Collar Torque⚠ unverified
Mechanical / Power Screws · Compute the torque due to collar (thrust bearing) friction
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| F | F | N | 1.0 | Axial load on the screw |
| 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 | Tcollar | N*m | Collar friction torque, in newton-metres (N*m) |
The science & history
Understanding the Parameters
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Axial load $F$ — the full load presses on the collar, so the friction force is $\mu_c F$ and the torque scales directly with load.
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Collar diameter $d_c$ — the mean diameter of the annular contact, which is the effective radius ($d_c/2$) at which the friction force acts. A larger collar means a longer lever arm and thus more friction torque — the opposite of the thread, where a larger diameter is unavoidable.
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Collar friction $\mu_c$ — the make-or-break parameter. A plain sliding collar ($\mu_c \approx 0.15$) can add as much torque as the thread itself; a thrust bearing ($\mu_c \approx 0.005$–$0.01$) makes $T_c$ almost vanish. This single substitution is the most effective way to raise a screw system's overall efficiency.
Derivation (Approaching a Proof)
Model the collar as an annular contact carrying the axial load $F$. As the screw turns, every element of the contact slides against the stationary seat, generating friction that resists rotation. Assuming the load is uniformly distributed and acts at a mean radius $r_c = d_c/2$, the total friction force is $\mu_c F$ and it acts at that radius, giving the friction torque
$$T_c = (\mu_c F)\,r_c = \mu_c F\,\frac{d_c}{2} = \frac{F d_c \mu_c}{2}.$$
More precisely, integrating the friction torque of a uniform-pressure annulus of inner/outer radii $r_i, r_o$ gives an effective radius $r_c = \tfrac{2}{3}\dfrac{r_o^3 - r_i^3}{r_o^2 - r_i^2}$; the simplified form here uses the mean collar diameter as that effective radius, which is accurate for a narrow collar. It is exactly analogous to a disc clutch/brake friction torque — the same $\mu F r$ physics.
Dimensional check. $[T_c] = \text{N}\cdot\text{m}$ ($\mu_c$ dimensionless). ✓
History and Development
Thrust-collar friction is a standard term in power-screw analysis (Shigley), and the historical shift from plain thrust collars to thrust ball bearings (early 20th century) transformed the usability of screw jacks and machine-tool feeds by slashing $\mu_c$. The same uniform-pressure/uniform-wear friction-torque theory governs disc clutches and brakes.
Related Concepts: Total Torque Raise, Power Screw Torque raise, Acme Thread Torque, Power Screw Efficiency, Friction
Notes: Uses the mean collar diameter as the effective friction radius (accurate for a narrow collar). Use a thrust bearing to minimise $\mu_c$. Combine with the thread torque via Total Torque Raise.