1. ## Torque-Forward Drive

T_f = (LP)/(2pie_f)

2. ## Torque-Backdrive

T_b = (LPe_b)/(2pi)

3. ## Key Torque-Forward Drive

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

4. ## 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

5. ## Speed

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

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

6. ## Drive Horsepower-Rotary

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

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

7. ## Drive Horsepower-Linear

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

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

8. ## 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

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

10. ## Efficiency - Power Screws - Forward Drive

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

11. ## 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.

12. ## Lead Angle

lamda = arctan(L/(piD))

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

13. ## 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

14. ## 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.)

15. ## 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 = 1/8WD^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.