Spinning Spindle Vibration Resonance & Critical Speed

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 6 inputs are read from the form on every keystroke: Rotating Mass, Bolster Stiffness, Residual Unbalance, Damping Ratio, Operating Speed and Danger Band Width.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves First Critical Speed together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Operating Speed Ratio, Dynamic Amplification, Whirl at Operating Speed, Whirl at Resonance, Danger Band Lower and Danger Band Upper — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the First Critical Speed shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Rotor and Operation. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read First Critical Speed in the dark results panel — that is the headline figure, expressed in rpm.
4. Check the supporting rows underneath (Operating Speed Ratio, Dynamic Amplification, Whirl at Operating Speed, Whirl at Resonance, Danger Band Lower and Danger Band Upper) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing First Critical Speed before a trial is booked, so machine time and material in Textile Machinery Kinematics & IoT Analytics are committed against a calculated figure rather than an estimate.
• Costing and quotation — First Critical Speed is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Rotating Mass) shows how much of the gap in First Critical Speed each variable explains.
• Teaching and study — the accepted ranges bracket normal Textile Machinery Kinematics & IoT Analytics practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• A single lumped mass on a linear spring is the whole model, and a real spindle has several modes — the second and third criticals can sit inside the running range even when the first is safely below it. Bolster stiffness is also not linear: it is a damped flexible mounting whose stiffness varies with amplitude and with the oil, so the critical speed drifts with temperature and wear rather than staying where a datasheet puts it. Unbalance changes continuously through the build as the bobbin fills, and the worst case is rarely the full package. Use this to locate the band to avoid, then confirm with a run-up vibration measurement.
• Every input is bounded to the range normal practice occupies (Rotating Mass 0.05 to 5 kg, Bolster Stiffness 10 to 5000 kN/m and Residual Unbalance 0.1 to 200 g·mm, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask