A spindle steady-state accurate thermal analysis method and system based on implicit thermal network

Abstract

The present invention discloses an implicit thermal network method and system for precise steady-state thermal analysis of a spindle, the method comprising the following steps: analyzing the internal heat transfer mode of the spindle to divide the thermal network nodes and form a thermal network model; determining each thermal resistance model and the bearing heat generation model, and expressing them through the steady-state temperature value of the node to be solved as the boundary condition; constructing a steady-state implicit heat flow balance equation group of the spindle; selecting the initial temperature value and the allowable error limit; solving the steady-state temperature value through the Newton method and outputting it; compared with the traditional thermal network method, the present method directly uses the steady-state temperature of the system to be solved as the boundary condition of the thermal network method for calculation, takes into account the influence of the boundary conditions on the thermal resistance and heat generation, converts the explicit linear equation group of the heat flow balance equation into an implicit nonlinear equation group, takes into account the solution efficiency of the traditional steady-state thermal network method and the solution accuracy of the transient thermal network method, and can more accurately and efficiently obtain the temperature field distribution of the spindle system to be solved.

Description

Technical Field

[0001] The present invention belongs to the field of machinery, and in particular relates to a spindle steady-state precise thermal analysis method and system based on an implicit thermal network. Background Art

[0002] The machine tool spindle is one of the core functional components of high-end CNC machine tools. Its performance determines the quality of part machining and is crucial to the machining accuracy and production efficiency of the machine tool. It is the most important factor restricting the improvement of CNC machine tool precision. Research shows that among the factors affecting machine tool machining accuracy, thermal error is the largest source of error in CNC machine tools, accounting for 40% to 70% of the total manufacturing error.

[0003] Currently, most thermal analysis of spindles is based on the finite element method (FEM) and the thermal network method (TTM). While the FEM offers high computational accuracy and reliability, it suffers from modeling complexity, low solution efficiency, and difficulty coupling with rotor mechanics models. The TTM offers higher solution efficiency and is more suitable for engineering applications requiring rapid modeling and analysis. In practical applications, the TTM is often combined with a bearing local heat generation model and a type-specific thermal resistance calculation method to ensure both accuracy and efficiency.

[0004] However, in the traditional steady-state thermal network method, since the temperature when the system reaches steady state is an unknown quantity, when calculating the thermal resistance and heat generation, the node temperature at the initial moment or the node temperature where the thermal resistance is located is often used as the boundary condition, and then the heat flow balance equation is constructed through the thermal resistance and heat generation. Because the influence of the steady-state temperature of the node on the thermal resistance and heat generation when the system reaches thermal stability is ignored, the elements of the thermal conductivity matrix G and the heat generation matrix Q formed by the thermal resistance and heat generation are constants, so the constructed heat flow balance equation group GT=Q is a linear equation group. This method is an explicit solution method. Although the solution speed is fast, due to the unreasonable boundary conditions, there is a large error between the theoretical calculated value of the steady-state temperature of the system and the actual result;

[0005] The transient thermal network method discretizes the period from the initial moment to the point of thermal stability into smaller time steps for calculation. Specifically, the system's temperature field at time t+Δt is calculated using the system's temperature field at time t as a boundary condition. The temperature difference between the two adjacent moments is considered to be less than the allowable error limit. The system is then considered to have reached thermal stability, and the calculated temperature at that moment is the temperature field at the thermally stable state. Because the boundary conditions are continuously updated during the calculation process, the transient thermal network method can produce more accurate results than the steady-state explicit thermal network method. However, due to the use of an iterative method and the large number of iterations, the solution efficiency is low when solving for the steady-state value, and the steady-state results inevitably suffer from the accumulation of truncation errors. Summary of the Invention

[0006] In order to solve the problems existing in the prior art, the present invention provides a spindle steady-state precise thermal analysis method based on implicit thermal network, which directly uses the steady-state temperature of the system to be solved as the boundary condition of the thermal network method for calculation, takes into account the influence of the boundary conditions on thermal resistance and heat generation, and takes into account the solution efficiency of the traditional steady-state thermal network method and the solution accuracy of the transient thermal network method.

