WO2020155226A1 - 基于热误差和温升加权的丝杠预紧量确定方法 - Google Patents

基于热误差和温升加权的丝杠预紧量确定方法 Download PDF

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WO2020155226A1
WO2020155226A1 PCT/CN2019/075710 CN2019075710W WO2020155226A1 WO 2020155226 A1 WO2020155226 A1 WO 2020155226A1 CN 2019075710 W CN2019075710 W CN 2019075710W WO 2020155226 A1 WO2020155226 A1 WO 2020155226A1
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preload
temperature
screw
thermal error
temperature sensor
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PCT/CN2019/075710
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English (en)
French (fr)
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刘阔
王永青
刘海波
李旭
沈明瑞
牛蒙蒙
班仔优
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大连理工大学
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Priority to US16/470,925 priority Critical patent/US11467066B2/en
Publication of WO2020155226A1 publication Critical patent/WO2020155226A1/zh

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q5/00—Driving or feeding mechanisms; Control arrangements therefor
    • B23Q5/22—Feeding members carrying tools or work
    • B23Q5/34—Feeding other members supporting tools or work, e.g. saddles, tool-slides, through mechanical transmission
    • B23Q5/38—Feeding other members supporting tools or work, e.g. saddles, tool-slides, through mechanical transmission feeding continuously
    • B23Q5/40—Feeding other members supporting tools or work, e.g. saddles, tool-slides, through mechanical transmission feeding continuously by feed shaft, e.g. lead screw
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form

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  • the invention belongs to the technical field of numerical control machine tool assembly, and is specifically a method for determining the preload of a lead screw based on the weighting of thermal error and temperature rise.
  • the friction between the nut and the lead screw will generate a lot of heat, and the transfer of this heat to the lead screw will cause the lead screw to stretch.
  • the feed axis adopts a semi-closed loop control mode, the thermal elongation of the lead screw will cause a change in the positioning accuracy of the axis, and this change is the thermal error of the feed axis.
  • the thermal error will eventually affect the machining accuracy of the workpiece and the accuracy consistency of batch processing.
  • the commonly used method is to pre-tighten the screw, that is, to apply an axial pre-tightening force to the screw through the pre-tightening nut, so that the screw produces an appropriate amount of axial pre-tension.
  • the current method of reducing the thermal error of the feed axis through the screw pre-tightening method has the following shortcomings:
  • the pre-tightening amount of the screw is generally determined based on experience and mainly considers the suppression effect of the thermal error. This method is difficult to achieve the optimal effect . If the screw preload is too small, the thermal error suppression effect is insufficient; if the screw preload is too large, although the thermal error suppression effect is better, it will cause excessive temperature rise of the front and rear bearings of the screw. Accelerate the wear of the bearing and shorten the service life.
  • the present invention proposes a method for determining the amount of screw preload based on the thermal error and temperature rise weighting, which comprehensively considers the thermal error of the feed shaft Suppress and control the temperature rise of key measuring points to obtain the optimal preload of the lead screw.
