Coil Spring Calculator

Coil Spring Calculator

(e.g., Steel: ~79 GPa, Bronze: ~40 GPa)

(Enter to calculate deflection)

(Enter to calculate required load)

Spring Rate (k): — N/mm

Deflection (δ) under Applied Load: — mm

Required Load (F) for Desired Deflection: — N

function calculateSpringProperties() { var wireDiameter = parseFloat(document.getElementById('wireDiameter').value); var meanCoilDiameter = parseFloat(document.getElementById('meanCoilDiameter').value); var numActiveCoils = parseFloat(document.getElementById('numActiveCoils').value); var modulusRigidityGPa = parseFloat(document.getElementById('modulusRigidity').value); var appliedLoad = parseFloat(document.getElementById('appliedLoad').value); var desiredDeflection = parseFloat(document.getElementById('desiredDeflection').value); var springRateResultDiv = document.getElementById('springRateResult'); var deflectionResultDiv = document.getElementById('deflectionResult'); var loadResultDiv = document.getElementById('loadResult'); // Reset results springRateResultDiv.innerHTML = 'Spring Rate (k): — N/mm'; deflectionResultDiv.innerHTML = 'Deflection (δ) under Applied Load: — mm'; loadResultDiv.innerHTML = 'Required Load (F) for Desired Deflection: — N'; // Input validation for primary spring rate calculation if (isNaN(wireDiameter) || wireDiameter <= 0) { alert('Please enter a valid positive Wire Diameter.'); return; } if (isNaN(meanCoilDiameter) || meanCoilDiameter <= 0) { alert('Please enter a valid positive Mean Coil Diameter.'); return; } if (isNaN(numActiveCoils) || numActiveCoils <= 0) { alert('Please enter a valid positive Number of Active Coils.'); return; } if (isNaN(modulusRigidityGPa) || modulusRigidityGPa = 0 && !isNaN(springRate) && springRate > 0) { var deflection = appliedLoad / springRate; deflectionResultDiv.innerHTML = 'Deflection (δ) under Applied Load: ' + deflection.toFixed(4) + ' mm'; } else if (!isNaN(appliedLoad) && appliedLoad = 0 && !isNaN(springRate) && springRate > 0) { var requiredLoad = springRate * desiredDeflection; loadResultDiv.innerHTML = 'Required Load (F) for Desired Deflection: ' + requiredLoad.toFixed(4) + ' N'; } else if (!isNaN(desiredDeflection) && desiredDeflection < 0) { loadResultDiv.innerHTML = 'Required Load (F) for Desired Deflection: Deflection must be non-negative'; } }

Understanding Coil Springs and Their Properties

Coil springs are ubiquitous mechanical components, found in everything from vehicle suspensions and industrial machinery to pens and toys. Their primary function is to store and release mechanical energy, providing resistance to a force or maintaining a specific position. The behavior of a coil spring is largely defined by its 'spring rate' or 'spring constant', which quantifies how much force is required to compress or extend the spring by a certain unit of distance.

What is Spring Rate (k)?

The spring rate (k) is a fundamental characteristic of a spring. It's the ratio of the change in force to the corresponding change in deflection. A higher spring rate means the spring is stiffer, requiring more force to achieve the same amount of compression or extension. Conversely, a lower spring rate indicates a softer spring. The standard unit for spring rate is Newtons per millimeter (N/mm) or pounds per inch (lbs/in).

Key Parameters for Coil Spring Calculation:

The spring rate of a helical compression or extension spring is determined by several physical and material properties:

• Wire Diameter (d): This is the diameter of the wire material used to form the coils. A thicker wire generally results in a stiffer spring.
• Mean Coil Diameter (D): This is 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 can be calculated as Outer Diameter – Wire Diameter. A larger mean coil diameter tends to make the spring softer.
• Number of Active Coils (Na): These are the coils that are free to deflect under load. The more active coils a spring has, the softer it will be. The number of active coils depends on the spring's end type (e.g., plain, squared, ground).
• Modulus of Rigidity (G): Also known as the shear modulus, this is a material property that describes a material's resistance to shear deformation. It's a measure of the material's stiffness. Common values for steel are around 79 GPa, while bronze might be around 40 GPa.

The Spring Rate Formula:

The formula used in this calculator for the spring rate (k) of a helical compression or extension spring is:

k = (G * d⁴) / (8 * D³ * Na)

Where:

• k = Spring Rate (N/mm)
• G = Modulus of Rigidity (N/mm², converted from GPa)
• d = Wire Diameter (mm)
• D = Mean Coil Diameter (mm)
• Na = Number of Active Coils (unitless)

Calculating Deflection and Load:

Once the spring rate (k) is known, you can easily determine the deflection (δ) for a given applied load (F), or the required load for a desired deflection, using Hooke's Law:

F = k * δ

Therefore:

• Deflection (δ) = F / k (If you know the applied load and spring rate)
• Load (F) = k * δ (If you know the desired deflection and spring rate)

Example Calculation:

Let's consider a spring with the following properties:

• Wire Diameter (d): 2 mm
• Mean Coil Diameter (D): 20 mm
• Number of Active Coils (Na): 10
• Modulus of Rigidity (G): 79 GPa (which is 79,000 N/mm²)

Using the formula:

k = (79,000 N/mm² * (2 mm)⁴) / (8 * (20 mm)³ * 10)

k = (79,000 * 16) / (8 * 8000 * 10)

k = 1,264,000 / 640,000

k ≈ 1.975 N/mm

If an applied load of 100 N is placed on this spring:

Deflection (δ) = 100 N / 1.975 N/mm ≈ 50.63 mm

This calculator helps you quickly determine these critical values, aiding in the design and analysis of spring-based systems.