Modeling method of spindle axial thermal error model based on machine tool power

Abstract

The present invention discloses a spindle axial thermal error modeling method based on machine tool power, comprising the following steps: step one: constructing a theoretical cutting power model; step two: considering the influence of axial thermal error on cutting power on the basis of the theoretical cutting power model, and constructing a cutting power model considering thermal error; step three: constructing a support vector regression machine model using the constructed cutting power model considering thermal error; step four: optimizing the parameters of the support vector regression machine model to obtain the spindle axial thermal error model. The spindle axial thermal error modeling method based on machine tool power of the present invention can identify the spindle axial thermal error through the change of machine tool power.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical error analysis, and specifically relates to a spindle axial thermal error modeling method based on machine tool power. Background Art

[0002] Machine tool errors mainly include geometric errors and thermal errors, among which thermal errors account for as much as 60% to 70%. Thermal errors are caused by the combined effects of internal and external heat sources on the components of the machine tool during operation, forming a complex, non-uniform, and non-steady-state temperature field, which leads to thermal deformation of the entire machine and its components, thus affecting the corresponding position of the machine tool tool and the workpiece being processed. Therefore, accurate mathematical modeling and compensation of spindle thermal errors are the key to improving the accuracy of CNC machine tools.

[0003] At present, thermal error modeling mainly involves establishing a mapping relationship between temperature points and thermal errors, and using temperature changes to predict the thermal errors of machine tools. Although the thermal error modeling method based on machine tool temperature can be applied to corresponding error compensation, it also has some disadvantages: (1) There is no unified standard for the selection of temperature sensitive points, and the collinearity of temperature sensitive points will affect the robustness of the thermal error prediction model; (2) The temperature sensitive points will change, which will seriously affect the robustness of the model prediction. Summary of the invention

[0004] In view of this, an object of the present invention is to provide a spindle axial thermal error modeling method based on machine tool power, which can identify the spindle axial thermal error through machine tool power changes.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for modeling a spindle axial thermal error model based on machine tool power comprises the following steps:

[0007] Step 1: Construct theoretical cutting power model;

[0008] Step 2: Based on the theoretical cutting power model, the influence of axial thermal error on cutting power is considered, and a cutting power model considering thermal error is constructed;

[0009] Step 3: Use the cutting power model considering thermal error to build a support vector regression model;

[0010] Step 4: Optimize the parameters of the support vector regression model to obtain the spindle axial thermal error model.

[0011] Furthermore, in step 1, the method for constructing the theoretical cutting power model is:

[0012] 11) Construct the power model of micro-element cutting edge:

[0013] dP cutting (θ,z)=|dP n |+|dP f |=|(K te dS+K tc s t sinψdz)·2πnr|+|(dF t sinψ+dF r cosψ)·f|

[0014] Among them, dP cutting (θ,z) is the power of the micro-element cutting edge; θ represents the position angle of the micro-element cutting edge at the tool tip; z represents the position of the micro-element cutting edge in the tool axial direction; dP n Indicates the power consumed by the tool rotation at the micro-element cutting edge; dP f Indicates the power consumed by the tool feed at the micro-element cutting edge; K te K represents the tangential plowing force cutting coefficient of the micro-element cutting edge; tc represents the tangential shear force cutting coefficient of the micro-element cutting edge; dS represents the length of the micro-element cutting edge; dz represents the axial thickness of the micro-element cutting edge; s t represents the feed per tooth; ψ represents the micro-element cutting edge position angle; n represents the cutting speed; r represents the tool radius; dF t Indicates the tangential cutting force of the micro-element cutting edge; dF r represents the radial cutting force of the micro-element cutting edge; f represents the feed rate, and f = n·s t ·M, M is the number of teeth;

[0015] 12) Construct the instantaneous power model of the cutting edge based on the power model of the micro-element cutting edge:

[0016]

[0017] P cutting Indicates the instantaneous cutting power of the cutting edge; a p Indicates cutting depth;

[0018] 13) Construct the rate model of the cutting edge based on the instantaneous power model of the cutting edge:

[0019]

[0020] in, Indicates the average cutting power of the cutting edge in one cycle; φ p Indicates the tooth angle of the tool.

[0021] Furthermore, in step 2, the cutting power model considering thermal error is constructed as follows:

[0022]

[0023] in, It represents the average cutting power of the cutting edge in one cycle after considering the thermal error; ΔZ represents the additional cutting depth caused by the elongation of the tool in the Z direction due to the axial thermal error of the spindle.

