micro-units j in a single macro-unit i, I represents the identity matrix, represents the equivalent heat conduction matrix of macro unit i; f() represents the interpolation function; (2.2) The equivalent heat conduction matrix of each macro unit is summed to obtain the heat conduction matrix K of the planar structure T : Where NE represents the total number of macro units; (2.3) According to the structural heat conduction finite element equation K T T=P to obtain the structural temperature matrix T, where P is the temperature load matrix; (2.4) The temperature change ΔT of each macro unit i is obtained according to the structural temperature matrix T, and then the thermal stress load matrix of the macro unit i caused by the temperature field is obtained according to the following formula Among them, B is the macro unit strain displacement matrix, D H is the homogenized constitutive matrix, ε T is the thermal strain of macro unit i, T' represents the matrix transpose; α represents the thermal expansion coefficient; ΔT represents the temperature change of macro unit i; (2.6) The thermal stress load matrix of each macro unit i Add together to obtain the overall thermal stress load matrix F of the plane structure th : Where NE represents the total number of macro units.

3. The multi-scale topology optimization method for a machine tool spindle box considering temperature constraints according to claim 2, characterized in that: The interpolation function in (2.1) and interpolation functions Calculated as: Where c is the parameter to avoid singularity of heat conduction matrix, and p is the penalty parameter.

4. The multi-scale topology optimization method for a machine tool spindle box considering temperature constraints according to claim 2, characterized in that: The homogenized constitutive matrix D in (2.4) is H Calculated as: Among them, D0 is the constitutive matrix under normal conditions, B j and u j are the strain-displacement matrix and displacement matrix of microelement j, respectively.

5. The multi-scale topology optimization method for a machine tool spindle box considering temperature constraints according to claim 2, characterized in that: The temperature change ΔT of the macro unit i in (2.4) is calculated as: in, and are the temperatures of the four nodes of macro unit i, is the ambient temperature of the workshop where the machine tool is located; the node refers to the four corners of the macro unit i, and the temperature of the four nodes of each macro unit i is extracted from the structural temperature matrix T.

6. The multi-scale topology optimization method for a machine tool spindle box considering temperature constraints according to claim 1, characterized in that: Said (3) is specifically: First calculate the element stiffness matrix K of the macro element i i for: The unit stiffness matrix K of each macro unit i is i Add together to obtain the overall stiffness matrix K: Then substitute the overall stiffness matrix K into the following formula to obtain the overall displacement matrix U composed of the displacements of each node in the plane structure: KU=F m +F th Among them, F m is the mechanical load matrix of the planar structure.

7. The multi-scale topology optimization method for a machine tool spindle box considering temperature constraints according to claim 1, characterized in that: Said (4) is specifically: (4.1) First, calculate the flexibility C with respect to the macro design variable ρ M Sensitivity for: in, Represents the effect of the overall thermal stress load on the macro design variable p M Sensitivity, The macro design variable ρ represents the overall stiffness matrix for element i M sensitivity; The above overall thermal stress load has an impact on the macro design variable p M Sensitivity Calculated as: (4.2) Calculate the flexibility C for the microscopic design variable ρ m Sensitivity for: in, Represents the effect of the overall thermal stress load on the micro-design variable ρ m Sensitivity, represents the microscopic design variable ρ of the overall stiffness matrix for element i m sensitivity; The above overall thermal stress load has an impact on the micro-design variable ρ m Sensitivity Calculated as: in, Denotes the homogenized constitutive matrix D H For micro-design variables ρ m sensitivity; The above homogenized constitutive matrix D H For micro-design variables ρ m Sensitivity Calculated as: Among them, B j and u j are the strain-displacement matrix and displacement matrix of microelement j, respectively.

8. The multi-scale topology optimization method for a machine tool spindle box considering temperature constraints according to claim 1, characterized in that: Said (5) is specifically: The flexibility C is respectively related to the macro design variable ρ M and micro-design variables ρ m sensitivity to the current macro design variables ρ M and micro-design variables ρ m The two design variables are used as input parameters and input into the MMA algorithm to obtain the optimized two design variables, and the optimized macro design variable ρ M and micro-design variables ρ m Determine whether the optimization results meet the convergence conditions; If the convergence condition is met, the macro design variable ρ obtained in the last iteration is M and micro-design variables ρ m Characterization is performed as the optimal machine tool spindle box structure; If the convergence condition is not met, return to step (2) and execute each step repeatedly until the convergence condition is met.

9. The multi-scale topology optimization method for a machine tool spindle box considering temperature constraints according to claim 8, characterized in that: In the sensitivity and sensitivity The two sensitivities are input into the MMA algorithm after being filtered.

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