CALCULATE WITH CONFIDENCE

Engineering · Machine Design

Shaft Critical Speed and Rotor Unbalance Calculator

Estimate the first critical speed of an ideal simply supported shaft with a centered disk, or calculate rotating unbalance force from entered mass eccentricity and speed.

Engineering · Machine Design

Enter the engineering model

Explicit properties, geometry, units and assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Visual modelSchematic · not to scale
Machine Design: critical visual explanationA simplified diagram showing the relationship represented by the selected calculator mode. It is explanatory and not a fabrication, safety or scale drawing.shaft flexibility → ideal critical speedreal rotor response also depends on bearings and damping
The diagram explains the selected relationship only. Dimensions, symbols and proportions are illustrative; use the entered values and stated assumptions for the calculation.

Keep every unit basis, sign convention, property source and idealization consistent. Values stay in this browser.

Engineering calculation result

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Understand the machine model

What this calculator is for

Rotors can respond strongly near a natural bending frequency, while eccentric mass creates a rotating force that grows with speed squared. The two modes expose these related but distinct ideas.

1Choose flexibility or unbalance mode.
2Keep weight, mass, gravity and geometry definitions consistent.
3Do not infer a safe operating band from the ideal result alone.

Visual explanation

The critical-speed model links static shaft flexibility to an ideal natural frequency. The unbalance model follows a small mass offset as it rotates around the shaft axis.

The governing relationship

Centered disk: δ=WL³/(48EI), ωn=√(g/δ). Unbalance force amplitude Fu=meω².

Keep the boundary visible

Single-degree idealizations only. Distributed shaft mass, gyroscopic effects, bearing stiffness, damping, multi-disk modes, run-up response, balance grade and safe operating range are excluded.

Quick guide

How to use this calculator

  1. Choose the analysis mode that matches the physical model before entering values.
  2. Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
  3. Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.

Calculation method

Transparent engineering model

Centered disk: δ=WL³/(48EI), ωn=√(g/δ). Unbalance force amplitude Fu=meω².

The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.

Worked example

Worked example

A 2 kg eccentric mass at 0.5 mm and 3000 rpm creates an ideal unbalance-force amplitude of about 98.696 N.

Centered disk: δ=WL³/(48EI), ωn=√(g/δ). Unbalance force amplitude Fu=meω².

Supported inputs

Precision and limits

Analysis, not approval

Single-degree idealizations only. Distributed shaft mass, gyroscopic effects, bearing stiffness, damping, multi-disk modes, run-up response, balance grade and safe operating range are excluded.

Standards and properties

Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.

Units and precision

Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.

Privacy

Entered engineering values and results stay in this browser and are not sent to analytics or third parties.