DSC TOC
Proceedings of IMECE’03
2003 ASME International Mechanical Engineering Congress
Washington, D.C.,
Novemberof15–21,
2003
Proceedings
IMECE2003
2003 ASME International Mechanical Engineering Congress and R&D Expo
November 15-21, 2003, Washington, DC USA
IMECE2003-41360
IMECE2003-41360
ANALYSIS OF SLIP IN A CONTINUOUSLY VARIABLE TRANSMISSION
B. Bonsen, T.W.G.L. Klaassen, K.G.O. van de Meerakker,
M. Steinbuch and P.A. Veenhuizen
Eindhoven University of Technology
Mechanical Engineering
Control Systems Technology
PO Box 513, WH -1.126
5600 MB Eindhoven, The Netherlands
Email: b.bonsen@tue.nl
ABSTRACT
High clamping force levels reduce the efficiency of the Continuously Variable Transmission (CVT). However, high clamping force levels are necessary to prevent slip between the belt
and the pulleys. If a small amount of slip is allowed, the clamping force level can be reduced. To achieve this, slip in a CVT
is investigated. From measurements on an experimental setup,
Traction curve data and efficiency measurements are derived. A
model describing slip in a CVT is verified using measurements
with a belt with increased play. It is found that small amounts
of slip can be controlled in a stable way on the setup. The traction curve was mostly dependent on the CVT ratio. Efficiency is
found to be highest for 1 to 2% slip depending on the ratio. The
model is in reasonable agreement with the measurements.
pulleys which are wedge shaped. By changing the position of the
pulleysheaves the ratio of the CVT can be adjusted. The V-belt
consists of blocks which are held together by two rings that in
turn exist of a set of bands. To achieve torque transmission sufficiently high clamping force levels are needed to prevent slip in
the variator. Because the torque level is not exactly known at all
times, since no torque sensor is used due to cost considerations, a
safe clamping force level based on the maximum possible load is
maintained at all times. This safety level is based upon assumed
maximum shockload levels from the road, like bumps, and the
engine torque.
In order to maintain these safety levels higher clamping force
levels are maintained then needed. Higher clamping force levels
cause more losses in the CVT. These losses are caused by increases in power consumed by the hydraulic pump, by increases
in the losses due to slip in the belt if a pushbelt is used, and by
increases in deformation in the belt and in the pulleys. Furthermore wear is increased and fatigue life is reduced.
In order to reduce these clamping force levels a method is needed
to detect slip in the variator fast enough to prevent slip from
reaching destructive levels. A method to detect and control slip
is therefore needed.
In this paper measurements are presented of the traction curve
in a V-belt CVT. Also a quantitative evaluation is made of the
model proposed by [1].
1
Introduction
Applying a Continuously Variable Transmission (CVT) in
an automotive driveline has several advantages. A CVT can operate at a wider range of transmission ratios, therefore the engine
can be operated more efficiently than with a stepped transmission. Also, a CVT does not interrupt the torque transmission
when shifting. This gives a more smooth ride than a stepped
transmission does. A V-belt based Continuously Variable Transmission uses a belt or a chain to transmit torque from a driving
side to a driven side by means of friction. The layout of the CVT
and the V-belt are shown in figure 1. The variator consists of two
1
c 2003 by ASME
Copyright Active arc
T
Q
Secondary side
β
α
Primary side
Idle arc
Figure 2.
CVT torque transmission scheme
The second variable in the traction curve is the slip in the variator.
Slip is defined as:
ν=|
ωs
− 1|
ω p r0
(2)
Where ωs is the angular speed of the secondary axle, ω p is
the angular speed of the primary axle and r0 is the geometrical
ratio, which is defined by:
r0 =
Figure 1.
2
Traction curve
The V-belt type CVT utilizes friction to transmit power
from the primary pulley to the secondary pulley. The traction
curve is the dimensionless relationship between transmitted torque and the slip. The maximum input torque that
can be transmitted by the CVT is dependent on the applied
clamping force. The traction coefficient is therefore chosen to
be a dimensionless value. The traction coefficient µ is defined as:
Tq cos φ
2Fs Rs
(3)
R p is the running radius on the primary pulley. A model of
the torque transmitting mechanism of the V-belt is given by [2].
This model gives insight on the tensile and compressive forces
acting within the bands and between the blocks of the belt (see
figure 2).
Layout of a CVT and a metal pushbelt
µ=
Rp
Rs
2.1
Tangential slip
Slip is defined in equation 2. When the CVT transmits
power a certain amount of slip can be measured almost linear
with the applied torque. This is called the microslip regime of
the CVT, because traction is still increasing in this regime with
increasing slip. The microslip is caused by gaps between the
blocks on the idle part of the driving pulley as shown in figure
3 [1]. On the driving pulley an idle arc exists where no slip occurs. Also an active arc exists (see figure 2), where slip occurs
relative to the total play in the belt and the active arc length.