[0024] Furthermore, in step 3, the method for constructing the support vector regression model is:

[0025] According to the principle of structural risk minimization, the function modeling problem of support vector regression machine is to find the objective function f(x) with the minimum risk:

[0026] f(x,ω)=ωφ(x)+b

[0027] Among them, ω is the weight vector; φ(x) represents the corresponding value of x mapped to the high-dimensional feature space; x=[Δp,n,s t ] represents the input vector, Δp represents the change in the total power of the machine tool before and after the thermal error occurs; b is the threshold value;

[0028] Introducing the insensitive function ε, the constrained optimization problem is expressed as:

[0029]

[0030] Where C represents the penalty factor; l represents the number of support vector machines; ξ i and represents the slack variable; y i represents the target value; φ(x i ) represents the corresponding value of x mapped to the high-dimensional feature space;

[0031] Introducing the Lagrangian function transforms it into a dual problem:

[0032]

[0033] in, and α i represents the Lagrange multiplier; α j is not equal to and α i Variables;

[0034] The Lagrange coefficients are solved by solving the dual convex quadratic programming problem of the constrained optimization problem:

[0035]

[0036] In the formula represents the optimal solution; φ(x i )φ(x j)=K(x i ,x j ); K(x i ,x j ) is the kernel function that satisfies the Mercer condition;

[0037] Depend on Find The decision function is constructed as:

[0038]

[0039] Rewrite the decision function as a support vector regression model:

[0040]

[0041] in, is the coefficient; x i is the support vector; K(x i ,x) is the kernel function, and l is the number of support vector machines.

[0042] Furthermore, the kernel function uses the Gaussian radial basis kernel function:

[0043] K(x,x i ) = exp(-||x i -x|| 2 / σ 2 )

[0044] Among them, σ is the width parameter of the function, which controls the radial range of the function, denoted by 1 / σ 2 is the parameter g.

[0045] Furthermore, in the step 4, the parameters g and C of the support vector regression machine model are optimized by using a network traversal parameter search algorithm or a cross-validation method to obtain the spindle axial thermal error model.

[0046] The beneficial effects of the present invention are:

[0047] The present invention provides a modeling method for a spindle axial thermal error model based on machine tool power. Based on the characteristic that the spindle axial thermal error causes the tool to elongate in the axial direction to produce additional cutting depth, thereby causing a change in the cutting power of the machine tool, on the basis of a theoretical cutting power model, after considering the spindle axial thermal error, a cutting power model considering the thermal error is obtained. The cutting power model considering the thermal error is constructed as a support vector regression machine model using a support vector regression machine. At the same time, the parameters of the support vector regression machine model are optimized to construct a spindle axial thermal error model, which reflects the mapping relationship between the spindle axial thermal error and the change in the cutting power of the machine tool. The thermal error of the spindle axis can be identified by using the before and after changes in the cutting power of the machine tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0049] Figure 1 It is a flow chart of an embodiment of a method for modeling a spindle axial thermal error model based on machine tool power according to the present invention;

[0050] Figure 2 Schematic diagram of the additional cutting depth of the heat-conducting tool due to the spindle axial thermal error;

[0051] Figure 3 It is the power distribution diagram of non-cutting state and cutting state;

[0052] Figure 4 It is a schematic diagram of the milling process of the end mill;

[0053] Figure 5 This is the power distribution diagram of the cutting state considering thermal error. DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0055] like Figure 1 As shown, the spindle axial thermal error modeling method based on machine tool power in this embodiment includes the following steps:

[0056] Step 1: Construct a theoretical cutting power model.

[0057] Among the total error sources of machine tools, geometric errors and thermal errors account for the majority. Therefore, this embodiment only considers the influence of geometric errors and thermal errors on cutting processing. Figure 2 As shown in the figure, in actual machining, the tool tip will deviate from the theoretical position due to the influence of the machine tool geometric error. Because the geometric error does not change with time, after the machine tool has been working for a long time, the axial thermal elongation error of the spindle caused by the thermal deformation of the machine tool will cause the tool to elongate in the Z direction to produce an additional cutting depth ΔZ on the basis of the geometric error, thereby causing additional power consumption.

