Conical Roller Thrust Bearing: Geometry, Motion and Surface-Speed Calculator

Conical rollers between mating races

The perspective view removes the upper race so the tapered rollers can be seen. The lower conical race stays fixed. Each roller both revolves around the bearing axis and spins about its own radial axis. The separate axial section shows both race surfaces meeting the roller generators; their dashed extensions meet at one common apex.

The illustration is a symmetric idealization with horizontal radial roller axes. At radial position r, the cone radius is r tan(alpha), where alpha is the roller half-angle. The upper and lower raceways therefore slope at equal and opposite angles. Real bearing designs also have retaining and guiding details that are simplified here.

With the lower race fixed and upper race rotating at n RPM, ideal no-slip contact gives an orbital rate of n/2. The roller spin relative to that orbiting frame is −n/(2 tan(alpha)); the minus sign gives the opposing direction. Blue witness stripes make the spin visible separately from the orbital motion. All motion is slowed by a factor of 20 for viewing.

The number of displayed rollers reduces for larger half-angles so their ideal cones do not overlap. It is illustrative, not a proposed cage design or a capacity calculation.

Recognizing a tapered-roller thrust arrangement

Timken’s thrust bearing catalog shows the TTHD family with two mating thrust races, tapered rollers and a common-apex arrangement. It lists applications including crane hooks, extruders and thrust blocks. That catalog drawing is the reference for the form shown here; this animation is not a dimensional reproduction of a catalog part.

Spherical roller thrust bearings are a different geometry. Product load ratings, alignment allowances, lubricant requirements and speed limits must come from the selected bearing’s documentation. No catalog product is selected by this calculator.

Race surface speed and ideal roller motion

For race speed n in RPM, angular speed is omega = 2 pi n/60 radians per second. Convert each entered radius from millimetres to metres. Surface speeds are V1 = omega r1 and V2 = omega r2. Their ratio is V2/V1 = r2/r1.

The fourth result is S = 100(V2 − V1)/((V1 + V2)/2). This describes the relative spread of the two race speeds. It is not a measured slip percentage, friction loss, heat rate or wear prediction. A cylindrical roller cannot provide a different circumferential speed at each end simply by spinning, but actual slip requires a full contact and motion model.

For the symmetric geometry drawn here, a roller point on the upper contact line has height +r tan(alpha); the corresponding lower point has height −r tan(alpha). If the orbital angular speed is c and the radial spin is s, their tangential velocities are r(c − s tan(alpha)) and r(c + s tan(alpha)). Setting these equal to omega r and zero gives c = omega/2 and s = −omega/(2 tan(alpha)).

These relations explain why angle changes the roller spin and thickness while leaving the four race-speed comparisons unchanged. They do not determine force, stiffness or fatigue life. If r2 is not greater than r1, the diagram identifies the invalid radius order.

Example at 50 and 100 mm radii

At 60 RPM, omega = 2 pi rad/s. For r1 = 0.050 m and r2 = 0.100 m, V1 = 0.3142 m/s and V2 = 0.6283 m/s. The outer/inner ratio is 2, and the normalized speed spread is 66.7%.

For a 12° roller half-angle in the illustrated symmetric arrangement, the orbital rate is 30 RPM and the roller spin relative to its orbiting frame is approximately −141.1 RPM. At the two radial endpoints, roller radii are 50 tan(12°) = 10.63 mm and 100 tan(12°) = 21.26 mm.

Doubling the race speed doubles both surface speeds and both motion rates, while leaving their ratio and normalized spread unchanged. Increasing the half-angle makes the rollers thicker and reduces their spin rate; it does not alter V = omega r at the specified contact radii.

What this calculator does not determine

The common-apex geometry is a kinematic explanation of ideal rolling. It does not guarantee that a loaded physical bearing has no sliding, deformation or loss. This page does not solve contact stresses, roller-end/rib friction, cage forces, skew or lubricant-film behavior.

No load rating, applied axial force or reliability target is entered. A fatigue-life calculation would require additional data and a suitable catalog model; the speed-spread percentage describes only relative race speeds. Universal preload values, temperature thresholds, surface-finish limits and replacement intervals cannot be obtained from these four inputs.

The rollers are drawn as ideal conical frusta. End profiling, relief, cage pockets, shoulders and race thickness are simplified. This is an explanatory animation, not a manufacturing drawing.

Conical roller thrust bearing questions

Why does the angle slider leave the four numerical results unchanged?

Those results describe race speeds at fixed radii. The angle changes the drawn cone thickness and roller spin, while race speed remains omega times radius.

Is the speed-spread result actual sliding?

No. It is a normalized difference between two race speeds. Actual slip cannot be inferred from that number alone.

Why do the rollers orbit more slowly than the moving race?

In the symmetric idealization with one race fixed, satisfying no-slip contact on both sides gives an orbital rate equal to half the moving-race speed.

Are the two races flat?

No. The section shows mating inclined surfaces whose extensions meet the rollers at a common apex.

What radius order does the bearing require?

The outer radius must exceed the inner radius. If the entered values do not meet that condition, the diagram shows the selected radii and identifies the needed change.