TECHNICAL UNIVERSITY OF CLUJ-NAPOCA
24 - 25 September 2009
EXPERIMENTAL INVESTIGATIONS OF ROLLING FRICTION IN
MECHATRONICS MICROSYSTEMS
Dumitru OLARU, Ciprian STAMATE, Alina DUMITRASCU, Gheorghe PRISACARU
Abstract: To evaluated the rolling friction in a micro rolling contact the authors developed a new micro
tribometer with a rotating glass disc supported by 3 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 micro balls having the diameter of 1.588 mm and normal load of 9.42 mN both in
dry and condensed water conditions.
Key words: Rolling friction, micro tribometer, microball, microsystem.
1. INTRODUCTION
The use of the micro linear or rotating ball
bearings in the MEMS applications implies the
simplification in construction, low level of
friction and high stability, so that the microball
bearings seem promising for future MEMS
applications. Some experiments to determine
the friction in the linear or rotating microball
bearings was realized in the last period.
Lin et al. [1] determined the static and
dynamic coefficient of friction for a microball
linear system consisting of micromachined
silicon V-grooves and stainless-steel microballs
with diameter of 0.285 mm and established that
the dynamic coefficient of friction
was
between 0.007 to 0.015 if there is no interaction
between balls. Ghalichechian et al. [2]
determined the coefficient of friction in an
encapsulated rotary microball bearing realized
by silicon microfabrication and stainless steel
microballs with 0.285 mm diameter. The
coefficient of friction 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. The global friction coefficient between
rotor, microballs and stator was determined as a
linear dependence with acceleration and value
of 0.02 have been obtained.
Using spin-down testing McCarthy et al. [3]
experimentally investigated the dependence of
speed and normal load on dynamic friction in a
planar-contact encapsulated microball bearing
having 0.285mm diameter steel balls and
silicon races. The authors determined the
dynamic friction coefficient varying from
0.0005 to 0.025, for speeds of 250–5000 r/min
and for loads of 10–50 mN.
Using the integration of the free oscillations
equations of a microball on a spherical surface,
Olaru et al. [4] evaluated the rolling friction
coefficient on the basis of the number and
amplitude of the experimentally determined
ball oscillations. For a microball having a
diameter of 1 mm, Olaru et al. [4] obtained in
dry conditions values for rolling friction
coefficient up to 0.015 – 0.03.
The experimental results obtained by [1,2,3]
reefer to the global rolling friction coefficient
both in a microball linear system [1] and in a
rotary microball bearing [2,3]. The global
friction coefficient is a result both of the
rolling friction and of the sliding friction caused
by the pivoting motion of the microballs over
the races.
To evaluated only the rolling friction in a
micro rolling contact the authors developed a
new micro tribometer with a rotating glass disc
supported by 3 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 micro balls having the
diameter of 1.588 mm and normal load of 9.42
mN.
2. EQUIPMENT AND PROCEDURE
In the figure 1 is presented the micro
tribometer used for experiments.
equilibrium of the disc 2, following equation
for rolling friction coefficient µ is obtained:
J ⋅ cos( α ) d 2 φ2
(2)
µ=
⋅ 2
G⋅r
dt
where: J is the moment of inertia for the disc 2,
d 2 φ2 dt 2 is angular acceleration of the disc 2
and φ2 is angular position of the disc 2 as a
function of the time t.
To determine the angular acceleration of the
disc 2 a high – speed camera with 90
frames/seconds was used to capture the angular
position of the disc 2 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
synchronism time. In figure 2 are presented the
registered positions of the disc 2, of a ball and
of the disc 1, respectively φ2 , φb , and φ1 at a
short time t after the start of the rotation.
Fig. 1 Micro tribometer disc on 3 balls
The disc 1 is rotated with a constant rotating
speed. Three micro balls are in contact with the
race of the disc 1 at the equidistance position
(120 degrees). All the three microballs
sustained a glass disc 2 and are normal loaded
G
with a force Q =
, where G is the
3 ⋅ cos α
weigh of the disc 2 and α is the contact angle
between microballs and spherical surface of the
disc 2.
When the disc 1 start to rotate with a
constant speed ω1, the balls start to rolls on the
raceway of the disc 1 and start to rotate the disc
2, as a result of rolling friction forces between
the balls and the disc 2. The tangential forces
between the balls and the disc 2 (F) are the
traction forces for the disc 2 and can be
expressed as:
F = µ ⋅Q
(1)
where µ is the rolling friction coefficient
between balls and disc 2.
The disc 2 is accelerated from zero to the
rotational speed of the disc 1 in a time t
(seconds) as a result of inertial effect.
Considering only friction between disc 2 and
the three balls
and using the dynamic
Fig. 2: Angular positions of the disc 1, 2 and of the balls
after the time t
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
φ2 corresponding to every frame. The camera
was installed vertically 15-cm above the disc 2,
to minimize the measurement errors. A white
mark was placed both on disc 2 and on disc 1 as
it can be observed in the figure 2 and the
angular positions φ2 and φ1 was measured
according to the reference line (position at t =
0) and these marks. At the initial time (t = 0)
the marks on the two discs and one of the three
ball was placed at zero position corresponding
to reference line.
