Screw Theory Applied to a Rigid Cylinder Moving on a Plane

2011 ◽  
Author(s):  
James Di´az-Gonza´lez ◽  
Lourdes Rosario
Keyword(s):  
Coulomb Friction ◽  
Screw Theory ◽  
Cylindrical Part ◽  
Rolling Motion ◽  
Harmonic Force ◽  
Friction Forces ◽  
Dimensionless Variable ◽  
Static Plane ◽  
Vibration Parameters ◽  
External Harmonic Force

In this work a mathematical model of the motion of a cylinder moving on a plane is deduced using screw theory. The linear Coulomb friction equations are applicable for the maximum static and kinetic friction forces. In the case of the rolling motion of a cylinder, the friction forces are not necessarily maxima. This paper describes the dynamic states of motion of a cylindrical part moving in three separate scenarios by the Euler dual equation. The first scenario is when the cylinder is moving on a horizontal static plane due to an external harmonic force proportional to the mass of the part. For this case, the sliding conditions are expressed as a function of the vibration parameters and generalized based on a harmonic dimensionless variable. The second and third scenarios are when the cylinder is moving by translational displacements on a horizontal and inclined plane.

scholarly journals Vibroimpact Mobile Robot

2021 ◽  
Vol 17 (4) ◽  
pp. 429-436
Author(s):  
A. P. Ivanov ◽  
Keyword(s):  
Simple Model ◽  
Mobile Robot ◽  
Periodic Motion ◽  
Horizontal Plane ◽  
Coulomb Friction ◽  
Average Velocity ◽  
Moving Mass ◽  
Harmonic Force ◽  
Maximal Average ◽  
The Right

A simple model of a capsule robot is studied. The device moves upon a rough horizontal plane and consists of a capsule with an embedded motor and an internal moving mass. The motor generates a harmonic force acting on the bodies. Capsule propulsion is achieved by collisions of the inner body with the right wall of the shell. There is Coulomb friction between the capsule and the support, it prevents a possibility of reversal motion. A periodic motion is constructed such that the robot gains the maximal average velocity.

Model-Based Analysis of Friction-Induced Sub-Synchronous Whirl for a Rotor Contacting With Clearance Bearings Under Axial Load

2015 ◽  
Author(s):  
Matthew O. T. Cole ◽  
Lawrence Hawkins
Keyword(s):  
Axial Load ◽  
Coulomb Friction ◽  
Friction Forces ◽  
Root Finding ◽  
Model Based ◽  
Simple Physical Interpretation ◽  
Level Of Agreement ◽  
Model Based Analysis

For rotors supported by active magnetic bearings (AMBs), clearance bearings are commonly used to provide backup support under loss of AMB functionality. Test data from real machines shows that rotor vibration during touchdown on backup bearings may involve steady forward whirling at a sub-synchronous frequency. This excitation is believed to be due to friction forces transmitted between the rotor and a bearing end-face under axial load. This paper proposes a new analytical approach to model and predict such friction-driven forward whirl behaviors. A set of constraint equations are derived that relate a circular whirl motion of arbitrary orbital speed to the frequency response functions of the rotor-housing structure. This model is coupled with an evaluation of Coulomb friction associated with slip between the rotor and the supporting end-face of a thrust bearing. The resulting equations can be used to compute a set of possible whirl motions via a root-finding procedure. A case study is undertaken for a 140 kW energy storage flywheel. Model-based predictions are compared with measured data from spin-down tests and show a good level of agreement. The study confirms the role of friction-related forces in driving forward-whirl response behaviors. It also highlights the key role of housing and machine support characteristics in response behavior. This influence is shown to be complex and not open to simple physical interpretation. Therefore, the proposed analytical method is seen as a useful tool to investigate this influence while avoiding the need for time consuming numerical simulations.

On Some Problems With Modeling of Coulomb Friction in Self-Locking Speed Reducers

2014 ◽  
Author(s):  
Marek Wojtyra
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Equations Of Motion ◽  
Velocity Ratio ◽  
Friction Forces ◽  
Friction Law ◽  
Rigid Body Model ◽  
Feasible Sets ◽  
Unstable Solutions ◽  
Coulomb Friction Law

A simple mathematical model of friction in speed reducers is presented and discussed. A rigid body approach, typical for multibody simulations, is adopted. The model is based on the Coulomb friction law and exploits the analogy between reducers and wedge mechanisms. The first version of the model is purely rigid, i.e. no deflections of the mechanism bodies are allowed. Constraints are introduced to maintain the ratio between input and output velocity. It is shown that when friction is above the self-locking limit, paradoxical situations may be observed when kinetic friction is investigated. For some sets of parameters of the mechanism (gearing ratio, coefficient of friction and inertial parameters) two distinct solutions of normal and friction forces can be found. Moreover, for some combinations of external loads, a solution that satisfies equations of motion, constraints and Coulomb friction law does not exist. Furthermore, for appropriately chosen loads and parameters of the mechanism, infinitely many feasible sets of normal and friction forces can be found. Examples of all indicated paradoxical situations are provided and discussed. The second version of the model allows deflection of the frictional contact surface, and forces proportional to this deflection are applied to contacting bodies (no constraints to maintain the input-output velocity ratio are introduced). In non-paradoxical situations the obtained results are closely similar to those predicted by the rigid body model. In previously paradoxical situations no multiple solutions of friction force are found, however, the amended model does not solve all problems. It is shown that in regions for which the paradoxes were observed only unstable solutions are available. Numerical examples showing behavior of the model are provided and analyzed.

