Mechanical Actuators, Acme Lead Screws & Lifting Jacks
Acme Power Screw Raising/Lowering Torque & Efficiency Formula
Calculate Acme Thread Raising Torque T_R (N·m) including Thrust Collar Friction, Load-Lowering Torque T_L (N·m), Overall Screw+Collar Efficiency (%), and Overhauling Check.
Include BOTH 14.5° Acme flank wedging cos(alpha) AND thrust-collar torque—or stall your jack motor!
In machine-tool lead screws, scissor lifts, and sluice-gate actuators using 29° Acme threads (flank half-angle alpha = 14.5°, versus 0° for square threads), normal thread force rises by 1 / cos(alpha), increasing friction! For axial load F, pitch diameter d_m, screw lead l (axial advance per revolution = N_starts * pitch), thread friction mu, thrust-collar friction mu_c, and mean collar diameter d_c, Total Raising Torque is T_R = F * (d_m / 2) * ((tan_lambda * cos_alpha + mu) / (cos_alpha - mu * tan_lambda)) + F * mu_c * (d_c / 2) where tan_lambda = l / (PI() * d_m)! Lowering Torque replaces the numerator/denominator signs with (mu - tan_lambda * cos_alpha) / (cos_alpha + mu * tan_lambda): if T_L <= 0, the screw OVERHAULS (spins down on its own under gravity)!
Verify on a 25,000 N (2.5-ton) Screw Jack—Axial_Load F = 25,000 N (B2), Mean_Screw_Dia d_m = 32.0 mm (B3), Screw_Lead l = 6.0 mm (B4), Flank_Half_Angle alpha = 14.5 deg (B5), Thread_Friction mu = 0.12 (B6), Collar_Friction mu_c = 0.10 (B7), and Mean_Collar_Dia d_c = 45.0 mm (B8): Total Raising Torque hits 130.25 N·m (E2, including 56.25 N·m collar torque!), Lowering Torque is safely positive at +81.77 N·m (E3 -> "SELF-LOCKING" in E5), and Overall Mechanical Efficiency T_ideal / T_R equals 18.33% (E4)!
| Acme Screw Jack KPI (25 kN, dm=32, l=6, alpha=14.5°, mu=0.12, muc=0.10, dc=45) | Formula | Verified Output |
|---|---|---|
| Total Raising Torque T_R (N·m) | Thread_Raise_Torque + F * muc * (dc / 2000) | 130.25 N·m (171.77 @ l = 16 mm) |
| Total Lowering Torque T_L (N·m) | Thread_Lower_Torque + F * muc * (dc / 2000) | 81.77 N·m (42.44 @ l = 16 mm) |
| Overall Screw+Collar Efficiency (%) | (((F * l / 1000) / (2 * PI())) / T_R) * 100 | 18.33% (37.06% @ l = 16 mm) |
| Jack Self-Locking Status | T_L > 0 -> SELF-LOCKING else OVERHAULING | SELF-LOCKING |
Acme Thread + Thrust Collar Raising Torque Formula
Validate Axial_Load > 0, d_m > 0, Lead > 0, alpha in [0, 30], mu in (0, 0.50], mu_c in [0, 0.50], and d_c > 0!
=LET(ld_f, B2, dm_s, B3, ld_l, B4, al_d, B5, mu_t, B6, mu_c, B7, dc_m, B8, IF(OR(ld_f <= 0, dm_s <= 0, ld_l <= 0, al_d < 0, al_d > 30, mu_t <= 0, mu_t > 0.5, mu_c < 0, mu_c > 0.5, dc_m <= 0), "Invalid Screw Input", LET(tl_m, ld_l / (PI() * dm_s), ca_l, COS(al_d * PI() / 180), IF(ca_l <= mu_t * tl_m, "Invalid Screw Input", ROUND(ld_f * (dm_s / 2000) * ((tl_m * ca_l + mu_t) / (ca_l - mu_t * tl_m)) + ld_f * mu_c * (dc_m / 2000), 2)))))Fast Multi-Start Lead Screw Efficiency Jump Check (Set Lead l = 16 mm)
Increase Screw_Lead B4 from 6.0 mm (single-start) to 16.0 mm (multi-start fast actuator): Raising Torque E2 rises moderately to 171.77 N·m, Lowering Torque E3 drops to 42.44 N·m, and Mechanical Efficiency E4 more than doubles from 18.33% to 37.06%!
=IF(ISTEXT(E2), E2, LET(tl_m, B4 / (PI() * B3), ca_l, COS(B5 * PI() / 180), tr_q, B2 * (B3 / 2000) * ((tl_m * ca_l + B6) / (ca_l - B6 * tl_m)) + B2 * B7 * (B8 / 2000), ROUND((((B2 * B4 / 1000) / (2 * PI())) / tr_q) * 100, 2)))Try the example
Use the original values or change them to test your understanding.