Thermal error modeling method for large and medium-sized machine tool foundation structure

Abstract

The invention discloses a thermal error modeling method for a large and medium-sized machine tool foundation structure, and belongs to the field of precision manufacturing. The method comprises the following steps: firstly, dividing a complex structure into a few regular finite element units, and arranging a temperature sensor at a key position of each unit so as to obtain temperature distribution in the units through accurate interpolation; the equivalent node force of each unit is calculated through the temperature distribution, and a node-based static thermal error model is constructed. And then, through a matrix displacement method and in combination with convolution of a historical temperature sequence, a dynamic thermal error model related to the position is further obtained. Compared with the prior art, the calculation amount can be effectively reduced, the precision of the thermal error model is improved, a reliable basis is provided for real-time thermal error compensation of large and medium-sized machine tools, and the machining precision and stability are remarkably improved. The method is suitable for basic structure thermal error modeling and precision compensation systems of various large and medium-sized machine tools.

Description

Technical Field

[0001] The invention relates to a thermal error modeling method for a large and medium-sized machine tool infrastructure, relates to the field of CNC machine tool processing and precision, and can provide effective technical means for thermal error compensation and machining precision improvement of large and medium-sized machine tools. Background Art

[0002] In the modern precision manufacturing process, large and medium-sized machine tools (such as five-axis horizontal milling and turning machining centers, vertical machining centers, etc.) have increasingly higher requirements for machining accuracy. The basic structural components of large and medium-sized machine tools (such as the columns and beams of the machine tools) have a large length. Affected by changes in ambient temperature or thermal radiation generated during the operation of the machine tools, these components will produce significant thermal deformation, which will affect the machining accuracy. In addition, since the thermal deformation on the basic structure will produce an amplification effect at the terminal processing position of the machine tool, the thermal error will have a serious impact on the stability and accuracy of the entire machining process. However, the existing thermal error modeling technology often has problems such as high computational complexity and insufficient model accuracy, which makes it difficult to meet the needs of real-time compensation. Therefore, there is an urgent need for an accurate and computationally efficient thermal error modeling method to improve the machining accuracy of large and medium-sized machine tools in temperature fluctuation environments. Summary of the invention

[0003] The purpose of the present invention is to provide a thermal error modeling method for the basic structural components of large and medium-sized machine tools. Through reasonable unit division, temperature measurement and data interpolation methods, a thermal error model with both accuracy and computational efficiency is constructed to meet the real-time compensation requirements of thermal errors of machine tools.

[0004] The thermal error modeling method provided by the present invention comprises the following steps:

[0005] Step 1: Structural division: Divide the basic structure of large and medium-sized machine tools into multiple finite element units to reduce model complexity while ensuring calculation accuracy. Each unit is set to have a regular geometric shape to facilitate error calculation and data processing.

[0006] The thermal error modeling method of a large and medium-sized machine tool foundation structure according to claim 1 is characterized in that it includes: in the step 1, the large and medium-sized machine tool structure component unit is specifically as follows:

[0007] Step 1.1. The structural components of large and medium-sized machine tools are all composed of thin-walled hollow beams, which can be regarded as plane rigid frame structures. Since the divided units have the following properties: the length-to-width ratio or length-to-height ratio of the unit is small; the unit is a hollow beam structure. Therefore, according to the beam theory in the finite element, the influence of shear deformation needs to be considered in this unit.

[0008] Step 2: Arrangement of temperature measurement points: Arrange temperature sensors at key locations of each unit (such as boundary vertices) to collect the real-time temperature value of the unit. The arrangement of temperature measurement points between units has a common design to optimize the number of sensors.

[0009] The thermal error modeling method for a large and medium-sized machine tool infrastructure according to claim 1 is characterized in that it includes: in the step 2, the temperature measurement point positions are specifically as follows:

[0010] Step 2.1. According to the result of unit structure simplification, the actual physical structure corresponding to each unit is simplified to a square tube composed of four plates. Therefore, arranging temperature measurement points at the 8 vertices of the square tube is a reasonable method to obtain the unit temperature distribution. And every two adjacent units share 4 temperature measurement points, thereby reducing the total number of temperature measurement points. The total number of temperature measurement points of the entire structure is defined as n t . Note that the simplified square tube unit has four straight lines parallel to the unit axis (the four edges of the square tube). In order to further use these temperature measurement points to describe the temperature distribution of the entire structure, all temperature measurement points are divided into four groups based on these four lines.

[0011] Step 3: Temperature distribution calculation: Based on the temperature data collected by the sensor, the temperature distribution model in the unit is constructed using the cubic spline interpolation method. Through the interpolation function, the temperature changes at different locations in each unit can be accurately calculated, providing the basis for subsequent error calculations.

[0012] Based on each temperature measurement point group, a temperature curve can be obtained. The horizontal axis of the curve represents the coordinate along the axis of this structural unit (i.e. the axis of the square tube), defined as l; the vertical axis of the curve represents the temperature change value, defined as Δt. Then, the temperature change value of the temperature measurement point is the interpolation point of the curve, and the temperature curve inside each unit can be represented as a part of the curve.

[0013] By using cubic spline curves

[103] to interpolate a single temperature curve, a smooth curve represented by an explicit function can be obtained, and the expression is simple enough to facilitate further temperature distribution calculations and equivalent force calculations. The interpolation process is as follows:

[0014] (1) In the i-th unit, the unit length is lei, and the temperature curve can be represented by the cubic polynomial Ti(l). The coordinates of the two interpolation points in unit i are defined as (li, Δtci) and (li+1, Δtci+1).

[0015] (2) Definition Represents a cubic polynomial T i (l) The second-order derivative with respect to l, M i(l) can be obtained by linear interpolation from M i It is expressed as:

[0016] Integrate equation (1-1) twice, and use the side condition as T i (l i )=Δt ci and T i (l i+1 )=Δt ci+1 , we can get T i The expression of (l) is as follows:

[0017] (3) M in formula (1-2) i and M i+1 Still unknown, according to the temperature T in formula (1-2) i (l) when l = l i The first-order continuity at , we get: Repeating formula (1-3) from i=1 to i=m-1, we can get n-1 equations, which can be expressed in the form of a matrix, namely: in, n represents the total number of units. Formula (1-4) can be written as: M = C -1 d(1-6)where C is the coefficient matrix in formula (1-4).

[0018] According to formula (1-4), the temperature variable only exists in vector d, so C -1 There are no variables in it, and the expression of the temperature curve is still an explicit expression to facilitate subsequent calculations.

[0019] In order to further obtain the overall temperature distribution and equivalent nodal force of the i-th unit, equation (1-2) is expressed in the local coordinate system {xyz} of the unit and written as:

[0020] Therefore, the expressions of the four temperature curves of the ith unit can be obtained by substituting equation (1-6) corresponding to each curve into equation (1-7). The expressions of these four temperature curves are: (1) The expression of the temperature of the outer straight line 1 with respect to the x-axis coordinate is defined as T out1,i (x); (2) The temperature of the outer line 2 with respect to the x-axis coordinate is defined as T out2,i(x); (3) The temperature of the inner line 1 with respect to the x-axis coordinate is defined as T in1,i (x); (4) The temperature of the inner line 2 with respect to the x-axis coordinate is defined as T in2,i (x);

[0021] Furthermore, the temperature distribution of the four plates of the simplified i-th unit with respect to coordinates x, y, and z is defined as: T i1 (x,z),T i2 (x,z),T i3 (x,y) and T i4 (x,y). T out1,i (x), T out2,i (x), T in1,i (x) and T in2,i (x) are located on the four edges of the i-th unit (the connecting lines of two adjacent plates), so assuming that the temperature inside each plate is distributed linearly along the width direction (y-axis or z-axis direction), the temperature distribution of the four plates can be expressed by T out1,i (x), T out2,i (x), T in1,i (x) and T in2,i (x) is obtained by linear interpolation, that is:

[0022] Different from the traditional finite element method, the unit temperature distribution function obtained above is not only related to the temperature measurement point value of the unit, but also to the temperature measurement point values ​​of adjacent units and other units, thereby improving the accuracy of the obtained unit temperature distribution.

