a study on the thermal characteristics of the grinding ... study on the thermal characteristics of...

A STUDY ON THE THERMAL CHARACTERISTICS OF THE GRINDING MACHINEAPPLIED HYDROSTATIC BEARING

Bo-Sung Kim1, Gyeong-Tae Bae1, Gwi-Nam Kim1, Hong-Man Moon2, Jung-Pil Noh1 and Sun-Chul Huh11Department of Energy and Mechanical Engineering, Gyeonsang National University, South Korea

2Duck Heung Co. Ltd., South KoreaE-mail: [email protected]

ICETI-2014 W-1031_SCINo.15-CSME-54,E.I.C.Accession 3829

ABSTRACTIn order to activate the high precision and multi-functional machine tool, adequate technical level of thehigh-precision products is required. The hydrostatic bearings is used as a method for producing the high-precision products. The hydrostatic bearing has a relatively small run-out compared to its shape error byfluid film effect in hydrostatic state similar to pneumatic bearing and has high stiffness, load capacity anddamping characteristics. In this study, we conducted a study on the thermal deformation of the grindingmachine that has a great influence on the machining accuracy of the product. The temperature of the frontbearing is 10◦C or higher than the temperature of the rear bearing. Thermal deformation of the spindle wasfound to be dependent on the temperature of the hydrostatic bearing and could identify the overall thermalcharacteristics of the grinding machine.

Keywords: hydrostatic bearing; built-in motor; multi-functional machine tool.

UNE ÉTUDE DES CARACTÉRISTIQUES THERMIQUES DE LA MACHINEÀ MEULER À PALIER HYDROSTATIQUE

RÉSUMÉPour activer la haute précision d’une machine-outil multifonction de haute précision, le niveau technique dehaute précision des produits est nécessaire. Les paliers hydrostatiques sont utilisés comme procédé pour laproduction de produits de haute précision. Les paliers hydrostatiques ont un épuisement relativement faiblecomparable à la relative erreur de forme par effet de film de fluide à l’état hydrostatique tel que le roulementpneumatique, et ils ont une grande rigidité, une capacité de charge et des caractéristiques d’amortissement.Dans cette recherche, nous avons mené une étude sur la déformation thermique de la machine à meuler, cettedernière ayant une grande influence sur la précision de l’usinage du produit. La température du palier avantde 10◦C ou plus haute que la température du palier arrière, et la déformation thermique de la broche, se sontavérées dépendantes de la température du palier hydrostatique et pouvaient identifier les caractéristiquesthermiques globales de la machine à meuler.

Mots-clés : palier hydrostatique; moteur intégré; machine-outil multifonction.

Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015 717

1. INTRODUCTION

A grinding machine is a type of machine tool used to precisely cut machine parts using a rotating grindingstone and is used for ensuring successful implementation of the final performance of key parts in the man-ufacturing process of most products.For example, its application plays an important role in assuring the thequality of products from manufacture of auto parts, electric/electronic parts, data communication equipmentrequired in these times of informatization, general machinery, molds, optical communication parts, to pre-cision optical devices used in the aerospace and military fields. In particular, in the case of the spindle ofa machine tool rotating at a high speed, the degree of precision of the machined product apparently variesdepending on the condition of the grinding machine [1–3].

In order to materialize the high precision work of a grinding machine, a high precision of the spindlerotating system, which mostly dominates the geometric accuracy of a machined part and the surface profile,is required. Though in the past, cheap and standardized rolling bearings that have superior replaceabilitywere used as a method for the precision of the spindle and maintaining its rigidity in high speed rotation,it is said that rolling bearing is vulnerable to friction between metal pieces, thermal deformation caused byheat, and vibration. Accordingly, hydrostatic bearings are essentially used for the spindle of a machine toolas an alternative, which has an advantage that it can maintain high precision and stiffness with no abrasionsince only viscous friction of fluid left as solid friction is eliminated by the hydraulic pressure that is formedbetween the journal bearing and the spindle [4–6].

As the existing hydrostatic spindle has a structure in which the power is transmitted by an external motorusing a belt, vibration and noise generated during a high speed machine work affect the machining accuracyof the machine part. In this study model, the existing hydrostatic spindle structure of transmitting the powerapplies the design of a built-in motor to enhance the stability during high speed rotation. In addition, thedeformation caused by heat should be minimized to obtain the superior machining accuracy.