[0007] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a spindle steady-state accurate thermal analysis method based on implicit thermal network, comprising:

[0008] According to the spindle model, the internal heat transfer mode of the spindle is analyzed, the thermal network nodes are divided, and the thermal network nodes are replaced by thermal resistance. A two-dimensional plane heat transfer network model based on the thermal network is established, and heat is transferred between nodes.

[0009] Simplify the thermal resistance model structure, determine the parameters of the two-dimensional planar heat transfer network model, analyze the calculation expressions of different types of thermal resistance in the spindle system based on heat conduction theory, treat the steady-state temperature value T of the spindle system as a variable, and express the relevant thermal resistance R(T) through the steady-state temperature of the node;

[0010] A bearing heat generation model is established, and the bearing heat generation is analyzed using the overall method. The heat generation is implicitly expressed as Q(T) through the steady-state temperature T.

[0011] Based on the thermal network analysis method, a steady-state heat flow balance equation group is formed;

[0012] The Newton method is used to calculate the steady-state temperature of the spindle. The initial temperature value T0 is set, and the thermal resistance R(T0) and heat generation Q(T0) at the initial temperature are calculated. The allowable error limit ε is given, and the iterative calculation is performed until |T (k+1) -T (k) |<ε,take T=T (k +1) ; Get the temperature value T when the spindle system reaches steady state.

[0013] The system thermal network nodes are divided and the model is established, and the node density is increased at key joint surfaces such as the heat source and bearings of the main shaft. At the same time, the structures in the three-dimensional main shaft model that have negligible effects on the temperature field are ignored and simplified into two-dimensional cross-sections for analysis.

[0014] Simplify the thermal resistance model structure and construct the function expression of thermal resistance R and node steady-state temperature T as follows:

[0015] The inner and outer rings of the bearing are equivalent to hollow cylinders.

[0016] The radial thermal resistance of a hollow cylinder is:

[0017]

[0018] The axial thermal resistance of a hollow cylinder is:

[0019]

[0020] Where: r2 is the outer radius of the hollow cylinder; r1 is the inner radius of the hollow cylinder; λ(T) is the thermal conductivity of the hollow cylinder, which is a function of the steady-state temperature of the node; L is the length of the hollow cylinder; d2 is the outer diameter of the hollow cylinder; d1 is the inner radius of the hollow cylinder;

[0021] Considering the principal axis as a cylinder,

[0022] Radial thermal resistance of a cylinder:

[0023]

[0024] Axial thermal resistance of the cylinder:

[0025]

[0026] Where: λ(T) is the thermal conductivity of the hollow cylinder, which is a function of the steady-state temperature node; L is the length of the cylinder; d is the outer diameter of the cylinder;

[0027] Natural convection heat transfer thermal resistance of the outer surface of the bearing seat and the outer surface of the end cover:

[0028] Where: h is the convective heat transfer coefficient, which is a function of the node steady-state temperature; A is the convective heat transfer area;

[0029] Forced convection heat transfer coefficient:

[0030]

[0031] Where: a (T) is the thermal conductivity of air, which is a function of the steady-state temperature of the node; d is the characteristic diameter; N u is the Nusselt number, which can be obtained from the Reynolds number R e and Prandtl number P r Obtain

[0032] Thermal resistance of grease and rolling element:

[0033]

[0034] Where: B is the bearing width; D w is the diameter of the bearing rolling element; λ(T) is the thermal conductivity of the grease, which is a function of the steady-state temperature of the node.

[0035] The overall method is used to analyze the heat generation of the bearing. The implicit expression of the steady-state temperature value is used. The heat generation is obtained based on the calculated power loss. Specifically,

[0036] Friction losses caused by load:

[0037] M1=f1p1d m

[0038] Where: f1 is a coefficient related to the bearing type and load; p1 is the equivalent dynamic load of the bearing; d m is the bearing pitch diameter;

[0039] Losses caused by lubrication:

[0040]

[0041] Where: f0 is a coefficient related to the bearing type and lubrication method; ν(T) is the kinematic viscosity of the grease at steady-state temperature, which is a function of steady-state temperature; n is the bearing speed; d m is the bearing pitch diameter;

[0042] Overall friction torque of the bearing:

[0043] M=M0+M1

[0044] Heat generation of bearings:

[0045] Q = 1.047 × 10 -4 M

[0046] Distribute the heat generated by the bearing evenly to the inner and outer raceways.

