Development Journal

Universal Washing Machine Damper

1 Introduction

This is the development journal for an open source hardware washing machine damper. The damper is the most important part for long mechanical life of a washing machine. …

2 General technical facts

what are typical damper types? which one fail sooner, which ones last? damper parameters? loads/stresses/frequencies/ damping-power /thermal losses/ differential equations that describe the system of mass/spring coeff/damper —> forces —-> design

length: tbd.
mounting holes: 8.0 mm for fitting screw

3 fundamental differential equations for mass-spring-damper-sytsem

3.1 amplitude vs. frequency

The following GNU Octave script calculates and plots the amplitude of a damped mass-spring oscillator depending on the excitation frequency.

% spring_dampe_mass_amplitude.m
% Calculates and plots the amplitude of a damped
% spring–mass oscillator as a function of the excitation frequency.

clear all; close all; clc;

% ---- Parameters -------------------------------------------------
m  = 40.0;        % Mass / kg
k  = 15000.0;      % Spring constant / N/m
c  = 1.0;        % Damping constant / N·s/m (0 = undamped)
F0 = 1.0;        % Amplitude of the excitation force / N

% Natural angular frequency and natural frequency
omega0 = sqrt(k/m);           % / rad/s
f0     = omega0/(2*pi);       % / Hz

% Frequency axis around the natural frequency
f_min = 0.0 * f0;             % Lower limit / Hz
f_max = 3.0 * f0;             % Upper limit / Hz
N     = 1000;                 % Number of support points

f     = linspace(f_min, f_max, N);  % Frequency [Hz]
omega = 2*pi*f;                     % Angular frequency [rad/s]

% ---- Amplitude calculation --------------------------------------
% A(omega) = F0 / sqrt((k - m*omega^2)^2 + (c*omega)^2)
num  = F0;
den  = sqrt( (k - m.*omega.^2).^2 + (c.*omega).^2 );
A    = num ./ den;

% ---- Spring force calculation -----------------------------------
% Peak spring force magnitude: |F_spring| = k * A (from F_s = -k x)
F_spring = k .* A;  % / N

% ---- Plot ------------------------------------------------------
figure;
plot(f, A, 'LineWidth', 2, 'DisplayName', 'Amplitude');
hold on;
plot(f, F_spring/1000, 'LineWidth', 2, 'DisplayName', 'Spring Force /kN');  % Scaled for visibility
grid on;
xlabel('Frequency f /Hz');
ylabel('Amplitude A /m , Force / kN');
title('Amplitude and Spring Force of Damped Spring-Mass Oscillator');
legend('Location', 'best');

% Enlarge font size for all axes text (title, labels, ticks, legend)
set(gca, 'FontSize', 16);  % Adjust 16 to your preferred size (e.g., 20 for even larger)

% Mark the natural frequency
y_eig = interp1(f, A, f0);     % Amplitude at natural frequency
plot(f0, y_eig, 'ro', 'MarkerSize', 8, 'LineWidth', 2);
text(f0, y_eig, sprintf('  f_0 = %.2f Hz', f0), ...
     'VerticalAlignment', 'bottom');

drawnow;
% pause;    % Optionally enable if you want the window to remain open

3.2 unbalanced forces vs. rpm

The following scipt calculates the unbalance forces as a funktion of the rotations per minute. Huge forces arise out of a unproper balance which is why the Fairdevices control unit needs to have function to minimise the unbalance of loundry inside the machine.

% Unbalance force of a rotating mass
% m in kg, r in m, n in 1/min

clear all; close all; clc;

% Parameters
r = 0.25;                 % Radius in m (example value 0.1 m)
n = linspace(0, 1400, 500);   % Speed from 0 to 1400 rpm

% Convert speed to angular velocity
omega = 2*pi*n/60;       % rad/s

% Family of curves for masses 1 ... 8 kg
m_vec = 1:1:8;

figure;
hold on; grid on;

for m = m_vec
    F = m * r .* (omega.^2);    % Unbalance force in N
    plot(n, F, 'DisplayName', sprintf('m = %d kg', m));
end

xlabel('Speed n [rpm]');
ylabel('Unbalance force F [N]');
title(sprintf('Unbalance force F(n) for r = %.3f m and m = 1...8 kg', r));
legend('show', 'Location', 'northwest');

DIAGRAM placeholder —

3.3 spring constant

Assumptions:

mass of tub = 30 kg
water mass = 10 kg
loundry mass = 1..8 kg

max delta for static load: 2.5 cm

Spring constant for 3 parallel springs: 15000 N/m

2Do / Next Steps

Documatation of physical and mathematical fundamentales to calculate load / stresses / amplidudes / optimum values by equations, figures, etc. All ‘scientific’ knowledge should be gathered. It’s the base for opimisation by calculations and not trying ;)
Determination of typical values for
- spring constants
- damper constants
- massrange of empty and fully loaded washing drum in washing machines.
Note values in this document
calculation of forces and amplitudes, maximum allowable amplitudes / imbalance of loundry
Investigation / List of available oil damper
concept of frictionless, wearless, electromagnetic damper by Eddy Current or by generator coil
estimation of unbalance force

…