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工程设计学报
Chin J Eng Design  2023, Vol. 30 Issue (4): 456-466    DOI: 10.3785/j.issn.1006-754X.2023.00.055
Tribology and Surface/Interface Technology     
Research on the effect of thermal deformation of feed system on the motion repeatability errors of machine tool
Guangming SUN1,2(),Jingjing YANG1,Siqi CHEN1,Jian ZHAO1(),Heshuai ZHANG2
1.School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin 300384, China
2.Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China
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Abstract  

In order to analyze the effect of thermal deformation of feed system on the motion repeatability errors of machine tool, a modeling method for thermal deformation of feed system based on a layered model-moving heat source was proposed. The feed system was divided into a screw layer and worktable layer, and the moving joint surface was equivalent to a spring. The finite element model was established by using solid element and contact element. The temperature field and thermal deformation of the feed system were obtained by applying moving heat source to the screw and guide rail. On this basis, the effect of worktable feed speed, bearing preload torque, and slider support distance on the motion repeatability errors of machine tool was analyzed and verified by experiments. The research showed that the worktable feed speed and bearing preload torque had a significant impact on the motion repeatability errors of machine tool, while the slider support distance had a relatively small impact on the motion repeatability errors of machine tool. The research results provide a basis for reducing the motion repeatability errors of machine tool in machine tool design and assembly.

Key words： feed system      thermal deformation      move thermal load      motion repeatability error     
Received: 03 March 2023      Published: 04 September 2023
CLC:  TH 128  
Corresponding Authors: Jian ZHAO     E-mail: gmsun@tju.edu.cn;zhaojiantcu@163.com
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Guangming SUN
Jingjing YANG
Siqi CHEN
Jian ZHAO
Heshuai ZHANG
Cite this article:

Guangming SUN,Jingjing YANG,Siqi CHEN,Jian ZHAO,Heshuai ZHANG. Research on the effect of thermal deformation of feed system on the motion repeatability errors of machine tool. Chin J Eng Design, 2023, 30(4): 456-466.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2023.00.055     OR     https://www.zjujournals.com/gcsjxb/Y2023/V30/I4/456


进给系统热变形对机床运动重复性误差的影响研究

为了分析进给系统热变形对机床运动重复性误差的影响，提出了一种基于分层模型-移动热源的进给系统热变形建模方法。将进给系统分为丝杠层和工作台层，将移动结合面等效为弹簧。采用实体单元和接触单元建立了有限元模型，在丝杠和导轨上施加移动热源，获得进给系统的温度场和热变形。在此基础上，分析了工作台进给速度、轴承预紧力矩和滑块支撑距离对机床运动重复性误差的影响，并进行了实验验证。研究表明，工作台进给速度和轴承预紧力距对机床运动重复性误差的影响较大，滑块支撑距离对机床运动重复性误差的影响较小。研究结果为在机床设计和装配中减小机床运动重复性误差提供了依据。


关键词： 进给系统,  热变形,  移动热载荷,  运动重复性误差 
Fig.1 Structure of linear feed system of precision machine tool
Fig.2 Layered model of feed system
Fig.3 Equivalent stiffness treatment of ball screw nut pair
Fig.4 Finite element model of guide rail slider pair
Fig.5 Finite element model of feed system
边界条件计算公式字符意义计算结果
轴承生热率q1[22]

q1=0.104?7n1(M1+M2)V

M1=10-7f0vn23dm3vn1>2?000?mm2/s?r/min160×10-7f0dm3vn1<2?000?mm2/s?r/min??????????????????????????????M2=f1Fβdm

n1为轴承转速；M1为轴承所受的黏性摩擦力矩；M2为轴承所受的机械摩擦力矩；V为热源体积；?0为取决于润滑类型和轴承参数的常数；ν为润滑剂运动黏度；dm为轴承中径；?1为与载荷和轴承结构相关的系数；Fβ 为轴承摩擦力矩的计算载荷1 510 520 W/m3

滚珠丝杠与螺母间的

热流密度q2[23]

q2=0.104?7n2(0.94Mp+Md)A2

Md=FαPh2πη11-?η12

Mp=FpPh2πη1(1-?η12)

n2为丝杠转速；Mp为滚珠螺旋阻力矩；Md为驱动力矩；Α2为丝杠与螺母的接触面积；Fα 为丝杠的轴向载荷；Ρh为丝杠的导程；η1为丝杠的传动效率；Fp为丝杠的轴向预紧力10 300 W/m2
电机热流密度q3[24]q3=Mt?n39?550?A31-?η2Mt为电机输出扭矩；n3为电机转速；η2为电机机械效率；A3为电机表面积1 500 W/m2

导轨与滑块间的

热流密度q4[24]

q4=μWgv0J?A4μ为导轨与滑块间的动摩擦因数；W为施加在摩擦面上的力；g为重力加速度，取9.8 m/s2；J为热功当量，取4.2 J/cal；ν0为滑动速度；A4为导轨与滑块的摩擦面积580 W/m2

自然对流换热系数

h1[25]

h1=Nu?κL

Nu=CGr?Prn

Gr=L3gavΔTv2

Pr=cpρvk

Nu为努塞尔数；κ为流体的热传导系数；L为定型尺寸；Gr为格拉晓夫数；Pr为普朗特系数；av为关于流体体积的膨胀系数；?T为试验台表面与液体之间的温度差；cp为流体的等压比热容；ρ为流体密度；C, n为常数，与液体的流动状态和发生导热表面的形状有关

轴承座表面、

电机座表面：

55 W/（m2·℃）

强迫对流换热系数

h2[25]

h2=Nu?κL

Nu=Re23·Pr23(Re<4.3×105,?0.7<Pr<670)Re=ω×d0vf

Re为雷诺数；ω为角速度；d0为公称直径；vf为空气的运动黏度

丝杠螺母座表面：

230 W/（m2·℃）；

丝杠表面：

650 W/（m2·℃）
Table 1 Analysis of thermal boundary conditions for machine tool
Fig.6 Flow of layered simulation of feed system based on layered-moving heat source
Fig.7 Temperature field of screw layer
Fig.8 Structure field of screw layer
Fig.9 Temperature field of worktable
Fig.10 Structure field of worktable
Fig.11 Simulation results of worktable motion errors
区域线性位移重复性误差/μm偏摆角重复性误差/(μm/m)俯仰角重复性误差/(μm/m)
P11.483.7211.00
P21.391.540.83
P31.462.1410.85
P41.331.240.80
P50.710.521.05
Table 2 Motion repeatability error of worktable
Fig.12 Simulation results of motion repeatability errors of machine tool under different worktable feed speeds
Fig.13 Simulation results of motion repeatability errors of machine tool under different bearing preload torques
Fig.14 Simulation results of motion repeatability errors of machine tool under different slider support distances
Fig.15 Site of the test experiment of motion repeatability errors of machine tool
Fig.16 Experimental results of motion repeatability errors of machine tool under different worktable feed speeds
Fig.17 Experimental results of motion repeatability errors of machine tool under different bearing preloading torques
Fig.18 Experimental results of motion repeatability errors of machine tool under different slider support distances
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