Calculates for various motion-related values:
Motion profiles are assumed to be trapezoidal in nature, with constant accel, decel, and max speed.
The following calculation order is observed…
The “Forces” dropdown calculates the force required to move a load given the motion values determined above. Several cases are provided:
A friction coefficient input is provided as well.
The “Power” dropdown calculates an estimated power requirement based on the motion values and force values above.
$D$ = Total distance of move, ft
$D_{a}$ = Accel distance, *ft*
$D_{d}$ = Decel distance, *ft*
$T$ = Total time of move, second
$T_{a}$ = Accel time, *second*
$T_{d}$ = Decel time, *second*
$a$ = Acceleration, ft / sec2
$d$ = Deceleration, ft / sec2
$v$ = Max speed, ft per sec
Accel Distance: $$ D_{a} = \frac {a \, T_{a}^2} {2} $$
Decel Distance: $$ D_{d} = \frac {d \, T_{d}^2} {2} $$
Total Time of move: $$ T = \left( \frac {v}{a} \right) + \left( \frac {v}{d} \right) + \left( \frac { D - \left( D_{a} + D_{d} \right)} {v} \right) $$
$m$ = Mass of moved load, lbm
$F_{a}$ = Force required to accelerate, *lbf*
$F_{d}$ = Force required to decelerate, *lbf*
$\mu$ = Coefficient of friction, unitless
For Horizonal & CWA movement: $$ F_{a} = \frac {m}{32.2} \, a + (m \mu) $$ $$ F_{d} = \frac {m}{32.2} \, d + (m \mu) $$
Lift on acceleration: $$ F_{a} = m + \left( \frac {m}{32.2} \, a \right) + (m \mu)$$ $$ F_{d} = m - \left( \frac {m}{32.2} \, d \right) + (m \mu)$$
Lower on Acceleration: $$ F_{a} = m - \left( \frac {m}{32.2} \, a \right) + (m \mu)$$ $$ F_{d} = m + \left( \frac {m}{32.2} \, d \right) + (m \mu)$$
$P_{hp}$ = power, *hp*
$P_{kW}$ = power, *kW*
η = System efficiency, percentage
$$ F = \left|F_{a}\right| \vee \left|F_{d}\right| $$ $$ P_{hp} = \frac {F \, v}{550 \eta} $$
$$ P_{kW} = 0.7457 P_{hp} $$