Page 606 - Mechanical Engineers' Handbook (Volume 2)

10 Steady-State and Dynamic Behavior of Servoactuators and Servosystems 597

Figure 40 Schematic diagram of an electromechanical servoactuator.

A simplified dynamic model may be derived based on the following assumptions:
1. The amplifier bandwidth is considerably greater than that of the servomotor load
portion of the system.
2. The gears have zero backlash and infinite stiffness.
3. The connecting shafts all have infinite stiffness.

Assumptions 2 and 3 eliminate some important dynamic effects that may need to be included
in some cases. 41
Definitions of the critical parameters and variables are as follows:

B viscous damping in the load (N m s/rad)
L
J polar moment of inertia of the load (N m s /rad)
2
L
K voltage gain of amplifier (V/V)
a
K ac current gain of amplifier (A/V)
n gear ratio, / , / L
L
m
m
T external load torque (N m)
e
T (s) Laplace transform of T d
d
T ƒL Coulomb friction torque in load (N m)
T total load torque reflected to the motor shaft (N m)
m
T total load torque (N m)
L
v voltage output of amplifier (V)
a
v voltage input to amplifier (V)
i
V (s) Laplace transform of v i
i
angular displacement of the load (rad)
L
angular velocity of the load (rad/s)
L
Other parameters are as defined in Section 3.
Mathematical Model
The basic equations which describe the dynamic behavior of the servoactuator in Fig. 40 are
as follows:
Amplifier equation:
v K v (67)
a i
a