[0047] The formation of the thermal equilibrium differential implicit equations, according to the heat flow principle, heat flow is due to the existence of temperature gradient, the formula is as follows:

[0048]

[0049] Where: H is the heat flow; R i is the thermal impedance; T1, T2 are the node temperatures.

[0050] For general heat transfer conditions, Kirchhoff's heat flow law gives:

[0051]

[0052] Where: T0 is the temperature at the heat source; T i is the temperature of the node adjacent to the heat source; R ij is the thermal impedance between the heat source and the surrounding adjacent areas. If it is related to the temperature value, it is expressed by the steady-state temperature value of the corresponding node. Q is the heat generated by heat. If it is related to the temperature value, it needs to be expressed by the steady-state temperature value of the corresponding node.

[0053] The steady-state heat balance implicit equations are expressed in matrix form:

[0054] G(T)T=Q(T)

[0055] Where: G is the thermal conductivity matrix, which is formed by the thermal resistance R and is a function of the steady-state temperature of the node; T is the temperature matrix, which is formed by the steady-state temperature T of the node; Q is the heat generation matrix, which is formed by the heat generation Q and is a function of the steady-state temperature of the node.

[0056] The Newton method is used to calculate the spindle steady-state temperature, as follows:

[0057] Calculation equation g(T (k) )=[G (k) ]{T (k)}-{Q (k)} and the Jacobian matrix J(T (k) );

[0058] Solve for ΔT (k) The linear equation system J(T (k) )ΔT (k) =-g(T (k) );

[0059] Let T (k+1) =T (k) +ΔT (k) ;

[0060] If the absolute error of the calculated values ​​of the two adjacent steps is less than the allowable error limit |T (k+1) -T (k) |<ε, take the steady-state temperature value T=T (k+1) , and stop the calculation.

[0061] Based on the technical concept described in the present invention, a spindle steady-state precise thermal analysis system based on an implicit thermal network is also provided, which includes a spindle model construction module, a thermal resistance model expression module, a bearing heat generation calculation module, a steady-state heat flow balance equation group construction module, and a Newton iteration module;

[0062] The spindle model construction module is used to analyze the internal heat transfer mode of the spindle according to the spindle model, divide the thermal network nodes, replace the thermal network nodes with thermal resistance, and establish a two-dimensional planar heat transfer network model based on the thermal network, with heat transfer between nodes;

[0063] The thermal resistance model expression module is used to determine the parameters of the two-dimensional planar heat transfer network model based on the simplified thermal resistance model structure. It analyzes the calculation expressions of different types of thermal resistance in the spindle system based on heat conduction theory, treats the steady-state temperature value T of the spindle system as a variable, and expresses the relevant thermal resistance R(T) through the steady-state temperature of the node.

[0064] The bearing heat generation calculation module is used to analyze the bearing heat generation using the overall method based on the bearing heat generation model, and implicitly express the heat generation Q(T) through the steady-state temperature T;

[0065] The steady-state heat flow balance equations building module is used to form a steady-state heat flow balance equations based on the thermal network analysis method;

[0066] The Newton iteration module uses the Newton method to calculate the steady-state temperature of the spindle, sets the initial temperature value T0, calculates the thermal resistance R(T0) and heat generation Q(T0) at the initial temperature, gives the allowable error limit ε, and performs iterative calculations until |T (k+1) -T (k) |<ε,take T=T (k+1) ; Get the temperature value T when the spindle system reaches steady state.

[0067] The Newton iteration module solves the spindle steady-state temperature as follows:

[0068] Calculation equation g(T (k) )=[G (k) ]{T (k)}-{Q (k)} and the Jacobian matrix J(T (k) );

[0069] Solve for ΔT (k) The linear equation system J(T (k) )ΔT (k) =-g(T (k) );

[0070] Let T (k+1) =T (k) +ΔT (k) ;

[0071] If the absolute error of the calculated values ​​of the two adjacent steps is less than the allowable error limit |T (k+1) -T (k) |<ε, take the steady-state temperature value T=T (k+1) , and stop the calculation.

[0072] In addition, the present invention also provides a computer device, including a processor and a memory, the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and when the processor executes the computer executable program, it can implement the spindle steady-state precise thermal analysis method based on the implicit thermal network.

