Study On Dynamics And Vibration Suppression Of The Spin Drying Process Of A Vertical Axis Automatic Washing Machine

The development of domestic washing machine industry has taken about 30 years. Now, the annual output of domestic washers ranks first worldwide and accounts for about 40 percent of the global output. However, because domestic washer industry started from technology introductions or technology imitations, not enough studies have been carried out and core technologies have not yet been completely grasped. All these factors are restricting a further development of this domestic industry. Because domestic design methods of washers are lagging behind, native washers are uncompetitive in the global market. Now, most of domestic washers can only occupy part of the relatively low-end market, and are uncompetitive in obtaining market share in the high-end market.Vibration and noise requirements have become two of the most important performance indexes of a washing machine. Because strong vibrations often occur in the spin drying process, vibration problems have attracted lots of attentions from producers. This paper studies dynamics and vibration suppression of the spin drying process of a vertical axis automatic washing machine. Steady-state response, stability and transient response are three main research aspects for dynamic systems. Up till now, most studies on the spin drying process have focused on the first aspect, and few papers have ever been published to analyze the other two. Thus stability of the spin drying process is chosen as our research emphasis, besides, some work is also done for analyzing the steady-state response. For further development of our research, a method of building a flexible model for the vertical axis automatic washing machine is at last provided.Both of the suspension system and the hydraulic balancer show great influences on vibrations of the spin drying process, thus, basic characteristics and stability analyses of the suspension structure of the washing machine are carried out in Chapters 2 and 3 respectively, and detailed characteristics of the hydraulic balancer are studied in Chapter 4, based on studies above, mutual influences between the suspension system and the balancer are studied in Chapter 5.For discussing basic characteristics of the suspension system, the effect of the hydraulic balancer is not considered in Chapters 2 and 3. In Chapter 2, damping properties of the suspension system are analyzed and a mathematical model for describing damping forces is built; Kinetic energies of different parts of the washing machine are deduced and submitted into Lagrange's Equation to derive a vibration model for the spin drying process; Different methods of adjusting the static equilibrium position of the washing machine are studied; Rigid modals are analyzed. In Chapter 3, a rotating coordinate transformation is performed and an autonomous formulation is derived based on which stability analyses are carried out; A hopf bifurcation phenomenon is discovered while decreasing the tangential damping coefficient of the suspension system; The numerical continuation method is used in analyzing stability of the spin drying process with instabilities observed validated by both simulations and experiments at last. From the two chapters, basic characteristics of the machine's suspension structure including its influence on the stability of the spin drying process could be clearly identified. Considering the work principle of a hydraulic balancer originates from the self-alignment phenomenon occurred in planar rotators, a planar model is used in Chapter 4 to analyze basic characteristics of the hydraulic balancer. For analyzing its stability, a two-ball model generally used in researches is employed for describing its effect. An autonomous form is built and constrains on its equilibrium points are derived; Stability changes of the equilibrium points upon variations of different parameters are analyzed; The difference between a two-ball model and a steady state description is analyzed, and the limitation of a hydraulic balancer is illustrated: the hydraulic balancer with only one layer can hardly overcome total unbalance of the system, fortunately, an improving method with multi-layers can be used to enhance the balancer's capability under small eccentricities. From this chapter, basic characteristics of the hydraulic balancer could be comprehensively understood which is useful for analyzing the balancer's effect on a three-dimensional system.Based on discussions above, in Chapter 5,a two-ball description of the balancer is employed to develop a three-dimensional model for the washing machine which is then translated into an autonomous form; The equilibrium points of the autonomous form are solved and similarities between these points and those of a planar model are discussed; Local bifurcation analyses are carried out and the balancer's effect to decrease the value of the tangential damping coefficient at the hopf bifurcation point discussed in Chapter 3 is pointed out. Furthermore, two unstable regions denoted by M and N of the spin drying process when the axial damping coefficient of the suspension system is small are observed; Influencing factors of the stable region N are analyzed and validated by experiments; The importance of the hydraulic balancer for suppressing vibrations in stable regions is illustrated,and a governing equation for a smaller deflection angle is presented. From this chapter, the balancer's effect on the stability and the steady-state response of the spin drying process could be clearly understood.Besides studies above, a method for building a flexible model for the washing machine is illustrated in Chapter 6. A floating-reference-frame and the modified Craig-Bampton method are used to obtain a mathematical description of the tub based on which Euler-Lagrange equation is employed for deriving a flexible model for the washing machine; The generalized-αmethod is used for solving the flexible model and deformations of the tub during the spin drying process are obtained; Correctness and effectiveness of the flexible model are validated through a comparison between results obtained in this chapter and those from ANSYS. This chapter provides a foundation for further development of our research.At last, in Chapter 7, for the convenience of analyzing dynamics of the spin drying process, a software package with a graphic user interface is developed for designers, and a design method for vibration suppression is also provided.