Friction Experiment of Linear Motion Roller Guide THK SRG25

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3, pp. 545-551 MARCH 2014 / 545 DOI: 10.1007/s12541-014-0369-y Friction Experiment of Linear Motion Roller Guide THK SRG25 De-Jun Cheng 1, Wan-Suk Yang 1, Je-Hong Park 1, Tae-Jo Park 1, Su-Jin Kim 1,#, Gyung-Ho Kim 2, and Chun-Hong Park 2 1 Department of Mechanical Engineering, Gyeongsang National University, Jinju, Korea 2 Korea Institute of Machinery & Materials, Daejeon, Korea # Corresponding Author / E-mail: sujinkim@gnu.ac.kr, TEL: +825-5772-1636, FAX: +825-5772-1577 KEYWORDS: LM roller guide, External load, Dynamic friction, Stribeck effect, Coulomb friction, Viscous friction Friction is a characteristic that can be found in machine elements in common engineering use, and it has great effect on the machining performance of a machine tool. Linear motion (LM) guides supported by rolling elements are used for accurate positioning of precision machine. For accurate positioning, the frictional behavior of the LM guide must be understood. In this investigation, a new experiment is conducted to measure friction, and the behavior of LM roller guide friction is measured under various external loads, preloads, velocities, and lubricants. The results obtained from experiment are compared with reference data, and the experimental friction equation of LM roller guide THK SRG25 is achieved from experiment, which can be used to calculate LM roller guide friction and control positioning accuracy. Manuscript received: September 6, 2013 / Revised: December 10, 2013 / Accepted: January 12, 2014 1. Introduction NOMENCLATURE F = Friction force (N) f 0 = Base friction force (N) k 1 = Factor dependent on the type of bearing k 2 = Factor dependent on the type of bearing (1/µm) P = External load (N) 1.5 for Normal p c = Preload class (µm) 2.5 for C 1 preload 3.5 for C 0 preload V St = Sliding speed coefficient in the Stribeck force (m/s) V = Sliding speed (m/s) ν = Kinematic viscosity (mm 2 /s) µ St = Stribeck effect force coefficient (knmm/s) µ v = Viscous friction coefficient (Ns 2 /mm 4 ) Linear motion (LM) guides have been widely used for precise positioning devices to transport machine parts through a linear path in machining centers and X-Y tables etc. As machine parts becoming smaller and finer, the required order of precision has been increased. 1 LM guides using roller bearing have many advantages such as high stiffness, smooth motion. Linear motion guides also have a low friction coefficient compared with sliding contact bearings. Usually, the static friction is small and almost the same as dynamic friction. However, high static friction with lower kinematic viscosity results in stick slip, wherein the coefficient is separated and the difference between them increases with increasing preload. 2 Therefore, the study of LM guide friction plays a crucial role in the machining center. Andersson et al. 3 deals with different friction models for sliding contacts running under different conditions, friction models which have been studied are: Coulomb friction model, Viscous friction model, Stribeck effect model, Combined Coulomb and Viscous friction model. The friction was observed by several authors 4-9 that the variation of friction depends on interfacial conditions such as sliding speed, the normal load, temperature, stick slip and vibration. When using an LM system, it is necessary to provide effective lubrication, where the main function of lubricant is the reduction of both friction and wear of the rolling elements. There has been a great deal of research conducted in relation to the influence of lubrication on journal bearing friction. However, only few studies have been proposed to learn the influence of lubrication on the LM guide friction. KSPE and Springer 2014

