Order of Authors: DUMITRU N OLARU, Professor; CIPRIAN STAMATE, Dr.; ALINA DUMITRASCU, Doctoral student; GHEORGHE PRISACARU, Ass.

Transcription

1 Editorial Manager(tm) for Tribology Letters Manuscript Draft Manuscript Number: TRIL Title: NEW MICRO TRIBOMETER FOR ROLLING FRICTION Article Type: Tribology Methods Keywords: Rolling friction, Friction test methods, Dynamic modelling. Corresponding Author: Prof. Dumitru OLARU, Ph.D Corresponding Author's Institution: Technical University First Author: DUMITRU N OLARU, Professor Order of Authors: DUMITRU N OLARU, Professor; CIPRIAN STAMATE, Dr.; ALINA DUMITRASCU, Doctoral student; GHEORGHE PRISACARU, Ass. Professor Abstract: To determine the rolling friction coefficient in the micro rolling systems the authors developed a new micro tribometer consist in a driving rotational disc in contact with microballs which sustain an inertial driven rotational disc. The driving disc has a constant rotational speed and the rotational motion is transmitted from driving disc to the inertial driven disc by friction between the rolling contacts between the microballs and the two discs. A camera monitors the angular position of the inertial driven disc, from the start to the synchronism rotation and friction coefficient between the microballs and the inertial disc was determined as a function of the angular acceleration of the inertial disc. Kinematics and dynamics of the microballs have been developed and analytical equations for friction coefficient between the microballs and the driving disc have been obtained also. Experimental investigations with the microballs having 1. mm evidenced values for friction coefficient between to 0.000, for rotational speed between 0 to rpm. By increasing the microball diameter to mm an increasing of the friction coefficient up to 0.00 has been obtained. Suggested Reviewers: DANIEL NELIAS Professor Laboratoire de Mecanique des Contacts et des Structures, INSA-Lyon, France daniel.nelias@insa-lyon.fr Professor Nelias work in the field of contact mechanics and tribology of rolling bearings DIK SCHIPPER Professor Laboratory of Surface Technology and Tribology, Twente University D.J.Schipper@ctw.utwente.nl Professor Schipper has important researches in the field of tribology and microtribology with expermental investigations using microtribometers Tudor Andrei Professor Machine Elements and Tribology, POLITEHNICA University of Bucharest tudor@meca.omtr.pub.ro Professor Tudor Andrei is the head of the Dept. of Machine Elements and Tribology and is a very active professor in the field of tribology of rolling and sliding contacts.

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3 Manuscript Click here to download Manuscript: MANUSCRIPT_OLARU_TRIBOLOGY LETTERS.doc NEW MICRO TRIBOMETER FOR ROLLING FRICTION Dumitru N. OLARU Technical University Gheorghe Asachi Iasi, Department of Machine Elements and Mechatronics, Bld. D. Mangeron 1-, 000, Iasi, Romania dolaru@mail.tuiasi.ro; dumitru_olaru@yahoo.com Ciprian STAMATE Technical University Gheorghe Asachi Iasi, Department of Machine Elements and Mechatronics, Bld. D. Mangeron 1-, 000, Iasi, Romania Alina DUMITRASCU Technical University Gheorghe Asachi Iasi, Department of Machine Elements and Mechatronics, Bld. D. Mangeron 1-, 000, Iasi, Romania Gheorghe PRISACARU Technical University Gheorghe Asachi Iasi, Department of Machine Elements and Mechatronics, Bld. D. Mangeron 1-, 000, Iasi, Romania 1

4 ABSTRACT To determine the rolling friction coefficient in the micro rolling systems the authors developed a new micro tribometer consist in a driving rotational disc in contact with microballs which sustain an inertial driven rotational disc. The driving disc has a constant rotational speed and the rotational motion is transmitted from driving disc to the inertial driven disc by friction between the rolling contacts between the microballs and the two discs. A camera monitors the angular position of the inertial driven disc, from the start to the synchronism rotation and friction coefficient between the microballs and the inertial disc was determined as a function of the angular acceleration of the inertial disc. Kinematics and dynamics of the microballs have been developed and analytical equations for friction coefficient between the microballs and the driving disc have been obtained also. Experimental investigations with the microballs having 1. mm evidenced values for friction coefficient between to 0.000, for rotational speed between 0 to rpm. By increasing the microball diameter to mm an increasing of the friction coefficient up to 0.00 has been obtained. Keywords: Rolling friction, Friction test methods, Dynamic modelling. 1 Introduction The use of the linear or rotating microball bearings in the MEMS applications (micromotors, microgenerators, microactuators, micropumps) implies the simplification in construction, low level of the friction, low level of the wear, high stability, and thus the microball bearings seem to be a promising solution for future MEMS applications. In the last period some experimental evaluations of the friction in the linear and rotating microball bearings was realized.

