A rapid measurement method for thermal expansion error in a fully closed-loop feed system of a CNC machine tool

Abstract

The present invention discloses a method for rapidly measuring thermal expansion errors in a fully closed-loop feed system of a numerically controlled machine tool. The method involves simplifying a grating into a one-dimensional model, establishing a heat conduction differential equation for the grating based on the Green's function method, and preliminarily establishing a grating temperature field model. A preliminarily established thermal expansion error model for the fully closed-loop feed system is also established based on the linear thermal expansion of the grating. Temperature and thermal error data for the grating at different positions and times within the first 30 minutes are measured using a temperature sensor and a laser interferometer, constructing a multivariate equation system for thermal characteristic parameters. The thermal characteristic parameters are identified using a particle swarm optimization algorithm. The identified thermal characteristic parameters are then substituted into the preliminarily established grating temperature field model and thermal error model to establish a full-process grating temperature field model and thermal error model. The method can obtain grating temperature and thermal error data at different positions and times throughout the entire process through only short-term measurements, reducing measurement time and improving measurement efficiency.

Description

Technical Field

[0001] The invention belongs to the field of error measurement of numerically controlled machine tools, and in particular relates to a method for quickly measuring thermal expansion errors of a fully closed-loop feeding system of a numerically controlled machine tool. Background Art

[0002] Currently, high-end CNC machine tools are all equipped with fully closed-loop feed systems featuring high-precision gratings. Thermal expansion errors are primarily caused by thermal deformation of the gratings. During machine tool motion, the grating temperature changes due to heat sources such as frictional heat, cutting heat, motor heat dissipation, and ambient temperature fluctuations. This causes thermal deformation and thermal errors, affecting part machining accuracy. Thermal error data measurement technology is fundamental to thermal error compensation. To obtain a highly accurate and robust thermal error model, thermal error measurement technology is required to accurately measure machine tool thermal errors. Thermal error measurement technology for CNC machine tools primarily involves collecting the error caused by thermal deformation of key moving components and the temperature near the relevant heat sources. During the thermal error data measurement process, the machine tool must be stopped for multiple thermal error measurements and temperature acquisitions using temperature sensors, laser interferometers, eddy current displacement sensors, and other sensors. This entire process can take several days, resulting in low measurement efficiency and making it unacceptable for most companies. Summary of the Invention

[0003] In response to the shortcomings of the existing technology, the present invention provides a method for quickly measuring the thermal expansion error of a fully closed-loop feed system of a CNC machine tool, so as to improve the measurement efficiency of the thermal error in the actual measurement process, solve the problems of the thermal expansion error measurement cycle of the fully closed-loop feed system of a CNC machine tool being too long, too time-consuming, and difficult to measure, and improve the thermal error measurement efficiency of the CNC machine tool.

[0004] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0005] A method for quickly measuring thermal expansion errors of a fully closed-loop feed system of a CNC machine tool, the method comprising the following steps:

[0006] 1) Preliminary establishment of the grating temperature field model: The grating is simplified into a one-dimensional model along the direction of the readhead movement, and the establishment of the grating temperature field model is simplified to a one-dimensional heat conduction problem. The grating heat conduction differential equation is established, and the differential equation is solved based on the Green's function method to preliminarily establish the grating temperature field model;

[0007] 2) Preliminary establishment of grating thermal error model: Based on the preliminarily established grating temperature field model and the linear thermal expansion of the grating, a preliminarily established grating thermal error model is established;

[0008] 3) Identification of thermal characteristic parameters of the grating temperature field model and thermal error model: After the grating temperature field model and thermal error model are initially established, the temperature data and thermal error data of the grating at different positions and times within the first 30 minutes are measured using a temperature sensor and a laser interferometer. The position and time data are substituted into the temperature field model and the thermal error model to construct a multivariate equation system for the thermal characteristic parameters of the grating temperature field model and the thermal error model. The thermal characteristic parameters of the grating temperature field model and the thermal error model are identified using a particle swarm optimization algorithm.

[0009] 4) Establishment of the full-process grating thermal error model: Substitute the identified thermal characteristic parameters into the preliminarily established grating temperature field model and thermal error model to obtain the full-process grating temperature field model and thermal error model, that is, measure the thermal error of the temperature field at each moment after 30 minutes.

