Bosch rexroth MCL, Project Planning Manual

Page: 144 / 206

11.2 Basic formulae
11.2.1 General movement equations
The variables required for sizing and selecting the motor are calculated using
the equations shown in the following.
The process-related feed forces and speeds are used directly for
drive selection during project planning of linear direct drives with‐
out conversions.
v(t) Velocity profile over time in m/s
s(t) Distance course over time in m
a(t) Acceleration profile vs. time in m/s²
F(t) Force course over time in N
m Moved mass in kg
F
0
(t) Base force and friction in N
F
P
(t) Processing force or operation force in N
F
eff
Effective force in N
v
avg
Average velocity in m/s
t Time in s
T Total time in s
Fig. 11-2: General equations of motion
In most cases the mathematical description of the required positions vs. the
time is known (NC-program, electronic cam disk). By means of path function,
the calculation of velocity, acceleration and force can be done. Standard soft‐
ware (such as MS Excel or MathCad) can be used for calculating the re‐
quired variables, even with complex motion profiles.
The following chapter provides a more detailed correlation for tra‐
pezoidal, triangular or sinusoidal speed curves.
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Motor dimensioning
MCL Ironless Linear Motors
Bosch Rexroth AG R911330592_Edition 06