5 Lin et al. [1] determined the static and dynamic friction coefficient for a linear microball system consisting of micromachined silicon V-grooves and stainless-steel microballs having 0.- mm diameter. By determining the acceleration of the free slider in the linear microball system, the authors have established that the dynamic friction coefficient is found to be in between 0.00 and 0.01 if there is no interaction between balls. It can be mentioned that in the experiments of Lin et al [1] the friction coefficient included both rolling friction and pivoting friction in the contacts between microballs and the guides. Tan et.al [] continued the experimental research from [1] and proposed a viscoelastic model for friction force developed in a rolling contact between a microball and a plane. This viscoelastic model includes material parameters, ball diameter, normal load and linear speed and was applied to the rolling contacts from the linear microball system used in [1]. For a steel microball having 0.-mm diameter, loaded with a normal force of mn and rolling with a linear speed between 0.0 m/s to m/s the friction coefficient values up to 0.00 being obtained. Ghalichechian et al. [] experimentally determined the friction coefficient in an encapsulated rotary microball bearing mechanism using silicon microfabrication and stainless steel microballs of 0. - mm diameter. The friction coefficient was indirectly obtained by measuring the transient response of the rotor in the deceleration process from a constant angular velocity until it completely stops due to friction. Using a high speed camera system, the angular position of the rotor in the deceleration process was determined. The measured angular positions θ( t ) was fitted b t to an exponential function in the form θ( t ) = a e + c t + d, where t is the time (in seconds) and a, b, c and d are constants. The acceleration of the rotor was obtained by differentiation of the function θ ( t ). The global friction coefficient between rotor, microballs and stator was determined as a linear dependence with acceleration and value of 0.0 has been obtained for an angular speed of 0. rad/s.

6 McCarthy et al. [] experimentally investigated the influence of the speed and of the normal load on dynamic friction in a planar-contact encapsulated microball bearing having 0.- mm diameter steel balls and silicon races. Using the spin-down testing the authors determined the dynamic friction coefficient for rotational speed between - and 00 - rpm and for axial load between - and - mn. The friction coefficient obtained for these conditions was from (at rpm and mn) to 0.0 (at 00 rpm and mn). Also, an empirical power-law model for dynamic friction torque in a planar-contact encapsulated microball bearing has been developed []. Using the integration of the free oscillations equations of a microball on a spherical surface, Olaru et al. [] evaluated the rolling friction coefficient on the basis of the number and amplitude of the experimentally determined microball oscillations. The influence of condensing atmospheric water on the rolling friction coefficient was also determined. For a microball having a diameter of 1- mm, Olaru et al. [] obtained in dry conditions values for rolling friction coefficient up to and in presence of the condensed water on spherical surface obtained values for rolling friction coefficient up to All the experimental results obtained by [1,,] reefer to the global rolling friction coefficient both in a microball linear system [1] and in a rotary microball bearing [,]. It is important to be evidenced that both in the microball linear system and in the rotary microball bearing the global friction coefficient is a result of the rolling friction and of the sliding friction caused by the pivoting motion of the microballs over the races. To determine only the rolling friction coefficient in the micro rolling systems the authors developed a new micro tribometer with a rotating inertial glass disc supported by steel microballs. A camera monitors the angular position of the rotating disc, from start to the synchronism rotation and friction coefficient was determined as a function of the angular acceleration of the rotating disc. Experimental investigations were realized with the microballs having the diameter of 1. mm and mm.

