KEVOS® MAKEOS · Power Transmission
Engine Flywheel Rim Weight and Arm Proportions (Energy Excess Factor, Speed Variation)
For a reciprocating engine or compressor flywheel, what rim mass keeps the speed within my allowed variation, given the indicated power or the work per revolution and the factor of energy excess, and what width and thickness should the elliptical arms have at the hub?
Flywheel rim weight for engines by the handbook formulas W = 387,587,500 c n HP ÷ (D² N³) when the indicated horsepower is given and W = 11,745 n E ÷ (D² N²) when the work per revolution is given, here in SI as rim mass m = n E ÷ v² with E = c × work per revolution, the factor of energy excess c entered from the table for the engine and cut-off, 1/n the allowed speed variation and v the speed of the mean rim diameter; with the rim cross-section for the material density, and the arm proportions: width at the hub 1.3 × shaft diameter for six arms or 1.2 × for eight, thickness half the width, and the area at the rim at least two-thirds of the area at the hub.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Energy from | choice | Find the work per revolution from the indicated power and speed, or enter the work per revolution directly (piston force × twice the stroke for a double-acting engine). |
| Indicated power | kW | Indicated power of the engine, used when energy is found from power. |
| Work done by the engine per revolution | J | Average work done by the engine in one revolution, used when entered directly. |
| Factor of energy excess (from the table for the engine) | Factor of energy excess for the engine type and point of cut-off, from the handbook table or engine data; the rim must absorb this share of the work per revolution. | |
| Flywheel speed | rpm | Rotational speed of the flywheel. |
| Allowed speed variation 1/n | % | Allowed variation in speed as a percentage of the mean speed (1/n; the handbook gives 1/50 to 1/100, that is 2 % to 1 %). |
| Mean diameter of the rim | m | Mean diameter of the rim, to the centre of the rim section. |
| Rim | ||
| Density of the rim material | kg/m³ | Density of the rim material from your material data (for the rim cross-section). |
| Arms | ||
| Number of arms | choice | Number of arms (spokes) in the wheel; the handbook gives proportions for six and eight. |
| Shaft diameter at the hub | mm | Diameter of the shaft at the hub, which sets the arm proportions. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Energy from
- What it is
- Whether the energy comes from the indicated power or from the work per revolution.
- Units and format
- Choose one of 2 options from the list: Indicated power of the engine; Work done per revolution.
- Example
- The form opens with “Indicated power of the engine” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Chooses which of the two inputs sets the work per revolution.
- Get it right
- Use the work per revolution when you know the mean effective pressure, piston area and stroke.
What this means: Indicated power
- What it is
- Indicated power developed in the engine cylinders.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 1000000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 112 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rim mass rises in proportion.
- Get it right
- Indicated power is above the shaft power by the mechanical losses; 1 hp = 0.7457 kW.
What this means: Work done by the engine per revolution
- What it is
- Average work the engine does in one revolution, entered directly.
- Units and format
- Enter a number in J: joules. The form accepts 0.000001 J or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20000 J as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rim mass rises in proportion.
- Get it right
- Double-acting engine: mean pressure × piston area × twice the stroke.
What this means: Factor of energy excess (from the table for the…
- What it is
- Factor of energy excess: the share of the work per revolution the flywheel must absorb and give back.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.209 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rim mass rises in proportion.
- Get it right
- Read it from the handbook table for the engine type and point of cut-off, or from engine data.
What this means: Flywheel speed
- What it is
- Rotational speed of the flywheel in revolutions per minute.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rim mass falls with the square of the speed for given work.
- Get it right
- Use the running speed of the engine shaft that carries the flywheel.
What this means: Allowed speed variation 1/n
- What it is
- Allowed variation in speed during a revolution as a percentage of the mean speed.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.000001% to 50%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Halving the variation doubles the rim mass.
- Get it right
- The handbook range is 1/50 to 1/100, that is 2 % to 1 %; finer for generators.
What this means: Mean diameter of the rim
- What it is
- Mean diameter of the flywheel rim, measured to the centre of the rim section.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 50 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.8 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rim mass falls with the square of the diameter.
- Get it right
- Outside diameter less the rim depth.
Rim
What this means: Density of the rim material
- What it is
- Density of the rim material, for the cross-section that gives the rim mass.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 30000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7200 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only changes the rim cross-section.
- Get it right
- Cast iron is about 7200 kg/m³ and steel about 7850 kg/m³; use your material data.
Arms
What this means: Number of arms
- What it is
- Number of arms (spokes) between the hub and the rim of the flywheel.
- Units and format
- Choose one of 2 options from the list: 6 arms; 8 arms.
- Example
- The form opens with “6 arms” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Sets the arm width factor: 1.3 for six arms, 1.2 for eight.
- Get it right
- The handbook gives arm proportions for six and eight arms.
What this means: Shaft diameter at the hub
- What it is
- Diameter of the shaft where the flywheel hub sits.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Arm width and thickness grow in proportion.
- Get it right
- Use the shaft size at the hub, not a reduced journal.
Method and formulas
- Work per revolution = power × 60 ÷ N (or entered); E = c × work per revolution.
- Rim mass m = n E ÷ v² with v = π D N ÷ 60 and n = 100 ÷ allowed variation in per cent; this is the handbook’s W = 11,745 n E ÷ (D² N²) (and 387,587,500 c n HP ÷ (D² N³)) in consistent units.
- Rim cross-section = m ÷ (ρ π D).
- Arm width at the hub W = 1.3 × shaft diameter (6 arms) or 1.2 × (8 arms); thickness = W ÷ 2; elliptical area π W t ÷ 4; area at the rim at least two-thirds of that.
- Example: 112 kW at 200 rpm with c = 0.209 and 2 % variation needs a rim of about 988.22 kg on a 1.8 m mean diameter.
Limitations
- The rim is taken to store all the energy; arms and hub add a little, which the handbook formulas neglect.
- The factor of energy excess depends on the engine type, cut-off, reciprocating masses and connecting rod; enter it from the table or engine data.
- Check the rim stress and bursting speed for the material (flywheel-rim-design) before use.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the rim of an engine or compressor flywheel
- Check an existing flywheel against a tighter speed variation
- Proportion cast flywheel arms for the shaft
Who it is for
- Machine designers
- Engine and compressor restorers
- Mechanical engineering students
What you get
- Rim mass (and in pounds)
- Energy excess E the rim absorbs
- Rim speed at the mean diameter
- Rim cross-section area
- Arm width and thickness at the hub
- Arm section area at the hub and the least area at the rim
Interpreting the result
- Halving the allowed speed variation doubles the rim mass; doubling the mean diameter at the same speed cuts it to a quarter.
- Arms should be about three-quarters as strong as the shaft in torsion and taper towards the rim.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3010–3011. Topic reference; no source tables or recommended settings are reproduced.
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