Formula Calculators

Torque-Forward Drive

`T_f = (LP)/(2pie_f)`

Torque-Backdrive

`T_b = (LPe_b)/(2pi)`

Key Torque-Forward Drive

`T_g = (LP)/(2pi) (1-1/e_f)`

Key Torque-Backdrive

`T_c = (LP)/(2pi) (1-e_b)`

`T_f` = Forward drive torque, in.-lbs.
`T_b` = Backdrive torque, in.-lbs.
`T_g` = Forward Drive Key Torque
`T_c` = Backdrive Key Torque
L = Lead, in./rev.
P = Load, lbs.
`e_f` = Forward drive efficiency
`e_b` = Backdrive efficiency

Speed

`text{ipm} = L(text{rpm})`

ipm = Linear speed, in./min.
L = Lead, in./rev.
rpm = Rotational speed, rev./min.

Drive Horsepower-Rotary

`hp = ((r p m)T)/(63,025)`

hp = Horsepower
rpm = Rotational speed, rev./min.
T = Drive torque, in.-lbs.

Drive Horsepower-Linear

`hp = (P(i p m))/(396,000)`

hp = Horsepower
P = Load, lbs.
ipm = Speed-linear, in./min.

Critical Speed

`text{rpm} = ((4.76)(10^6)dF_s)/(Kl^2)`

rpm = Maximum safe rotational speed, rev./min.
d = Minor diameter, in.
l = Unsupported length, in.
K = Factor of safety (user defined 1.25 to 3 common)
`F_s` = End fixity factor
= .32 fixed-free
= 1.00 supported-supported
= 1.55 fixed-supported
= 2.24 fixed-fixed

Column Loading

`P_s = (P_mF_l)/K`

`P_s` = Maximum safe column load, lbs.
`P_m` = Basic maximum column load, lbs.
K = Factor of safety (1.25 to 3 common)
`F_t` = End fixity factor
= .25 fixed-free
= 1.00 supported-supported
= 2.00 fixed-supported
= 4.00 fixed-fixed

Efficiency - Power Screws - Forward Drive

`e_f = (tanlambda)[(cosphi_n-mutanlambda)/(cosphi_ntanlambda+mu)]`

Efficiency - Power Screws - Backdrive

`e_b = (1/tanlambda)[(cosphi_ntanlambda-mu)/(cosphi_n+mutanlambda)]`

`e_f` = Forward drive efficiency
`e_b` = Backdrive efficiency
`lamda` = Lead angle
`phi` = Thread angle in axial plane
`phi_n` = Thread angle in normal plane, `arctan(coslamdatanphi)`
`mu` = coefficient of friction
D = Screw pitch diameter, in.
L = Lead, in./rev.

Lead Angle

`lamda = arctan(L/(piD))`

D = Screw pitch diameter, in.
L = Lead, in./rev.

Wear Life for Ballscrews*

`text{Life} = (P_r/P_a)^3(1,000,000 text{ in.})`

Life = Expected travel life, in.
`P_r` = Operating load rating, lbs.
`P_a` = Actual load, lbs. (as determined by application)
* Applies to conventional Ballscrews only. For Freewheeling Ballscrew life, contact Roton

Acceleration Force^† - Objects in Linear Motion

`F_a = (WDeltaFPM)/(1,930t)`

`F_a` = Force to accelerate (lbs.)
W = Weight of object (lbs.)
`DeltaFPM` = Change in linear speed (ft./min.)
t = Time period to accelerate (sec.)

Acceleration Torque^† - Objects in Rotary Motion

`T_a = (WK^2DeltaRPM)/(307t)`

`T_a` = Torque to accelerate (ft.-lbs.)
`WK^2` = Rotational inertia of object (lbs.-`ft.^2`)
(for solid screw shaft, use `WK^2` = 1/8`WD^2`
where W = weight of screw (lbs.)
D = diameter of screw (ft.))
`DeltaRPM` = Change in rotational speed (rpm)
t = Time period to accelerate (sec.)

^†Formulas for acceleration torque and acceleration force are average values only for the time period values used. Actual peak torques and peak forces to accelerate can be several order of magnitude greater than formula values for short periods of time. The shorter the acceleration time period the greater actual peak values will exceed formula values. This can be important to designers when sizing drives and drive components.