# Dynamics of a milkshaker - Passage through resonance and frequency transformation

## Abstract

Rotor dynamics is a fascinating subject both from an experimental and a theoretical point of view. Most often experiments on various phenomena require more or less sophisticated test rigs, either because the experiments are dangerous or because the effects are difficult to reproduce. In teaching it is, however, beneficial to have experiments that are simple and can be performed by the students themselves. One of these examples is a standard milkshaker, which at a closer look, exhibits rich dynamical phenomena. The first phenomenon that can be observed and studied is the passage through resonance. Depending on the eccentricity of the rotor, the driving torque of the motor is strong enough or not to reach supercritical speeds. If for a given torque the eccentricity is too large, the system gets stuck in the resonance with a rather large amplitude. A second phenomenon that can be observed is the following: When the milkshaker is placed on an even surface it starts to move on the surface. The movement is caused by a wobbling motion of the system due to the eccentricity. Although the angular velocity of the rotor is high, the motion on the surface is quite slow in comparison. This is an interesting phenomenon that can be related to mechanical frequency transformation which occurs in the contact between the milkshaker and the ground. Depending on whether the rotor is running in a supercritical range or stuck below the resonance frequency, different motions can be observed. The system can be analyzed with a relatively simple nonlinear rigid body model. In this paper we study both phenomena mentioned above from a theoretical point of view. The equations of motion are derived in analytical form and their nonlinear behavior is investigated. Due to its relatively simple nature, the system has been used in lectures as a demonstrator and for student tutorial projects.

Item Type: Article 2012 Spelsberg-Korspeter, G. and Heffel, Eduard Dynamics of a milkshaker - Passage through resonance and frequency transformation English Rotor dynamics is a fascinating subject both from an experimental and a theoretical point of view. Most often experiments on various phenomena require more or less sophisticated test rigs, either because the experiments are dangerous or because the effects are difficult to reproduce. In teaching it is, however, beneficial to have experiments that are simple and can be performed by the students themselves. One of these examples is a standard milkshaker, which at a closer look, exhibits rich dynamical phenomena. The first phenomenon that can be observed and studied is the passage through resonance. Depending on the eccentricity of the rotor, the driving torque of the motor is strong enough or not to reach supercritical speeds. If for a given torque the eccentricity is too large, the system gets stuck in the resonance with a rather large amplitude. A second phenomenon that can be observed is the following: When the milkshaker is placed on an even surface it starts to move on the surface. The movement is caused by a wobbling motion of the system due to the eccentricity. Although the angular velocity of the rotor is high, the motion on the surface is quite slow in comparison. This is an interesting phenomenon that can be related to mechanical frequency transformation which occurs in the contact between the milkshaker and the ground. Depending on whether the rotor is running in a supercritical range or stuck below the resonance frequency, different motions can be observed. The system can be analyzed with a relatively simple nonlinear rigid body model. In this paper we study both phenomena mentioned above from a theoretical point of view. The equations of motion are derived in analytical form and their nonlinear behavior is investigated. Due to its relatively simple nature, the system has been used in lectures as a demonstrator and for student tutorial projects. Mathematical Modelling 7 1 IFAC 16 Department of Mechanical Engineering16 Department of Mechanical Engineering > Dynamics and VibrationsExzellenzinitiativeExzellenzinitiative > Graduate SchoolsExzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)Zentrale Einrichtungen 28 May 2014 12:52 doi:10.3182/20120215-3-AT-3016.00207 ASCII CitationReference ManagerBibTeXSimple MetadataMultiline CSVHTML CitationDublin CoreJSONEndNoteAtomMODST2T_XMLEP3 XMLRDF+XML TUfind oder in Google

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