Modeling of vibrational non-impact motion of mobile-based body

The paper deals with vibrational non-impact displacement of a mobile-based body on an inclined plane. Two cases are considered: when the body is subjected to kinematical excitement, and when the plane is excited in two perpendicular directions. This phenomenon is used in vibratory assembly devices, where vibration excitement compensates interdependent orientation errors of the components subjected to assembly. Transient and periodic regimes of the body motion from static to dynamic equilibrium are investigated. Dependencies of maximum displacement and average creeping displacement speed upon the elastic resistance force, body pressure to the plane force, the ratio of mutually perpendicular vibration amplitudes, and the phase of these vibrations are presented. The possibilities and conditions of automatic components assembling by applying vibration displacement are characterized.     

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.     

Extending the Thorin class

We prove that the Thorin class $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 , is the minimal class of probability distributions on \mathbbR₊ {\mathbb{R}_{+} } that is closed under convolutions and weak limits and contains the Tweedie distributions Tw_(κ+1)/κ (μ, λ), μ > 0, λ > 0.     

Modeling of vibrational impact motion of mobile-based body

The paper deals with vibrational impact motion of a mobile-based body on an inclined plane, which is a characteristic for vibrational alignment of components subjected to an automated assembly. The alignment model is presented by a two-degree-of-freedom vibro-impact system in which the moving body is impacting the plane obliquely. Properties of the vibrational impact motion under kinematical excitement of the moving body and under the excitement of the plane in two perpendicular directions were investigated by numerical methods. It was determined that impact displacement occurs under transient regimes of motion from static to dynamic state of equilibrium. Dependencies of maximum displacement of the body and average displacement velocity on force of elastic resistance, amplitude of plane vibration in the direction of the displacement, and phase angle between the perpendicular members of vibration components were established. Zones of system and excitement parameter combination when the vibrational impact motion occurs were defined.     

On the Hougaard subordinated Gaussian Lévy processes

The Hougaard subordinated multivariate Gaussian Lévy processes are characterized. Necessary and sufficient conditions for their self-decomposability are given and related Ornstein-Uhlenbeck type processes are described.