  • the method of determining the preload of the screw based on the weighted thermal error and temperature rise First, under different preload states of the screw, conduct the thermal behavior test of the feed shaft under typical working conditions to obtain the screw under various preload states The maximum thermal error and the temperature rise of the key temperature measurement points; then, the mathematical model of the screw preload and the maximum thermal error and the temperature rise of the key temperature measurement points are established; finally, the maximum thermal error and the temperature rise of each temperature measurement point
  • the weighting function of is optimized for the objective function to obtain the optimal preload of the screw; the specific steps are as follows:
  • the first step the thermal behavior test of the feed shaft under typical working conditions
  • the first temperature sensor 3 is arranged on the front bearing 2 of the feeding system, the second temperature sensor 7 is arranged on the nut 6, the third temperature sensor 10 is arranged on the rear bearing 11 of the feeding system, and the fourth temperature sensor 9 is arranged On the bed 8 near the screw;
  • the pre-tightening amount of the screw is measured by the pre-tightening angle of the pre-tightening nut 12, and the thermal behavior test of the feed axis is performed separately: in the initial thermal steady state, the laser interferometer is used to test the feed axis The positioning error of the whole stroke is recorded, and the temperature values of the first temperature sensor 3, the second temperature sensor 7, the third temperature sensor 10 and the fourth temperature sensor 9 are recorded; then, the feed axis is heated under the motion information, and the motion process Test the full-stroke positioning error at regular intervals (about 15 minutes), and record the temperature of each measuring point; repeat the heat engine and test process until the lead screw reaches thermal equilibrium;
  • the second step is to calculate the maximum thermal error of the feed axis and the temperature rise of the key temperature measurement point
  • the maximum thermal error of the feed axis in each preload state is calculated according to formula (1):
  • E max_i E i (M i ,N)-E i (1,N) (1)
  • E max_i is the maximum thermal error when the i-th preload is used
  • M i is the number of positioning error tests when the i-th preload is used
  • N is the number of points for the positioning error test
  • E i (M i , N) is the N- th point data of the Mi- th positioning error test when the i- th preload is used
  • E i (1,N) is the N-th point of the first positioning error test when the i-th preload is used data
  • ⁇ T i,j is the temperature rise of the j-th temperature sensor when the i-th preload is used
  • T i,j (M i ) is the j-th temperature sensor when the i-th preload is used.
  • measured values M i, T i, j (1) is an amount of preload using the i-th measured value of the first temperature sensors j, T i, 4 (M i ) of the i-th amount of preload using The Mi- th measurement value of the fourth temperature sensor 9 at time, Ti ,4 (1) is the first measurement value of the fourth temperature sensor 9 when the i-th preload is used;
  • the third step is to establish the mathematical model of the screw preload and the maximum thermal error and the temperature rise of the key temperature measurement points.
  • E max is the maximum thermal error of the feed shaft
  • A is the screw preload, that is, the locking angle of the preload nut 12
  • a 0 and a 1 are coefficients
  • ⁇ T j is the temperature rise of the j-th temperature sensor, b j,0 , b j,1 and b j,2 are coefficients;
  • the coefficients a 0 , a 1 , b j,0 in equations (3) and (4) are identified based on the least square method , B j,1 and b j,2 ;
  • the fourth step is to calculate the optimal preload of the screw
  • ⁇ 0 is the weight coefficient of the maximum thermal error of the feed axis
  • ⁇ j is the weight coefficient of the temperature rise of the j-th temperature sensor
  • a min and A max are the lower limit and upper limit of the screw preload A during the automatic optimization process.
  • the beneficial effect of the present invention is that the thermal error of the feed shaft and the temperature rise of the moving parts are comprehensively considered, and the optimal preload of the lead screw is obtained through the thermal behavior test of the feed shaft under typical working conditions and the preload calculation method , Solve the problem that the current screw preloading method based on experience is difficult to achieve the optimal effect.
  • Pre-tightening the screw according to the method for determining the pre-tightening amount of the screw provided by the present invention can effectively reduce the thermal error of the feed shaft while effectively controlling the temperature rise of the moving parts such as the bearing, thereby improving the machining accuracy and precision stability of the machine tool Performance and ensure the service life of moving parts such as bearings.
  • Figure 1 is a schematic diagram of the temperature measuring point layout of the feed shaft.
  • Figure 2 shows the effect diagram of the maximum thermal error modeling.
  • Figure 3(a) is the effect diagram of the temperature rise modeling of the first temperature sensor.
  • Figure 3(b) shows the effect of temperature rise modeling of the second temperature sensor.
  • Figure 3(c) shows the effect of temperature rise modeling of the third temperature sensor.
  • the X-axis stroke of the machining center is 0 ⁇ -500mm, and the maximum feed speed is 32000mm/min.
  • the first temperature sensor 3 is arranged on the front bearing 2 of the feed system
  • the second temperature sensor 7 is arranged on the nut 6
  • the third temperature sensor 10 is arranged on the On the rear bearing 11 of the feed system
  • the fourth temperature sensor 9 is arranged on the bed 8 near the screw.
