Coefficient of Linear Thermal Expansion: Machining Guide

Quick take: Thermal expansion is not just a materials-table topic. In machining, it changes fit, tolerance, and process stability as tools, holders, and workpieces heat up through the cut.

Related references: Calculated Forces When Turning: Quick Guide, Understanding Hardness in Metalworking, and Understanding Cutting Equations.

Most materials expand when their temperature increases and contract when their temperature decreases. The size change is approximately proportional to the temperature change, but the amount of size change varies from material to material.

The amount of size change is calculated by the equation:

ΔL = αL0ΔT

where ΔL is the change in length measured along one dimension, α is the coefficient of linear thermal expansion, L0 is the length of the object at the original temperature and ΔT is the temperature change. Both ΔL and L0 have units of length, such as meters, and ΔT has units of degrees, such as ° C, so α has units of 1 ÷ degrees. Alternatively, the units of α could be expressed as m ÷ (m – ° C), for example.

Thermal Expansion Calculator

Original Length (L₀) in meters or inches:
Coefficient of Linear Thermal Expansion (α) in 1/°C or 1/°F:
Temperature Change (ΔT) in °C or °F:
Calculate Change in Length (ΔL)

function calculateExpansion() { const length = parseFloat(document.getElementById(‘length’).value); const alpha = parseFloat(document.getElementById(‘alpha’).value); const tempChange = parseFloat(document.getElementById(‘tempChange’).value); if (!isNaN(length) && !isNaN(alpha) && !isNaN(tempChange)) { const deltaL = alpha * length * tempChange; document.getElementById(‘result’).textContent = “Change in Length (ΔL): ” + deltaL.toFixed(6) + ” meters or inches”; } else { document.getElementById(‘result’).textContent = “Please enter valid values for all fields.”; }}

Formula: ΔL = α × L₀ × ΔT

where: