Research on real time compensation of thermal errors of CNC lathe based on linear regression theory Qiu Yongliang

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1 d Iteratioal Coferece o Machiery, Materials Egieerig, Chemical Egieerig ad Biotechology (MMECEB 015) Research o real time compesatio of thermal errors of CNC lathe based o liear regressio theory Qiu Yogliag Guagdog polytechic of idustry ad commerce. Guagzhou yogliag.qiu@163.com Keywords: Precisio machiig; CNC lathe; Liear regressio theory; Thermal error compesatio Abstract.I the field of precisio machiig, thermal error is oe of the mai error sources i CNC machiig. The thermal error compesatio of CNC lathe ca effectively improve the machiig accuracy of machie tools. O the basis of the research of local thermal error compesatio techology i NC lathe the temperature of the ey poits i CNC machiig is real-time measured by platium resistace temperature sesor. Ad the thermal error model is established by meas of the fit of the measured temperature ad liear regressio theory. Accordig to the thermal error model, the experimet of thermal error compesatio is coducted, ad the experimetal results idicate that better surface quality is achieved with the implemetatio of the thermal error compesatio. Itroductio With the developmet of sciece ad techology, the requiremets for the accuracy of product are higher ad higher. The methods of improvig the machiig accuracy of CNC lathe have maily error avoidace method ad error compesatio method [1-]. Error avoidace method which improves the machiig accuracy of the lathe by improvig the accuracy of parts of machie tools, usig costat temperature worshop ad so o will lead to a icrease i the cost of worpiece. Error compesatio method which is both ecoomical ad reliable has bee a focal poit of the research of CNC machiig techology [3-4]. There are may factors which affect the machiig accuracy of machie tools. Ad the thermal error which accouts for 40%-70% of the total machiig error is oe of the biggest error sources [5-6]. The ifluece of thermal error o the machiig accuracy is more obvious for the CNC lathe of machiig rotary parts because of the temperature of the worpiece is raisig fast i the process of machiig. The temperature of the motor, the rotary shaft, the feed shaft ad the cuttig tool ad so o are measured by the platium resistace temperature sesor. The thermal error model of CNC lathe is established based o liear regressio theory. The temperature of the same measurig poit is measured real-time i the CNC lathe machiig, ad real-time thermal error is calculated by thermal error model. Real-time compesatio of thermal errors for CNC lathe is realized through thermal error compesatio system. Placemet of temperature sesor Both the frictio heat betwee the movig parts ad the eviromet temperature have some effects o the machiig accuracy of the lathe. The machiig poit of the lathe ca ot be accurately positioed due to the thermal expasio of the lathe guide, thermal expasio of worpiece ad so o. The machiig error caused by the temperature chage is called thermal error. The thermal error of the worpiece i lathe machiig is maily reflected i the machiig accuracy of the Z axis, as show i fig The authors - Published by Atlatis Press 530

2 Fig.1 SJ30 oblique body CNC lathe The placemet of the temperature sesor is the ey of the thermal error compesatio effect. For CNC lathe machiig, the mai heat sources: heat of electric motor, frictio heat betwee gears i the spidle box, cuttig heat betwee the cuttig tool ad the worpiece, the frictio heat betwee the guide rail ad the ball screw, ad so o. Therefore, the heat source affectig the accuracy of the worpiece is maily cocetrated i the spidle box, X axis guide, cuttig tools, electric motor ad so o. These heat sources are the ey positios placig temperature sesor. The temperature sesor should be placed as close as possible to the heat source, ad its umber should be more tha the umber of heat source of the CNC lathe. If the coditios permit, the more temperature sesors are placed at the ey poit ad the better the statistical effect. Thermal error model of CNC lathe The liear relatioship betwee thermal error ad temperature is established by usig multiple liear regressio theory, which is a commo method of thermal error modelig [7-8].The thermal error model established by this method has good reliability ad high accuracy of predictio. Accordig to the distributio of the heat source of the CNC lathe, temperature measurig poits are placed o the lathe. The temperature measured at each measurig poit is recorded as: T 1, T,, T. Observe the chage of the temperature, the K(=1,,,m) group sample observatio data were recorded as: T 1, T,, T. At the same time, the machiig error of the worpiece i the directio of the Z axis is recorded: z1, z,, z.liear equatios ca be obtaied as follows: z1 a0 at 1 11 at 11 z a0 at 1 1 at z3 a0 at 1 13 at3 3 (1) z a0 at 1 1 at The eq. (1) is chaged ito a matrix formula: Z BA () Where, 531

