附录A
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.
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 ba
sed 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 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.
Figure 1. Layout of a CVT and a metal pushbelt  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:  S S q R F T 2cos φ
μ=                            （1）
In which q T  represents the input torque, S R  represents the secondary running radius of the belt on the pulley, S F  represents the secondary clamping force and φ is the pulley wedge angle.
Figure 2. CVT torque transmission scheme
The second variable in the traction curve is the slip in the variator.
Slip is defined as:
10
-=r P S ωων                          （2） Where s ω is the angular speed of the secondary axle, p ω is the angular speed of the primary axle and 0r  is the geometrical ratio, which is defined by:
S
P R R r =0                              （3） P R  is the running radius on the primary pulley.
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. 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 dt is evenly distributed along the idle arc of the driving pulley. The traction
Figure 3. Gaps in the belt
curve (figure 5) shows that torque transmission increases almost linearly with an increase in slip, until a certain maximum torque is reached. dt can be estimated by adding an initial gap do 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.
dL t +=0δδ                            （4）
To calculate the slip caused by these gaps we can use the following equations:
d
R d t ps t m ++⨯=δαδδ                        （5） m
m d v δδ+=                            （6） In equation 5, a is the idle arc, d is the width of a belt element and dt is the total gap between the elements in the belt. To calculate the amount of slip the total gap dt has to be known. 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.
v c f 0=                                （7）
12
10v v e a a g -+=                          （8）
f g v v +=)sin(μ                        （9）
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.
pulleys2.2 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 const
ant. 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.
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.
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 torqu
e 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.
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 pulley. This ratio ring limit the movement of the pulley. Primary and secondary pressure was held constant (clamping forces were held constant) during the experiments.
Figure 4. Experimental setup
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).

版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系QQ:729038198，我们将在24小时内删除。