Selection of Acceleration and Jerk Parameters for Function Blocks
Definition
Acceleration is the first derivative of velocity, or the rate of change of velocity. The Acceleration rate therefore specifies how quickly an axis may change its velocity.
Jerk
In physics, jerk is the rate of change of acceleration; more precisely, the derivative of acceleration with respect to time is the second derivative of velocity, or the rate change of acceleration. The Jerk rate therefore specifies how quickly an axis may change its acceleration. Jerk therefore controls how abrupt the axis begins and ends the acceleration and deceleration curves.
See also Motion Profile.
Rules
The amount of time an axis takes to change its velocity from one velocity to another is a function of both Acceleration and Jerk. The larger the values of acceleration and jerk In physics, jerk is the rate of change of acceleration; more precisely, the derivative of acceleration with respect to time, the more quickly an axis will attain its programmed velocity. The following are generalizations that can be made about acceleration, jerk and their relationships to each other.
- The higher the acceleration rate, the faster the axis will obtain programmed velocity
- The higher the jerk rate, the more responsive the axis will be to changes in command
- Excessive jerk typically, more noticeably contributes to harsh acceleration than excessive acceleration
- Too low of a jerk value contributes to slow axis responsiveness to changing commands
- Lower jerks tend to soften the beginning and end of acceleration, while higher jerks sharpen the beginning and end of acceleration
- Typically, Jerk > Acceleration, Acceleration > Velocity
Methods
There are several methodologies to determine proper acceleration and jerk values. These methodologies allow you to calculate parameters given different desired profiles. Once parameters are calculated, you can then modify them as desired to obtain the results you want. Acceleration and Jerk values are subject to the limits of ratios as explained below.
1/3,1/3,1/3 time, given velocity and time. This allows you to calculate an appropriate acceleration and jerk, if you would like an axis acceleration/deceleration profile to “jerk” or ramp acceleration up for 1/3 of the time, accelerate 1/3 of the time and ramp acceleration down 1/3 of the time. Time is the desired amount of time to reach desired velocity. Note, this is the time to change velocity, not the time to complete the move.
Acceleration = (3 * Velocity)/(2 * time) Jerk = 3* Acceleration / time
1/3,1/3,1/3 velocity, given velocity and time. This allows you to calculate an appropriate acceleration and jerk, if you would like an axis acceleration/deceleration profile to “jerk” or ramp acceleration up for 1/3 of the velocity change, accelerate 1/3 of the velocity change and ramp acceleration down 1/3 of the velocity change. Where velocity is the desired velocity change, and time is the desired amount of time to reach the desired velocity change. Note, this is the time to change velocity, not the time to complete the move.
Acceleration = (5 * Velocity) / (3 * time) Jerk = (3 * Acceleration ^2) / (2 * velocity)
Calculate Jerk, given Velocity, acceleration and time. If you already know the maximum acceleration of the axis, and want to simply calculate a Jerk given the velocity and time, you can use the following equation. Note, this is the time to change velocity, not the time to complete the move.
Jerk = (2 * Acceleration) / ( time – ( velocity / (2 * acceleration)))
Limitations on Acceleration and Jerk
The ratios of Acceleration to Jerk and Velocity to Jerk are limited on most function blocks.
- The ratio of Velocity to Acceleration must be less than 20. A value of 20 suggests a time to accelerate to velocity of approximately 20 seconds, assuming infinite jerk. As jerk is decreased, this acceleration time would be increased.
- The ratio of Acceleration to Jerk must be less than 2. A value of 2 suggests the time to jerk to the acceleration rate is approximately 2 seconds.
