Modelling the mechanical action of a front loading washing machine

Fisher & Paykel Appliances is a major New Zealand appliance manufacturing company who, amongst other products, develops front- loading washing machines. Their development teams are committed to improving the machine performance. Machine performance is a combination of wash performance (soil removal and wear and tear), power and water consumption, and ease of use. The problem Fisher & Paykel Appliances posed to Mathematics-in-Industry New Zealand was to investigate mathematical models for the wash performance of front-loading washing machines due to mechanical action. Analysis of experimental data supplied by Fisher & Paykel Appliances did not identify the expected inverse relationship between soil removal and wear and tear, indicating that both metrics could be simultaneously improved. The experimental data is further used to identify a rela- tionship between drum speed and the spin dynamics, indicating that a re-configuration of the machine vanes could improve wash perfor- mance. A physical model of wash behaviour is developed to explore the relationship between drum speed and the actions of clothing. A video analysis approach demonstrates that a simple video set-up can be used to gain further insight into the trajectories and mixing of both experimental and genuine wash behaviour.