HEIDENHAIN TNC 430 PA/M - Relation between Jerk, Acceleration, Velocity and Distance; Maximum Acceleration

December 2001 The Control Loop 6 – 111
6.8.1 Relation Between Jerk, Acceleration, Velocity and Distance
To ensure proper operation of an axis, the following two conditions must be
fulfilled:
n The desired maximum speed v
max
and maximum jerk r
max
result in a
maximum acceleration a
max
.
n A minimum distance s
min
must be traversed in order to attain the maximum
speed v
max
.
Maximum
acceleration
Taking into account the motor and the power stage, the machine should be
specified in such a way that acceleration during the acceleration phase is as
constant as possible. This ensures maximum utilization of the drive current.
The machine, on the other hand, should be designed to fulfill the following
dynamic requirements: The jerk should be kept to a minimum and the jerk
phase should be maximized in order to prevent the machine from oscillating.
The result is no constant acceleration, but a short acceleration peak. If the
maximum velocity and the maximum permissible jerk of the machine are
preset, the maximum attainable velocity can be determined.
Jerk r
t
Velocity v
Acceleration a
a
max
v
max
r
max
⋅=
t
Acceleration a
Velocity v
Jerk r