Ball bearings, rolling and friction: sources & model

Make a wheel see-through, follow a marked ball and test which motions can roll. Then discover why a longer spin does not always mean less friction.

What supports the explanation?

What this model assumes

1. Ideal zero-angle, no-gross-slip kinematics; no contact-force, wear, life or lubrication solver.
2. Published nominal dimensions inform original geometry. Groove/cage/wheel details are authored.
3. The wheel is held off the ground; no riding, braking-distance or road-contact prediction.
4. Coast inertia and torque are authored effective parameters, not measured products or material rankings.
5. Coast loss is lumped and constant; no heating law or lubricant optimization.
6. The gold inertia rim is symbolic; effective inertia is not derived from its displayed mesh.
7. NASA research bearings and the plotted test differ from our model. No raw data is invented from the scan.
8. Teardown displacement is for inspection; separated components are paused, not operating as a bearing.
9. Name the parts: A raceway is the curved track where a rolling element meets a ring. This bearing has balls, an inner ring, an outer ring and a cage. A cage is not a seal or a motor. Covers and seals are omitted here so the contacts remain visible.
10. One sourced geometry, one original model: GMN’s 608 sheet specifies an 8 × 22 × 7 mm envelope, seven balls of diameter 3.969 mm and a 14.7 mm pitch diameter. This gives ball-center radius R = 7.35 mm and ball radius a = 1.9845 mm. The internal geometry is not guaranteed for every bearing called 608. Our groove curvature, cage, wheel and spacer are original teaching geometry, not manufacturer CAD or a production drawing.
11. Two contact constraints: At zero contact angle, inner and outer contact radii are ri = R − a and ro = R + a. Let Ωi and Ωo be ring angular velocities, Ωc the ball-center orbit velocity and ωb the ball’s orientation velocity relative to the desk. Ideal rolling requires RΩc − aωb = riΩi and RΩc + aωb = roΩo. These are tangential speeds, not equal-rpm rules.
12. Solving for travel and turn: Adding the constraints gives Ωc = (riΩi + roΩo)/(2R). Subtracting gives ωb = (roΩo − riΩi)/(2a). Positive rotation is counterclockwise viewed from the positive axle end. A cage-mounted observer sees ωb − Ωc. Rendering that relative value directly as the ball’s world rotation would create false sliding.
13. One wheel turn: With the inner ring fixed and outer ring at 60 rpm, the cage travels at 38.1 rpm. The ball turns at 141.1111 rpm relative to the desk, or 103.0111 rpm relative to the cage. One outer-ring revolution gives 228.6° of orbit and 846.6667° of marked-ball orientation change. The familiar “half speed” intuition needs contact radii and reference frames.
14. A flat bridge to the idea: For a cylinder between parallel strips, bottom fixed and top traveling 20 mm without slip, the center travels 10 mm. Translation and turning cancel at the lower contact and add at the upper contact. The circular bearing’s two contact radii differ, so the same reasoning does not make the cage’s angular speed exactly half the outer ring’s.
15. Real rolling still loses energy: Real contacts are finite patches, and surfaces deform. Rolling and local sliding effects, lubricant motion, cage interactions, seals and other mechanisms contribute losses. Less apparent contact area is not a universal explanation of lower friction. SKF’s engineering account separates mechanisms and their operating conditions.
16. Our coast-down apparatus: The authored effective inertia is 4 × 10⁻⁵ or 8 × 10⁻⁵ kg·m². The constant opposing torque is 2 × 10⁻⁵ or 4 × 10⁻⁵ N·m. Both rotors start at 6 rad/s. Their exact numbers are not measured skateboard parameters. The gold rim is a symbol for added effective inertia, not a mass calculated from that visible rim’s material.
17. A complete energy account: While rotating, ω = ω₀ − Mt/J and θ = ω₀t − Mt²/(2J). Stop at t = Jω₀/M and keep the rotor stopped; resistance is not a reverse motor. Stored energy K = Jω²/2 and dissipated work Mθ sum to the initial energy. With baseline settings, stopping takes 12 seconds and 0.00072 joules are dissipated. No temperature rise is calculated.
18. The hidden-variable trap: Double inertia alone and stopping takes twice as long. Double both inertia and loss torque and the speed traces coincide because M/J is unchanged, although energy and loss torque double. Motion alone cannot identify both unknowns. Match or independently measure what matters before interpreting a free-spin comparison.
19. What the real research tests: NASA TN D-7356 examined a thrust-loaded, cageless angular-contact research bearing. Figure 7 compares experimental solid lines with calculated dashed lines for three balls, 26° contact angle and specified lubrication at 1,000, 2,000 and 3,000 rpm. Those conditions differ from our radial teaching bearing. A scan is not an exact raw-data table, and it cannot supply a skateboard rider limit.
20. Which bearing belongs where?: Ball bearings support many rotating shafts and wheels. Roller bearings use other rolling-element shapes; plain bearings use sliding surfaces and may rely on lubrication films. Load direction, speed, stiffness, environment, space and life requirements guide engineering choices. There is no universal winner or safe load calculated by this lesson.

What has been checked

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Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Actual render of the original 608-size bearing and translucent skateboard wheel. GMN nominal bearing dimensions; cage, wheel, marks and scene are authored teaching geometry, not manufacturer CAD or a measured performance test.