Time to Accelerate

The amount of time required to accelerate from one speed to another can be extremely helpful to know when setting up continuous press systems where a mechanical press will cycle at a constant rate (strokes per minute) while the servo feed system must move press targets into position between press strokes.  For instance, when running a mechanical press at 250 strokes per minute with a pressing angle of 20º the servo has a mere 0.229 seconds to move the material so that the last press location is out of the way and the next pressing target is in position.

Continuing the example, the longer the distance the material has to travel between press operations, the less time the system has to be in position.  How much time does your servo spend moving material?  How much of that time is consumed physically coming up to speed and then decelerating to a stop at the end of the travel?  The time to accelerate equation can help answer those questions.

The equation for acceleration time is:

t = s / a

Where:

t = time in seconds

s = speed in inches per second

a = acceleration in inches per second2

This equation assumes a constant acceleration rate.  The speed in the equation is the total change in speed, so this formula works for calculating the time required to go from 0 to a target speed, or to calculate the time required to change from one speed to another.  It also works for accelerations and decelerations, because in physics, they are the same thing.

Example

While setting up a continuous punch system, you calculate that if the press is running at 300 spm, and your pressing angle is 26º, the servo system will have only 0.1834 s to position targets between punch operations.

The servo system was sized for a maximum acceleration rate of 550 ips2.  You’ve calculated that the system must reach a maximum speed of 16 ips (80 fpm), which will give you a remaining 0.064 s to accelerate and decelerate for each move.  So, one half of the total acceleration time is 0.032 s.

t = s / a

t = 16 ips / 550 ips2

t = 0.0291 s

You can actually lower the programmed acceleration for the move to help avoid mechanical slip.  By rearranging the equation, you can calculate the acceleration required.

t = s / a

t · a = s

a = s / t

a = 16 ips / 0.032 s

a = 500 ips2

By lowering the accelerations by 10%, the system will still achieve the move in the required time, but you will have also reduced wear on the mechanics of the system.