[0023] Step 4: Calculate the equivalent nodal force: Calculate the equivalent nodal force of each unit according to the temperature distribution of the unit. Introduce the equivalent nodal force into the static thermal error model to accurately describe the impact of unit temperature changes on structural displacement and angle.

[0024] The unit equivalent node force can be divided into the unit equivalent node tension F ie and the unit equivalent node bending moment M ie According to the simplified unit structure, the equivalent node tension can be expressed as the sum of the equivalent tension of each plate due to thermal expansion, that is: Here, α represents the thermal expansion coefficient of the material.

[0025] The equivalent node bending moment M ieIt can also be expressed as the sum of the equivalent bending moments of each plate due to thermal expansion. For the plates located at the top and bottom (j=1,2), the equivalent bending moment can be obtained by the difference between the thermal expansion of the plate and the average thermal expansion of the unit; and for the plates located at the front and rear (j=3,4), the equivalent bending moment can be expressed as the product of the equivalent force and the y-axis coordinate integrated along the y-axis. Therefore, the total expression of the equivalent node bending moment can be written as: in, It represents the average temperature of the entire i-th unit distributed along the axial direction (x-axis direction).

[0026] In order to express equations (1-9) and (1-10) in a simple explicit form, replace T in equation (1-7) with i (x) Integrate x and divide by the unit length to obtain the average value T of each temperature curve in the i-th unit. i . And T i There is a simpler expression:

[0027] Thus, the four temperature curves in the i-th unit, T out1,i (x), T out2,i (x), T in1,i (x) and T in2,i The average value of (x) can be calculated according to formula (1-12) and is defined as T out1,i , T out2,i , T in1,i and T in2,i . However, in formulas (1-9) and (1-10), there is T i1 (x,z),T i2 (x,z),T i3 (x,y) and T i4 The integral of (x,y) along the x-axis can be converted to T according to formula (1-8) out1,i (x), T out2,i (x), T in1,i (x) and T in2,i (x) is the integral along the x-axis and can be further expressed by T out1,i , T out2,i , T in1,i and T in2,i Substitution. After the substitution is completed, the integrals along the y-axis and z-axis are calculated, and equations (1-9) and (1-10) can be transformed into: Equations (1-13) and (1-14) are the expressions for the equivalent nodal tension and bending moment of the i-th unit, and the equivalent nodal forces in 6 directions at the nodes at both ends of the unit are written in vector form as follows:

[0028] Step 5, dynamic thermal error model: The equivalent nodal force is converted into nodal thermal error using the matrix displacement method, and combined with the historical temperature series convolution method, a position-dependent dynamic thermal error model is obtained. The hysteresis effect of the model can be further reduced by moving average smoothing the temperature data, thereby improving the prediction accuracy of the thermal error.

[0029] Although the temperature around the machine tool changes very slowly, the thermal error can be regarded as a quasi-static error (which can be approximately calculated using a static thermal error model). However, in order to obtain a thermal error model with higher accuracy, the thermal error needs to be regarded as a "dynamic error" in the quasi-static error. At this time, the change in thermal error often lags behind the change in temperature, which is called hysteresis. Figure 4 Therefore, in this section, the dynamic thermal error model of the machine tool will be established based on the static thermal error model.

