A cone brake uses axial force to press a rotating conical member into a stationary lined housing. Friction around the conical surface resists shaft rotation. The calculator estimates the normal contact load and friction torque for an entered axial force, cone half-angle, friction coefficient and mean friction radius.
Cone Brake Interactive Calculator
Estimate ideal friction torque when an axial force presses a rotating cone into a stationary lined housing. Adjust the half-angle, axial force, effective friction radius and friction coefficient.
Equation Used
- One conical friction interface is fully engaged.
- Axial equilibrium neglects axial sliding friction during engagement.
- The entered mean friction radius is the effective torque radius.
- Friction coefficient is constant.
- The animation is illustrative slow driven rotation, not calculated braking deceleration.
Ideal fully engaged cone brake. No stopping time, heat, wear, release force, shaft strength or bearing load is calculated. Driven rotation in the end view illustrates opposing friction only.
A rotating cone inside a fixed brake housing
The blue cone and shaft rotate together. The gray housing is fixed to the frame, and the gold lining lies between the two mating surfaces. Applying axial force toward the small end seats the cone against the lining. The housing carries the reaction torque to the frame.
The upper drawing is a longitudinal cutaway through the shaft axis. An axisymmetric cone has the same section as it rotates, so that section does not wobble or slide artificially. The lower end view shows rotation and an opposing friction-torque arrow.
The cone stays fully engaged in this model. Engagement travel, release springs, operating linkage and actual braking deceleration are not solved. No rotational inertia or initial speed is entered, so the animation does not predict a stopping time.
Conical friction braking
A conical contact can provide friction torque with an axial operating load. Unlike a cone clutch, which transfers torque between two rotating members, this brake transfers torque from a rotating member to a fixed housing.
This generic illustration does not represent a rated product or a particular machine. Its support fittings and shaft dimensions are schematic. Selecting materials, lining area, operating linkage and thermal capacity requires additional design information.
Normal load and friction torque
Let Fₐ be axial force and α the cone half-angle measured between the conical surface and the shaft axis. The axial component of the total normal contact load N is N sin α. Equilibrium gives N = Fₐ / sin α.
With friction coefficient μ and effective mean friction radius rₘ in metres, T = μ N rₘ. This follows the conical-brake equation in the Machine Design Databook, Figure 19-24. A smaller half-angle increases ideal normal load for the same axial force.
N is the sum of the magnitudes of the distributed normal contact forces, not a single net radial force on the shaft. The reported axial/normal percentage is 100 sin α. It is a geometric force ratio, not a risk or safety score.
Worked cone-brake example
At Fₐ = 1000 N, μ = 0.35, rₘ = 100 mm and α = 12°, normal load is approximately 4810 N. Torque is 0.35 × 4810 × 0.1 = 168.3 N·m.
The normal/axial force ratio is approximately 4.81, and axial/normal force is 20.79%. Doubling axial force, friction coefficient or radius doubles the ideal torque when the other inputs stay fixed. Changing the half-angle changes the force conversion through its sine.
What this model does and does not establish
A shallow cone raises the ideal normal-force multiplier, but that fact alone does not establish release behavior, allowable pressure or service life. Assess release behavior using the lining friction, cone geometry and release mechanism.
The torque calculation assumes constant friction and an effective mean radius. It does not determine the contact-pressure distribution, lining temperature, available cooling, wear, dynamic response or the axial force needed to release a real brake.
The displayed cone width and housing thickness are illustrative proportions. The radius dimension and cone taper follow their controls. Rotation remains visible at all input settings without implying that a physical brake is continuously slipping under a rated load.
Cone-brake questions
Which part is fixed?
The outer lined housing is fixed to the frame. The cone and shaft rotate.
Is the angle the full cone angle?
No. It is the half-angle between the conical surface and shaft axis.
Why does changing friction affect torque but not normal load?
In this fully seated model, axial equilibrium sets normal load. Friction then sets tangential resistance and torque.
Does the animation show stopping time?
No. It shows slow driven rotation to make the opposing friction torque visible. Inertia and initial speed are not inputs.
What does the cone-angle comparison mean?
A defined force ratio: axial force divided by total normal load, expressed as a percentage. It is not a safety rating.
Engineering reference
Machine Design Databook, McGraw-Hill (2004), Chapter 19, page 19.34, Figure 19-24 provides the conical brake section and equations Fₙ = Fₐ/sin α and T = μFₐD/(2 sin α), where D is the mean friction diameter. This calculator uses radius rₘ = D/2.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
