Figure 1 Electromechanical car mirror wiper system
The motor shown is a servomotor, a dc motor designed in particular for
use in a control system. The operation of this device is as follows: A
fixed voltage is carried out to the field winding. A voltage is
implemented as an input to the servo motor and the angular position c of
the wiper arm is the output of the device. The input voltage is
implemented to the armature circuit of the dc motor. A constant voltage
is carried out to the field winding. If an errors exists, the motor
develops a torque to rotate the output load in the sort of way as to
reduce the error to zero. For constant field current, the torque evolved
by using the motor is
Where K1 is the motor torque constant and ia is the armature current.
When the armature is rotating, a voltage proportional to the fabricated
from the flux and angular velocity is brought on within the armature.
For a constant flux, the brought about voltage eb is without delay
proportional to the angular velocity or
Where eb is the back emf, K 2 is the back emf constant of the
motor, and is the angular displacement of the motor shaft.
The speed of an armature-managed dc servomotor is managed via the
armature voltage e(t). The differential equation for the armature
circuit is
Substituting Equation (2) in to Equation (3) yields:
Taking the Laplace transform the equation will be
The equation for torque equilibrium is
Taking the Laplace transform the equation will be
Where J0 is the inertia of the combination of the motor, load, and gear
train referred to the motor shaft and b0 is the viscous-friction
coefficient of the aggregate of the motor, load, and gear train
mentioned the motor shaft.
By eliminating from Equations (5) and (7), we obtain
We assume that the gear ratio of the gear train is such that the output
shaft rotates n times for each revolution of the motor shaft. Thus,
The wiper arm speed can be evaluated by using an integrator to the wiper
arm position as
Substituting Equation (10) in to Equations (9) and to Equations (8)
gives us the transfer function between the applied voltage and the wiper
speed as
The parameters of the system is shown in Table 1 below.
Table 2 Parameters of the system