[0010] As a preferred solution of the present invention, the grating temperature field model in step 1) is initially established, specifically: the grating is simplified into a one-dimensional model along the movement direction of the reading head, and the establishment of the grating temperature field model is simplified to a one-dimensional heat conduction problem, and the one-dimensional heat conduction differential equation of the grating is established as follows:

[0011]

[0012] The boundary conditions are as follows:

[0013]

[0014] The initial temperature distribution is as follows:

[0015] θ(x,t)=0,t=0,0≤x≤L

[0016] Where θ(x, t) is the grating temperature field model, g is the heat source, which is the friction heat generated by the friction between the grating reading head and the grating during machine tool processing, δ is the δ(x) function, P is the circumference of the grating cross section, A is the area of ​​the grating cross section, and θ is the grating temperature field model. f (t) is the ambient temperature, v is the movement speed of the grating reading head during machine processing, k is the thermal conductivity of the grating medium material, h, h1, h2 are the relative temperatures of the grating and the ambient temperature θ f (t), α is the thermal diffusion coefficient of the grating, and L is the length of the grating in the one-dimensional model. The one-dimensional heat transfer differential equation of the grating is solved by the Green's function method, and the grating temperature field model is preliminarily established as follows:

[0017]

[0018] Where θ(x, t) is the initially established grating temperature field model, and:

[0019]

[0020] λ m is the root of the following transcendental equation:

[0021]

[0022] As a preferred embodiment of the present invention, a grating thermal error model is preliminarily established in step 2), specifically: based on the preliminarily established grating temperature field model, the one-dimensional thermal deformation of the grating is calculated by the linear thermal expansion of the grating, and the preliminarily established grating thermal error model is shown in the following formula:

[0023]

[0024] Where E(x,t) is the one-dimensional thermal deformation of the grating, α E is the grating expansion coefficient, which is assumed to be constant along the grating.

[0025] As a preferred solution of the present invention, the identification of thermal characteristic parameters of the grating temperature field model and thermal error model in step 3) is specifically as follows: after the grating temperature field model and thermal error model are initially established, the temperature data θ1(x1, t1), θ2(x2, t2), ..., θ3 of the grating at different positions and times within the first 30 minutes are measured by a temperature sensor and a laser interferometer. n (x n ,t n ) and thermal error data E1(x1,t1), E2(x2,t2), ..., E n (x n ,t n ), the temperature data θ1(x1,t1), θ2(x2,t2), ..., θ n (x n ,t n ) and thermal error data E1(x1,t1), E2(x2,t2), ..., E n (x n ,t n ) is substituted into the initially established grating temperature field model and thermal error model, and a multivariate equation group about the thermal characteristic parameters of the temperature field model and thermal error model is established, where h, h1, h2, α E , g is the parameter to be determined, λ m is the root of the transcendental equation, v, k, α, L are known parameters, θ f (t) can be obtained by actual calculation; calculate the transcendental equation λ m Partial solutions (λ1,λ2,…,λ n ,n<m), and combined with the known measured temperature data θ1(x1,t1), θ2(x2,t2), ..., θ n (x n ,t n) and thermal error data E1(x1,t1), E2(x2,t2), ..., E n (x n ,t n ) The temperature prediction values ​​θ1′(x1,t1), θ2′(x2,t2), ..., θ are iterated through the particle swarm optimization algorithm. n ′(x n ,t n ) and the thermal error prediction values ​​E1′(x1,t1), E2′(x2,t2), ..., E n ′(x n ,t n ),make:

[0026]

[0027] Where F is the fitness function, i = 1, 2, ..., n, and n is the number of actual temperature measurement data sets;

[0028] The minimum value of F is obtained through the iterative loop of the particle swarm optimization algorithm. When F takes the minimum value, the thermal characteristic parameters h, h1, h2, and α of the grating temperature field model and the thermal error model can be identified. E 、g.

[0029] As a preferred solution of the present invention, the whole process grating thermal error model of step 4) is established, specifically: the identified thermal characteristic parameters (h, h1, h2, α E , g), known parameters (v, k, α, L), transcendental equation λ m Partial solutions (λ1,λ2,…,λ n ,n<m) and the actual θ f Substituting (t) into the grating temperature field model and thermal error model established in steps 1) and 2), we can obtain the full-process grating temperature field model θ(x, t) and thermal error model E(x, t), that is, the thermal errors at each time and position after measuring for 30 minutes.

[0030] Compared with the prior art, the technical effects of the present invention are:

[0031] The present invention proposes a method for quickly measuring the thermal expansion error of a fully closed-loop feed system of a CNC machine tool, establishes a full-process grating temperature field and thermal error model, and combines short-time temperature and error measurements to quickly obtain grating temperature and thermal error data at different positions and times during the entire measurement process, thereby shortening the temperature and thermal error measurement time and improving measurement efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of a method for quickly measuring thermal expansion errors in a fully closed-loop feed system of a CNC machine tool;

[0033] Figure 2 Schematic diagram of one-dimensional heat conduction of grating. DETAILED DESCRIPTION

[0034] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0035] like Figure 1 As shown, a method for quickly measuring thermal expansion error of a fully closed-loop feed system of a CNC machine tool comprises the following steps:

[0036] 1) Preliminary establishment of grating temperature field model

[0037] The grating is simplified into a one-dimensional model along the direction of movement of the reading head. Figure 2 As shown, the establishment of the grating temperature field model is simplified to a one-dimensional heat conduction problem, and the one-dimensional heat conduction differential equation of the grating is established as follows:

[0038]

[0039] The boundary conditions are as follows:

[0040]

[0041] The initial temperature distribution is as follows:

[0042] θ(x,t)=0,t=0,0≤x≤L

[0043] Where θ(x, t) is the grating temperature field model, g is the heat source, which is the friction heat generated by the friction between the grating reading head and the grating during machine tool processing, δ is the δ(x) function, P is the circumference of the grating cross section, A is the area of ​​the grating cross section, and θ is the grating temperature field model. f (t) is the ambient temperature, v is the movement speed of the grating reading head during machine processing, k is the thermal conductivity of the grating medium material, h, h1, h2 are the relative temperatures of the grating and the ambient temperature θ f (t), α is the thermal diffusion coefficient of the grating, and L is the length of the grating in the one-dimensional model.

[0044] The Green function method is used to solve the one-dimensional heat transfer differential equation of the grating, and a preliminary grating temperature field model is established, as follows:

[0045]

[0046] Where θ(x, t) is the initially established grating temperature field model, and:

[0047]

[0048] λ m is the root of the following transcendental equation:

[0049]

[0050] 2) Preliminary establishment of grating thermal error model

[0051] Based on the preliminarily established grating temperature field model, the one-dimensional thermal deformation of the grating is calculated through the linear thermal expansion of the grating, and a preliminarily established grating thermal error model is shown in the following formula:

[0052]

[0053] Where E(x,t) is the one-dimensional thermal deformation of the grating, α E is the grating expansion coefficient, which is assumed to be constant along the grating.

[0054] 3) Identification of thermal characteristic parameters of grating temperature field model and thermal error model

[0055] After the grating temperature field model and thermal error model were initially established, 10 sets of temperature data θ1(x1, t1), θ2(x2, t2), ..., θ 10 (x 10 ,t 10 ) and thermal error data E1(x1,t1), E2(x2,t2), ..., E 10 (x 10 ,t 10 ), the temperature data θ1(x1,t1), θ2(x2,t2), ..., θ 10 (x 10 ,t 10 ) and thermal error data E1(x1,t1), E2(x2,t2), ..., E 10 (x 10 ,t 10 ) is substituted into the initially established grating temperature field model and thermal error model, and a multivariate equation group about the thermal characteristic parameters of the temperature field model and thermal error model is established, where h, h1, h2, α E , g is the parameter to be determined, λ m is the root of the transcendental equation, v, k, α, L are known parameters, θ f (t) can be obtained by actual calculation. Calculate the transcendental equation λ m The 10 basic solutions (λ1,λ2,…,λ 10 ), and combined with the known measured temperature data θ1(x1,t1), θ2(x2,t2), ..., θ 10 (x 10 ,t 10 ) and thermal error data E1(x1,t1), E2(x2,t2), ..., E10 (x 10 ,t 10 ) The temperature prediction values ​​θ1′(x1,t1), θ2′(x2,t2), ..., θ are iterated through the particle swarm optimization algorithm. 10 ′(x 10 ,t 10 ) and the thermal error prediction values ​​E1′(x1,t1), E2′(x2,t2), ..., E 10 ′(x 10 ,t 10 ),make:

[0056]

[0057] Where F is the fitness function.

[0058] The minimum value of F is obtained through the iterative loop of the particle swarm optimization algorithm. When F takes the minimum value, the thermal characteristic parameters h, h1, h2, and α of the grating temperature field model and the thermal error model can be identified. E 、g.

[0059] 4) Establishment of the whole process grating thermal error model:

[0060] The identified thermal characteristic parameters (h, h1, h2, α E , g), known parameters (v, k, α, L), transcendental equation λ m The 10 basic solutions (λ1,λ2,…,λ 10 ) and the actual θ f Substituting (t) into the grating temperature field model and thermal error model established in steps 1) and 2), we can obtain the full-process grating temperature field model θ(x, t) and thermal error model E(x, t), that is, the thermal errors at each time and position after measuring for 30 minutes.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for quickly measuring thermal expansion error of a fully closed-loop feed system of a CNC machine tool, characterized in that: The method comprises the following steps: 1) Preliminary establishment of the grating temperature field model: The grating is simplified into a one-dimensional model along the direction of the readhead movement, and the establishment of the grating temperature field model is simplified to a one-dimensional heat conduction problem. The grating heat conduction differential equation is established, and the differential equation is solved based on the Green's function method to preliminarily establish the grating temperature field model; 2) Preliminary establishment of grating thermal error model: Based on the preliminarily established grating temperature field model and the linear thermal expansion of the grating, a preliminarily established grating thermal error model is established; 3) Identification of thermal characteristic parameters of the grating temperature field model and thermal error model: After the grating temperature field model and thermal error model are initially established, the temperature data and thermal error data of the grating at different positions and times within the first 30 minutes are measured using a temperature sensor and a laser interferometer. The position and time data are substituted into the temperature field model and the thermal error model to construct a multivariate equation system for the thermal characteristic parameters of the grating temperature field model and the thermal error model. The thermal characteristic parameters of the grating temperature field model and the thermal error model are identified using a particle swarm optimization algorithm. 4) Establishment of the full-process grating thermal error model: Substitute the identified thermal characteristic parameters into the initially established grating temperature field model and thermal error model to obtain the full-process grating temperature field model and thermal error model, that is, the thermal error of the temperature field at each moment after measuring 30 minutes; The grating temperature field model of step 1) is initially established. Specifically, the grating is simplified into a one-dimensional model along the direction of movement of the reading head, and the establishment of the grating temperature field model is simplified to a one-dimensional heat conduction problem. The one-dimensional heat conduction differential equation of the grating is established as follows: The boundary conditions are as follows: The initial temperature distribution is as follows: θ(x,t)=0,t=0,0≤x≤L Where θ(x, t) is the grating temperature field model, g is the heat source, which is the friction heat generated by the friction between the grating reading head and the grating during machine tool processing, δ is the δ(x) function, P is the circumference of the grating cross section, A is the area of ​​the grating cross section, and θ is the grating temperature field model. f (t) is the ambient temperature, v is the movement speed of the grating reading head during machine processing, k is the thermal conductivity of the grating medium material, h, h1, h2 are the relative temperatures of the grating and the ambient temperature θ f (t) is the heat transfer coefficient, α is the thermal diffusion coefficient of the grating, and L is the length of the grating in the one-dimensional model; The Green function method is used to solve the one-dimensional heat transfer differential equation of the grating, and a preliminary grating temperature field model is established, as shown below: Where θ(x, t) is the initially established grating temperature field model, and: λ m is the root of the following transcendental equation: In step 2), the grating thermal error model is initially established. Specifically, based on the initially established grating temperature field model, the one-dimensional thermal deformation of the grating is calculated through the linear thermal expansion of the grating, and the grating thermal error model is initially established, as shown in the following formula: Where E(x,t) is the one-dimensional thermal deformation of the grating, α E is the grating expansion coefficient, which is assumed to be constant along the grating; Step 3) Identification of thermal characteristic parameters of the grating temperature field model and thermal error model: After the grating temperature field model and thermal error model are initially established, the temperature data θ1(x1, t1), θ2(x2, t2), ..., θ3 of the grating at different positions and times within the first 30 minutes are measured by temperature sensor and laser interferometer. n (x n ,t n ) and thermal error data E1(x1,t1), E2(x2,t2), ..., E n (x n ,t n ), the temperature data θ1(x1,t1), θ2(x2,t2), ..., θ n (x n ,t n ) and thermal error data E1(x1,t1), E2(x2,t2), ..., E n (x n ,t n ) is substituted into the initially established grating temperature field model and thermal error model, and a multivariate equation group about the thermal characteristic parameters of the temperature field model and thermal error model is established, where h, h1, h2, α E , g is the parameter to be determined, λ m is the root of the transcendental equation, v, k, α, L are known parameters, θ f (t) can be obtained by actual calculation; calculate the transcendental equation λ m Partial solutions (λ1,λ2,…,λ n ,n<m), and combined with the known measured temperature data θ1(x1,t1), θ2(x2,t2), ..., θ n (x n ,t n ) and thermal error data E1(x1,t1), E2(x2,t2), ..., E n (x n ,t n ) The temperature prediction values ​​θ1′(x1,t1), θ2′(x2,t2), ..., θ are iterated through the particle swarm optimization algorithm. n ′(x n ,t n ) and the thermal error prediction values ​​E1′(x1,t1), E2′(x2,t2), ..., E n ′(x n ,t n ),make: Where F is the fitness function, i = 1, 2, ..., n, and n is the number of actual temperature measurement data sets; The minimum value of F is obtained through the iterative loop of the particle swarm optimization algorithm. When F takes the minimum value, the thermal characteristic parameters h, h1, h2, and α of the grating temperature field model and the thermal error model can be identified. E , g; The whole process of the grating thermal error model of step 4) is established, specifically: the identified thermal characteristic parameters (h, h1, h2, α E , g), known parameters (v, k, α, L), transcendental equation λ m Partial solutions (λ1,λ2,…,λ n ,n<m) and the actual θ f Substituting (t) into the grating temperature field model and thermal error model established in steps 1) and 2), we can obtain the full-process grating temperature field model θ(x, t) and thermal error model E(x, t), that is, the thermal errors at each time and position after measuring for 30 minutes.

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