Although a spindle with a built-in motor spindle can resolve the problems caused by the belt and gearmoving at high speed, a thermal deformation problem can occur due to the internal heat generated duringthe rotation. As the degree of this thermal deformation is as big as several tens of µm, differently fromseveral µm that is dealt with in static or dynamic deformation, it is a problem preferentially considered toimprove the accuracy of the machine tool [7, 8].

In this study, the grinding machine (hereinafter ‘Hydrostatic Wheel Head’) has a grinding wheel of /O400size or bigger and peripheral velocity of 60 m/s, and is comprised of a built-in motor, hydrostatic bearings,and a hydrostatic spindle. Thus, the thermal deformation characteristics at different temperatures of thehydrostatic bearings are evaluated through the results of the finite element analysis and the test that areconducted for the structural stability of the operating wheel head based on the theoretical calculation.

2. THEORETICAL DESIGN METHOD OF A HYDROSTATIC BEARING

The important problem of grinding machine which is also the biggest cause for deterioration of the machin-ing accuracy of machine parts is the thermal deformation. Accordingly, the hydrostatic wheel head in thisstudy is a type of a driving motor which is embedded in the structure as shown in Fig. 1, and the thermaldeformation takes place in front-rear direction. Also, though each deformation is small, it is advantageousin the overall tip stiffness as the overhang is small [9–11].

The power consumption of hydrostatic bearing can be expressed as the sum of the pumping power (Np)and the friction power (N f ) as shown in Eq. (1), and the pumping power (Np) can be expressed as follows:

Np = QPs =Bh3

η· P2

r

P= np

1P· W 2h3

ηA2p

(1)

Here np is a dimensionless quantity, which depends only on the shape of the bearing surface, which is called

718 Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015

Fig. 1. Diverse constructions of spindle system.

the pump power factor and is expressed as np = B/A2. And P is the pressure ratio, which is calculated usingP = Pr/Ps.

The friction power (N f ) can be expressed as follows:

N f = F ·υ = n f ·ηApυ2

h(2)

where the driving power is F and the speed is v.Here n f is a dimensionless quantity, which depends only on the shape of the bearing surface, that is

called the friction power factor, and is expressed as n f = AL/AP. AL and AP represent the land area and thepressure receiving area of the bearing, respectively. The change in the temperature of the bearing (∆t) canbe expressed as Eq. (3), using Eqs (1) and (2):

∆t =Nt

ρcQ(3)

Since the heat generating phenomenon, which deteriorates the tip stiffness, should be suppressed in orderto enhance the stiffness of the spindle, the effect on the increase in the temperature should be consideredalong with the bearing rigidity.

3. DESIGN MODEL

The wheel head is comprised of a hydrostatic spindle, hydrostatic bearings, a grinding wheel flange, agrinding wheel, a built-in motor, a cooling jacket and a body as shown in Fig. 2.

The operating principle of the wheel head is in the structure wherein a turned machine part is groundusing the rotating force of the grinding wheel that is mechanically coupled with the hydrostatic spindlesthrough the built-in motor.

4. TEMPERATURE CHARACTERISTICS EXPERIMENT

4.1. Thermocouple TestIn the test, the temperature was measured using a thermocouple which converts the thermal energy generatedin the motor embedded hydrostatic wheel head into electric energy and measures it. The instruments usedfor measurement were Agilent 34972A and GAP-SENSOR AEC-5505 as shown in Fig. 3. As per the testconditions shown in Table 1, the maximum rotating speed was set considering the peripheral velocity of60 m/s. It shows that the atmospheric temperature was set to 24.4◦C and the humidity to 44◦C. Also, thetemperature of the oil chiller, which is the cooling oil, was originally set to 18◦C and the viscosity of the oilused was 2.1 cSt.


Fig. 2. Drawings of CNC grinding machine.

Fig. 3. Measuring instrument of thermocouple test.

Fig. 4. Measuring points of thermocouple test.

Table 1. Experimental conditions of thermocouple test.Conditions Speed [m/s] Temperature [◦C] Humidity [%] Oil-Chiller Temperature [◦C]– 60 24.4 44 18

The test method was to set the setting temperature of the oil chiller to 18◦C under the room temperaturecondition, and to increase the speed by 500 rpm at an interval of an hour if the temperature range was


Fig. 5. Results of thermocouple test.