[0058] The power of a CNC machine tool in cutting state includes the net cutting power of the CNC machine tool used to remove material, also known as the material removal power P. cutting , based on the cutting power studied by the micro-element cutting force theory, specifically refers to the net cutting power of CNC machine tools used only for removing material. The power of CNC machine tools in the cutting state also includes the power P in the non-cutting state under this working condition. idle , additional load power loss (including spindle and feed axis) P a-n , P a -f, such as Figure 3 shown.

[0059] Specifically, the construction method of the theoretical cutting power model is:

[0060] 11) Construct the power model of micro-element cutting edge:

[0061] The milling process of flat cutter is as follows Figure 4 As shown in the figure, the tool is divided into N layers along the tool axis, and the micro-element cutting force on the cutting edge can be decomposed into tangential cutting force, radial cutting force and axial cutting force; the micro-element cutting force model is:

[0062]

[0063] Among them, dF t ,dF r ,dF a They represent the tangential cutting force, radial cutting force and axial cutting force of the micro-element cutting edge respectively; K te ,K re ,K ae They represent the tangential, radial and secondary normal plowing force cutting coefficients of the micro-element cutting edge, K tc ,K rc ,K ac They represent the shear cutting coefficients of the micro-element cutting edge in the tangential, radial and secondary normal directions respectively; θ represents the position angle of the micro-element cutting edge at the tool tip; z represents the position of the micro-element cutting edge in the tool axial direction; dS and dz represent the length of the micro-element cutting edge and the axial thickness of the micro-element chip edge respectively; ψ represents the position angle of the micro-element cutting edge; s t represents the feed per tooth. Then:

[0064] ψ=θ+(i-1)φ p -ztan(i0) / r

[0065] Where i0 represents the helix angle; φ p represents the tooth angle of the tool, and φ p =2π / M, M is the number of teeth; i represents the i-th tooth; r is the tool radius.

[0066] The instantaneous cutting power of the micro-element cutting edge can be calculated as the power due to tool rotation (dP n ) and tool feed (dP f ) is the sum of the cutting power generated by the cutting edge. In the tool rotation motion, dFr and dFa are perpendicular to the cutting speed, so they do not consume power, while dFt is consistent with the cutting speed and needs to consume power. Therefore, the power consumed by the micro-element cutting edge in the tangential, radial and axial directions is:

[0067]

[0068] Among them, dPn,t 、dP n,r and dP n,a They respectively represent the power consumed by the micro-element cutting edge in the tangential, radial and axial directions when the tool rotates; V is the cutting speed, V=2πnr, n is the cutting speed.

[0069] Then, the power consumed by the micro-element cutting edge due to tool rotation can be expressed as:

[0070] dP n +dF t ·V

[0071] Similarly, the power consumed by tool feed is:

[0072]

[0073] Among them, dP f,t 、dP f,r and dP f,a They represent the power consumed by the micro-element cutting edge in the tangential, radial and axial directions when the tool is fed; f is the feed speed, f = n·s t ·M.

[0074] Then, the power consumed by the micro-element cutting edge due to tool feed can be expressed as:

[0075] dP f =dF t cosψ·f+dF r sinψ·f

[0076] Then, the power model of the micro-element cutting edge is constructed as follows:

[0077] dP cutting (θ,z)=|dP n |+|dP f |=|(K te dS+K tc s t sinψdz)·2πnr|+|(dF t sinψ+dF r cosψ)·f|

[0078] Among them, dP cutting (θ,z) is the power of the micro-element cutting edge; θ represents the position angle of the micro-element cutting edge at the tool tip; z represents the position of the micro-element cutting edge in the tool axial direction; dP n Indicates the power consumed by the tool rotation at the micro-element cutting edge; dP f Indicates the power consumed by the tool feed at the micro-element cutting edge; K te K represents the tangential plowing force cutting coefficient of the micro-element cutting edge; tcrepresents the tangential shear force cutting coefficient of the micro-element cutting edge; dS represents the length of the micro-element cutting edge; dz represents the axial thickness of the micro-element cutting edge; s t represents the feed per tooth; ψ represents the micro-element cutting edge position angle; n represents the cutting speed; r represents the tool radius; dF t Indicates the tangential cutting force of the micro-element cutting edge; dF r represents the radial cutting force of the micro-element cutting edge; f represents the feed rate, and f = n·s t ·M, M is the number of teeth;

[0079] 12) Construct the instantaneous cutting power model of the cutting edge based on the power model of the micro-element cutting edge:

[0080]

[0081] P cutting Indicates the instantaneous cutting power of the cutting edge; a p Indicates cutting depth;

[0082] 13) Construct the rate model of the cutting edge based on the instantaneous power model of the cutting edge:

[0083]

[0084] in, Indicates the average cutting power of the cutting edge in one cycle; φ p Indicates the tooth angle of the tool.