7 Equipment and procedure Figure 1 presents the new micro tribometer. The driving disc 1 is rotate with a constant rotational speed and has a radial groove race. Three microballs are in contact with the race of the disc 1 at the equidistance position ( degrees). All the three microballs sustain an inertial glass G disc and are normal loaded with a force Q = cos, where G is the weigh of the disc and α α is the contact angle between the microballs and the spherical surface of the disc. When the disc 1 start to rotate with a constant angular speed ω 1, the balls start to rolls on the raceway of the disc 1 and start to rotate the inertial disc, as a result of rolling friction forces between the balls and the disc. The tangential forces between the balls and the disc (F ) are the traction forces for the driven disc and can be expressed as: F = µ Q (1) where µ is the rolling friction coefficient between the balls and the disc. The disc is accelerated from zero to the synchronism rotational speed (which corresponds to the rotational speed of the disc 1) in a time t (seconds) as a result of inertial effect. Considering only friction between the disc and the three balls (neglecting the friction between the disc and air), and using the dynamic equilibrium of the disc, following equation for rolling friction coefficient µ is obtained: α µ φ J cos d = () G r dt where: J is the inertia moment for the inertial disc, and φ is angular position of the disc as a function of the time t. d φ dt is angular acceleration of the disc

8 To determine the angular acceleration of the disc a high speed camera Philips SPC00NC/00 VGA CCD with 0 frames/seconds was used to capture the angular position of the disc from start to the synchronism rotation. Also, the angular positions of the balls and of the disc 1 are captured by camera from start to the time when the angular speed of all three elements are the same (synchronism speed). In Fig. are presented the registered positions of the disc, of a ball and of the disc 1, respectively φ, φ b, and φ 1, at a short time t after the start of the rotation. The images captured by the camera was processed frame by frame in a PC using Virtual Dub soft and was transferred in AutoCAD to be measured the angular positions φ, φ b and φ 1 corresponding to every frame. The camera was installed vertically 1-mm above the disc, to minimize the measurement errors. A white mark was placed both on disc and on disc 1 as it can be observed in Fig. and the angular positions φ and φ 1 was measured according to the reference line (position at t = 0) and these marks. At the initial time (t = 0) the marks of the two discs and one of the three ball was placed at zero position corresponding to reference line.. Kinematics and dynamics analysis of the new micro tribometer.1 Theoretical angular speed of the disc In Fig. is presented the position of a ball in contact with the two discs during the running process. In vertical plane following forces acts on the microball: normal forces Q 1 and Q, centrifugal force F C and gravitational force G b. Also, two contact angles α1 and α are realized between vertical direction and the directions of the two normal load Q 1 and Q, respectively. The contact angle α was determined by relation: r α = arcsin () R S

9 where r is the distance from the rotational center to the center of the micro balls and R S is the radius of the spherical surface of the inertial disc. The contact angle α 1 can be determined as result of the equilibrium of the vertical and horizontal forces acting on the microball: α 1 = arctg where m b is the mass of the ball and Q = Q. Q sinα + mb r ω () m g + Q cosα b b Neglecting the sliding between the microballs and the two discs, the tangential speeds of the balls in the contact points v 1, and v, can be determined with relations: v 1 ( db = ω1 r1 = ω r + sin 1 ) () 1 α v ( d b = ω r = ω r sin ) () α where: r 1, r are the distances from the rotational center to the contact points between microballs and the two discs and d b is the microball diameter. relation: According to Fig., the tangential speed of the ball center, v b can be determined with v b v 1 + v = ω r b = () From Eqs., and it can be obtained theoretical angular speed of the inertial disc, ω,t, if is not sliding between balls and the disc, and considering low rotational speed ( α 1 α α ): ω, t Kb ωb K1 ω1 = () where K b and K 1 are two geometrical parameters constants defined by relations: K b r = () ( r 0. d sin α ) b ( r + 0. db sin α ) K1 = () ( r 0. d sin α ) b

10 Also, a theoretical angular position of the inertial disc, (): φ, t b φb 1 φ1 φ, t, can be obtained from the equation = K K () Using the differences between theoretical angular positions of the disc and measured angular positions of the disc it can be obtain information about the presence of the sliding between the microballs and the disc.. Friction coefficient between microballs and driving disc 1 To obtain information on the friction coefficient between the microballs and the driving disc 1, a dynamic analysis of the microballs has been made. In Fig. are presented the forces acting on a microball in the direction of the ball motion, when the driving disc 1 is rotate with a constant speed ω 1. It can be write equilibrium of the forces acting on the microballs: F + 1 = F F ib (1) where: F 1 is the tangential force in the contact of the microball with the disc 1, F is the tangential force in the contact of the microball with the disc, and F ib is the inertial force acting in the center of the microball. The force F is obtained by the dynamic equilibrium of the inertial disc and results: J dω = () r dt F The inertial force acting in the center of the microball is determined by relation: where m b is the mass of the microball. F ib = m b dω dt From Eqs. 1, and 1 the following equation for the force F 1 we obtained: b r (1)

