User`s manual

7-46 Motion Mate™ DSM314 for Series 90™-30 PLCs User's Manual – January 2001 GFK-1742A
7
Calculating Acceleration, Velocity and Position Values
One method of determining the value for APM or DSM motion program variables such as
Acceleration
,
Velocity
or
Position
is to plot the desired move or move segment as a velocity
profile. A velocity profile plots time on the horizontal axis of a graph and velocity on the vertical
axis. The key to understanding profile generation is to break the complete move into smaller
segments that may be analyzed geometrically. Most applications will use the economical
trapezoidal move, velocity profile as illustrated below. To move as quickly as possible, use a
triangular velocity profile if the servo has sufficient speed range. A triangular move would
accelerate half the distance then decelerate the remaining half. Another alternative is to use a
trapezoidal profile with a shorter slew segment.
Kinematic Equations
Kinematics is the branch of mechanics that studies the motion of a body or a system of bodies
without consideration given to its mass or the forces acting on it. The following table includes
transformations of the basic linear equations as applied to the acceleration portion of motion
profiles. Use these formulae to calculate the velocity and acceleration for the acceleration portions
of the move.
Table 7-2. Linear Equation Transformations
Given
Solve For
A, X A, V A, t V, t V, X X, t
A
cceleration
V/t V
2
/2X 2X/t
2
V
elocity
2
AX
At 2X/t
X
(Distance)
V
2
/2A At
2
/2 Vt/2
t
ime
2
X
A
V/A 2X/V
Let’s take a look at the figure below. Beginning at zero velocity the axis will accelerate in a
positive direction (t
a
), run (slew) at velocity for some time (t
s
), then decelerate back to zero
velocity (t
d
). That’s a complete move or move segment. Looking at the figure below we can
easily separate the different portions of the move.
A common rule of thumb is to divide the
trapezoidal move into three time portions, one-third for acceleration, one-third at slew velocity
and the remaining third to decelerate.
The slew (X
s
) section of an equally divided trapezoidal
velocity profile represents ½ of the distance moved and the acceleration and deceleration portions
each represent ¼ of the total distance. The rule of thirds minimizes the RMS torque current in the
motor and is the most economical use of energy.