[0085] Step 2: Based on the theoretical cutting power model, the influence of axial thermal error on cutting power is considered, and a cutting power model considering thermal error is constructed.

[0086] The axial thermal expansion of the spindle is as follows: Figure 2 As shown in the figure, the axial thermal expansion can be regarded as an additional cutting depth ΔZ on the basis of the theoretical cutting depth. Therefore, when creating a cutting power model considering thermal error, due to the influence of the spindle axial thermal expansion error, the tool cutting depth is greater than the theoretical cutting depth a. p On the basis of p +ΔZ). Then the cutting power model considering thermal error is constructed as follows:

[0087]

[0088] in, It represents the average cutting power of the cutting edge in one cycle after considering the thermal error; ΔZ represents the additional cutting depth caused by the elongation of the tool in the Z direction due to the axial thermal error of the spindle.

[0089] Under the same processing conditions, the cutting power will increase after thermal error occurs, such as Figure 5As shown in the figure, by comparing the change in the total power of the machine tool before and after the thermal error, the additional power consumption ΔP due to the thermal error can be obtained:

[0090] ΔP=P2-P1

[0091] Among them, P2 represents the total power of the machine tool after the thermal error occurs; P1 represents the total power of the machine tool before the thermal error occurs.

[0092] Step 3: Use the constructed cutting power model considering thermal error to build a support vector regression machine model.

[0093] Based on the influence of thermal error on cutting power, combined with the main influencing factors on cutting power: cutting speed (n) and feed per tooth (s t ), a spindle axial thermal error identification model based on machine tool power was established. The model takes the spindle axial thermal elongation error (Δz) as the dependent variable, the machine tool power change value before and after the thermal error (ΔP), the cutting speed (n), the feed per tooth (s t ) is the independent variable.

[0094] Support Vector Regression (SVR) is based on the VC dimension of statistical learning theory and adopts the principle of structural risk minimization. It not only has a simple structure, but also can effectively solve problems such as model selection and under-learning, small samples, nonlinearity, local optimality and dimensionality disaster, and has strong generalization ability.

[0095] Specifically, the construction method of the support vector regression model is:

[0096] According to the principle of structural risk minimization, the function modeling problem of support vector regression machine is to find the objective function f(x) with the minimum risk:

[0097] f(x,ω)=ωφ(x)+b

[0098] Among them, ω is the weight vector; φ(x) represents the corresponding value of x mapped to the high-dimensional feature space; x=[Δp,n,s t ] represents the input vector, Δp represents the change in the total power of the machine tool before and after the thermal error occurs; b is the threshold value;

[0099] Introducing the insensitive function ε, the constrained optimization problem is expressed as:

[0100]

[0101] Where C represents the penalty factor; l represents the number of support vector machines; ξ i and i * represents the slack variable; y i represents the target value; φ(xi ) represents the corresponding value of x mapped to the high-dimensional feature space;

[0102] Introducing the Lagrangian function transforms it into a dual problem:

[0103]

[0104] in, and α i represents the Lagrange multiplier; α j is not equal to and α i Variables;

[0105] The Lagrange coefficients are solved by solving the dual convex quadratic programming problem of the constrained optimization problem:

[0106]

[0107] In the formula represents the optimal solution; φ(x i )φ(x j )=K(x i ,x j ); K(x i ,x j ) is the kernel function that satisfies the Mercer condition;

[0108] Depend on Find The decision function is constructed as:

[0109]

[0110] Rewrite the decision function as a support vector regression model:

[0111]

[0112] in, is the coefficient; x i is the support vector; K(x i ,x) is the kernel function, and l is the number of support vector machines.

[0113] Compared with other kernel functions, Gaussian radial basis kernel function modeling has the advantages of fast training speed and high accuracy. The kernel function of this embodiment adopts Gaussian radial basis kernel function:

[0114] K(x,x i ) = exp(-||x i -x|| 2 / σ 2 )

[0115] Among them, σ is the width parameter of the function, which controls the radial range of the function, denoted by 1 / σ 2 is the parameter g.

[0116] Step 4: Optimize the parameters of the support vector regression model to obtain the spindle axial thermal error model.