[0073] At the same time, a computer-readable storage medium can be provided, in which a computer program is stored. When the computer program is executed by a processor, the spindle steady-state precise thermal analysis method based on the implicit thermal network can be implemented.

[0074] Compared with the prior art, the present invention has at least the following beneficial effects: the present invention directly uses the unknown system steady-state temperature T as the boundary condition of the steady-state thermal network method, converts the thermal resistance and heat generation into functions with T as the independent variable. Accordingly, the heat flow balance equation is also converted from the explicit linear equation group GT=Q of the traditional thermal network method to the implicit nonlinear equation group G(T)T=Q(T). The boundary condition of the method described in the present invention is the steady-state temperature of the system to be determined, and there is no error caused by unreasonable boundary conditions. Therefore, it is an accurate thermal network solution method; the advantage of the present invention is that when using the thermal network method, the need to assume or experimentally measure the steady-state temperature when calculating the thermal resistance and heat generation related to temperature and the truncation error existing in the transient thermal network method are avoided. The heat flow equation is expressed in an implicit form through the steady-state temperature value T, and can be directly solved by the Newton method. Compared with the traditional steady-state thermal network method, the solution accuracy is improved, and compared with the transient thermal network method, the accumulation of truncation errors is avoided, taking into account the advantages of high solution efficiency of the traditional steady-state thermal network method and high solution accuracy of the transient thermal network method. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 This is a flow chart of the spindle steady-state implicit algorithm of the present invention.

[0076] Figure 2 This is a schematic diagram of the main axis node division of the present invention.

[0077] Figure 3 Schematic diagram of the spindle thermal network model of the present invention.

[0078] Figure 4 Numerically evaluate results for multiple methods. DETAILED DESCRIPTION

[0079] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0080] In the description of the present invention, it is to be understood that the terms “include” and “comprise” indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0081] The present invention provides a spindle steady-state precise thermal analysis method based on an implicit thermal network. This method directly uses the unknown system steady-state temperature T as the boundary condition of the steady-state thermal network method, converting thermal resistance and heat generation into functions with T as the independent variable. Accordingly, the heat flow balance equation is also converted from the explicit linear equation group GT=Q of the traditional thermal network method to the implicit nonlinear equation group G(T)T=Q(T). The method specifically includes the following steps:

[0082] Step 1: According to the spindle model, analyze the internal heat transfer mode of the spindle, divide the thermal network nodes, and establish a two-dimensional plane heat transfer network model based on the thermal network. Figure 2 As shown, it is considered that the heat source is concentrated at the nodes;

[0083] Step 2: Based on the thermal network model, simplify the thermal resistance model structure, determine the network parameters, analyze the calculation expressions of different types of thermal resistance in the shaft system based on heat conduction theory, treat the steady-state temperature value T of the spindle system as a variable, and express the relevant thermal resistance through the steady-state temperature of the node;

[0084] Step 3: Establish a bearing heat generation model, use the overall method to analyze the bearing heat generation and implicitly express the heat generation through the steady-state temperature T;

[0085] Step 4: Based on the thermal network method, a steady-state heat flow balance implicit equation group is formed;

[0086] Step 5: Use Newton's method to calculate the steady-state temperature of the spindle, select the initial temperature value T0, calculate R(T0) and Q(T0), give the allowable error limit ε, and perform iterative calculation until |T (k+1) -T (k) |<ε,take T=T (k+1) ,stop;

[0087] Step six: output the temperature value T of the spindle system when it reaches a steady state.

[0088] In step 1, the system thermal network nodes are divided and the model is established. The node density is appropriately increased at key interfaces such as the spindle's heat source and bearings. At the same time, small structures such as fillets and screw holes in the 3D spindle model that have little impact on the temperature field are ignored and simplified to a 2D cross-section for analysis.

[0089] In step 2, the thermal resistance model structure is simplified, and the thermal resistance is implicitly expressed through the steady-state temperature of the node. The inner and outer rings of the bearing are equivalent to hollow cylinders.

[0090] Radial thermal resistance of a hollow cylinder:

[0091]

[0092] Axial thermal resistance of a hollow cylinder:

[0093]

[0094] Where:

[0095] r2—outer radius of hollow cylinder / mm;

[0096] r1—inner radius of the hollow cylinder / mm;

[0097] λ(T)—Hollow cylinder thermal conductivity / W·(mm·℃) -1 , is a function of the node steady-state temperature;

[0098] L—hollow cylinder length / mm;

[0099] d2—outer diameter of the hollow cylinder / mm;

[0100] d1—Inner radius of the hollow cylinder / mm.