  • the tested machining center is oriented to the consumer electronics industry, and the typical workpieces processed are the aluminum housings of mobile phones and tablet computers.
  • the typical working conditions are determined according to the processing process: the usual stroke range is -100 ⁇ -400mm; the usual feed speed is 2000mm/ min; The processing frequency is the average processing time of a single workpiece is 90s, and the workpiece processing interval is 15s.
  • the thermal behavior test of the feed shaft is carried out under the conditions of the locking angle of the pre-tightening nut of 0°, 60°, 120°, 180° and 270°:
  • the positioning error of the full stroke is tested every 15 minutes, and the temperature values of the first temperature sensor 3, the second temperature sensor 7, the third temperature sensor 10 and the fourth temperature sensor 9 are recorded. After the heat engine moves for 2 hours, the feed axis reaches thermal equilibrium and the test stops.
  • the second step is to calculate the maximum thermal error of the feed axis and the temperature rise of the key temperature measurement point
  • the maximum thermal error of the feed axis in each preload state is calculated according to formula (1):
  • E max_i E i (M i ,N)-E i (1,N) (1)
  • E max_i is the maximum thermal error when the i-th preload is used
  • M i is the number of positioning error tests when the i-th preload is used
  • N is the number of points for the positioning error test
  • E i (M i , N) is the N- th point data of the Mi- th positioning error test when the i- th preload is used
  • E i (1,N) is the N-th point of the first positioning error test when the i-th preload is used data.
  • ⁇ T i,j is the temperature rise of the j-th temperature sensor when the i-th preload is used
  • T i,j (M i ) is the j-th temperature sensor when the i-th preload is used.
  • measured values M i, T i, j (1) is an amount of preload using the i-th measured value of the first temperature sensors j, T i, 4 (M i ) of the i-th amount of preload using the fourth temperature sensor of the measured values M i 9, T i, 4 (1) the fourth temperature sensor 9 1st measurement value is employed when the i-th amount of preload.
  • the third step is to establish a mathematical model of the screw preload, the maximum thermal error and the temperature rise of the key temperature measurement point
  • E max is the maximum thermal error of the feed shaft
  • A is the screw preload (that is, the locking angle of the preload nut 12)
  • a 0 and a 1 are coefficients.
  • ⁇ T j is the temperature rise of the j-th temperature sensor
  • b j,0 , b j,1 and b j,2 are coefficients.
  • the maximum thermal error modeling effect is shown in Figure 2
  • the modeling effect of the temperature rise of the first to third temperature sensors is shown in Figure 3(a) ⁇ Figure 3(c).
  • the fourth step is to calculate the optimal preload of the screw
  • ⁇ 0 is the weight coefficient of the maximum thermal error of the feed axis
  • ⁇ j is the weight coefficient of the temperature rise of the j-th temperature sensor.
  • the optimal preload of the X-axis screw of the vertical machining center is 156°.