11 F J r dω 1 = dt + m r The normal force in the contact of the microball with the driving disc 1 can be expressed by equation: where g is the gravitational acceleration. b dωb dt (1) G mb g Q1 = + (1) cos α cos α The friction coefficient between the microball and the driving disc 1, as a ratio between the tangential force F 1 and the normal force Q 1 results: µ dω dω b 1 = A + B (1) dt dt where A and B are two inertial parameters with values expressed in s : J cosα A = r ( G + m b. Friction between disc and air g ) mb r cosα B = (1) ( G + m g ) For a disc with radius R having a rotational speed ω in a fluid with a kinematics viscosity υf and a density ρ f, a friction torque M f is developed which can be determined by relation: M f 0. KM ρ f R ω = (0) where K M is a coefficient depending on the Reynolds parameter. For laminar flow ( 0 < Re < ) the coefficient K M can be determined by relation:. K M = (1) Re where the Reynolds parameter Re is determined by relation b R ω Re =. Considering the friction between the disc and air, Eq. can be modified as: υ f

12 J cos α d φ cos α µ = + M f () G r dt G r For low rotational speeds and in the accelerated stage of the disc, the friction between the disc and air can be neglected and the friction coefficient depends only of the inertial effect as in Eq.. In the synchronism stage, the acceleration of the disc becomes zero and the friction coefficient depends only of the friction between air and the disc. In these conditions, the friction coefficient can be determined by equation: α µ M f. Experimental results and validation of the procedure = cos () G r In order to validate the proposed procedure and equipment, we have realized a lot of experiments for different rotational speeds of the driving disc 1. The driving disc 1 was mounted on the rotational table of a Tribometer CETR type UMT- having servo-controlled rotational speed. The inertial disc is a glass disc having following dimensions: the radius of the disc, R = 1. mm, the radius of the spherical surface of the disc, R S =0 mm. The weigh of the disc is G =.0 mn and the normal load acting on every ball is Q =. mn. The driving disc 1 is a steel ring of an axial ball bearing (series 10) having a rolling path at a radius r =.mm and a transversal curvature radius of. mm. Following dimensions of stainless - steel micro ball diameters was used: 1. mm (1/1 inch ) and mm. The roughness of the active surfaces of the two discs and of the balls was measured with Form Talysurf Intra System. Following values of Ra was obtained: spherical surface of the disc, Ra = 0.0 µm, rolling path of the disc 1, Ra = 0.00 µm and ball surface, Ra = 0.0 µm. The contact angle α has. 0 and the contact angle α 1 has values between (. 0 0 ), depending of the balls diameter and rotational speed as it can be observed in Eq.. The angular speed of the driving disc 1 was between 0- to 1 - rpm.

13 All measurements are performed in steady room environment at a temperature of (-) 0 C and a relative humidity of (0 )%RH. All the tests was realized in dry conditions (without lubricant or condensed water on contact surfaces). Figure presents the typically registrations of the three angular positions, φ1, φb and φ, when the driving disc 1 is rotate with an angular speed ω1=. s -1 (rotational speed of rpm), for three microballs having 1.-mm diameter. time It can be observed that angular position of the disc 1 is a linear function of the φ 1 ) = 1 ( t ω t, where ω 1 is angular speed of the disc 1, that means a constant rotational speed of the disc 1. The angular position of the balls and the angular position of the disc, φ b ( t ) and φ( t ) respectively, are non linear functions of the time and analytical expressions was obtained by curve fitting of the experimental results. For the time variation of the angular position of the inertial disc following exponential function we proposed: φ ( t ) a+ b ln( t ) + c ln( t ) = e () where a, b and c are constants obtained by curve fitting of the numerical values, using MatLAB soft. For the angular position variation of the disc presented in Fig., following values of the a, b and c constants was obtained: a =.; b =.; c = In Fig. is presented the differences between the measured and curve fitting values of the angular position for the disc, when the disc 1 has a angular speed ω 1 =. s -1. The angular acceleration of the disc was obtained by derivative process of the fitted angular position function φ ( ) described by Eq.. Using Eq. we obtained the friction coefficient between the t microballs and the inertial disc, as a function of the time, µ ( ). The time variation of this friction coefficient is presented in Fig.. t