[0101] Think of the main axis as a cylinder.

[0102] Radial thermal resistance of a cylinder:

[0103]

[0104] Axial thermal resistance of the cylinder:

[0105]

[0106] Where:

[0107] λ(T)—thermal conductivity of hollow cylinder / W·(mm·℃) -1 , is the function of the steady-state temperature node;

[0108] L—cylinder length / mm;

[0109] d—outer diameter of cylinder / mm.

[0110] Natural convection heat transfer thermal resistance of the outer surface of the bearing seat and the outer surface of the end cover:

[0111]

[0112] Where:

[0113] h—Convection heat transfer coefficient / W·(mm 2 ℃) -1 , is a function of the node steady-state temperature;

[0114] A—Convection heat transfer area / mm 2 .

[0115] Forced convection heat transfer coefficient:

[0116]

[0117] Where:

[0118] λ a (T)—heat conductivity of air / W·(m·K) -1 , is a function of the node steady-state temperature;

[0119] d—characteristic diameter / m;

[0120] N u —Nusel number, which can be obtained from the Reynolds number R e and Prandtl number P r Obtain

[0121] Thermal resistance of grease and rolling element:

[0122]

[0123] Where:

[0124] B—bearing width / mm;

[0125] D w —Diameter of bearing rolling element / mm;

[0126] λ(T)—is the thermal conductivity of the grease, a function of the steady-state temperature of the node.

[0127] In step 3, the bearing heat generation is analyzed using an integral approach, with an implicit expression of the steady-state temperature. The heat generation is obtained by calculating the power loss.

[0128] M1=f1p1d m

[0129] Where:

[0130] f1 - coefficient related to bearing type and load;

[0131] p1—equivalent dynamic load of bearing / N;

[0132] d m —Bearing pitch circle diameter / mm.

[0133] Losses caused by lubrication:

[0134]

[0135] Where:

[0136] f0—coefficient related to bearing type and lubrication method;

[0137] v(T)—The kinematic viscosity of grease at steady-state temperature, which is a function of steady-state temperature.

[0138] n—bearing speed, r / min;

[0139] d m —Bearing pitch circle diameter / mm.

[0140] Overall friction torque of the bearing:

[0141] M=M0+M1

[0142] Heat generation of bearings:

[0143] Q=1.047×10- 4 M

[0144] Distribute the heat generated by the bearing evenly to the inner and outer raceways.

[0145] In step 4, the implicit differential equations of thermal equilibrium are formed.

[0146] According to the thermal network method, the matrix form of the steady-state thermal equilibrium differential implicit equations is formed:

[0147] [G]{T}={Q}

[0148] Where:

[0149] [G]—thermal conductivity matrix, which is formed by thermal resistance and is therefore also a function of the steady-state temperature of the node to be determined;

[0150] {T}—temperature matrix, which is formed by the steady-state temperature of the node to be calculated;

[0151] {Q}—heat generation matrix, which is formed by the amount of heat generated and is therefore also a function of the steady-state temperature of the node to be determined.

[0152] Step 5: Use Newton's method to solve. First, select the temperature initial value T0, use the temperature iteration initial value to calculate the thermal resistance R(T0) and heat generation Q(T0), and give the allowable error limit ε, and iterate the solution of the nonlinear equation.

[0153] (1) Calculation equation g(T (k) )=[G (k) ]{T (k)}-{Q (k)} and the Jacobian matrix J(T (k) );

[0154] (2) Solve for ΔT (k) The linear equation system J(T (k) )ΔT (k) =-g(T (k) );

[0155] (2) Let T (k+1) =T (k) +ΔT (k);

[0156] (4) If the absolute error of the calculated values ​​of the two adjacent steps is less than the allowable error limit |T (k+1) -T (k) |<ε, take the steady-state temperature value T=T (k+1) , and stop the calculation.

[0157] Step seven: output the temperature when the spindle system temperature field reaches a steady state.

[0158] Through the above process, the numerical calculation results are as follows Figure 4 By comparing the calculated results of the steady-state temperature of the bearing seat at different speeds with the experimental results, it can be found that the implicit thermal network method proposed in this invention is in good agreement with the experimental results and has a smaller error than the traditional steady-state thermal network method and the transient thermal network method.

