# Calculating Acceleration for Linear Motion

• February 22, 2019
• News

By H2W Technologies

Every motion control problem begins with a need to move a certain payload over a certain distance. However, there are many types of moves possible, and determining the right motion control solution may require some calculations to match the specifications found on a given motors data sheet. Most sales engineers will ask you for three basic questions when directing you to the proper motor or motion control solution.

• What is the stroke or displacement required?
• What is the force or thrust required?
• At what duty cycle do you plan on operating the motor?

### Travel Distance

The travel distance is the first piece of information needed to unlock any specification, because a solution to move a few microns would utilize different motion technology from an application requiring several meters of travel. In addition to understanding the total travel required, it would be necessary to determine whether the travel is oscillatory, constant velocity, or the motion profile is defined by a pick-and-place application. Oscillatory systems typically will move back and forth at a specific frequency or range of frequencies. While constant velocity systems either need to operate for a known distance or time at a constant velocity, or they need to get a payload up to a velocity, in these cases the distance and time to accelerate up to the velocity needs to be understood and accounted for in the overall displacement. With this information you can determine the acceleration necessary to make the move. To learn more about calculating acceleration you can read our white paper about calculating acceleration for linear motion.

### Force

The next step is determining the amount of thrust or force required. Force is simply the amount of acceleration multiplied by the mass of the moving object. If the motion is horizontal, this equates to the mass of the payload added to the mass of the moving part of the linear motor or stage and multiplied by the amount of acceleration required by the motion. Vertical applications must add or subtract the acceleration due to gravity depending on the direction of motion.

### Duty Cycle

Finally, how long is power going to be applied to the motor? Many oscillatory systems will be operating continuously, and thus would have a duty cycle of 100%, while other applications will be short bursts of power, 1 second or less, while being off for several seconds, and will have a duty cycle of less than 10%. Duty cycle is defined as the time on divided by the total time per cycle (time on + time off). Depending on the linear motor selected, the amount of force available at a duty cycle of 10% can be as much as 3 times the continuous force rating. This last piece of the puzzle helps break down the necessary components required to properly size any motion control problem.

Once these three pieces are determined, any application can be sized and verified that it is sufficient based on the specifications found on any standard data sheet.