Use this calculator to determine the key performance characteristics of a rectangular wire wave spring based on its dimensions and material properties.
Understanding Wave Springs
Wave springs are precision elastic components designed to provide a specific force at a given deflection. Unlike traditional coil springs, wave springs are made from flat wire (often rectangular) formed into a wavy or corrugated shape. This unique design allows them to achieve the same force as a conventional coil spring but in a significantly smaller axial space, making them ideal for applications with tight radial and axial constraints.
Key Advantages of Wave Springs:
Space Saving: Can reduce spring height by up to 50% compared to coil springs, saving valuable space.
Precise Force: Offer accurate and repeatable force output.
Wide Range of Materials: Available in various materials to suit different environments and temperature requirements.
Versatility: Used in numerous industries, including aerospace, medical devices, automotive, and industrial equipment.
How the Calculator Works:
This calculator uses standard engineering formulas to estimate the performance characteristics of a single-turn, rectangular wire wave spring. The key parameters you input directly influence the spring's behavior:
Material Modulus of Elasticity (E): This is a measure of the material's stiffness. Higher E values result in stiffer springs. Common values for stainless steel (e.g., 302 SS) are around 193,000 MPa.
Wire Radial Wall (b) & Wire Thickness (t): These dimensions define the cross-section of the wire. The thickness (t) has a cubic effect on spring rate, making it a critical dimension for spring stiffness and stress.
Mean Coil Diameter (Dm): The average diameter of the spring coils.
Number of Waves (Nw): The number of peaks and valleys in the spring. More waves generally lead to a higher spring rate.
Number of Turns (Nt): The number of active coils. For single-turn wave springs, this is typically 1.
Free Height (Hf): The height of the spring when no load is applied.
Working Height (Hw): The height at which the spring is expected to operate, and where the working load and stress are calculated.
Solid Height (Hs): The height of the spring when fully compressed, where all coils are in contact.
Calculated Outputs:
Spring Rate (k): The force required to deflect the spring by one unit of length (N/mm).
Working Deflection (δw): The amount the spring is compressed from its free height to its working height.
Working Load (Pw): The force exerted by the spring at its working height.
Working Stress (σw): The bending stress experienced by the spring wire at its working height. It's crucial to ensure this is below the material's yield strength to prevent permanent deformation.
Solid Deflection (δs): The total deflection from free height to solid height.
Solid Load (Ps): The force exerted by the spring when fully compressed to its solid height.
Solid Stress (σs): The bending stress at solid height. This value is critical for determining if the spring will take a permanent set.
Important Considerations:
While this calculator provides valuable estimates, actual spring performance can be influenced by manufacturing tolerances, material variations, and specific application conditions. Always consult with spring manufacturers for critical applications and consider factors like fatigue life, operating temperature, and environmental resistance. High stress values, especially at solid height, indicate a risk of permanent deformation (taking a set).
Example Calculation:
Let's use the default values:
E = 193,000 MPa
b = 0.5 mm
t = 0.1 mm
Dm = 20.0 mm
Nw = 2
Nt = 1
Hf = 10.0 mm
Hw = 7.0 mm
Hs = 2.0 mm
Upon calculation, you would find:
Spring Rate (k): ~0.005 N/mm
Working Deflection (δw): 3.0 mm
Working Load (Pw): ~0.015 N
Working Stress (σw): ~289.4 MPa
Solid Deflection (δs): 8.0 mm
Solid Load (Ps): ~0.041 N
Solid Stress (σs): ~771.0 MPa
These values help engineers select the appropriate wave spring for their design requirements, ensuring it can handle the required loads without exceeding material stress limits. Note that the solid stress in this example is very high, suggesting that compressing this specific spring to solid height would likely cause permanent deformation.
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function calculateWaveSpring() {
// Get input values
var E_str = document.getElementById("modulusElasticity").value;
var b_str = document.getElementById("wireRadialWall").value;
var t_str = document.getElementById("wireThickness").value;
var Dm_str = document.getElementById("meanCoilDiameter").value;
var Nw_str = document.getElementById("numWaves").value;
var Nt_str = document.getElementById("numTurns").value;
var Hf_str = document.getElementById("freeHeight").value;
var Hw_str = document.getElementById("workingHeight").value;
var Hs_str = document.getElementById("solidHeight").value;
// Convert to numbers
var E = parseFloat(E_str);
var b = parseFloat(b_str);
var t = parseFloat(t_str);
var Dm = parseFloat(Dm_str);
var Nw = parseInt(Nw_str);
var Nt = parseInt(Nt_str);
var Hf = parseFloat(Hf_str);
var Hw = parseFloat(Hw_str);
var Hs = parseFloat(Hs_str);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Input validation
if (isNaN(E) || E <= 0 ||
isNaN(b) || b <= 0 ||
isNaN(t) || t <= 0 ||
isNaN(Dm) || Dm <= 0 ||
isNaN(Nw) || Nw < 2 || // Minimum 2 waves for a wave spring
isNaN(Nt) || Nt <= 0 ||
isNaN(Hf) || Hf <= 0 ||
isNaN(Hw) || Hw <= 0 ||
isNaN(Hs) || Hs <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields. Number of Waves (Nw) must be at least 2.";
return;
}
if (Hw >= Hf) {
resultDiv.innerHTML = "Working Height (Hw) must be less than Free Height (Hf).";
return;
}
if (Hs >= Hw) {
resultDiv.innerHTML = "Solid Height (Hs) must be less than Working Height (Hw).";
return;
}
if (Hs >= Hf) { // Redundant but good to catch
resultDiv.innerHTML = "Solid Height (Hs) must be less than Free Height (Hf).";
return;
}
// Calculations
var pi = Math.PI;
// Spring Rate (k) = (E * b * t^3 * N_w^4) / (12 * π * Dm^3 * N_t)
var k = (E * b * Math.pow(t, 3) * Math.pow(Nw, 4)) / (12 * pi * Math.pow(Dm, 3) * Nt);
// Working Deflection (δ_w) = H_f – H_w
var delta_w = Hf – Hw;
// Working Load (P_w) = k * δ_w
var P_w = k * delta_w;
// Working Stress (σ_w) = (3 * π * P_w * Dm) / (N_w * b * t^2)
var sigma_w = (3 * pi * P_w * Dm) / (Nw * b * Math.pow(t, 2));
// Solid Deflection (δ_s) = H_f – H_s
var delta_s = Hf – Hs;
// Solid Load (P_s) = k * δ_s
var P_s = k * delta_s;
// Solid Stress (σ_s) = (3 * π * P_s * Dm) / (N_w * b * t^2)
var sigma_s = (3 * pi * P_s * Dm) / (Nw * b * Math.pow(t, 2));
// Display results
var resultsHtml = "