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Abstract

本发明提供了基于热误差和温升加权的丝杠预紧量确定方法，属于数控机床装配领域。首先在丝杠的不同预紧状态下，进行典型工况下的进给轴热行为试验，获取丝杠在各种预紧状态下的最大热误差和关键温度测点的温升；然后，建立丝杠预紧量与最大热误差和关键温度测点温升的数学模型；最后，以最大热误差和各温度测点温升的加权函数为目标函数进行优化，得出丝杠的最优预紧量。该方法综合考虑进给轴的热误差和关键点温升确定丝杠的最优预紧量，解决了目前基于经验的丝杠预紧方法难以达到最优效果的问题，可以提高机床的加工精度和精度稳定性，并确保轴承等运动部件的使用寿命。

Description

基于热误差和温升加权的丝杠预紧量确定方法 技术领域
本发明属于数控机床装配技术领域，具体为一种基于热误差和温升加权的丝杠预紧量确定方法。
背景技术
在进给轴运行过程中，螺母与丝杠的摩擦会产生大量热量，该热量传递到丝杠上则会导致丝杠热伸长。若进给轴采用半闭环控制方式，丝杠热伸长就会引起该轴定位精度的变化，这种变化就是进给轴的热误差。该热误差最终会影响工件的加工精度和批量加工的精度一致性。
为了减小半闭环进给轴的热误差，常用的方法是对丝杠进行预紧，即通过预紧螺母对丝杠施加轴向预紧力，使丝杠产生适量的轴向预拉伸。预紧螺母的预紧角度越大，丝杠的预拉伸量就越大。当丝杠受热时，将会先抵消丝杠由于预拉伸产生的内部应力，而不会伸长。当内部应力被完全抵消后，丝杠才会受热伸长。这样可有效减小进给轴的热误差。
目前通过丝杠预紧方式减小进给轴热误差的方法存在以下不足：丝杠的预紧量一般基于经验确定且主要考虑对热误差的抑制效果，这种方式很难达到最优的效果。若丝杠预紧量偏小，则对热误差的抑制效果不够；若丝杠预紧量偏大，虽然对热误差抑制效果较好，但会造成丝杠的前后轴承温升过大，从而加速轴承的磨损，缩短使用寿命。在专利《一种数控机床进给系统滚珠丝杠预紧力的试验优化方法》(申请号：201610285987.5)中，虽然提出了以进给轴定位精度和动态特性为指标的丝杠预紧力优化方法，但没有考虑丝杠预紧力对热误差和前后轴承温升的影响，因此采用该方法得到的最优丝杠预紧力并不能满足对热误差抑制和温升控制的共同要求。
发明内容
本发明针对目前缺乏综合考虑热误差和温升的最优预紧量确定方法的现状，提出一种基于热误差和温升加权的丝杠预紧量确定方法，综合考虑进给轴热误差的抑制和关键测点温升的控制，得出丝杠的最优预紧量。
本发明的技术方案为：
基于热误差和温升加权的丝杠预紧量确定方法，首先在丝杠的不同预紧状态下，进行典型工况下的进给轴热行为试验，获取丝杠在各种预紧状态下的最大热误差和关键温度测点的温升；然后，建立丝杠预紧量分别与最大热误差和关键温度测点温升的数学模型；最后，以最大热误差和各温度测点温升的加权函数为目标函数进行优化，得出丝杠的最优预紧量；具体步骤如下：
第一步，典型工况下的进给轴热行为试验
将第一温度传感器3布置在进给系统的前轴承2上，第二温度传感器7布置在螺母6上，第三温度传感器10布置在进给系统的后轴承11上，第四温度传感器9布置在丝杠附近的床身8上；
对机床加工工件时的运动轨迹进行分析，提取进给轴的运动信息，包括行程范围、进给速度和运行频率；
在丝杠的不同预紧状态下，丝杠预紧量以预紧螺母12的预紧角度衡量，分别进行进给轴热行为试验：在初始热稳态时，使用激光干涉仪测试进给轴的全行程定位误差，并记录第一温度传感器3、第二温度传感器7、第三温度传感器10和第四温度传感器9的温度值；然后，让进给轴在运动信息下进行热机，运动过程中每隔一段时间(约15min)测试一次全行程定位误差，并记录各测点的温度；重复热机和测试过程，直至丝杠达到热平衡；
第二步，计算进给轴的最大热误差和关键温度测点的温升
基于第一步采集的热误差和温度数据，在每种预紧状态下进给轴最大热误差按式(1)计算：
E max_i＝E i(M i,N)-E i(1,N) (1)