14 Discussions: 1. The time variation of the friction coefficient, from start to the synchronism rotation is in accord with the physical phenomena. That means a rapid increasing of the friction coefficient at the start to a maximum value and followed by a decreasing to a low constant value, when is attained the synchronism of rotation for all elements (disc 1, disc and balls). In this stage, the angular acceleration of the disc is zero and friction between disc and air leads to a constant value for friction coefficient as in Eq.. For rotational speed of the disc 1 having between 0 - and - rpm and considering the following values for air kinematics viscosity and air density: υ = 1 m s -1 and ρ = 1. 1 kgm -, respectively, the friction coefficient caused only by the f f air resistance determined by Eq. has values between. and.. The experimental values of the friction coefficient obtained by proposed method suggest a dominance of the rolling process between the three microballs and the disc. Using the measured angular positions of the disc 1 and the measured angular positions of the microballs presented in the Fig., we determined the theoretical angular positions of the disc according to Eq., in the hypothesis of pure rolling motion between micro balls and the two discs. The difference between theoretical angular positions of the disc determined by Eq. and measured angular positions of the disc are presented in Fig.. The differences not exceed ± 0. radians.. The influence of the rotational speed on the friction coefficient was evidenced by the experiments realized with the micro balls having 1. mm with four rotational speed of the disc 1: 0-, -, 0- and - rpm. In Fig. are presented the variation of the angular position of the disc from start to the synchronism for following rotational speeds of the disc 1: 0-, -, 0- and - rpm. The time

15 from the start to the synchronism varies between 1 seconds (for the rotational speed of 0 rpm) to seconds (for the rotational speed of rpm). In Fig. are presented the variations of the friction coefficient in the contacts between microballs and the disc for the ball diameter of 1. mm, when the rotational speed of the disc 1 was 0-, -, 0- and - rpm. It can be observed that the maximum values of the friction coefficient varies between at 0 rpm and at rpm, and the increasing of the speed leads to the increasing of the maximum friction coefficient. At synchronism the friction coefficient obtained for all rotational speeds leads to a constant value of about In order to evidence the influence of the microball diameter on the friction coefficient was realized comparative experiments with balls having mm in diameter. In Fig. are presented the variations of the friction coefficient in the contacts between microballs having mm and the disc, when the rotational speed of disc 1 was 0- and - rpm. It can be observed that the maximum friction coefficient has values between to 0.00, when the rotational speed of the disc 1 has values between 0- and - rpm. The differences between the friction coefficients for the two microball diameters can be explained if considering the dependence between the friction torque and the normal load, obtained by McCarthy et al. [] in a planar-contact encapsulated microball bearing having 0.mm diameter steel balls and silicon races. So, McCarthy et al. established in [] that the ratio between the friction 0. torque and the angular speed can be expressed as a product between a constant factor and F, where F n is the normal force applied to the 0 microballs with 0.mm diameter situated between a silicon stator and a silicon rotor having plan surfaces. For normal forces between mn and mn tested in [], results the maximum Hertz contact pressure in the microball bearing having values between 0.1 GPa and 0.GPa, respectively. McCarthy et al.[] obtained for the normal n

16 force of mn and a rotational speed of rpm a friction coefficient of and for the normal force of mn and a rotational speed of 00 rpm obtained a friction coefficient of 0.0. Using the linear dependence of the friction torque with rotational speed obtained in [] it can be considered that at rpm and mn normal force, the friction coefficient is about In conclusion, the results obtained in [] shows that if the maximum Hertz contact pressure increases from 0.1 GPa to 0. GPa at a constant rotational speed, the friction coefficient decreases from to 0.000, respectively. 1 In our experiments for the maximum Hertz contact pressure of 0.1 GPa (for the ball having mm) we obtained friction coefficient values between and Also, for the maximum Hertz contact pressure of 0.1 GPa (for the ball having 1. mm) we obtained friction coefficient values between and 0.000, that means a good correlations with the results from [].. The proposed method can be extended to determine the friction coefficient between the driving disc 1 and microballs, by using both acceleration of the disc and acceleration of the microballs, as was demonstrated in Eqs. 1 and 1. For the ball angular position φ b ( t ) we considered an exponential function given by equation: ab + bb ln( t ) + cb ln( t ) φ ( t ) = e () b where a b, b b and c b are constants determined by curve fitting of the experimental results. By derivative of the function φ b ( t ) we obtained the angular acceleration of the microball motion, which was introduced in Eq.1. For the balls with 1. - mm diameter the inertial parameters A and B from Eqs. 1 and 1 have following values: A = 1.1 s and B = 1. s. Figure 1 presents the friction coefficient between balls and the two discs. No differences between the two friction coefficients can be observed as a result of very small influence of the inertial parameter B. It can be explained by the small influence of the inertial motions of the balls in the