3 z1 1 a0 1 T11 T1 T 1 z a1 1 T1 T T A ; B ; Z ; a 1 T1 T T z a0, a1,, a are +1 parameters to be estimated. Both T1, T,, Tad z1, z,, z ca be accurately measured. 0, 1,, are idepedet radom variables ad obey ormal distributio. Liear regressio equatio is established: y a at a T a T (3) The square sum of the deviatio is miimum to calculate the parameters a 0, a 1,, a, that is: ( ) mi ( j 0 1 1j j j) j1 j1 (4) M y y y a at a T a T Parameter a0, a1,, a is the solutio of the eq. (5) by the differetial theory. M ( yj a0 at 1 1j atj) a0 j1 M ( yj a0 at 1 1j atj) a1 j1 M ( yj a0 at 1 1j atj) a j1 Therefore, the thermal error model is: z a at a T a T (6) (5) Thermal error real-time compesatio systems The thermal error real-time compesatio system of CNC lathe which is composed of the software programmig system, the real-time temperature measuremet system ad the servo system is a closed loop system, as show i fig.. The origial CNC istructio of the CNC lathe eeds to be determied accordig to the desig of worpiece before the CNC machiig. However, the origial CNC istructio eeds to be corrected accordig to the thermal error model ad the feedbac of the ecoder because of thermal error. The temperatures of real-time measuremet are substituted ito the thermal model, ad the thermal errors are calculated. Fig.. Thermal error real-time compesatio systems 53

4 Implemetatio of thermal error compesatio Based o ey hot poits of CNC lathe ad priciples for temperature sesor placemet, four platium resistace temperature sesors were istalled i the spidle box, X axis guide rail, cuttig tools ad electric motor. I the machiig of pure alumium material, the temperature of the real-time measuremet is recorded: T 1, T,, T 4 ( 1,,,5). The machiig errors of worpiece diameter relative each group temperature are measured with a verier caliper. Five sets of machiig errors are recorded as: z1, z,, z5. Fig.3 Worpieces of SJ30 oblique body CNC lathe The temperature ad the machiig errors are substituted ito the eq. (5), to calculate the parameters a 0, a 1,, a 5. Therefore, the thermal error model is described as: z T 6.93T 3.96T 9.3T (7) The effect of thermal error compesatio is show i Figure 4. The results show that the effect of thermal error compesatio of CNC lathe is obvious. Thermal errors(um) Before compesatio After compesatio Machiig time(mi) Fig.4 Effect of thermal error compesatio Coclusios The thermal error compesatio ca effectively improve the machiig accuracy of the CNC lathe. I this paper, the structure of umerical cotrol lathe, heat source distributio ad the ifluece of thermal error o the accuracy of the worpiece ad so o are aalyzed i detail. The heat source of the CNC lathe is foud, which provides the basis for the placemet of the temperature sesor. The thermal error model of CNC lathe is established based o liear regressio theory ad the temperature measured by multiple temperature sesors. The thermal error real-time compesatio system based o thermal error model is developed. It is foud by experimets that the placemet of temperature sesor, thermal error model ad thermal error compesatio system are all reliable. 533

5 Refereces [1] Lv Fegyu, He Chegzhu, Gou Weidog. Thermal error compesatio system developmet of vertical machiig ceter. Modular machie tool & automatic maufacturig techique,014,6: [] Zhag Tig, Liu Shihao. Overview of thermal error compesatio modelig for umerical cotrol machie. Machie tool & hydraulics, 011,39(1):1-17. [3] Guo Qiajia, Yag Jiaguo, Wag Xiusha, et al. O lie measuremet ad compesatio machiig of thermal error for NC machie Tool. Maufacturig techology & machie tool, 007,4:3-37. [4] Guo Qiajia,Yag Jiaguo,Li Yogxiag, et al. Research o thermal error compesatio techique of gear hobbig machie. Chia mechaical egieerig,007,3(18): [5] Ma shuwe, Xu Zhogxig, Liu Lixi, et al. A study o thermal Error Compesatio for the spidle of XH718 machiig ceter. Mechaical sciece ad techology, 007,6(4): [6] Gog Ligyu, Che zeyu. Thermal error modelig ad compesatio of umericai cotrol machie tools, Maufacturig automatio, 01,34(1):4-69. [7] Ji Chagzhu. The research of CNC thermal error compesatio system. Master degree dissertatio, Hefei Uiversity of Techology, [8] Wag Shilog, Yag Yog, Zhou Jie, et al. Modelig of thermal error compesatio of large-scale umerical cotrol gear hobbig machie. Joural of cetral south uiversity, 011,4(10):