Total Torque Raise⚠ unverified
Mechanical / Power Screws · Compute the total torque to raise a load, including collar friction
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| F | F | N | 1.0 | Axial load on the screw |
| dm | dm | m | 1.0 | Mean (pitch) diameter of the thread |
| l | l | m | 1.0 | Lead of the thread (axial advance per revolution) |
| mu | μ | — | 1.0 | Coefficient of friction between the screw and nut threads (dimensionless) |
| dc | dc | m | 1.0 | Mean collar diameter |
| mu_c | μc | — | 1.0 | Coefficient of friction at the collar (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Ttotal | N*m | Total raising torque, in newton-metres (N*m) |
The science & history
Understanding the Parameters
-
Thread group ($d_m$, $l$, $\mu$) — feeds the thread raising torque $T_{\text{thread}} = \dfrac{F d_m}{2}\dfrac{l + \pi\mu d_m}{\pi d_m - \mu l}$ (square-thread form; see Power Screw Torque raise). This part does the useful lifting plus thread friction.
-
Collar group ($d_c$, $\mu_c$) — feeds the collar friction torque $T_{\text{collar}} = \dfrac{F d_c \mu_c}{2}$ (see Collar Torque). This part is pure loss — it does no lifting, only fights bearing friction.
-
Their balance — for a plain collar, $T_{\text{collar}}$ is frequently comparable to or larger than $T_{\text{thread}}$, so the collar can dominate the effort. Both parts scale with the load $F$, so the ratio (and hence the system efficiency) is independent of load and set purely by geometry and friction.
Derivation (Approaching a Proof)
The two torques act about the same axis (the screw axis) and resist the same rotation, so by simple superposition of moments they add:
$$T_{\text{total}} = T_{\text{thread}} + T_{\text{collar}}.$$
Substituting the two components:
$$T_{\text{total}} = \underbrace{\frac{F d_m}{2}\,\frac{l + \pi\mu d_m}{\pi d_m - \mu l}}_{\text{thread: lift + thread friction}} + \underbrace{\frac{F d_c \mu_c}{2}}_{\text{collar friction}}.$$
There is no interaction term because the two friction interfaces are physically separate (thread flanks vs collar face) and both simply oppose the applied torque. Only the thread part contains the useful lifting work ($F l$ per turn); the collar part is entirely dissipative, which is why minimising collar friction (a thrust bearing) is the biggest lever on overall efficiency (Power Screw Efficiency).
Dimensional check. Both terms are N·m, so $[T_{\text{total}}] = \text{N}\cdot\text{m}$. ✓
History and Development
Adding thread and collar torques is the standard complete power-screw design calculation in Shigley and machine-design practice. It makes explicit that a screw system has two friction budgets — thread and collar — and that the collar, easily overlooked, often governs the required input torque and the choice of a thrust bearing.
Related Concepts: Power Screw Torque raise, Collar Torque, Acme Thread Torque, Power Screw Efficiency, Screw Lead Angle
Notes: Thread part uses the square-thread form (use $\mu\sec\alpha$ for Acme/V). Collar part is pure loss — minimise $\mu_c$ with a thrust bearing. Multiply by the appropriate factor for lowering.