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Shaft critical speed from static sag calculator

Jeffcott single-disc shaft critical speed from supplied static sag.

shafts-critical-speed.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenariocriticalrad/sspeedFraction
221.4720.472834
247.6140.422916

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

speed separation screen0.47 ✓ passes

BASELINE INPUTS

CALCULATED

critical221.47 rad/s
speedFraction0.47283

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
speed separation screen0.47 ✓ passes
alternative · alternative
speed separation screen0.42 ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

critical
critical = sqrt(gravity/sag) [rad/s]
speed fraction
speedFraction = operatingSpeed/critical

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

sag
0.2 mm
gravity
9.81 m/s^2
operating speed
1000 rpm

Calculated

critical
221.472 rad/s
speed fraction
0.472834

Assumptions and limits

Jeffcott single-disc shaft critical speed from supplied static sag.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Shaft critical speed screening. Inputs: shaft stiffness; supported masses; span. Outputs: first critical-speed estimate. Model scope: Elastic shaft models and specified supports. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

  • Inputs: shaft stiffness, supported masses, span
  • Outputs: first critical-speed estimate
  • Modes: calculate, compare, sweep
  • Drawing: Shaft load diagram

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS

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