.compression-spring-calculator-container {
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max-width: 800px;
margin: 20px auto;
padding: 25px;
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border-radius: 10px;
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border: 1px solid #e0e0e0;
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box-sizing: border-box;
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margin-top: 20px;
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function calculateSpring() {
var wireDiameter = parseFloat(document.getElementById('wireDiameter').value);
var meanCoilDiameter = parseFloat(document.getElementById('meanCoilDiameter').value);
var numActiveCoils = parseFloat(document.getElementById('numActiveCoils').value);
var freeLength = parseFloat(document.getElementById('freeLength').value);
var shearModulus = parseFloat(document.getElementById('shearModulus').value);
var errorMessageDiv = document.getElementById('errorMessage');
errorMessageDiv.style.display = 'none';
errorMessageDiv.innerHTML = ";
// Input validation
if (isNaN(wireDiameter) || wireDiameter <= 0) {
errorMessageDiv.innerHTML = 'Please enter a valid positive Wire Diameter.';
errorMessageDiv.style.display = 'block';
return;
}
if (isNaN(meanCoilDiameter) || meanCoilDiameter <= 0) {
errorMessageDiv.innerHTML = 'Please enter a valid positive Mean Coil Diameter.';
errorMessageDiv.style.display = 'block';
return;
}
if (isNaN(numActiveCoils) || numActiveCoils <= 0 || !Number.isInteger(numActiveCoils)) {
errorMessageDiv.innerHTML = 'Please enter a valid positive integer for Number of Active Coils.';
errorMessageDiv.style.display = 'block';
return;
}
if (isNaN(freeLength) || freeLength <= 0) {
errorMessageDiv.innerHTML = 'Please enter a valid positive Free Length.';
errorMessageDiv.style.display = 'block';
return;
}
if (isNaN(shearModulus) || shearModulus <= 0) {
errorMessageDiv.innerHTML = 'Please enter a valid positive Material Shear Modulus.';
errorMessageDiv.style.display = 'block';
return;
}
if (meanCoilDiameter <= wireDiameter) {
errorMessageDiv.innerHTML = 'Mean Coil Diameter must be greater than Wire Diameter.';
errorMessageDiv.style.display = 'block';
return;
}
// Calculations
var springIndex = meanCoilDiameter / wireDiameter;
// Spring Rate (k) = (G * d^4) / (8 * Na * D^3)
// G is in MPa (N/mm^2), d, D in mm. Result k in N/mm
var springRate = (shearModulus * Math.pow(wireDiameter, 4)) / (8 * numActiveCoils * Math.pow(meanCoilDiameter, 3));
// Solid Height (Ls) – approximation for squared and ground ends
var solidHeight = wireDiameter * (numActiveCoils + 2);
var maxDeflection = 0;
var maxLoad = 0;
var stressSolidHeight = 0;
if (freeLength <= solidHeight) {
errorMessageDiv.innerHTML = 'Free Length must be greater than Solid Height for valid deflection calculation. Adjust Free Length or other parameters.';
errorMessageDiv.style.display = 'block';
// Still display other valid results
} else {
maxDeflection = freeLength – solidHeight;
maxLoad = springRate * maxDeflection;
// Wahl Factor (Kw) = (4C – 1) / (4C – 4) + 0.615 / C
var wahlFactor = (4 * springIndex – 1) / (4 * springIndex – 4) + 0.615 / springIndex;
// Stress at Solid Height (τ_s) = (8 * P_max * D * Kw) / (pi * d^3)
// P_max in N, D in mm, d in mm. Result τ_s in MPa
stressSolidHeight = (8 * maxLoad * meanCoilDiameter * wahlFactor) / (Math.PI * Math.pow(wireDiameter, 3));
}
// Display results
document.getElementById('springIndexResult').getElementsByTagName('span')[0].innerText = springIndex.toFixed(3);
document.getElementById('springRateResult').getElementsByTagName('span')[0].innerText = springRate.toFixed(3) + ' N/mm';
document.getElementById('solidHeightResult').getElementsByTagName('span')[0].innerText = solidHeight.toFixed(3) + ' mm';
document.getElementById('maxDeflectionResult').getElementsByTagName('span')[0].innerText = maxDeflection.toFixed(3) + ' mm';
document.getElementById('maxLoadResult').getElementsByTagName('span')[0].innerText = maxLoad.toFixed(3) + ' N';
document.getElementById('stressSolidHeightResult').getElementsByTagName('span')[0].innerText = stressSolidHeight.toFixed(3) + ' MPa';
}
// Run calculation on page load with default values
window.onload = calculateSpring;
Compression Spring Calculator
(e.g., Music Wire: ~79300 MPa, Stainless Steel 302: ~69000 MPa)
Calculation Results
Spring Index (C):
Spring Rate (k):
Solid Height (Ls):
Max Deflection (δmax):
Max Load (Pmax):
Stress at Solid Height (τs):
Understanding Compression Springs
A compression spring is an open-coil helical spring that resists a compressive force applied axially. It is designed to become shorter when a load is applied, storing mechanical energy, and then returning to its original length when the load is removed. These springs are ubiquitous, found in everything from ballpoint pens and automotive suspensions to industrial machinery and medical devices.