[0159] And as shown in Table 1, this method has high solution efficiency while ensuring solution accuracy.

[0160] Table 1

[0161] Traditional Steady-State Thermal Network Method Transient Thermal Network Method Method of the present invention Calculation time / s 0.108 240.29 0.209

[0162] The present invention provides a spindle steady-state precise thermal analysis method based on an implicit thermal network. This method converts thermal resistance and heat generation into functions with T as the independent variable by directly taking the unknown system steady-state temperature T as the boundary condition of the steady-state thermal network method. Correspondingly, the heat flow balance equation is also converted from the explicit linear equation group GT=Q of the traditional thermal network method to the implicit nonlinear equation group G(T)T=Q(T). Since the boundary condition of this method is the steady-state temperature of the system to be determined, there is no error caused by unreasonable boundary conditions, so it is an accurate thermal network solution method. In addition, although the heat flow balance equation of this method is a nonlinear equation group that needs to be solved by the Newton method, the solution efficiency is high and a numerical solution can be obtained with a small number of iterations. However, the numerical differentiation method of the transient thermal network method has many iterative steps, which not only leads to the accumulation of truncation errors, but also has a lower solution efficiency than the Newton method. Therefore, this method can avoid the shortcomings of unreasonable boundary condition setting of the existing thermal network steady-state algorithm and low efficiency and large cumulative error of the iterative solution of the transient thermal network method. Compared with the traditional method, it takes into account the solution efficiency of the traditional steady-state thermal network method and the solution accuracy of the transient thermal network method, and can obtain the temperature field distribution of the spindle system to be solved more accurately and efficiently, refer to Table 2.

[0163] Table 2

[0164]

[0165] Based on the technical concept described in the present invention, a spindle steady-state precise thermal analysis system based on an implicit thermal network is also provided, which includes a spindle model construction module, a thermal resistance model expression module, a bearing heat generation calculation module, a steady-state heat flow balance equation group construction module, and a Newton iteration module;

[0166] The spindle model construction module is used to analyze the internal heat transfer mode of the spindle according to the spindle model, divide the thermal network nodes, replace the thermal network nodes with thermal resistance, and establish a two-dimensional planar heat transfer network model based on the thermal network, with heat transfer between nodes;

[0167] The thermal resistance model expression module is used to determine the parameters of the two-dimensional planar heat transfer network model based on the simplified thermal resistance model structure. It analyzes the calculation expressions of different types of thermal resistance in the spindle system based on heat conduction theory, treats the steady-state temperature value T of the spindle system as a variable, and expresses the relevant thermal resistance R(T) through the steady-state temperature of the node.

[0168] The bearing heat generation calculation module is used to analyze the bearing heat generation using the overall method based on the bearing heat generation model, and implicitly express the heat generation Q(T) through the steady-state temperature T;

[0169] The steady-state heat flow balance equations building module is used to form a steady-state heat flow balance equations based on the thermal network analysis method;

[0170] The Newton iteration module uses the Newton method to calculate the steady-state temperature of the spindle, sets the initial temperature value T0, calculates the thermal resistance R(T0) and heat generation Q(T0) at the initial temperature, gives the allowable error limit ε, and performs iterative calculations until |T (k+1) -T (k) |<ε,take T=T (k+1) ; Get the temperature value T when the spindle system reaches steady state.

[0171] The Newton iteration module solves the spindle steady-state temperature as follows:

[0172] Calculation equation g(T (k) )=[G (k) ]{T (k)}-{Q (k)} and the Jacobian matrix J(T (k) );

[0173] Solve for ΔT (k) The linear equation system J(T (k) )ΔT (k) =-g(T (k) );

[0174] Let T (k+1) =T (k) +ΔT (k) ;

[0175] If the absolute error of the calculated values ​​of the two adjacent steps is less than the allowable error limit |T (k+1) -T (k) |<ε, take the steady-state temperature value T=T (k+1) , and stop the calculation.

[0176] In addition, the present invention can also provide a computer device, including a processor and a memory, the memory is used to store a computer executable program, the processor reads part or all of the computer executable program from the memory and executes it, and when the processor executes part or all of the computer executable program, it can implement the spindle steady-state precise thermal analysis method based on implicit thermal network described in the present invention.