Fig. 6. Experimental equipment of thermal deformation test.

stabilized after operating it at 0 rpm for the initial 10 minutes. The increase in the temperature of eachpart of the hydrostatic wheel heads was measured while the peripheral speed was increased up to 60 m/s(2,860 rpm). Figure 4 shows the process of the thermocouple test. After operating it at 0 rpm for the initial10 minutes, the speed was increased by 500 rpm at an interval of an hour if the temperature range wasstabilized. Figure 5 shows the result of the thermocouple test, and Fig. 5a shows the result of measuring thetemperatures of the front and rear bearings. In the result of the test, we can see that the temperatures of thefront and rear bearings have an overall trend of an increase as the rpm increases, and the temperatures ofthe front bearing and the rear bearing are measured to be respectively at 38.5 and 31◦C when the machine isoperated at 2,860 rpm after 6 hours.

As a result of measuring the temperature, the reason why the temperature of the front bearing is higherthan that of the rear bearing is presumed to be the effect of no load condition of not having the grindingwheel on the tip of the spindle. Next, natural cooling was done after six and half hours, and we can observea gradual decrease in the temperatures of the front and rear bearings. Figure 5b shows the result of measuringthe atmospheric temperature and the temperatures of the front and rear body parts. The temperatures showan overall trend of a increase as the rpm increases, and the temperature of the front and rear body parts at themaximum speed of 2,860 rpm is measured to be 35◦C. By comparing Figs. 5(a) and (b), it is noticeable thatthe temperature of the front and rear body parts is influenced by the temperature of the hydrostatic bearings.Figure 5(c) demonstrates the change in the temperature of the cooling jacket and the oil pump.

The temperature of the cooling jacket constantly reads 18◦C even when the rpm increases. Due to theinfluence of temperature change of the hydrostatic bearing, the mean temperature of the oil pump increasesand is measured as 27.5◦C at the maximum speed of 2,860 rpm.

4.2. Thermal Deformation Measurement TestThe thermal deformation of the hydrostatic wheel head was measured using LION (SEA V8.0). Figure 6shows the test measurement coordinates and the test process of the LION equipment for the rotation axis.The thermal deformation of the rotation axis was measured for X , Y and Z axes under the condition as shownin Fig. 7. During the test, the thermal deformations at the tip of the rotation axis were measured for a totalof 60 minutes at an interval of 10 minutes at the speed of 1,450, 2,175, 2,900, 1,450, 725, and 2,175 rpm.Consequently, the temperature of the hydrostatic bearing has a big effect on the thermal deformation ofthe rotation axis. The thermal deformation of the X axis was measured to be 3.68µm by the rpm and thetemperature of the hydrostatic bearing, and the direction of the Y axis, which is directly affected by thegrinding work, is influenced by the acceleration of gravity. For the Y axis, thermal deformation of 3.61 µmtook place due to the acceleration of gravity of the spindle and the temperature of the hydrostatic bearing.The spindle tip of the Z axis is less influenced by the temperature of the cooling oil, differently form that ofthe X and Y axes.


Fig. 7. Experimental conditions of thermal deformation test.

Fig. 8. Results of thermal deformation test.

Furthermore, the effect of the rotational inertia acts more heavily in the direction of the Z axis than in thedirection of X and Y axes due to the structural characteristics of the hydrostatic wheel head. Accordingly,the thermal deformation of the Z axis showed a relatively large value of 8.35 µm in comparison to other axesdue to the effect of the cooling oil temperature, structural characteristics, and the temperature of hydrostaticbearing.

5. THERMAL CHARACTERISTICS ANALYSIS

The analysis modeling of the hydrostatic wheel head was conducted using CATIA V5 considering the hydro-static bearing, body, and motor in which a problem occurs in thermal deformation. For thermal deformationanalysis, ANSYS Workbench v13, a commercial Finite Element Analysis Program, was used.

5.1. Analysis ConditionsThe following boundary conditions were applied in order to analyze the thermal deformation that occurswith the hydrostatic spindle and the grinding machine:


Fig. 9. Mesh of the wheel head.