Key Parameters and Their Importance
- Wire Diameter (d): The diameter of the wire used to form the spring. A larger wire diameter generally results in a stiffer spring.
- Mean Coil Diameter (D): The average diameter of the spring coils, measured from the center of the wire on one side to the center of the wire on the opposite side. It's calculated as Outer Diameter – Wire Diameter, or Inner Diameter + Wire Diameter.
- Number of Active Coils (Na): The number of coils that are free to deflect under load. This is a critical factor in determining the spring's flexibility. End types (e.g., squared and ground) can affect the number of active coils relative to the total coils.
- Free Length (Lo): The overall length of the spring in its uncompressed state.
- Material Shear Modulus (G): A material property that describes its resistance to shear deformation. It's crucial for calculating spring rate. Common values for steel alloys range from 69,000 MPa (for stainless steel) to 79,300 MPa (for music wire). Ensure your input units for G are consistent with your dimensional units (e.g., MPa for mm, psi for inches).
How the Calculator Works
This calculator uses fundamental spring design equations to determine key performance characteristics based on your input parameters:
- Spring Index (C): Calculated as
D / d. This dimensionless ratio indicates the relative tightness of the coil. A lower index (e.g., 12) might indicate a spring prone to buckling. - Spring Rate (k): Also known as spring constant, it's the force required to deflect the spring by a unit of length. The formula used is
k = (G * d^4) / (8 * Na * D^3). The unit will be N/mm if dimensions are in mm and G in MPa. - Solid Height (Ls): The length of the spring when it is fully compressed, with all active coils touching. For squared and ground ends, it's approximated as
d * (Na + 2). - Maximum Deflection (δmax): The maximum distance the spring can be compressed from its free length to its solid height:
δmax = Lo - Ls. This assumes the spring can be compressed to solid height without yielding. - Maximum Load (Pmax): The maximum force the spring can withstand when compressed to its solid height:
Pmax = k * δmax. - Stress at Solid Height (τs): The shear stress experienced by the wire when the spring is compressed to its solid height. This is a critical value to ensure the spring does not permanently deform (take a "set"). The formula involves the Wahl Factor (Kw) to account for curvature effects:
τs = (8 * Pmax * D * Kw) / (π * d^3), whereKw = (4C - 1) / (4C - 4) + 0.615 / C.
Important Considerations
While this calculator provides essential design parameters, real-world spring design involves more complex factors:
- End Types: The calculator uses an approximation for solid height suitable for squared and ground ends. Other end types (plain, plain and ground, squared) will have different solid height calculations and affect the number of active coils.
- Buckling: Long, slender compression springs can buckle under load before reaching solid height.
- Fatigue Life: For applications involving cyclic loading, fatigue analysis is crucial to predict the spring's lifespan.
- Material Properties: Temperature, corrosion, and relaxation can affect material properties and spring performance over time.
- Tolerances: Manufacturing tolerances can lead to variations in spring dimensions and performance.
Always consult with a spring manufacturer or a mechanical engineer for critical applications.