式中：E max_i为采用第i种预紧量时的最大热误差，M i为采用第i种预紧量时的定位误差测试次数，N为定位误差测试的点数，E i(M i,N)为采用第i种预紧量时第M i次定位误差测试的第N点数据，E i(1,N)为采用第i种预紧量时第1次定位误差测试的第N点数据；
每种预紧量下的各温度测点温升按式(2)计算：
ΔT i,j＝[T i,j(M i)-T i,j(1)]-[T i,4(M i)-T i,4(1)] (2)
式中：△T i,j为采用第i种预紧量时第j个温度传感器的温升，T i,j(M i)为采用第i种预紧量时第j个温度传感器的第M i次测量值，T i,j(1)为采用第i种预紧量时第j个温度传感器的第1次测量值，T i,4(M i)为采用第i种预紧量时第四温度传感器9的第M i次测量值，T i,4(1)为采用第i种预紧量时第四温度传感器9的第1次测量值；
第三步，建立丝杠预紧量分别与最大热误差和关键温度测点温升的数学模型
丝杠预紧量与进给轴最大热误差的关系如式(3)：
E max＝a 0-a 1×A (3)
式中：E max为进给轴最大热误差，A为丝杠预紧量即预紧螺母12的锁紧角度，a 0和a 1为系数；
丝杠预紧量与第j个温度传感器温升的数学模型如式(4)所示：
Figure PCTCN2019075710-appb-000001
式中：△T j为第j个温度传感器的温升，b j,0、b j,1和b j,2为系数；
根据第二步得到的丝杠在不同预紧量下的最大热误差和温升数据，基于最小二乘法辨识式(3)和式(4)中的系数a 0、a 1、b j,0、b j,1和b j,2；
第四步，计算丝杠的最优预紧量
最大热误差和关键温度测点温升的加权函数如式(5)所示：
Figure PCTCN2019075710-appb-000002
式中：λ 0为进给轴最大热误差的权系数，λ j为第j个温度传感器温升的权系数；
根据式(3)和式(4)将式(5)改写为：
Figure PCTCN2019075710-appb-000003
基于式(7)进行自动寻优，得出丝杠的最优预紧量；
Figure PCTCN2019075710-appb-000004
式中：A min和A max分别为自动寻优过程中丝杠预紧量A的下限和上限。
本发明的有益效果为：综合考虑了进给轴的热误差和运动部件的温升，通过典型工况下的进给轴热行为试验和预紧量计算方法得到丝杠的最优预紧量，解决了目前基于经验的丝杠预紧方法难以达到最优效果的问题。按照本发明提出的丝杠预紧量确定方法对丝杠进行预紧，可以在有效减小进给轴热误差的同时有效控制轴承等运动部件的温升，从而提高机床的加工精度和精度稳定性，并确保轴承等运动部件的使用寿命。
附图说明
图1为进给轴温度测点布置示意图。
图2为最大热误差建模效果图。
图3(a)为第一温度传感器温升建模效果图。
图3(b)为第二温度传感器温升建模效果图。
图3(c)为第三温度传感器温升建模效果图。
图中：1进给轴电机；2丝杠前轴承；3第一温度传感器；4丝杠；5工作台；6螺母；7第二温度传感器；8床身；9第四温度传感器；10第三温度传感器；11后轴承；12预紧螺母。
具体实施方式
为了使本发明的目的、技术方案和优点更加清晰明了，下面结合附图对本发明作详细说明。
以某型立式加工中心的X轴为例，详细说明本发明的实施方式。该加工中心X轴行程为0～-500mm，最大进给速度为32000mm/min。
第一步，典型工况下的进给轴热行为试验将第一温度传感器3布置在进给系统的前轴承2上，第二温度传感器7布置在螺母6上，第三温度传感器10布置在进给系统的后轴承11上，第四温度传感器9布置在丝杠附近的床身8上。
被测加工中心面向消费电子行业，加工的典型工件为手机和平板电脑的铝制外壳，根据加工过程确定其典型工况为：常用行程范围为-100～-400mm；常用进给速度为2000mm/min；加工频率为单个工件平均加工时间90s，工件加工间隔时间15s。
分别在预紧螺母的锁紧角度为0°、60°、120°、180°和270°的状态下进行进给轴热行为试验：