Table 2. Material properties of SM45C, GC300, and SCM415.Material Density Poisson’s Ratio Young’s modulus Thermal conductivityProperties [kg/m3] [ν] [GPa] [W/m·k]SM45C 7,850 0.28 209.0 51.9GC300 7,300 0.25 90.0 54SCM415 7,860 0.30 205.8 44.5

• A thermal conductivity was applied to each component, and the boundary surface was assumed tohave no thermal resistance. Also, the temperatures of the front and rear hydrostatic bearings were setas the heat sources considering the design parameters and the result of the test, and a caloric value of2900 W was given to the built-in motor referring to its specification.

• The temperature of the hydrostatic wheel head oil was applied based on the test result, and 2.1 cStof the viscosity of the oil was used. The temperature of the cooling jacket was applied to the contactplane of the motor and the cooling jacket considering the test result.

• In the thermal-structural coupled field analysis, the temperature of the hydrostatic wheel head gener-ated at 2,860 rpm was applied as the thermal load, and the weight of the hydrostatic wheel head itselfwas applied fixing the bed and the bolt fastened part which support the hydrostatic wheel head.

The materials used for the parts that consist of the hydrostatic wheel head were GC300, SM45C, andSCM415, of which the material properties are as shown in Table 2.

For meshwork of the hydrostatic wheel head, the Hex dominant method which can obtain accurate andhighly reliable analysis result by forming the mesh uniformly was applied, and the reliability of the analysison the thermal deformation which differs depending on the heat generating characteristics was improved bysetting the lattice dense. The mesh comprised of a total of 1,745,044 nodes and 504,190 elements.

5.2. Results of Thermal Characteristics AnalysisFigure 10 shows the temperature distribution of the wheel head at the peripheral velocity of 2,860 rpm. Thetemperatures of the front and the rear bearings are shown to be 39.5 and 32◦C, respectively. The reasonwhy the temperature of the front bearing is higher than that of the rear bearing is presumed to be becauseof the no load condition of not having the grinding wheel on the tip of the spindle. The temperature ofthe front and rear body parts is shown to be 35◦C, which corresponds to the value obtained from the test.The mean temperature of the spindle is shown to be 27◦C, and is presumed to have been influenced by thetemperature of the lubricant between the bearing and the spindle. Also, due to the effect of the cooling jackettemperature, the temperature of the motor is shown to be about 20◦C.


Fig. 10. Result of temperature analysis on wheel head.

Fig. 11. Results of thermal deformation analysis on spindle.

Figure 11 shows the thermal deformation of the hydrostatic spindle in the directions of X , Y and Z axes,and is the result of the analysis conducted applying the thermal load generated at 2,860 rpm. Figure 11(a)shows the deformation of the hydrostatic spindle rotation axis in the direction of the X axis, and the maxi-mum thermal deformation generated was 4.83 µm. The thermal deformation of the X axis was caused bythe heat generated by the lubricated friction between the front and rear hydrostatic bearings and the hydro-static wheel head, and the effect of the front and rear bearing temperature in the direction of the X axis.Figure 11(b) shows the deformation of the hydrostatic spindle rotation axis in the direction of the Y axis,and the maximum thermal deformation generated was 5.43 µm. For the Y axis, the acceleration of gravityof the spindle and the lubricated friction between the hydrostatic bearings and the hydrostatic spindle weregenerated in the direction of the Y axis as in the case of the X axis. Accordingly, the thermal deformationwas caused by the acceleration of gravity, the temperature of the front and rear bearing, and the effect of thelubricated friction in the direction of the Y axis. Figure 11(c) shows the thermal deformation of the spindlerotation axis in the direction of the Z axis, and the maximum thermal deformation generated was 14.25 µm.The maximum thermal deformation took place at the tip of the spindle, and, as to the cause, it is presumedthat the temperature of the front bearing had an effect on the tip of the spindle because the temperature ofthe lubricant between the hydrostatic bearings and the spindle was higher than that of the front bearing by12◦C. Also, a bigger thermal deformation was generated for the Z axis than that of the X and Y axes as thethermal load had a larger effect on the Z axis than on the X and Y axes due to its structural characteristics.In consequence, the directions of each axis of the hydrostatic spindle confirmed that the temperature of thehydrostatic was the main factor of generating heat for the hydrostatic spindle.