However, when the maximum torque capacity of the CVT is
reached slip will increase dramatically. This situation, macroslip,
is not stable during normal operation of the CVT, because the
traction coefficient decreases with increased slipspeed.
It is assumed that the total gap δt is evenly distributed along
(1)
In which Tq represents the input torque, Rs represents the
secondary running radius of the belt on the pulley, Fs represents
the secondary clamping force and φ is the pulley wedge angle.
2
c 2003 by ASME
Copyright Equation 7 gives a value for the friction caused by viscous
friction component. Equation 8 gives a value for the coulomb
friction component. a0,1 , c0 and v1 are coefficients which can be
chosen to match the measured values.
With these equations we can derive slip and traction from measured data as shown in section 4. With Asayama [1995] we can
obtain the tension and compression force distribution needed to
calculate the lengthening of the belt. Also, we can calculate the
idle arc from this model. From the idle arc, the length of the belt
and the initial gap we can calculate an estimate for slip in the belt
for a given load.
d
dm
2.2
Figure 3.
Radial slip
Not only slip in tangential direction occurs, but also slip in
radial direction. The first reason for radial slip is spiral running.
When the belt runs along the arc of contact the radius at which it
runs is not constant. This effect is caused by pulley deformation.
One type of deformation is the bending of the axle between both
pulley sheaves. The belt is not fully wrapped around the pulley,
therefore the resulting normal force of the blocks on the pulley is
not axial. This causes a bending moment in the axle [4].
A second effect is the bending of the pulley itself. This effect is
mostly dependent on the local normal force exerted on the pulley
by the blocks. This effect is small when the belt is running on a
small running radius, but on a large running radius this effect is
significant. The second reason for slip in radial direction is due
to shifting. When the CVT is shifted to a different transmission
ratio, radial slip is forced. This is done by changing the clamping
force ratio. The amount of radial slip that is forced depends on
the shifting speed and the (primary) angular speed.
Gaps in the belt
the idle arc of the driving pulley. The traction curve (figure 5)
shows that torque transmission increases almost linearly with an
increase in slip, until a certain maximum torque is reached. δt
can be estimated by adding an initial gap δo to the increase in
belt length due to the internal stresses in the bands and a decrease
in length of the blocks due to the compressive forces.
δt = δo + dL
(4)
To calculate the slip caused by these gaps we can use the following equations:
d · δt
αR p,s + δt + d
δm
ν=
d + δm
δm =
(5)
3
Experimental setup
In the experiments the geometric cvt ratio is fixed and the
clamping forces are constant, the traction coefficient then depends only on the slip in the system. The traction curve can
be constructed from output torque and slip measurements. The
test rig motors deliver a maximum torque of 298 Nm with a
maximum speed of 525 rad/s. Both motors are equipped with
a Heidenhain ERN1381 incremental rotary encoder with 2048
pulses/rev. The torque at both sides is measured using a HBM
T20WN torque sensor. The maximum allowable torque is 200
Nm with speeds up to 1050 rad/s. A separate hydraulic unit is
used to provide the required flow and pressure for the clamping
forces. Figure 4 gives a schematic overview of the experimental
setup.
(6)
In equation 5, α is the idle arc, d is the width of a belt element and δt is the total gap between the elements in the belt. To
calculate the amount of slip the total gap δt has to be known. Furthermore the decrease of the friction coefficient with increasing
slip speed has to be taken into account as shown by Kobayashi
[1998]. For this purpose a Stribeck curve is used [3]. This effect has an influence on the traction coefficient in the macroslip
regime. When macroslip occurs the traction will decrease with
increasing slip. The Stribeck effect is modelled using equation 9.
f = c0 v
(7)
− vv 2
g = a0 + a1 e 1
µv = sign(v) · g + f
4
Experimental results
The geometric ratio of the CVT was fixed during the experiments using a so-called ratio ring and the limits of the primary
(8)
(9)
3
c 2003 by ASME
Copyright M o to r 1
0.12
E n c o d e r
T o rq u e s e n s o r
0.1
M o to r 2
µ [−]
0.08
H y d r a u lic u n it
0.06
0.04
0.02
Figure 4. Experimental setup
0
0
0.12
µ [−]
0.08
3
Slip [%]
4
5
0.06
Medium
0.08
µ [−]
0.02
2
3
Slip [%]
= 150, 225, 300
0.1
Low
1
6
0.12
Overdrive
0.04
Figure 5.
2
Figure 6. Traction coefficient in overdrive, ωs
0.1
0
0
1
4
5
6
0.06
0.04
0.02
Traction coefficient at 300rad/s, ratio low(0.4), Medium (1.1)
and overdrive (2.26)
0
0
1
2
3
Slip [%]
4
Figure 7. Traction coefficient in low, ω p
pulley. This ratio ring limit the movement of the pulley. Primary
and secondary pressure was held constant (i.e. clamping forces
were held constant) during the experiments.
