Function Block Acceleration and Jerk Parameters

Acceleration is the first derivative of velocity, or the rate of change of velocity.

The acceleration rate specifies how quickly an axis may change its velocity.
Jerk 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 controls how abrupt the axis begins and ends the acceleration and deceleration curves.

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, the more quickly an axis will attain its programmed velocity.

These are generalizations that can be made about acceleration, jerk, and their relationships to each other.

The higher the acceleration rate, the faster the axis obtains programmed velocity.
The higher the jerk rate, the more responsive the axis is to changes in command.
Excessive jerk typically, and more noticeably, contributes to harsh acceleration rather 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.
- Higher jerks sharpen the beginning and end of acceleration.
Typically, Jerk > Acceleration; Acceleration > Velocity.

There are several methodologies to determine proper acceleration and jerk values.

These methodologies allow calculation of parameters given different desired profiles.
- Once parameters are calculated, they can be modified to obtain the designated results.
Acceleration and Jerk values are subject to the limits of ratios.

1/3,1/3,1/3 time, given velocity and time.

Acceleration = (3 * Velocity)/(2 * time)
Jerk = 3* Acceleration / time

This allows you to calculate an appropriate acceleration and jerk for an axis acceleration / deceleration profile to:
- Jerk or ramp acceleration up for 1/3 of the time.
- Accelerate 1/3 of the time.
- Ramp acceleration down 1/3 of the time.
Time is the desired amount of time to reach desired velocity.
- This is the time to change velocity, not the time to complete the move.

1/3,1/3,1/3 velocity, given velocity and time.

Acceleration = (5 * Velocity) / (3 * time)
Jerk = (3 * Acceleration ^2) / (2 * velocity)

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.
- 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.
- This is the time to change velocity, not the time to complete the move.

Calculate jerk, given velocity, acceleration, and time.

Jerk = (2 * Acceleration) / ( time – ( velocity / (2 * acceleration)))

If you know the maximum acceleration of the axis and want to calculate a jerk given the velocity and time, use this equation.

This is the time to change velocity, not the time to complete the move.

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 is 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.