[0030] For the basic structure of machine tools (especially large and medium-sized machine tools), from the perspective of physical process, the temperature distribution at each moment can be regarded as a temperature shock applied to the structure, and the thermal error value at the current moment can be regarded as the result of the accumulation of the shock response of all temperature shocks in the period before the moment. Since the convolution process can express the transient response at the current moment as an integral form of a series of shock responses generated by shocks at past moments, the dynamic thermal error of the structure can be expressed by convolution as: Among them, e(τ) represents the thermal error at time τ; s0 is named as the time constant; t(τ) represents the temperature change value at time τ; P(s) is the impulse response coefficient, which represents the proportional coefficient between the thermal error and the temperature shock.

[0031] Therefore, the average value of the impulse response coefficient within the range of time constant s0 can be written as: Among them, P is the proportional coefficient between thermal error and temperature, that is, the proportional coefficient between thermal error and temperature in the static thermal error model.

[0032] Therefore, formula (1-16) can be written as:

[0033] In practical applications, formula (1-18) is written in discrete form, that is: Where n0 represents the number of samples of temperature values ​​collected within the time constant s0; s n0 =s0 / n 0-1 Indicates the time interval between two samples.

[0034] Therefore, based on the concept of moving average, the value of the time constant can be obtained. In moving average, the lag time s t With time Constant s o The following approximate relationship is satisfied:

[0035] Therefore, a preliminary test can be used to determine the time constant S related to the thermal error of this basic structural component. o , namely: (1) first measure the curves of temperature and thermal error changing with time; (2) obtain the time corresponding to the peak of the temperature curve and the time corresponding to the peak of the thermal error curve in the same period, and make a difference to obtain the lag time S; (3) according to formula (3-56), obtain the time constant s o Each step in the thermal error calculation is an explicit basic operation, which means that the thermal error model can be explicitly expressed by the temperature value of the temperature measurement point and the coordinate value along the axial direction. Then, taking the temperature value of the temperature measurement point as the symbolic independent variable and simplifying the above equations using mathematical tool software (such as MATLAB), the complete thermal error model can be obtained with respect to the explicit expression between the temperature value of the temperature measurement point and the x-axis coordinate value of the local coordinate system of the i-th unit: Among them, C Yi For 2 rows n t The constant matrix of columns; C Zi For 4 rows n t The constant matrix of columns; C Ai For 3 rows n t A constant matrix of columns; Where t(τ-qs n0 ) indicates that in τ-qs n0 A vector consisting of the temperature change values ​​of the temperature measuring points at the moment.

[0036] At this point, a complete position-dependent explicit dynamic thermal error model shown in equations (1-20) and (1-21) has been established.

[0037] Furthermore, the computational effort of this thermal error model is evaluated: The floating point number calculation of the first equation in formula (1-20) is about 2×(2×n t×1+1×2×1)=4n t +4 times; the floating point calculation amount of the second equation in formula (1-20) is about 8n t +8 times; the floating point number calculation of the third equation in formula (1-20) is about 6n t +6 times. The amount of calculation of formula (1-21) can be significantly reduced by recursive calculation. Formula (1-21) can be written in recursive form, that is: Among them, t (1) Represents the value of t at the last sampling moment. The floating point number calculation amount of formula (1-22) is about 3n t Second-rate.

[0039] Based on the number of floating point calculations for each of the above equations, the number of floating point calculations for the total thermal error model is approximately 21n t +18 times. For the thermal error model, the number of temperature measurement points is n t = 36, and the total number of floating point calculations is about 700. Therefore, the thermal error model of the basic structural components of large and medium-sized machine tools has less calculation amount and is convenient for thermal error compensation.

[0040] Step 6: Application to thermal error compensation: Apply the dynamic thermal error model to the thermal error compensation system of the machine tool, so that the machine tool can automatically perform thermal error compensation in a temperature fluctuation environment, thereby effectively improving the processing accuracy and stability.