5
6
= 150, 225, 300
Traction curve
0.12
4.1
Traction coefficient
The traction coefficient was measured at different ratios, at
different primary speeds and at different pressures. In figure 6
and 7 can be seen that the traction coefficient depends little on
primary speed or secondary clamping pressure, but mostly on
the transmission ratio, as can be seen in figure 5. An increase in
clamping force causes more slip (see figure 8). This is caused by
an increase in tension in the bands and therefore in an increase in
length of the belt. This causes the play to increase.
0.1
0.08
µ [−]
8 bar
0.06
5 bar
0.04
0.02
0
0
4.2
Efficiency
The efficiency depends on pressure and on ratio. From figure
12 can be seen that an increase in pressure causes a decrease in
efficiency. This effect is caused by the internal friction in the
belt. Slip between the blocks and the bands also causes a strong
dependency on ratio (see figure 9). Efficiency is clearly higher
in medium than in overdrive or low. In medium no slip occurs
between the blocks and the bands, but in overdrive or low the
bands slip over the blocks. At high clamping levels this effect is
greater, because the normal forces acting between the blocks and
the bands increase linearly with an increase in clamping level.
1
2
3
Slip [%]
Figure 8. Traction coefficient for resp.
4
5
6
5bar and 8bar secondary clamp-
ing pressure
From figure 10 and 11 can be seen that input speed also has an
influence on efficiency.
4.3
Play
The microslip region is dependent on play in the belt. An
experiment has been carried out with a belt with increased play.
4
c 2003 by ASME
Copyright 1
1
0.98
Medium
0.98
0.94
0.94
0.92
0.9
η [−]
η [−]
0.92
LOW
0.9
0.88
OD
0.88
0.86
0.86
8bar
0.84
0.84
0.82
0.82
0.8
0
Figure 9.
5bar
0.96
0.96
1
Efficiency at
2
3
Slip [%]
300rad/s,
4
5
0.8
0
6
1
2
3
Slip [%]
Figure 12. Traction coefficient for resp.
clamping pressure
ratio low(0.4), Medium (1.1) and
overdrive (2.26)
4
5bar
5
and
6
8bar
secondary
1
0.08
225rad/s
0.96
0.94
0.07
0.92
0.06
µ [−]
η [−]
0.09
150rad/s
0.98
0.05
0.9
0.04
300rad/s
0.88
0.86
0.03
0.84
0.02
0.82
0.01
0.8
0
Figure 10.
1
2
3
Slip [%]
4
Efficiency in overdrive, ωs
1
5
0
0
6
= 150, 225, 300
1
2
3
Slip [%]
Figure 13. Effect of play in the belt,
creased gap (1.8mm)
4
5
ω p = 30rad/s,
6
in low, with in-
wp=300[rad/s] LOW
w =225[rad/s] LOW
p
wp=150[rad/s] LOW
0.98
0.96
0.94
0.1
η [−]
0.92
0.08
0.9
µ [−]
0.88
0.06
0.86
0.84
0.04
0.82
0.8
0
1
2
3
Slip [%]
Figure 11. Efficiency in low, ω p
4
5
0.02
6
0
0
= 150, 225, 300
1
2
3
Slip [%]
Figure 14. Effect of play in the belt,
increased gap (1.8mm)
One block was taken out of the belt. The performance of the belt
was measured with a total gap of 1.8mm. The cumulative gap
in the belt was 0.3mm in the other experiments. A significant
difference is measured in the LOW ratio of the CVT. In figure
4.3 the traction curve is shown for the low ratio of the CVT for
the belt with increased play. Also the result of the numerical
model is shown in figure 4.3. The results for overdrive show that
4
5
6
ω p = 30rad/s, in overdrive, with
in overdrive there is no significant change in the traction curve,
see figure 4.3. However, the model is less consistent with the
tractioncurve in overdrive than in low.
5
c 2003 by ASME
Copyright 5
Conclusion
The traction curve is mostly ratio dependent. This can be
explained with the shown model as explained in section 4.
Transmission efficiency is dependent on applied pressure, input
speed and the CVT ratio.
Gaps between the blocks of the belt cause at least part of the
tangential slip of the belt. This was confirmed by the experiment
with increased play in the belt. The consistency of the model is
better in low than in overdrive.
Future research will be directed at controlling slip in the CVT.
This can enhance the efficiency of the CVT.
REFERENCES
[1] Kobayashi, D., Mabuchi, Y., and Katoh, Y., 1998. “A study
on the torque capacity of a metal pushing v-belt for cvt’s”.
SAE Technical papers [].
[2] H. Asayama, J. Kawai, A. T. M. A., 1995. “Mechanism of
metal pushing belt”. JSAE Review 16 [], pp. 137–143.
[3] H. Olsson, K.J. Astrom, C. C. d. W. M. G. P. L., 1997. Friction models and frictino compensation. Tech. rep., Lund Institute of Technology.
[4] Sorge, F., 1996. “Influence of pulley bending on metal v-belt
mechanics”. Proceedings of the International Conference on
Continuously Variable Power Transmissions [].
6
c 2003 by ASME
Copyright