Page 218 - Mechatronics with Experiments

204 MECHATRONICS
(d) What happens if you use only the load-coupled position sensor, not the motor-coupled position
sensor? Show your claim with simulation results. Modify component parameters if necessary to
illustrate your point.
Simulate a condition as follows: the engine runs at a constant speed. The friction coefficient
at each tire–ground contact is constant and the same for all tires, and the vehicle weight is equally
distributed in all tires. The initial direction of motion and steering is a straight line motion. The
steering angle is zero at all times, which means all the wheels are aligned to move in a straight line.
Based on a different desired gear selection as a function of time (i.e., step changes in gears at specific
points in time), assume instantaneous gear shift and clutch engagement/disengagement. Assume the
clutch stays engaged at all times except when the neutral gear is selected.
12. (This problem can be assigned as a small research project for students).
Develop a mathematical model of a four wheel drive vehicle including the following compo-
nents of the powertrain (Figure 3.37):

Position sensors
Brake S ECM
Pedal sensor
S
Accelerator ECM Brakes
Pedal sensor ECM
Speed Speed
sensor sensor Vehicle speed
Torque Planetary Lower Tire & ground
Engine interaction
converter gear set powertrain
Traction force
FIGURE 3.37: Automotive powertrain block diagram: engine, transmission (torque converter
and planetary gear set), lower powertrain, brake, and tire–ground interaction.

1. Engine is to be modeled as a lug curve for different throttle values (without any transient
dynamics), T ( , w ,
eng throttle end
J eng ⋅ ̇ w eng (t) = T eng ( throttle , w eng ) − T imp (t) (3.339)
T eng ( throttle , w end ). This function is commonly referred as the “engine map.” The maximum
torque of the engine at full throttle is 1000 N m. Define an reasonable engine map based on
this information, that is, T eng ( throttle , w end ), look up table.
2. Transmission is to be modeled on a torque converter and a planetary gear set. We model the
torque converter with its steady-state torque ratio and primary torque functions, whereas the
planetary gear set is assumed to shift to the desired gear instantanously. The transient time
in the gear shifting is neglected, as well as the inertial and stiffness characteristics of the
transmission. Simply model the planetary gear set as an ideal gear ratio device.
1
T imp (t) = T (w turb ∕w eng ) ⋅ ⋅ w 2 eng (3.340)
p
w 2
r
T turb = N (w turb ∕w eng ) ⋅ T imp (t) (3.341)
t
N = N (gear) (3.342)
p
p
T (t) = N ⋅ T turb (t) (3.343)
out
p
1
w (t) = ⋅ w turb (t) (3.344)
out
N p
The torque converter is to be modeled as two steady-state functions: primary torque and torque
ratio, which are defined as a function of the speed ratio. The efficiency of the torque converter