Bearing friction decides how long a flywheel holds its charge: the friction torque is the friction coefficient times the wheel’s weight times the shaft radius. For a 500 kg, 180 kg·m² wheel on a 50 mm shaft at 1,500 rpm, lubricated bronze bearings (coefficient 0.02) cost 385 W and drain 53% of the stored energy in the first hour, while ball bearings that cut that friction by 10 to 50 times lose between 1% and 18% in the same hour.
Part of Flywheel Energy Storage
How bearing choice sets a flywheel’s self-discharge, and where the rest of the loss budget goes.
Friction Torque Is Coefficient × Load × Shaft Radius
Each bearing supports part of the wheel’s weight. The rubbing force is the load times the friction coefficient μ, and it acts at the shaft surface, so the friction torque on the wheel is
T = μ × W × r_shaft
with W the total weight in newtons and r_shaft the shaft radius. The power lost is P = T × ω. The wheel in this series has m = 500 kg (W = 4,905 N), a 50 mm shaft (r = 0.025 m), I = 180 kg·m² and ω = 157.1 rad/s at 1,500 rpm.
Coefficients: Bearing Materials gives a lubricated bronze-on-steel coefficient of 0.02 to 0.06. Roller Bearings says rolling friction is roughly 10 to 50 times lower than sliding friction for equal loads, so ball bearings are taken here as the sliding figure divided by 10 to 50.
| Bearing | Coefficient | Torque | Power at 1,500 rpm | Time to stop on friction alone | Share lost in hour 1 |
|---|---|---|---|---|---|
| Bronze, 0.02 | 0.02 | 2.45 N·m | 385 W | 3.2 h | 53% |
| Bronze, 0.06 | 0.06 | 7.36 N·m | 1,156 W | 1.1 h | almost all |
| Ball, 0.02 ÷ 50 | 0.0004 | 0.049 N·m | 7.7 W | 160 h | 1.2% |
| Ball, 0.06 ÷ 10 | 0.006 | 0.736 N·m | 116 W | 10.7 h | 18% |
Working, first row: T = 0.02 × 4,905 × 0.025 = 2.45 N·m; P = 2.45 × 157.1 = 385 W. A constant torque slows the wheel linearly: time to stop = I × ω ÷ T = 180 × 157.1 ÷ 2.45 = 11,540 s = 3.2 h. After one hour ω = 157.1 − 2.45 × 3,600 ÷ 180 = 108.1 rad/s, so the energy is (108.1 ÷ 157.1)² = 47% of the start: 53% is gone.
The result is a range, not a measurement. A hydrodynamic oil film (see Plain Bearings) can run at a lower coefficient than the table’s lubricated range at speed, and this page has no sourced film figure; measure your own wheel by timing its coast-down.
Measure The Real Loss By Coasting Down
- Spin the wheel to a known speed in the pit, then disengage the drive.
- Count or time the speed at two points, say at 100% and 90% of the start, with a stopwatch and a marked rim or a revolution counter on the shaft.
- Energy lost = I × (ω₁² − ω₂²) ÷ 2. From 157.1 to 141.4 rad/s (90%): ½ × 180 × (24,674 − 19,988) = 422 kJ, 19% of the stored energy.
- Divide by the time to get the loss power. Window it again at a lower speed to separate bearing friction (roughly constant torque) from air drag (steeply speed-dependent; see Reducing Windage Losses).
Where The Rest Of The Loss Goes
At high rim speed the bearing loss is often not the largest term. Air drag on the rim rises with the cube of the speed and can exceed the bearing loss of a ball-bearing wheel by an order of magnitude; the windage article works the numbers. The bearings also carry the unbalance force of Balancing, so a poor balance raises both the load and the loss.
Keeping The Bearings Alive
- Grease or oil on schedule; see Lubrication.
- A bearing running above 70 °C is failing (the corpus roller-bearing page’s figure). Put a temperature check on every housing.
- A horizontal-shaft wheel loads the bearings radially. A vertical-shaft wheel loads a single thrust bearing with its full weight; see Thrust Bearings.
Common Mistakes
- Counting bearing friction as the only loss. At speed, air drag can be larger.
- Assuming a long coast means a safe wheel. A wheel with good bearings stays dangerous for many hours.
- Using the weight of the wheel only. Add the belt pull and any unbalance force.
Safety
Low friction means a long time to stop
A wheel on good ball bearings can spin for more than a day on bearing friction alone, so it cannot be stopped by waiting. Plan a brake and a barrier to keep people out until it is stopped; see Speed Limiting. A bearing that seizes while the wheel is at speed jams the shaft in a way that can shear the shaft or tear the wheel loose.
What’s Next
- Learn next: Ball & Roller Bearings — the low-loss choice
- Combine with: Journal Bearings (Low-Tech) — the option you can make yourself