Clutches & Brakes Calculator — Torque Capacity, Contact Pressure & Thermal (Shigley's)
Governing standard: Shigley's Mechanical Engineering Design· Shigley §16 — uniform-wear and uniform-pressure disc/cone/drum models; capstan equation (e^μθ) for band brakes; engagement energy and thermal rise per engagement.
The MechanixCalc clutches and brakes calculator sizes and verifies friction clutches and brakes to the methods in Shigley's Mechanical Engineering Design (Chapter 16). Enter the clutch type — single-disc, multi-disc, cone, drum or band brake — the geometry, lining material and required torque, and the tool returns the torque capacity, safety factor, clamping-force requirement and peak contact pressure in one pass. Both the uniform-wear and uniform-pressure pressure-distribution models are available for disc and cone types, together with the capstan (e^μθ) equation for self-energising and de-energising band brakes.
It is built for drivetrain and machine-design engineers who need to size a clutch or brake to a transmitted torque, check that the contact pressure stays within the lining allowable and estimate the thermal rise per engagement — and who need a reviewer-ready calculation rather than a back-of-envelope estimate. The tool also includes an engagement-dynamics panel that computes the synchronisation speed, heat energy generated and maximum engagements per hour, and a lining material comparison across organic, semi-metallic, ceramic and carbon–carbon types.
What this calculator does
- Torque capacity and safety factor for single-disc, multi-disc, cone, drum and band-brake clutch types
- Uniform-wear and uniform-pressure pressure-distribution models for disc and cone clutches
- Capstan equation (e^μθ) for self-energising and de-energising band brakes with tight/slack-side force output
- Peak contact-pressure check against the lining material allowable
- Thermal rise per engagement — slip power, heat energy and estimated disc temperature rise
- Engagement dynamics panel — synchronisation speed, heat per engagement and engagements-per-hour thermal limit
- Lining material comparison table (organic, semi-metallic, ceramic, carbon–carbon) with torque-capacity utilisation ranking and PDF engineering report
Method & formulas
Disc and cone torque capacity (Shigley §16)
For a disc clutch the contact zone is an annulus between the inner radius ri and outer radius ro. Under the uniform-wear assumption the local pressure varies as p(r) = pmax · ri / r, which keeps the product p·r (proportional to wear rate) constant across the face. Integrating the friction moment over the annulus gives the torque capacity as a function of the actuating (clamping) axial force W. Under the uniform-pressure assumption the pressure is constant across the face at the allowable value, which gives a slightly higher torque for the same force but is the appropriate model for a new, unworn disc before bedding-in.
For a cone clutch the wedging action of the cone angle α amplifies the normal force on the contact face relative to the axial actuating force W. The torque capacity is derived from the normal force on the conical face and the cone's mean radius rm. Both uniform-wear and uniform-pressure cone equations are implemented; the uniform-wear form is generally preferred for design.
T = μ · W · N · (ro + ri) / 2where T = torque capacity (N·m); μ = friction coefficient; W = axial clamping force (N), where W = 2π · pmax · ri · (ro − ri); N = number of friction interfaces; ri, ro = inner and outer friction radii (m). The engine uses radii in mm and divides by 1000.
T = μ · W · N · (2/3) · (ro³ − ri³) / (ro² − ri²)where W = pmax · π · (ro² − ri²) under constant pressure; other symbols as above.
Band brake — capstan (Euler–Eytelwein) equation
A band brake wraps around a drum through angle θ (radians). Friction between the band and drum creates a tension ratio between the tight side (F1) and the slack side (F2) that depends exponentially on μθ — this is the capstan or Euler–Eytelwein equation. In the self-energising configuration the incoming (tight) side tension is amplified by the factor e^(μθ), which means a small actuating force F produces a large braking torque; in the de-energising configuration the ratio is inverted. The brake torque and peak lining pressure are then found from the tight-side tension and the drum geometry (Shigley §16-7).
F1 / F2 = e^(μ · θ)where F1 = tight-side tension (N); F2 = slack-side tension (N); μ = band–drum friction coefficient; θ = wrap angle (radians). Self-energising: F1 = F_applied · e^(μθ); de-energising: F2 = F_applied / e^(μθ).
T_brake = (F1 − F2) · R; p_max = F1 / (b · R)where R = drum radius (m); b = band width (m); p_max = peak lining pressure at the tight side (Shigley Eq. 16-17).
