Page 206 - Mechatronics with Experiments

192 MECHATRONICS
where N total is the total gear ratio from the torque converter output shaft to the tire–ground
contact point (it includes the average radius of the tire, R ave , in the gear ratio between the
shaft rotation and linear displacement of the tire),
N total = N planetary ⋅ N diff ⋅ N final drive ⋅ R ave (3.328)
where N planetary is the gear ratio at the currently selected gear (ratio between the speed of
the torque converter output shaft which is turbine and the speed of the planetary gear set
output shaft), N diff is the gear ratio at the differential, N final drive is the gear ratio of the final
drive, is the power transmission efficiency of the lower powertrain from turbine shaft to
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the tires.
For a given gear condition (i.e., gear 1, gear 2, gear 3), if we repeat this calculation
for different speed ratios of the torque converter, N = 0.0, 0.1, … ,1.0, we can plot the
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rimpull force developed at the tire–ground interaction at that gear as a function of machine
translational speed. If we repeat this for different gears (different N total values), then we
obtain different rimpull force versus machine speed curves for different gears (Figure
3.30b). This set of rimpull force–machine speed curves for different gear ratios defines the
tractive (rimpull) force capability of a machine. In steady state, for a given gear ratio of
the transmission, each curve shows the maximum rimpull force the machine can generate
at different machine speeds. Actual measured rimpull force curves versus machine speed
would be a little different than the calculated rimpull force curves due to slip between tires
and ground as well as friction losses, hence there is some error in calculating the machine
speed based on the engine speed.
Rimpull force versus machine speed curves for a machine which has a drive train
without torque converter (a direct coupling between engine and gear reducer set, i.e.,
planetary gear set) would look like the curves shown in Figure 3.24. When a torque
converter is included in the coupling between the engine and gear set, the rimpull force
versus machine speed curves are a little smoother, and the rimpull force is a little smaller
compared to the direct drive case. This is expected since the torque converter is less efficient
than the direct coupling.
The power delivered to the rim of the machine (rimpull power) is the engine power
minus the transmission losses. Notice that the maximum rimpull power is about same for all
gears. The difference is simply due to efficiency differences in the transmission at different
gear ratios. The shape of the rimpull power curve is simply stretched for different gears
(Figure 3.30c).
One simple measurement to confirm the engine and drive-train capabilities of a
machine is to measure the stall point. That is, for a given gear ratio (i.e., gear 1), set the
engine to full throttle, and load the machine such that the machine speed is zero (N = 0.0),
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and measure the rimpull force and the engine speed at that point (maximum rimpull at
machine stall speed). This measured data then can be compared with the specifications (i.e.,
maximum rimpull force on Figure 3.30b) to verify the accuracy of how well the machine
at hand meets the specified performance. About 3–5% variation between specifications and
actual measured values is normal as a result of manufacturing variations and measurement
errors.

3.8.5 Clutches and Brakes: Multi Disc Type

Clutches and brakes are very common components in motion transmission mechanisms
such as transmissions. They both involve two shafts. A clutch transmit torque from one
moving shaft to another moving shaft. In the case of brakes, the second shaft is stationary.
By controlling a combination of clutches and brakes, different gear ratios are obtained from
the transmission.