[0177] On the other hand, the present invention provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, the spindle steady-state precise thermal analysis method based on implicit thermal network described in the present invention can be implemented.

[0178] The computer device may be a laptop computer, a desktop computer or a workstation.

[0179] The processor can be a central processing unit (CPU), a graphics processing unit (GPU) / digital signal processor (DSP), an application-specific integrated circuit (ASIC), or an off-the-shelf field programmable gate array (FPGA).

[0180] The memory of the present invention may be an internal storage unit of a laptop computer, desktop computer or workstation, such as a memory or a hard disk; or an external storage unit, such as a mobile hard disk or a flash memory card.

[0181] Computer-readable storage media may include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. Computer-readable storage media may include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSD) or optical disks, etc. Among them, random access memory may include resistance random access memory (ReRAM) and dynamic random access memory (DRAM).

[0182] The above content is only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A spindle steady-state accurate thermal analysis method based on implicit thermal network, characterized in that: include: According to the spindle model, the internal heat transfer mode of the spindle is analyzed, the thermal network nodes are divided, and the thermal network nodes are replaced by thermal resistance. A two-dimensional plane heat transfer network model based on the thermal network is established, and heat is transferred between nodes. Simplify the thermal resistance model structure, determine the parameters of the two-dimensional plane heat transfer network model, analyze the calculation expressions of different types of thermal resistance in the spindle system according to the heat conduction theory, and convert the steady-state temperature value of the spindle system into Treated as a variable and expressing the relevant thermal resistance through the node steady-state temperature ; Establish a bearing heat generation model, use the overall method to analyze the bearing heat generation, and use the steady-state temperature Implicit expression of heat generation ; Based on the thermal network analysis method, the steady-state heat flow balance equations are formed; the steady-state heat balance implicit equations are expressed in matrix form: in: is the thermal conductivity matrix, and the thermal resistance Formation, is a function of the steady-state temperature of the node; is the temperature matrix, which is the node steady-state temperature T form; is the heat generation matrix, which is composed of Formation, is a function of the steady-state temperature of the node; Use Newton's method to calculate the spindle steady-state temperature and set the initial temperature value , calculate the thermal resistance at this initial temperature and heat generation , given the allowable error limit , and iterative calculation is performed until , k To set the number of iterations, take ; Get the temperature value when the spindle system reaches steady state ; Use Newton's method to calculate the spindle steady-state temperature, as follows: Calculation equation With the Jacobian matrix ; Solve about The linear equations ; make ; If the absolute error of the calculated values ​​of the two adjacent steps is less than the allowable error limit , take the steady-state temperature value , and stop the calculation.

2. The spindle steady-state precise thermal analysis method based on implicit thermal network according to claim 1 is characterized in that: The system thermal network nodes are divided and the model is established, and the node density is increased at the heat source of the main shaft and the key joint surface of the bearing. At the same time, the structures in the three-dimensional main shaft model that have negligible effects on the temperature field are ignored and simplified into two-dimensional cross-sections for analysis.

3. The spindle steady-state precise thermal analysis method based on implicit thermal network according to claim 1 is characterized in that: Simplify the thermal resistance model structure and build thermal resistance and node steady-state temperature The function expression is as follows: The inner and outer rings of the bearing are equivalent to hollow cylinders. The radial thermal resistance of a hollow cylinder is: The axial thermal resistance of a hollow cylinder is: ； Where: is the outer radius of the hollow cylinder; is the inner radius of the hollow cylinder; is the thermal conductivity of the hollow cylinder, which is a function of the steady-state temperature of the node; is the length of the hollow cylinder; is the outer diameter of the hollow cylinder; is the inner radius of the hollow cylinder; Considering the principal axis as a cylinder, Radial thermal resistance of a cylinder: Axial thermal resistance of the cylinder: Where: is the thermal conductivity of the hollow cylinder, which is a function of the steady-state temperature node; is the length of the cylinder; is the outer diameter of the cylinder; Natural convection heat transfer thermal resistance of the outer surface of the bearing seat and the outer surface of the end cover: Where: is the convective heat transfer coefficient, which is a function of the steady-state temperature of the node; ——Convection heat transfer area; Forced convection heat transfer coefficient: Where: ( T ) is the thermal conductivity of air, which is a function of the steady-state temperature of the node; is the characteristic diameter; is the Nusselt number, which can be obtained from the Reynolds number and Prandtl number Obtain ; Thermal resistance of grease and rolling element: Where: is the bearing width; is the diameter of the bearing rolling element; is the thermal conductivity of the grease as a function of the steady-state temperature of the node.

