Stability and dynamic analyses of a horizontal axis washing machine with a ball balancer

• Mathematical model of a horizontal axis washer with a ball balancer is built.
• Stability analysis considering the influence of gravity is carried out.
• Cone shape trajectory of the tub's axis is observed.
• Backward mass center design of the tub assembly can reduce vibration angle.

A mathematical model of a horizontal axis washing machine with a ball balancer is built. The Floquet multipliers are employed for judging the stability of the system based on which a special continuation program considering the influence of gravity is developed. Stability analysis is carried out with stable and unstable regions above 4 Hz discovered. Influences of several parameters on variations of the boundaries between the regions are discussed. Dynamics of the spinning cycle in Stable region 1 are studied. The phenomenon that the tub's axis moves along the lateral surface of a cone is discovered based on which equilibrium of the centrifugal forces is discussed and a potential method for getting a smaller vibration angle is proposed. A ball balancer is produced for experiment with its lubrication and defects due to friction discussed. Quantitative experiment is done on a commercial washing machine with instability of the balancer, the cone shape trajectory of the tub's axis and the method of obtaining a smaller vibration angle validated.