Formulas
The following are a set of equations that are used to calculate acceleration, peak force, RMS force, and duty cycle for stage sizing.
Newton’s Second law states:
| F = m x a | |
| where: | F = Force (lbs or [N]) |
| m = moving mass (lbs or [Kg]) | |
| a = acceleration (g’s) |
To size a stage properly the force must be known. If force is not known it must be calculated from the above equation. The mass is the total mass of the customer payload plus the mass of the moving components of the stage.
If the acceleration in g’s is not known it must be calculated from one of the following equations:
1. Triangular velocity profile:
 |
|
| where: | d = distance moved (in or [m]) |
| t = time to complete move (sec) | |
| G= gravitational constant (386 in/sec2 or [9.81 m/sec2]) |
2. Trapezoidal velocity profile:
 |
|
| where: | d = distance moved (in or [m]) |
| ta = time to get to speed (sec) | |
| G= gravitational constant (386 in/sec2 or [9.81 m/sec2]) |
3. Force RMS:
Once the force is determined, the duty cycle for all of the specific forces must be determined to calculate the RMS force, which is the average required force.
 |
|
| where: | Fa = Acceleration Force (lbs or [N]) |
| Fc = Constant Velocity Force (lbs or [N]) | |
| Fd = Deceleration Force (lbs or [N]) | |
| ta = time to accelerate to velocity (sec) | |
| tc = time at constant velocity (sec) | |
| td = time to decelerate to zero velocity (sec) | |
| ton = ta + tc + td (sec) | |
| toff = dwell time (sec) |
4. Duty Cycle:
5. Inch/Micron Conversion
Inch to Micron:
(Inch x 25.4) x 1000 = MicronExample: Convert 0.01” into microns
(0.010 x 25.4) x 1000 = 254 MicronsMicron to Inch:
(Micron / 1000) / 25.4 = InchExample: Convert 10 microns into inches
(10 / 1000) / 25.4 = 0.0004 Inch