在进给轴初始热稳态时，使用激光干涉仪测试进给轴的全行程定位误差，并记录第一温度传感器3、第二温度传感器7、第三温度传感器10和第四温度 传感器9的温度值。然后，让进给轴在典型运动信息下进行热机，热机程序如表1所示。
表1 热机的CNC程序
Figure PCTCN2019075710-appb-000005
运动过程中每隔15min测试一次全行程定位误差，并记录第一温度传感器3、第二温度传感器7、第三温度传感器10和第四温度传感器9的温度值。热机运动进行2小时后进给轴达到热平衡，测试停止。
第二步，计算进给轴的最大热误差和关键温度测点的温升
基于第一步采集的热误差和温度数据，在每种预紧状态下进给轴最大热误差按式(1)计算：
E max_i＝E i(M i,N)-E i(1,N) (1)
式中：E max_i为采用第i种预紧量时的最大热误差，M i为采用第i种预紧量时的定位误差测试次数，N为定位误差测试的点数，E i(M i,N)为采用第i种预紧量时第M i次定位误差测试的第N点数据，E i(1,N)为采用第i种预紧量时第1次定位误差测试的第N点数据。
每种预紧量下的各温度测点温升按式(2)计算：
ΔT i,j＝[T i,j(M i)-T i,j(1)]-[T i,4(M i)-T i,4(1)] (2)
式中：△T i,j为采用第i种预紧量时第j个温度传感器的温升，T i,j(M i)为采用 第i种预紧量时第j个温度传感器的第M i次测量值，T i,j(1)为采用第i种预紧量时第j个温度传感器的第1次测量值，T i,4(M i)为采用第i种预紧量时第四温度传感器9的第M i次测量值，T i,4(1)为采用第i种预紧量时第四温度传感器9的第1次测量值。
根据式(1)和式(2)计算出丝杠在每种预紧量时的最大热误差和各温度测点温升，具体结果如表2所示。
表2 最大热误差和温升数据汇总表
Figure PCTCN2019075710-appb-000006
第三步，建立丝杠预紧量与最大热误差和关键温度测点温升的数学模型
丝杠预紧量与进给轴最大热误差的关系如式(3)：
E max＝a 0-a 1×A (3)
式中：E max为进给轴最大热误差，A为丝杠预紧量(即预紧螺母12的锁紧角度)，a 0和a 1为系数。
预紧量与第j个温度传感器温升的数学模型如式(4)所示：
Figure PCTCN2019075710-appb-000007
式中：△T j为第j个温度传感器的温升，b j,0、b j,1和b j,2为系数。
根据第二步得到的丝杠在不同预紧量下的最大热误差和温升数据，基于最 小二乘法，根据式(3)和式(4)可以得出模型中的系数，具体为：a 0＝30.418、a 1＝0.083、b 1,0＝3.073、b 1,1＝0.15、b 1,2＝0.010、b 2,0＝0.718、b 2,1＝2.220、b 2,2＝0.0002、b 3,0＝1.814、b 3,1＝0.912和b 3,2＝0.005。最大热误差建模效果如图2所示，第一至第三温度传感器温升的建模效果如图3(a)～图3(c)所示。
第四步，计算丝杠的最优预紧量
最大热误差和关键温度测点温升的加权函数如式(5)所示：
Figure PCTCN2019075710-appb-000008
式中：λ 0为进给轴最大热误差的权系数，λ j为第j个温度传感器温升的权系数。
根据式(3)和式(4)将式(5)改写为：
Figure PCTCN2019075710-appb-000009
综合考虑对热误差抑制效果和温升控制，设置式(6)中的权系数为：λ 0＝0.15、λ 1＝0.8、λ 2＝0.1和λ 3＝0.8。
基于式(7)进行自动寻优，
Figure PCTCN2019075710-appb-000010
可以得到立式加工中心X轴丝杠的最优预紧量为156°。

Claims (1)