[0117] The support vector machine parameter selection method generally includes a network traversal-based parameter search algorithm and a cross-validation method, etc. The cross-validation method is a commonly used validation method in machine learning. This embodiment uses the cross-validation method to optimize the model parameters.

[0118] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A spindle axial thermal error modeling method based on machine tool power, characterized by: The steps include: Step 1: Construct theoretical cutting power model; Step 2: Based on the theoretical cutting power model, the influence of axial thermal error on cutting power is considered, and a cutting power model considering thermal error is constructed; Step 3: Use the cutting power model considering thermal error to build a support vector regression model; Step 4: Optimize the parameters of the support vector regression model to obtain the spindle axial thermal error model; In the step 1, the method for constructing the theoretical cutting power model is: 11) Construct the power model of micro-element cutting edge: dP cutting (θ,z)=|dP n |+|dP f |=|(K te dS+K tc s t sinψdz)·2πnr|+|(dF t sinψ+dF r cosψ)·f| Among them, dP cutting (θ,z) is the power of the micro-element cutting edge; θ represents the position angle of the micro-element cutting edge at the tool tip; z represents the position of the micro-element cutting edge in the tool axial direction; dP n Indicates the power consumed by the tool rotation at the micro-element cutting edge; dP f Indicates the power consumed by the tool feed at the micro-element cutting edge; K te K represents the tangential plowing force cutting coefficient of the micro-element cutting edge; tc represents the tangential shear force cutting coefficient of the micro-element cutting edge; dS represents the length of the micro-element cutting edge; dz represents the axial thickness of the micro-element cutting edge; s t represents the feed per tooth; ψ represents the micro-element cutting edge position angle; n represents the cutting speed; r represents the tool radius; dF t Indicates the tangential cutting force of the micro-element cutting edge; dF r represents the radial cutting force of the micro-element cutting edge; f represents the feed rate, and f = n·s t ·M, M is the number of teeth; 12) Construct the instantaneous power model of the cutting edge based on the power model of the micro-element cutting edge: P cutting Indicates the instantaneous cutting power of the cutting edge; a p Indicates cutting depth; 13) Construct the rate model of the cutting edge based on the instantaneous power model of the cutting edge: in, Indicates the average cutting power of the cutting edge in one cycle; φ p Indicates the tooth angle of the tool; In step 2, the cutting power model considering thermal error is constructed as follows: in, It represents the average cutting power of the cutting edge in one cycle after considering the thermal error; ΔZ represents the additional cutting depth caused by the elongation of the tool in the Z direction due to the axial thermal error of the spindle; In step 3, the method for constructing the support vector regression model is: According to the principle of structural risk minimization, the function modeling problem of support vector regression machine is to find the objective function f(x) with the minimum risk: f(x,ω)=ωφ(x)+b Among them, ω is the weight vector; φ(x) represents the corresponding value of x mapped to the high-dimensional feature space; x = [Δp, n, st] represents the input vector, Δp represents the change in the total power of the machine tool before and after the thermal error occurs; b is the threshold; Introducing the insensitive function ε, the constrained optimization problem is expressed as: Where C represents the penalty factor; l represents the number of support vector machines; ξ i and represents the slack variable; y i represents the target value; φ(x i ) represents the corresponding value of x mapped to the high-dimensional feature space; Introducing the Lagrangian function transforms it into a dual problem: in, and α i represents the Lagrange multiplier; α j is not equal to and α i Variables; The Lagrange coefficients are solved by solving the dual convex quadratic programming problem of the constrained optimization problem: In the formula represents the optimal solution; φ(x i )φ(x j )=K(x i ,x j ); K(x i ,x j ) is the kernel function that satisfies the Mercer condition; Depend on Find The decision function is constructed as: Rewrite the decision function as a support vector regression model: in, is the coefficient; x i is the support vector; K(x i ,x) is the kernel function, and l is the number of support vector machines.

2. The spindle axial thermal error modeling method based on machine tool power according to claim 1 is characterized in that: The kernel function uses the Gaussian radial basis kernel function: K(x,x i )=exp(-||x i -x|| 2 / σ 2 ) Among them, σ is the width parameter of the function, which controls the radial range of the function, denoted by 1 / σ 2 is the parameter g.

3. The spindle axial thermal error modeling method based on machine tool power according to claim 2 is characterized in that: In the step 4, the parameters g and C of the support vector regression model are optimized by using a network traversal parameter search algorithm or a cross-validation method to obtain the spindle axial thermal error model.

Images