Balance Rim Thermal Expansion Change Calculator
Calculate linear thermal expansion of a balance rim from its diameter, material coefficient, and signed temperature change.
Description
Linear thermal expansion scales a balance diameter with temperature change.
Linear thermal expansion scales a balance diameter with temperature change. Radius and circumference changes follow the same dimensional model.1
Calculate linear thermal expansion of a balance rim from its diameter, material coefficient, and signed temperature change.
When to use Balance Rim Thermal Expansion Change Calculator
Use this tool to calculate linear thermal expansion of a balance rim from its diameter, material coefficient, and signed temperature change.
Choose a supported reference focus or prepare the watch measurements, evidence and explicit limits requested. Confirm units and date conventions before running.
How to use Balance Rim Thermal Expansion Change Calculator and understand its results
- Choose a supported reference focus or prepare the watch measurements, evidence and explicit limits requested. Confirm units and date conventions before running.
- Enter balanceDiameterMillimeters, linearExpansionCoefficientPerCelsius, temperatureChangeCelsius using the field table and calculation rules, then run the tool.
- Read circumferenceChangeMillimeters, diameterChangeMillimeters, finalDiameterMillimeters, radialChangeMillimeters. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| balanceDiameterMillimeters | Balance diameter (mm) | number; minimum: 0 | Required |
| linearExpansionCoefficientPerCelsius | Linear expansion coefficient (1/degC) | number; minimum: 0 | Required |
| temperatureChangeCelsius | Temperature change (degC) | number | Required |
Enter positive diameter mm, nonnegative coefficient/°C and finite signed temperature change. Require positive final diameter. Return signed diameter/radius/circumference changes and final diameter.
diameterChange=diameter×coefficient×deltaT; final=diameter+change Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| circumferenceChangeMillimeters | Circumference change (mm) | number |
| diameterChangeMillimeters | Signed diameter change (mm) | number |
| finalDiameterMillimeters | Final diameter (mm) | number; minimum: 0 |
| radialChangeMillimeters | Signed radial change (mm) | number |
{
"input": {
"balanceDiameterMillimeters": 10,
"linearExpansionCoefficientPerCelsius": 0.0000115,
"temperatureChangeCelsius": 10
},
"output": {
"circumferenceChangeMillimeters": 0.003612831551628262,
"diameterChangeMillimeters": 0.00115,
"finalDiameterMillimeters": 10.00115,
"radialChangeMillimeters": 0.000575
}
}Limitations and assumptions
No bimetal compensation, spring response or timekeeping effect is inferred.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Balance–Spring Temperature Rate Change: Estimate relative period and rate change from T proportional to the square root of balance inertia divided by hairspring stiffness, using caller-supplied first-order coefficients. For a complementary task, use Middle Temperature Rate Error Calculator: Calculate the middle-temperature departure from the straight line between caller-supplied low- and high-temperature daily rates.
References
Similar or alternative tools
- Balance–Spring Temperature Rate Change
Estimate relative period and rate change from T proportional to the square root of balance inertia divided by hairspring stiffness, using caller-supplied first-order coefficients.
- Middle Temperature Rate Error Calculator
Calculate the middle-temperature departure from the straight line between caller-supplied low- and high-temperature daily rates.