17 friction coefficient. In these conditions, the friction coefficients between the balls and the two discs are equals and can be determined by equation (). By increasing the diameter of the three balls to.mm (/1 inch) the inertial parameters A and B has values with the same order of magnitude ( A =.01 s, B =.0 s ) and the differences between the two friction coefficients can be evidenced. Figure presents the friction coefficient between balls with.-mm diameter and the two discs, the driving disc 1 having a constant rotational speed of 0 rpm. Increasing of the microballs mass leads to the increasing of the inertial influence on the friction coefficient and the friction coefficient between the microballs and the two discs must be determined by different equations: Eq. for the contact between the microballs and the driven disc and Eq. for the contact between the microballs and the driving disc 1.. To verify the correspondence between our method and the spin - down method realized by [] and [], the transient response of the inertial disc in the deceleration process from a constant angular velocity until it completely stops due to friction has been determined. So, the disc 1 was rotated with constant speed until the disc and the balls attainted the synchronism rotation, after that was stopped. The angular position of the disc, from the constant rotational speed to his completely stop in the deceleration process was registered by camera. The measured angular positions φ ( ) was fitted to an exponential function used in [], having the following expression: t D t φ( t ) = C (1 e ) () where t is the time (in seconds) and C and D are constants. The C and D constants was obtained by the curve fitting of the experimental data imposing dφ ( t ) the initial condition: at t = 0, = ω1, where ω 1 is angular speed of the driving disc 1 before it dt was stopped. 1

18 The acceleration of the disc was obtained by differentiation of the function φ ( ). Figure 1 presents the experimental variations of the angular positions of the disc from the rotational speed of 0-, -, 0- and - rpm until it completely stops due to friction, the microballs having 1.- mm diameter. In the deceleration process, the kinematics energy of the disc in rotation is dissipated by friction process in the contacts between balls and the two discs. Using the deceleration of the disc in Eq., the variations of the friction coefficient have been obtained and are presented in Fig. 1. It can be observed that the maximum friction coefficient (for t = 0) determined by the spin - down method has values between and when the rotational speed of the disc 1 varied between 0- and - rpm while the maximum friction coefficient obtained by our method, for the same rotational speeds varies between and ( as in Fig. ). Conclusions The authors developed a new methodology to determine the rolling friction coefficient by monitoring the variation in time of angular position of an inertial rotating disc sustained and put in rotational motion by three microballs in the acceleration process, from start to the synchronism of the rotational speed. The kinematics and dynamics both of the inertial disc and of the microballs have been developed and analytical equations for friction coefficient between the microballs and the disc was obtained. Linear dependence between friction coefficient and angular acceleration of the inertial disc has been used. A new microtribometer consist in a steel driving disc having a constant rotational speed, an glass inertial driven disc and three stainless steel microballs was made and a lot of experiments to validate the methodology have been realized. The values of rolling friction coefficient we have obtained by this methodology lead to the following conclusions: 1 t

19 (a) The time variation of the friction coefficient, from start to the synchronism rotation is in accord with physical phenomena. A rapid increasing of the friction coefficient at the start to a maximum value followed by a decreasing to a low constant value was obtained. (b) A dominance of the rolling process between the three microballs and the inertial disc has been evidenced. Small differences between measured angular positions of the inertial disc and theoretical angular positions of the inertial disc have been obtained. (c) For the three steel microballs having 1.-mm diameter loaded with. mn per microballs, the maximum rolling friction coefficient between microballs and a glass inertial disc in dry conditions has values between and The variation of the rotational speed from 0 rpm to rpm lead to the increasing of the rolling friction from to 0.000, respectively. (d) By increasing of the ball diameter to mm and maintaining the normal load of. mn was obtained increasing of the maximum friction coefficient up to 0.00, for rotational speed of the driving disc 1 of rpm. (e) The values of friction coefficient obtained by proposed methodology both for 1. mm diameter and - mm diameter of the microballs was compared with the results obtained by [] using spin - down method and good correlations was obtained. Acknowledgements This work was supported by CNCSIS Grant ID_ No. 1/ The authors thanks to professor Dik Schipper from Twente University for technical discussions and to facilitate the preliminary experiments in the laboratory of Surface Technology and Tribology. 1

20 References [1] Lin, T.W., Modafe, A., Shapiro, B., Ghodssi, R.: Characterization of Dynamic Friction in MEMS Based Microball Bearings. IEEE Transaction of Instrumentation and Measurement, - (00) [] Tan, X., Modafe, A., Ghodssi, R.: Measurement and Modeling of Dynamic Rolling Friction in Linear Microball Bearings. Journal of Dynamic Systems, Measurement, and Control 1, 1- (00) [] Ghalichechian, N., Modafe, A., Beyaz, M. I., Ghodssi, R.: Design, Fabrication, and Characterization of a Rotary Micromotor Supported on Microball Bearings. Journal of Microelectromechanical Systems 1, - (00) [] McCarthy, M., Waits, C. M., Ghodssi, R.: Dynamic Friction and Wear in a Planar-Contact Encapsulated Microball Bearing Using an Integrated Microturbine. Journal of Microelectromechanical Systems 1, - (00) [] Olaru, D. N., Stamate, C., Prisacaru, Gh.: Rolling Friction in a Microtribosystem. Tribology Letters, 0-, (00) 1

21 FIGURES Fig. 1 The new micro tribometer with microballs Fig. The angular positions of the disc 1, and of the balls, after the time t 1

22 Fig. The position of a ball in contact with the two discs during the running process. Fig. The forces acting on the microball in the running process

23 Angular position ( radians ) 00 Angular position of the disc 1 Angular position of the micro balls 00 Angular position of the disc Time ( s ) Fig. The variation of the angular positions φ1, φb and φ for angular speed ω1=. s -1 and for three micro balls having 1,- mm diameter 1

24 Angular position ( radians ) Angular position of the disc obtained by curve fitting Measured angular position of the disc Time ( s ) Fig. The differences between the measured and the curve fitting angular position values of for the disc, Friction coefficient when the disc 1 has an angular speed ω 1 =. s Time ( s ) Fig. The variation of the friction coefficient between the microballs and the inertial disc, for an angular speed ω1=. s -1.

25 Differences between theoretical and measured angular positions of the disc ( radians) 1 0, 0, 0, 0, 0-0, -0, -0, -0, Time ( s ) Fig. The differences between theoretical positions of the disc determined by Eq. and measured angular positions of the disc, for angular speed ω1=. s -1

26 Angular position of the disc ( radians ) rpm rpm 0 rpm rpm Time ( s ) Fig. The variation of the angular positions of the disc for microballs having 1. mm and for angular speed of the disc 1 of: 0-, -, 0- and -rpm Friction coefficient r rpm rpm 0 rpm rpm Time ( s ) Fig. The variation of the friction coefficient between the microballs having 1.mm and the disc when the driving disc 1 was rotated with 0-, -, 0- and - rpm

27 Friction coefficient Time ( s ) rpm 0 rpm Fig. The variation of the friction coefficient between the microballs having mm diameter and Friction coefficient the disc for two rotational speeds of the disc 1: 0- and - rpm Time, seconds Friction coefficient between balls and disc Friction coefficient between balls and disc 1 Fig. 1 The variation of the friction coefficient between the balls having 1. - mm diameter and the two discs (1 and ), for rotational speed of the disc 1 of rpm..

28 Friction coefficient Time ( s ) Friction coefficient between balls and disc Friction coefficient between balls and disc 1 Fig. The variation of the friction coefficient between the microballs having. mm diameter Angular position ( radians ) and the two discs for the rotational speed of the disc 1 of 0 rpm 0 rpm rpm 0 rpm rpm Time ( s ) Fig. 1 The variation of the angular position for the disc when the disc 1 is stopped from the rotational speed of 0-, -, 0- and - rpm, the microballs having 1.- mm diameter..

29 Friction coefficient rpm rpm 0 rpm rpm Time ( s ) Fig. 1 The variation of the friction coefficient between the balls having 1. mm diameter and the two discs using the spin - down method, for the rotational speed of 0-, -, 0- and - rpm.