546 / MARCH 2014 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3 The purpose of this research is to characterize the friction force of LM Roller guide. A series of experiments are carried out to measure friction, which consider the effects of external load, preload, velocity and lubricant on LM roller guide friction. To characterize these components, a new experimental method in which external load can be applied easier is suggested to measure friction. Finally the experimental equation achieved from experimental results can be used to calculate LM Roller guide (THK SRG25) friction and the relationship among friction characteristic, external load, preload, velocity and lubrication can be analyzed using this empirical equation. 2. Experiment Method and Equipment LM Roller Guide (THK SRG25) that consists of rail and block is transported by 4 rows of rollers and each row has 58 rollers. Each row of rollers is arranged at a contact angle of 45 so that the LM block receives an equal load rating in all four directions (radial, reverse radial and lateral direction), and the use of a roller cage can eliminate friction between rollers, increase grease retention and minimize heat generation. The preload codes of it are Normal (1.5 µm), C 1 (2.5 µm) and C 0 (3.5 µm), respectively. Fig. 1 shows schematic of the LM roller guide and Table 1 shows the specification of the experimented LM roller guide. In the previous research, the traditional method which fixes two rails and places table on four blocks and the feed driven system controlled by linear motor is used to measure friction. Besides, the external load is applied to the LM guide by putting heavy work piece on the working table, as shown in reference. 4 In this investigation, a new experimental method is conducted to measure friction. The double rails and four blocks are fixed by using vice and compression load cell is put on the center of the face of the block, moreover, the LM rail is connected to tension load cell which is moved by NC machine. Furthermore, the steady-state LM guide velocity is also controlled by NC machine. In this measurement system, the external load is given by rotating vice handle which is measured by compression load cell and the friction force affected by external load is measured directly by tension load cell. A data acquisition system is used to measure the force continuously when the system is working and these data are sent directly to the computer. Fig. 2 shows the graph of LM roller guide experiment method. Comparing with previous methods, this one does not have global error, slope error or rail paralleled error. In order to reduce the effect of the moment on friction, double blocks are added on the other side of the rail. Besides, the large external load can be applied easier than traditional methods. Even though large external load is given, the inertia force does not increase because the mass of inertia force is rail not external weight, moreover, the inertia force is small because the mass of rail is small. Fig. 3 shows the friction of single block without external load test method. In Fig. 2 test method, subtracting the double block friction force without external load from measured friction force, the results are the friction of LM guide. In this experiment, symmetrical method is used, then measured friction force is twice the friction force of each rail, therefore, the calculated friction of LM roller guide should be divided by 2. Fig. 1 Schematic of the LM roller guide THK SRG25 Table 1 Specifications of the LM roller guide THK SRG 25 Normal Preload class C 1 (Light preload) C 0 (Medium preload) Basic dynamic load rating 27.9 kn Normal (2.47 mm) Diameter of roller C 1 (2.48 mm) C 0 (2.49 mm) Normal (3.76mm) Length of roller C 1 (3.78 mm) C 0 (3.79 mm) Number of rollers 58 4 Fig. 2 LM roller guide experiment method In this study, the LM rail moved along the horizontal direction in a single direction motion and the single stroke is 200 mm. The friction behavior of LM roller guide is measured under various external loads, velocities, preloads and lubricants. Table 2 indicates the experimental

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3 MARCH 2014 / 547 Fig. 4 Relationship among external load, preload and friction force Fig. 3 The graph of single block test method Table 2 Experiment conditions and equipments Travel distance 200 mm External load From 1.5 to 10 kn Velocity From 0.0017 to 0.13 m/s AFE-CA Grease Kinematic viscosity at 40 o C 99 mm 2 /s AFA grease Kinematic viscosity at 40 o C 25 mm 2 /s Compression load cell CAS-Korea C1E-2TS 2000 kg Tension load cell CAS-Korea CSBA-10LS 10 kg Data logger Radian INC. SDL-350R NC machine HYUNDAI-KIA machine KV 25 conditions and equipments. 3. Experimental Results 3.1 Relationship among external load, preload and friction In order to study the effects of the load and preload on the friction force, the friction force is measured for various loads. The external load is changed from 1.5 kn to 10 kn, which is 5.3~35.8% of the basic dynamic load rating. In this experiment, the velocity is 0.11 m/s, kinematic viscosity is 99 mm 2 /s and three different preloads are used. Fig. 4 shows how the friction force varied with respect to the external load and preload. Selected experimental points are used to demonstrate the effect; the results for combinations of different preloads are indicated. It is noticed that the friction force increases as external load increases, and friction force also increases as preload increases. The Fig. 5 Comparison of the calculated and friction coefficient reference diagram from THK catalog slope of friction curve from Normal, C 1 to C 0 is decreasing, because the deflection of LM bearing guide with a preload under a given load is smaller, and the rigidity is much greater than that without a preload. 10 Since an LM system makes rolling motion via its rolling elements such as rollers between the raceways, its frictional coefficient is much smaller than a sliding guide. The THK Company suggests the different friction coefficients for different LM Roller Guides, and from THK company catalog, the average coefficient of LM roller guide SRG friction range is from 0.001 to 0.002. 10 Friction coefficient, in general, has been determined as a function normal force and friction force. Using this method, the average coefficient of LM roller guide friction is calculated from Normal, C 1 and C 0. In Fig. 5, the results concerning the friction coefficient are compared with friction coefficient reference diagram from THK catalog. The reference diagram is drawn by calculating the average of different types of the LM systems, preloads, velocities, temperatures and so on. As shown in Fig. 5, the friction coefficient has values between 0.001 and 0.0177. When the applied load ratio is smaller than 0.18, the friction coefficient is decreasing large as the applied load ratio increases. However, when the applied load ratio is larger than 0.18, the friction coefficient decreases between 0.001 and 0.002. The value of friction coefficient calculated from experiment results is the same as the value of THK Company catalog.