[0041] The beneficial effects of the present invention are:

[0042] The present invention simplifies the complex large and medium-sized machine tool infrastructure into a few regular finite element units, realizes accurate thermal error modeling of the infrastructure, reduces the amount of calculation, and facilitates real-time application. Compared with the traditional model, the thermal error model of the present invention can more accurately describe the dynamic error characteristics of large and medium-sized infrastructure under temperature changes, and has good engineering applicability and practical promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the overall process of the thermal error modeling method of the present invention.

[0044] Figure 2 This is the layout diagram of temperature measurement points for basic structural components of large and medium-sized machine tools.

[0045] Figure 3 Schematic diagram of calculating the equivalent nodal force of the element through temperature distribution.

[0046] Figure 4 This is an illustration of the dynamic thermal error lagging behind the temperature change. DETAILED DESCRIPTION

[0047] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] In the embodiment, the present invention is applied to the thermal error modeling of the basic structure of large and medium-sized machine tools. Taking the column and ram of the KTX1250 five-axis horizontal milling and turning composite machining center as an example, the basic structure is divided into 4 finite element units, and 8-9 temperature sensors are arranged at the key position of each unit. Figure 2 As shown, the cubic spline interpolation method is used to obtain the temperature distribution of each unit, such as Figure 3 Combining the node displacement method and the historical temperature convolution formula, the dynamic thermal error model is obtained, as shown in Figure 4 Theoretically, the model can meet the error compensation requirements of large and medium-sized machine tools in terms of real-time calculation accuracy and efficiency, and significantly improve the machining accuracy of machine tools.

[0049] The present invention provides a thermal error modeling method for basic structural components of large and medium-sized machine tools, which can accurately capture thermal errors caused by temperature changes, provide effective technical support for thermal error compensation and precision improvement of machine tools, and has wide industrial application value.

Claims

1. A thermal error modeling method for the basic structure of large and medium-sized machine tools, characterized in that: include: Step 1, dividing the machine tool infrastructure into a plurality of finite element units, each finite element unit having a regular geometric shape; Step 2: Arrange temperature sensors at key positions of each finite element unit to collect temperature data within the finite element unit; Step 3: Based on the collected temperature data, calculate the temperature distribution of each finite element unit by interpolation method; Step 4: Calculate the equivalent nodal force according to the temperature distribution of each finite element unit to form a node-based static thermal error model; Step 5: Use the matrix shift method combined with the historical temperature sequence convolution to obtain a position-dependent dynamic thermal error model.

2. The thermal error modeling method for a large and medium-sized machine tool infrastructure according to claim 1 is characterized in that: include: In the step 1, the finite element unit is divided in a manner of decomposing the support structure into a small number of regular geometric units to reduce the computational complexity of the machine tool infrastructure model.

3. The thermal error modeling method for a large and medium-sized machine tool infrastructure according to claim 1 is characterized in that: include: In the step 2, the temperature sensor is arranged at the boundary vertex position of the unit, and the temperature distribution of the unit is obtained by using the temperature data of the sensor using the cubic spline interpolation method.

4. The thermal error modeling method for a large and medium-sized machine tool infrastructure according to claim 1, characterized in that: include: In the step 3, a static thermal error model is generated based on the equivalent nodal force of the node by calculating the equivalent nodal force of the temperature distribution unit.

5. The thermal error modeling method for a large and medium-sized machine tool infrastructure according to claim 1, characterized in that: include: In step 4, the dynamic thermal error model calculated by combining the matrix shift method with the historical temperature sequence convolution is used to compensate for the thermal error of the support structure in real time.

6. The thermal error modeling method for a large and medium-sized machine tool infrastructure according to claim 1, characterized in that: include: In step 5, the dynamic thermal error model smoothes the temperature value by a moving average method to reduce the lag effect of the thermal error model.

7. The thermal error modeling method for a large and medium-sized machine tool infrastructure according to claim 1, characterized in that: The method is applicable to thermal error modeling and precision compensation systems of supporting structure components of various large machine tools.

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