Fig. 12. Results of thermal deformation analysis on wheel head.

Fig. 13. Results of the thermal deformation test and analysis on spindle.

Figure 12 shows the result of the thermal behavior-structure coupled analysis of the wheel head. Thermaldeformation of about 18 µm was generated for the front and rear body parts due to the transferred heatby the front and rear hydrostatic bearings, and the thermal deformation generated for the motor was about10 µm. This result is presumed to be because of the decrease in the thermal deformation due to the effectof the cooling jacket. Also, the result of checking the thermal behavior of the hydrostatic wheel head’s frontbearing confirmed that it had an effect on the tip of the spindle, and the maximum thermal deformation of thehydrostatic wheel head caused by the temperature of the front hydrostatic bearing was 29 µm. This resultis presumed to because the heat generated in the front bearing had a big effect on the thermal deformationdue to the no load condition of the grinding wheel on the spindle tip. Thermal deformation bigger than theanalysis value will be generated by the grinding resistance that occurs during the actual grinding work andthe load of the grinding wheel.

5.3. Results Comparison of Test and AnalysisFigure 13 shows the graph which compares the test values and analysis values of the thermal deformation ofthe hydrostatic spindle. The analysis values of the thermal deformation of each axis were shown to be bigger


than the test values. Such a result was brought about during the process of simplifying the model consideringonly the elements which may cause a big problem in the initial thermal deformation. Accordingly, thedifference between the test and analysis results is presumed to be reduced if all the elements are considered.

The test and analysis values of the thermal deformation of the X axis appeared to be similar. This resultis presumed to be because the increase in the temperature of the hydrostatic bearings had an effect on thethermal deformation of the hydrostatic spindle in the direction of the X axis, both in the case of the testvalues and the analysis values. The test and analysis values of the thermal deformation in the direction ofthe Y axis also appeared to be similar. The direction of the Y axis is the direction directly influenced by agrinding process, and it is confirmed that the acceleration of gravity and the temperature of the hydrostaticbearings have an effect on the thermal deformation of the hydrostatic spindle.

The test and analysis values of the thermal deformation of the spindle in the direction of the Z axis showedsome differences, which is presumed to be because not all the fastening forces of the elements supporting theZ axis were considered in the process of simplifying the analysis model. It seems that the difference betweenthe test and analysis values will decrease if all the elements that support the Z axis are considered. Both thetest values and the analysis values of the thermal deformation of the Z axis show the same trend. As to thecause, it was confirmed that the temperature of the front bearing had an effect on the thermal deformationof the spindle tip because the temperature of the front bearing was the higher that of the lubricant betweenthe hydrostatic bearing and the wheel head by more than 10◦.

6. CONCLUSIONS

Based on the analysis of the structural stability of the wheel head and a test to grasp its thermal characteristicsin this study, the following conclusions can be drawn:

• The result of measuring the temperature distributed over the bearings of the hydrostatic wheel headshowed that the temperature of the front bearing was the highest as there was no load of the grind-ing wheel. As a result of the thermal deformation test conducted for the hydrostatic spindle, it wasconfirmed that the temperature of the hydrostatic bearings is the main cause for the occurrence of thethermal deformation in all the cases of X , Y and Z axes.

• The result of conducting a thermal-structural coupled field analysis of the hydrostatic wheel headverified that the temperature of the front and rear hydrostatic bearings is the main cause for the occur-rence of the thermal deformation of the spindle, and it was confirmed that there is a trend of the testresult and the analysis result corresponding to each other. Accordingly, the thermal deformation ofthe spindle will decrease if the increase in the temperature of the hydrostatic bearing is reduced.

• It was confirmed that, as a result of measuring the thermal deformation of the hydrostatic spindle,the analysis values and the test values are similar, and the thermal behavior characteristics of thehydrostatic wheel head can be ascertained based on its reliability. Accordingly, it is presumed to beuseful for the studies on thermal deformation of the hydrostatic wheel head that utilize the hydrostaticbearing.

ACKNOWLEDGEMENT

This paper is the result of a study conducted as a Wide Economic Region Leading Industry Fostering Project(No. A002200821) of the Dongnam Institute for Regional Program Evaluation supported by the Ministry ofKnowledge Economy, and the Korea Institute for Advancement of Technology.


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