The directional motion of the compliant body under vibratory excitation

The paper discusses the directional motion of the vibratory excited compliant body in respect to the stationary support which has the internal slot. Such a model and proposed mathematical approach represent a part-to-part interaction in the assembly position, whereas the motion of the compliant body characterizes the alignment of the mating parts. The characteristics of the motion of the compliant body under kinematical excitation along the direction of the joining axis are analyzed using the numerical technique. The dependences of the alignment duration upon the force of the body pressing to the support, the stiffness of the elastic constraints and the amplitude and frequency of the excitation are determined. The directional motion is performed by the body in respect to the support only when the parameters of the mechanical systems and excitation are adjusted. The areas of the parameter sets are defined considering the occurrence of the successful alignment of the connective surfaces. The body can move from the static to the dynamic position of equilibrium. The distance between these positions determines the maximum error of the interdependent position of the connective surfaces when the alignment of the parts is still possible. To explore the shaft alignment in respect to the bushing the experimental setup is made and the experiments of the alignment under kinematical excitation of the shaft along the bushing direction are accomplished. The experimental dependences of the alignment duration both on the shaft pressing force to the bushing and the excitation frequency are defined and the areas of the parameter sets are determined when the shaft is aligned successfully in respect to the bushing. The experimental results confirm the applicability of the mathematical approach.

► We model the vibratory motion of the compliant body considering the automated assembly.
► The success and duration of the alignment depend on the parameters of the system and vibratory excitation.
► Experimental analysis of the shaft-to-bushing alignment confirms the proposed mathematical approach.
► The vibratory alignment of the parts occurs under proper adjustment of the parameters.