Thermal rise per engagement
During an engagement the driver and driven sides slip while friction transmits torque. The slip power equals the design torque multiplied by the angular velocity difference. The energy dissipated in a single engagement is approximately half the slip power multiplied by the engagement time (assuming linear synchronisation). This energy heats the disc mass (steel, cp ≈ 500 J/kg·K), giving the temperature rise ΔT. The engagement panel extends this by computing the synchronisation speed from the inertia ratio, the maximum engagements per hour the thermal budget allows, and a speed-versus-time chart.
E = T · ω_slip · t_e / 2where E = energy per engagement (J); T = clutch torque (N·m); ω_slip = angular-velocity difference at engagement start (rad/s); t_e = engagement time (s). Factor ½ reflects linear synchronisation from ω_slip to 0.
Worked example
Size a single-disc clutch (uniform-wear model) to transmit 200 N·m with an organic lining on cast iron. Inner radius ri = 80 mm, outer radius ro = 120 mm, 2 friction interfaces, friction coefficient μ = 0.35, allowable contact pressure pmax = 0.7 MPa.
Given
- Inner radius ri80 mm
- Outer radius ro120 mm
- Friction interfaces N2
- Friction coefficient μ0.35
- Allowable contact pressure pmax0.7 MPa
- Required torque T_in200 N·m
Result
- Clamping force W14 074 N
- Torque capacity T985 N·m
- Safety factor SF4.93
- Peak contact pressure pmax0.7 MPa (at limit)
- Compute the clamping force at the pressure limit using the uniform-wear relation: W = 2π · pmax · ri · (ro − ri) = 2π × 0.7 × 80 × 40 = 14 074 N.
- The mean friction radius for uniform wear is (ro + ri)/2 = (120 + 80)/2 = 100 mm = 0.100 m.
- Torque capacity: T = μ · W · N · r_mean = 0.35 × 14 074 × 2 × 0.100 = 985 N·m.
- Safety factor: SF = T_capacity / T_in = 985 / 200 = 4.93 — well above 1 (the disc is sized conservatively or could be reduced).
- Peak contact pressure equals pmax = 0.7 MPa ≤ allowable 0.7 MPa — lining pressure check passes.
Illustrative example only — verify against your own design inputs. The large SF here shows the disc can handle much more than 200 N·m at these dimensions; a designer would reduce ri/ro or N to minimise size and cost, or target a required SF (typically 1.25–2.0 for power-transmission clutches).
Frequently asked questions
Which standard does this clutch and brake calculator use?
The torque capacity, contact pressure and clamping-force equations follow the methods in Shigley's Mechanical Engineering Design, Chapter 16 (uniform-wear and uniform-pressure disc/cone models; capstan equation for band brakes; Shigley Eq. 16-17 for peak lining pressure). The governing equations are shown in the generated PDF report. Note: the thermal fade sub-panel uses a heuristic linear fade model that is not tied to a specific standard, and is labelled as an engineering estimate in-product.
What is the difference between uniform-wear and uniform-pressure models?
Uniform-pressure assumes a constant contact pressure across the lining face, which is most accurate for a new disc before bedding-in occurs; it predicts slightly higher torque capacity for the same actuating force. Uniform-wear assumes the product p·r is constant (p(r) = pmax·ri/r), which better represents a worn-in disc in service. For design purposes Shigley recommends the uniform-wear model as the more conservative and realistic long-run condition; both models are available in the calculator.
What does self-energising mean for a band brake?
A band brake is self-energising when the rotation of the drum tends to pull the tight side of the band further onto the drum, amplifying the braking force. The capstan equation (F1/F2 = e^μθ) shows this exponential multiplication: a small actuating force at the slack side produces a much larger tight-side tension and therefore a higher braking torque. De-energising is the opposite configuration — the drum rotation tries to lift the band, requiring a larger actuating force for the same torque. The calculator covers both configurations and displays the self-energising gain ratio e^(μθ).
How does the thermal analysis work?
The primary thermal output is the temperature rise per engagement, computed from the slip energy (torque × slip speed × engagement time / 2) and the effective disc mass (steel density, disc geometry, cp ≈ 500 J/kg·K). The engagement-dynamics panel extends this to multi-engagement scenarios, computing the maximum engagements per hour before the lining temperature budget is exceeded. The thermal fade sub-panel is a separate engineering-estimate model (1-D Fourier surface temperature + a linear friction-fade heuristic) and is labelled accordingly — it is suitable for preliminary work but should be verified against test or catalogue data before final design.
Is the clutch and brake calculator free?
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