3. EXPERIMENTAL RESULTS
The disc 1 was mounted on the rotational
table of the pin on disc machine CETR type
UMT-2 having servo-controlled rotational
speed. The disc 2 and the balls has following
dimensions: the radius of the disc 2 is R =
14.25mm, the radius of the spherical surface of
the disc 2 is RS =70mm. The weigh of the disc
2 is G = 28.05 mN and the normal load on
every ball is about Q = 9.42mN. The disc 1 is a
steel ring of an axial ball bearing (series 51100)
with a curvature radius of 2.63 mm and having
the radius of the rolling path for the three
microballs r = 8.4 mm. The ball diameters was
1.588 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 roughness parameter Ra was
obtained: surface of the disc 2 has Ra =
0.028µm , rolling path of the disc 1 has Ra =
0.030 µm and ball surface has 0.022 µm. The
contact angle α has 6.90 The angular speed of
the disc 1 was between (40 –90) rpm. All
measurements are performed in steady room
environment at a temperature of (22-24)0 C and
a relative humidity of (40 – 60)%RH.
In Figure 3
are presented the typically
registrations of the three angular positions, φ1,
φb and φ2 , when the disc 1 has a rotational
speed of 60 rpm, for dry conditions.
φ2 ( t ) respectively, are non linear functions of
the time and analytical expressions was
obtained by curve fitting of the experimental
results.
The following exponential function was
proposed for angular position of the disc 2:
2
φ2 ( t ) = e a + b⋅ln( t )+ c⋅ln( t )
(3)
where a, b and c are constants obtained by
curve fitting of the numerical values.
Angular acceleration of the disc 2 was
obtained by derivative process from fitted
function of angular position described by
equation (3). Also, by equation (2) was
obtained the friction coefficient between balls
and disc 2 as a function of the time µ2 ( t ). In
the figure 4 are presented the variations of the
friction coefficient between balls and disc 2 for
3 rotational speeds of 40, 60 and 90 rpm of the
disc 1, in dry conditions.
Fig. 4: Variation of the friction coefficient between the
balls and the disc 2 for three rotational speed
of the disc 1: 40,60 and 90 rpm
Fig.3: Variation of the angular positions φ1, φb and φ2 for
angular speed ω1=6.28 s-1
It can be observed that angular position of the
disc 1 is a linear function of the
time: φ1( t ) = ω1 ⋅ t , where ω1 is angular speed
of the disc 1, that means a constant rotational
speed of the disc 1. The angular position of the
balls and of the disc 2, φb ( t ) and
The variation of the friction coefficient with
the time, from start to the synchronism rotation
is in accord with 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 3 elements (disc 1, disc 2 and
balls).
The experimental values of the friction
coefficient obtained by proposed method
suggest a dominance of the rolling process
between balls and disc 2.
To verify the correspondence between our
method and the spin-down method realized by
[2] and [3], the transient response of the disc 2
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 until the disc 2 and the balls attainted
the synchronism rotation after that was stopped.
The angular position of the disc 2 from the
constant rotational speed to his completely stop
in the deceleration process was registered by
camera. The measured angular positions
φ2 ( t ) was fitted to an exponential function
used in [3], having the form:
φ2 ( t ) = A ⋅ ( 1 − e − B ⋅t )
(4)
where t is the time (in seconds) and A and B
are constants determined by curve fitting the
experimental data. The deceleration of the disc
2 was obtained by differentiation of the
function φ2 ( t ) . Using the deceleration in
equation (2), the variations of the friction
coefficient have been obtained. In the figure 5
are presented the variations of the friction
coefficient from the rotational speed of 40, 60,
and 90 rpm until it completely stops due to
friction.
Fig. 5: Variation of the friction coefficient between the
balls having 1.588 mm and the two discs using spindown method for rotational speed 40, 60 and 90 rpm
the spin – down method (fig. 5) are in the same
interval of values 0.0002 to 0.0004 that
evidence a good agreement between the two
methods.
4. CONCLUSIONS
It is possible to estimate rolling friction
coefficient by monitoring the variation in time
of angular position for a rotating disc in contact
with 3 micro balls in the acceleration process.
For dry conditions, rolling friction coefficient
between 3 steel micro balls with diameter of
1.588 mm and a glass disc with 2.8 grams is
about 0.0002 – 0.0004, for a rotational speed
between 40 to 90 rpm and for dry conditions.
Acknowledgements
This work was supported by CNCSIS Grant
ID_607 No. 381/1.10.2007.
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 53, 839-846 (2004).
[2] 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 17, 632-642 (2008).
[3] McCarthy,M., Mike Waits, C. and Ghodssi, R.,
Dynamic Friction and Wear in a Planar-Contact
Encapsulated Microball Bearing Using an Integrated
Microturbine, Journal of Microelectromechanical
Systems, 18, 263-273, (2009)
[4] Olaru,D.N., Stamate, C., Prisacaru, Gh., Rolling
Friction in a Microtribosystem, Tribology Letters, 35,
205-210, 2009.
The maximum values of friction coefficient
obtained by proposed method (fig. 4) and by
CERCETARI EXPERIMENTALE PRIVIND FRECAREA DE ROSTOGOLIRE
IN MICROSISTEME MECATRONICE
Dumitru Olaru, Prof. Dr. Ing., Dept. of Machine Elements and Mechatronics, Technical University “Gheorghe Asachi”
of Iasi, [email protected], phone: 0232 232337
Ciprian Stamate, Doctoral student, Dept. of Machine Elements and Mechatronics, Technical University “Gheorghe
Asachi” of Iasi
Alina Dumitrascu, Doctoral student, Dept. of Machine Elements and Mechatronics, Technical University “Gheorghe
Asachi” of Iasi
Gheorghe Prisacaru, Conf. dr. ing., Dept. of Machine Elements and Mechatronics, Technical University “Gheorghe
Asachi” of Iasi