  1. 一种基于热误差和温升加权的丝杠预紧量确定方法，首先在丝杠的不同预紧状态下，进行典型工况下的进给轴热行为试验，获取丝杠在各种预紧状态下的最大热误差和关键温度测点的温升；然后，建立丝杠预紧量分别与最大热误差和关键温度测点温升的数学模型；最后，以最大热误差和各温度测点温升的加权函数为目标函数进行优化，得出丝杠的最优预紧量；其特征在于，步骤如下：
    第一步，典型工况下的进给轴热行为试验
    将第一温度传感器(3)布置在进给系统的前轴承(2)上，第二温度传感器(7)布置在螺母(6)上，第三温度传感器(10)布置在进给系统的后轴承(11)上，第四温度传感器(9)布置在丝杠附近的床身(8)上；
    对机床加工工件时的运动轨迹进行分析，提取进给轴的运动信息，包括行程范围、进给速度和运行频率；
    在丝杠的不同预紧状态下，丝杠预紧量以预紧螺母(12)的预紧角度衡量，分别进行进给轴热行为试验：在初始热稳态时，使用激光干涉仪测试进给轴的全行程定位误差，并记录第一温度传感器(3)、第二温度传感器(7)、第三温度传感器(10)和第四温度传感器(9)的温度值；然后，让进给轴在运动信息下进行热机，运动过程中每隔一段时间测试一次全行程定位误差，并记录各测点的温度；重复热机和测试过程，直至丝杠达到热平衡；
    第二步，计算进给轴的最大热误差和关键温度测点的温升
    基于第一步采集的热误差和温度数据，在每种预紧状态下进给轴最大热误差按式(1)计算：
    E max_i＝E i(M i,N)-E i(1,N)  (1)
    式中：E max_i为采用第i种预紧量时的最大热误差，M i为采用第i种预紧量时的定位误差测试次数，N为定位误差测试的点数，E i(M i,N)为采用第i种预紧 量时第M i次定位误差测试的第N点数据，E i(1,N)为采用第i种预紧量时第1次定位误差测试的第N点数据；
    每种预紧量下的各温度测点温升按式(2)计算：
    ΔT i,j＝[T i,j(M i)-T i,j(1)]-[T i,4(M i)-T i,4(1)]  (2)
    式中：△T i,j为采用第i种预紧量时第j个温度传感器的温升，T i,j(M i)为采用第i种预紧量时第j个温度传感器的第M i次测量值，T i,j(1)为采用第i种预紧量时第j个温度传感器的第1次测量值，T i,4(M i)为采用第i种预紧量时第四温度传感器(9)的第M i次测量值，T i,4(1)为采用第i种预紧量时第四温度传感器(9)的第1次测量值；
    第三步，建立丝杠预紧量分别与最大热误差和关键温度测点温升的数学模型
    丝杠预紧量与进给轴最大热误差的关系如式(3)：
    E max＝a 0-a 1×A  (3)
    式中：E max为进给轴最大热误差，A为丝杠预紧量即预紧螺母(12)的锁紧角度，a 0和a 1为系数；
    丝杠预紧量与第j个温度传感器温升的数学模型如式(4)所示：
    Figure PCTCN2019075710-appb-100001
    式中：△T j为第j个温度传感器的温升，b j,0、b j,1和b j,2为系数；
    根据第二步得到的丝杠在不同预紧量下的最大热误差和温升数据，基于最小二乘法辨识式(3)和式(4)中的系数a 0、a 1、b j,0、b j,1和b j,2；
    第四步，计算丝杠的最优预紧量
    最大热误差和关键温度测点温升的加权函数如式(5)所示：
    Figure PCTCN2019075710-appb-100002
    式中：λ 0为进给轴最大热误差的权系数，λ j为第j个温度传感器温升的权系数；
    根据式(3)和式(4)将式(5)改写为：
    Figure PCTCN2019075710-appb-100003
    基于式(7)进行自动寻优，得出丝杠的最优预紧量；
    Figure PCTCN2019075710-appb-100004
    式中：A min和A max分别为自动寻优过程中丝杠预紧量A的下限和上限。
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