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Investigation on the spindle thermal displacement and its compensationof precision cutter grindersYung-Cheng Wanga, Ming-che Kaoa, Chung-Ping ChangbaInstitute of Mechanical Engineering, National Yunlin University of Science and Technology, No. 123, Uni. Road, Section 3, 640 Douliu, Yunlin, TaiwanbDepartment of Mechanical Engineering, National Central University, Taiwana r t i c l ei n f oArticle history:Received 24 July 2010Received in revised form 7 March 2011Accepted 16 March 2011Available online 30 March 2011Keywords:Cutter grinderSpindle thermal displacementLaser displacement sensorCompensation mechanisma b s t r a c tThe axial performance of cutter grinders will have direct effects on the precision of groundcutters. Therefore, error elimination will be beneficial for the precision improvement ofcutter grinders. One of the main axial error sources is the spindle thermal displacement.General cutter grinders are not equipped with the cooling systems, because of their rel-ative lower rotating frequencies (8000 rpm), small working range and slower thermal gra-dient. On condition without cooling, there will be obvious thermal errors at the beginninghours of operations or the restarting of machines. That will cause materials waste andlower working efficiency.In this investigation, an efficient measurement system and the compensation mechanismhave been established for the minimization of thermal displacements. About 80% of thethermal displacement can be reduced and the thermal displacement error becomes lessthan 5lm. With this solution, the precision of cutter grinders can be improved.? 2011 Elsevier Ltd. All rights reserved.1. IntroductionPrecision cutter grinders (Fig. 1) can be widely appliedin either traditional mechanical industries or high-techindustries. The so-called maternal genetic effect availablein products would mean that the precision of products de-pends mainly on the machine tools, of which the errors canbe classified as: geometrical errors, temperature rise errorsand dynamic errors, etc. According to relevant studies,4070% of errors of machine tools result from the thermaldisplacement 1,2, where the main source of heat lies inthe friction between spindle and transmission belt, andthat between spindle and ball bearings.So far, some companies have developed the sensors laidinside the spindles by which to compensate the errors ofthermal displacement 3. Yet machines equipped withsuch spindles would increase working cost for small andmiddle sized cutter grinder manufacturers, while therewill be certain limits on the varieties and adoption of spin-dles, and on the promotion of performances of usedmachines.In this study, we have integrated an optical displace-ment sensor system, a temperature sensor system, and asignal acquisition and analysis system to construct anindependent module measurement system of spindle, bymeans of which it can be easy to find out the mathematicalcorrelation between temperature and thermal displace-ment for the spindle of cutter grinders. That can be usedto test the quality of spindles and also provides the basisfor compensation of thermal displacement during practicalmanufacturing process.2. Construction of measurement systemTemperature sensors and a displacement sensor wereinstalled in the measurement system (Figs. 2 and 3). Fromthe spindle test system, temperature and displacement sig-nals have been gained. After processes of signal converters0263-2241/$ - see front matter ? 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.measurement.2011.03.018Corresponding author. Tel.: +886 5 5342601x4122; fax: +886 55312062.E-mail address: wangyc.tw (Y.-C. Wang).Measurement 44 (2011) 11831187Contents lists available at ScienceDirectMeasurementjournal homepage: /locate/measurementFig. 1. Five-axis cutter grinder.Fig. 2. Module measurement system of spindle.Fig. 3. Installation of sensors.1184Y.-C. Wang et al./Measurement 44 (2011) 11831187and signal acquisitions, they would be recorded and ana-lyzed in the measurement program, by which the correla-tion between temperature drift and thermal displacementcan be established (Fig. 4).2.1. Temperature measurement systemTemperature sensors were fixed on the experimentalmachine, in which the spindle was installed. To acquirethe internal temperature relatively proximate to that ofthe spindle and reduce the influences of external environ-ment, the temperature sensor was installed inside the wallof spindle holder to contact the surface of spindle nearly.The PT-100 temperature sensor 4 was selected to mea-sure the temperature on different positions of spindle.It is generally appropriate to restrict the current of PT-100 within the range of 0.5 mA2 mA. Its resolution canbe set at 0.1 ?C. After testing it can be shown that temper-ature drifts of all temperature sensors are similar (Fig. 5).To simplify the measurement process and obtain a betterFig. 4. Signal processing.Fig. 5. Temperature changes of different positions.Fig. 6. Different starting temperatures.Y.