4. The spindle steady-state precise thermal analysis method based on implicit thermal network according to claim 1 is characterized in that: The overall method is used to analyze the heat generation of the bearing. The implicit expression of the steady-state temperature value is used. The heat generation is obtained based on the calculated power loss. Specifically, Friction losses caused by load: Where: It is a coefficient related to the bearing type and the load it bears; is the equivalent dynamic load of the bearing; is the bearing pitch diameter; Losses caused by lubrication: Where: It is a coefficient related to bearing type and lubrication method; is the kinematic viscosity of the grease at steady-state temperature, a function of steady-state temperature, is the bearing speed; is the bearing pitch diameter; Overall friction torque of the bearing: Heat generation of bearings: Distribute the heat generated by the bearing evenly to the inner and outer raceways.

5. The spindle steady-state precise thermal analysis method based on implicit thermal network according to claim 1 is characterized in that: The formation of the thermal equilibrium differential implicit equations, according to the heat flow principle, heat flow is due to the existence of temperature gradient, the formula is as follows: Where: is the heat flow; is the thermal impedance; is the node temperature; For general heat transfer conditions, Kirchhoff's heat flow law gives: Where: is the temperature at the heat source; is the temperature of the node adjacent to the heat source; is the thermal impedance between the heat source and the surrounding adjacent areas. If it is related to the temperature value, it is expressed by the steady-state temperature value of the corresponding node; For heat generation, if it is related to the temperature value, it needs to be expressed through the steady-state temperature value of the corresponding node.

6. A spindle steady-state precise thermal analysis system based on implicit thermal network, characterized in that: It includes the spindle model construction module, thermal resistance model expression module, bearing heat generation calculation module, steady-state heat flow balance equation group construction module and Newton iteration module; The spindle model construction module is used to analyze the internal heat transfer mode of the spindle according to the spindle model, divide the thermal network nodes, replace the thermal network nodes with thermal resistance, and establish a two-dimensional planar heat transfer network model based on the thermal network, with heat transfer between nodes; The thermal resistance model expression module is used to determine the parameters of the two-dimensional plane heat transfer network model based on the simplified thermal resistance model structure, analyze the calculation expressions of different types of thermal resistance in the spindle system based on the heat conduction theory, and convert the steady-state temperature value of the spindle system into Treated as a variable and expressing the relevant thermal resistance through the node steady-state temperature ; The bearing heat generation calculation module is used to analyze the bearing heat generation using the overall method according to the bearing heat generation model, and Implicit expression of heat generation ; The steady-state heat flow balance equations building module is used to form a steady-state heat flow balance equation system based on the thermal network analysis method; the steady-state heat balance implicit equation system is expressed in matrix form: in: is the thermal conductivity matrix, and the thermal resistance Formation, is a function of the steady-state temperature of the node; is the temperature matrix, which is the node steady-state temperature T form; is the heat generation matrix, which is composed of Formation, is a function of the steady-state temperature of the node; The Newton iteration module uses the Newton method to calculate the spindle steady-state temperature and set the initial temperature value. , calculate the thermal resistance at this initial temperature and heat generation , given the allowable error limit , and iterative calculation is performed until ,Pick ; Get the temperature value when the spindle system reaches steady state ; Use Newton's method to calculate the spindle steady-state temperature, as follows: Calculation equation With the Jacobian matrix ; Solve about The linear equations ; make ; If the absolute error of the calculated values ​​of the two adjacent steps is less than the allowable error limit , take the steady-state temperature value , and stop the calculation.

7. A computer device, characterized in that: It includes a processor and a memory, the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and when the processor executes the computer executable program, it can implement the spindle steady-state precise thermal analysis method based on implicit thermal network as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that A computer program is stored in the computer-readable storage medium. When the computer program is executed by a processor, the spindle steady-state precise thermal analysis method based on an implicit thermal network as claimed in any one of claims 1 to 5 can be implemented.

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