548 / MARCH 2014 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3 Fig. 6 Relationship between velocity and friction force Fig. 8 Relationship between lubricant and friction force Fig. 7 Stribeck curve and regimes of lubrication (η: Kinematic viscosity, P: Normal load and V: Velocity) 3.2 Relationship between velocity and friction In order to investigate the effect of the velocity on the friction force, the friction is measured at various constant velocities and different preloads. In this experiment the single block test method is used which has its velocities from 0.0017 m/s to 0.13 m/s and the kinematic viscosity is 99 mm 2 /s. In Fig. 6, a comparison of the results from different velocities and preloads are illustrated. The results for this graph indicate that the friction force takes a maximum value at very low velocity in three kinds of preload. When the velocity is smaller than 0.005 m/s, the friction force decreases exponentially with the increasing of velocity, which is due to mixed lubrication. The mixed lubrication can be defined as a friction contribution at low velocities, which is decreasing exponentially, as shown in Fig. 7. The Stribeck curve presents the relationship among friction coefficient, kinematic viscosity, velocity and normal load. Regions I, II and III in the Stribeck curve correspond to boundary lubrication, mixed lubrication and hydrodynamic lubrication respectively. The mixed lubrication regime refers to a combination of boundary lubrication with hydrodynamic lubrication. Generally, the minimum friction coefficient appears in the mixed lubrication regime (region II). 11,12 In this regime, the two surfaces are partly separated, partly in contact. As the speed increases, the metal-to-metal contact surface is reduced, then, the friction force decreases. When the preload increases, the fluid film thickness is further reduced and metal-to-metal contact become stronger, and then friction force increases. Besides, the slope of friction curve also becomes larger as the preload increases. For velocities above 0.005 m/s, the friction force linearly increases with increasing velocity due to hydrodynamic lubrication. In the hydrodynamic lubrication friction regime where the viscous friction is dominant, the dynamic viscosity of the fluid, the velocity and contact area of the moving object determine the friction force to be overcome, and the viscous friction force is assumed to be proportional to the velocity. 11 In addition, for three different preloads, the friction forces increase as preload increases because the fluid film thickness becomes thinner as the preload increases. 3.3 Relationship between lubricant and friction In order to investigate the effect of lubricant on the friction force, the friction force is measured under C 1 preload without external load, and the dynamic friction characteristics are studied under two viscosities of grease (99 mm 2 /s and 25 mm 2 /s). In Fig. 8, a comparison of the results from different greases is illustrated. It can be seen from this graph that the friction force with high kinematic viscosity is smaller than friction force with low kinematic

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3 MARCH 2014 / 549 viscosity when the velocity is smaller than 0.005 m/s. The drop-off in friction is called the mixed lubrication, for low value of kinematic viscosity fluid, fluid film thickness is reduced, then the friction force with low viscosity makes metal-to-metal contact stronger, therefore, the friction force with low kinematic viscosity is higher than friction force with high kinematic viscosity. This phenomenon is also shown at mixed lubrication curve in Fig. 7. For velocities above 0.005 m/s, the friction force with low kinematic viscosity is smaller than friction force with high kinematic viscosity because of viscous friction. In viscous friction regime, a lower viscosity decreases the fluid film thickness which will also decrease the friction force, then for small value of kinematic viscosity, friction force is small. Fig. 9 Friction vibration for different constant velocities 3.4 Relationship between velocity and friction vibration The friction force is measured under Normal preload at various velocities (0.0017, 0.003, 0.025 and 0.042 m/s) along horizontal motion direction and the external load is zero. Fig. 9 shows the friction force variations with time. It can be seen that the magnitude of friction vibration decreases with the increase of velocity, which is due to stick-slip behavior. The stick-slip phenomenon is the spontaneous jerky motion that can occur while two objects are sliding each other. However, the steady sliding motion is achieved, without stick-slip behavior, as the velocity increases. 14,15 In this experiment, the value of friction force is calculated from the mean value of the kinematic friction curve. 4. Discussion 4.1 Experimental equation In this experiment, the effects of velocity, external load, lubricant and preload on the friction force are taken into account. The empirical equation is composed of Coulomb friction, Stribeck effect and Viscous friction which is to estimate the friction of LM roller guide, and the factors include the external load, preload, velocity and lubricant. Coulomb and Viscous friction are modeled as shown in Eqs. (1) and (2). f Coulomb = ( k 1 k 2 p c )P 10 3 f Viscous = µ ν p c νv+ f 0 (1) (2) The Stribeck effect force is considered using an exponential model similar to the model proposed by Jeong: 13 f Stribeck = µ St p c ν ---- e V ------- V St (3) A Stribeck curve 11 presenting the relationship among velocity, kinematic viscosity and normal load can be obtained by summing up the Coulomb friction, Viscous friction and Stribeck effect force. Therefore, the frictional equation of LM roller guide THK SRG25 can be expressed as Eq. (4): V ------- F ( k 1 k 2 p c )P 10 3 p c µ ν νv µ V St St = + + ------ e +f ν 0 (4) Fig. 10 Friction force simulations The values of k 1, k 2, µ ν, V St, µ St and f 0 cannot be known before an experiment is carried out. Therefore, their values are determined by experiment results. The values of k 1, k 2 are achieved from Fig. 4, and the values of µ ν, V St, µ St and f 0 are achieved from Figs. 6 and 8. The