-C. Wang et al./Measurement 44 (2011) 118311871185resolution, only temperatures of the top position are mea-sured for analysis, because of its more temperaturechanges.2.2. Displacement measurement systemFor thermal displacement measurement of the rotatingspindle, high resolution in submicrometer range and non-contact measurement method are required. Thus the tradi-tional mechanical measurement devices are unsuitable forit.What used in this study was a laser displacement mea-surement device with the resolution of 0.2lm 5. The sta-bilitytestwascarriedoutundergeneralworkingcondition, while the drift of displacement signal was lessthan 2lm. That would meet the requirement of thermaldisplacement measurement.3. Experiments and resultsBoth the structure of machine tool and its surroundingconditions can become the factors affecting the processingprecision. Obviously, the system errors of machine toolcannot be maintained at a fixed level and can vary as timegoes by. Besides, the thermal deformation created due tothe operation of machine tool can lead to the thermal dis-placement, whose development can be very intricate 6.Though theoretical simulations as differential equationsand finite element method can provide a great deal ofinformation for the analysis of thermal displacement, themost effective way of analysis of such development wouldbe the direct measurement of thermal displacement bymeans of experiments. Therefore, this investigation wasbased on measurements of temperature and thermal dis-placement of spindles. With these data, their correlationcan be formulated and then the formulation is appliedfor compensation of thermal displacement, while onlythe temperature is measured during practical manufactur-ing process.It is impossible for ordinary processing factory to placethe machine tool in a state of constant starting tempera-ture. Besides, the starting temperatures of operation candiffer in each of the four seasons. To inspect the effect ofdifferent starting temperature, measurements were madeon different starting temperatures of spindle on the cuttergrinder. For instance, in Fig. 6, this test shows the resultedthermal displacement curves are fast no differences whenthe starting temperature was 19 ?C and 27 ?C separately.Thus for a spindle, the thermal displacement is only depen-dent on temperature changes, the starting temperature ofoperation should have no influence on it.Because the rotary speed of spindle is different at thepractical applications, it is necessary to investigate, if therotary speed of spindle will affect the thermal displace-ment amount due to a fast or slow speed. According tothedisplacementdifferencebetween3000 rpmand6000 rpm as measured (Fig. 7), a fast or slow rotary speedFig. 7. Thermal displacements in different rotary speeds.Fig. 8. Results of compensation.1186Y.-C. Wang et al./Measurement 44 (2011) 11831187would only result in a difference of the temperaturechanges, but have no effects on the thermal displacementamount. And there would be a very high repeatability.Thus, this feature can even more benefit the compensationofthermaldisplacement.ThecorrectionequationisL3000= 3.44T + 5.68 at 3000 rpm, and L6000= 3.95T + 4.95at 6000 rpm. (where L is the displacement, and T is thetemperature change)Above experiments show that temperature and thermaldisplacement changes of one spindle can be used to estab-lish a correlation, when both changes are increasing. Toverify this correlation also suitable for falling temperature,experiments for rising and falling temperature have beenperformed. The results show that the curve of thermal dis-placement in rising temperature can match with that infalling temperature. Hence, the physical properties of thespindle would not change due to either rising or fallingtemperature.According to the thermal displacement curve fromexperiments, results of compensation for thermal displace-ment of spindle are shown in Fig. 8. By the correlation ac-quired in previous experiments, the spindle is operated at aspeed of 6000 rpm and the thermal displacement will be34lm after 2 h. By the compensation of each 2 ?C temper-ature interval, the thermal displacement can be reduced toapproximately 4lm. That corresponds to a relativereduction of about 80%. By the compensation process theprecision of cutter grinder will be enhanced distinctly.4. ConclusionBy the application of temperature and displacementsensors, the correlation equation between thermal dis-placement and temperature has been formulated. Andwith this equation, thermal displacement of spindle canbe compensated during the manufacturing process.The experimental results have shown that effectivecompensation could make it possible to use the theoreticalestimate for compensation. By compensation processes foreach of above experiments, the thermal displacement canbe reduced to 4lm in short time. The reduction ratio isabout 80%.It was obviously proved that the processing error couldbe decreased to the range of micrometer so that theenhancement of the precision and working efficiency couldbe indeed achieved.AcknowledgmentThe authors wo