Helical Compression Spring Design Calculator

import math

def spring_design(d, D, Na, L0, F, G, end_inactive=2):
    """
    Helical compression spring design analysis.
    
    d  = Wire diameter (mm)
    D  = Mean coil diameter (mm)
    Na = Active coils
    L0 = Free length (mm)
    F  = Applied load (N)
    G  = Shear modulus (MPa = N/mm²)
    """
    
    if d <= 0 or D <= 0 or Na <= 0 or G <= 0:
        raise ValueError("All dimensions must be positive.")
    if d >= D:
        raise ValueError("Wire diameter must be smaller than coil diameter.")
    
    C = D / d                          # Spring index
    Kw = (4*C - 1)/(4*C - 4) + 0.615/C # Wahl correction factor
    k = (G * d**4) / (8 * D**3 * Na)   # Spring rate (N/mm)
    delta = F / k                      # Deflection (mm)
    tau = Kw * (8 * F * D) / (math.pi * d**3) # Shear stress (MPa)
    Nt = Na + end_inactive
    Ls = Nt * d                        # Solid height (mm)
    pitch = (L0 - d) / Na              # Pitch (mm)
    
    return {
        'spring_index': C,
        'wahl_factor': Kw,
        'spring_rate': k,
        'deflection': delta,
        'shear_stress': tau,
        'solid_height': Ls,
        'pitch': pitch,
        'total_coils': Nt
    }

# Example
d = 2.0
D = 16.0
Na = 8
L0 = 50.0
F = 100
G = 79300

results = spring_design(d, D, Na, L0, F, G, end_inactive=2)
for key, val in results.items():
    print(f"{key}: {val:.3f}")

function results = spring_design(d, D, Na, L0, F, G, end_inactive=2)
    % Helical compression spring design analysis
    % d  = Wire diameter (mm)
    % D  = Mean coil diameter (mm)
    % Na = Active coils
    % L0 = Free length (mm)
    % F  = Applied load (N)
    % G  = Shear modulus (MPa)
    
    if d <= 0 || D <= 0 || Na <= 0 || G <= 0
        error('All dimensions must be positive.');
    end
    if d >= D
        error('Wire diameter must be smaller than coil diameter.');
    end
    
    C = D / d;
    Kw = (4*C - 1)/(4*C - 4) + 0.615/C;
    k = (G * d^4) / (8 * D^3 * Na);
    delta = F / k;
    tau = Kw * (8 * F * D) / (pi * d^3);
    if nargin < 7
        end_inactive = 2;
    end

    Nt = Na + end_inactive;
    Ls = Nt * d;
    pitch = (L0 - d) / Na;
    
    results = struct('spring_index', C, 'wahl_factor', Kw, ...
        'spring_rate', k, 'deflection', delta, ...
        'shear_stress', tau, 'solid_height', Ls, ...
        'pitch', pitch, 'total_coils', Nt);
end

% Example
d = 2.0;
D = 16.0;
Na = 8;
L0 = 50.0;
F = 100;
G = 79300;

res = spring_design(d, D, Na, L0, F, G, 2);
disp(res);