550 / MARCH 2014 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3 changed. 4.2 Validation of the experimental equation To validate the developed experimental equation in this paper, the predictions from experimental equation are compared with experimental data. The friction forces are measured at various velocities (0.008, 0.025, 0.042 and 0.075 m/s) along horizontal motion direction, external loads (2, 4, 6 and 8 kn) and three different preloads (Normal, C 1 and C 0 ). Fig. 11 plots the comparison between the friction force from experimental Eq. (5) and those from experimental data. The maximum difference between experiment values and prediction values are about 18.3%, 17.8% and 14% with respect to Normal, C 1 and C 0 preload, respectively. Although the predicted values of friction force are different from experimental friction force, the agreement is reasonable. And the same trend that friction force increases with increasing external load and velocity is observed. 5. Conclusion Fig. 11 Predicted and experimental friction forces for different preloads experimental friction equation of LM roller guide THK SRG25 can be changed as Eq. (5): In this paper, a new experiment method is conducted to measure LM guide friction force. And the friction behavior of LM roller guide THK SRG25 in response to the external load, velocity, preload and lubrication is examined experimentally. The experimental result proves that the friction force increases as the external load increases and the value of friction coefficient decrease with the increase of external load. When the velocity is smaller than 0.005 m/s, the friction force with high kinematic viscosity is smaller than friction force with low kinematic viscosity. However, for velocities above 0.005 m/s, the friction force with high kinematic viscosity is higher than friction force with low kinematic viscosity. Furthermore, when a preload is applied to increase rigidity, the friction force also increases. Therefore, the friction force increases as the preload increases. The experimental friction equation of LM roller guide is achieved for the calculation of friction force. For verification, the friction forces predicted from the equation are compared with those from the additional experiment data. It is found from comparison that there is a good agreement between friction forces predicted from derived equation and those from the experiment. Therefore, the experimental friction equation can express the behavior of LM roller guide THK SRG25, and the relationship among friction characteristic, external load, preload, velocity and lubrication can be analyzed using this empirical equation. F ( 0.315 0.03p c )P 10 3 p c 0.244νV 30 --------- 0.01 = + + -----e +3 ν V (5) REFERENCES For three kinds of preload Normal, C 1 and C 0, the friction force F in response to the external load, velocity and lubricant can be calculated by Eq. (5), respectively. Fig. 10 shows the simulation results for different velocities and external loads. In this case, kinematic viscosity is 99 mm 2 /s and Normal, C 1 and C 0 are calculated. As shown in Fig. 10, the friction graph calculated from experimental friction equation is similar trend to the graph of experiment results. If kinematic viscosity, external load and velocity are changed, the value of friction force will be 1. Yi, Y. S., Kim, Y. Y., Choi, J. S., Yoo, J. H., Lee, D. J., and et al., Dynamic Analysis of a Linear Motion Guide Having Rolling Elements for Precision Positioning Devices, Journal of Mechanical Science and Technology, Vol. 22, No. 1, pp. 50-60, 2008. 2. Oiwa, T., Friction Control using Ultrasonic Oscillation for Rolling- Element Linear-Motion Guide, Review of Scientific Instruments, Vol. 77, No. 1, Page No. 016107, 2006.

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