scholarly journals Manipulating Single Enzymes by an External Harmonic Force

2007 ◽  
Vol 98 (16) ◽  
Author(s):  
Michael A. Lomholt ◽  
Michael Urbakh ◽  
Ralf Metzler ◽  
Joseph Klafter
Keyword(s):  
Harmonic Force ◽  
External Harmonic Force

Nonlinear argumental oscillators: A few examples of modulation via spatial position

2016 ◽  
Vol 23 (18) ◽  
pp. 2888-2911 ◽  
Author(s):  
Daniel Cintra ◽  
Pierre Argoul
Keyword(s):  
Magnetic Field ◽  
Spatial Localization ◽  
Spatial Position ◽  
Experimental Results ◽  
Harmonic Force ◽  
Van Der Pol ◽  
Stable Regime ◽  
Van Der Pol Representation ◽  
Localized Magnetic Field ◽  
External Harmonic Force

Under certain conditions, an oscillator can enter a stable regime when submitted to an external harmonic force whose frequency is far from the natural frequency of the oscillator. This may happen when the external force acts on the oscillator in a way which depends on the oscillator's spatial position. This phenomenon is called “argumental oscillation”. In this paper, six argumental oscillators are described and modeled, and experimental results are given and compared to numerical simulations based on the models. A polar Van der Pol representation, with embedded time indications, is used to allow a precise comparison. The pendulums are modeled as Duffing oscillators. The six models are based on various pendulums excited by spatially localized magnetic-field sources consisting of wire coils. Each pendulum receives the excitation via a steel element, or a permanent magnet, fitted at the tip of the pendulum's rod. The spatial localization induces another nonlinearity besides the Duffing nonlinearity. A control system allowing a real-time Van der Pol representation of the motion is presented. Attractors are brought out from experimental results.

scholarly journals REACTANCES AND SUSCEPTANCES OF MECHANICAL SYSTEMS

2021 ◽  
pp. 64-75
Author(s):  
I.P. Popov ◽  
Keyword(s):  
Steady State ◽  
Mechanical System ◽  
Mechanical Systems ◽  
Harmonic Force ◽  
Parallel Connection ◽  
Electrical Circuits ◽  
Major Interest ◽  
Inert Body ◽  
Complex Mechanical Systems ◽  
External Harmonic Force

The classical solution to the problems associated with calculating the velocities and reactions of elements of complex mechanical systems under harmonic force consists in the compilation and integration of systems of differential equations and is rather cumbersome and time-consuming. In most cases, a steady state is of major interest. The purpose of this study is to develop essentially compact methods for calculating systems under steady-state conditions. The problem is solved by the methods which are typically used to calculate electrical circuits. Representation of harmonic quantities as rotating vectors in a complex plane and the operations with their complex amplitudes can greatly facilitate the calculation of arbitrarily complex mechanical systems under harmonic effects in the steady state. In the proposed method, a key role is played by mechanical reactance, resistance, and impedance for the parallel connection of consumers of mechanical power, as well as susceptance, conductance, and admittance for the serial one. At force resonance, the total reactance of the mechanical system is zero. This means that the system does not exhibit reactive resistance to the external harmonic force. At velocity resonance, the total susceptibility of the mechanical system is zero. This means that the system has infinitely high resistance to the external harmonic force. As a result, the stock of the source of harmonic force is stationary, although the inert body and the elastic element oscillate.

Model-Based Analysis of Friction-Induced Subsynchronous Whirl for a Rotor Contacting With Clearance Bearings Under Axial Load

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Matthew O. T. Cole ◽  
Lawrence Hawkins
Keyword(s):  
Axial Load ◽  
Coulomb Friction ◽  
Friction Forces ◽  
Root Finding ◽  
Model Based ◽  
Simple Physical Interpretation ◽  
Level Of Agreement ◽  
Model Based Analysis

For rotors supported by active magnetic bearings (AMBs), clearance bearings are commonly used to provide backup support under loss of AMB functionality. Test data from real machines shows that vibration during touchdown on backup bearings may involve steady forward whirling of the rotor with a subsynchronous frequency. This excitation is believed to be due to friction forces transmitted between the rotor and a bearing end-face under axial load. This paper proposes a new analytical approach to model and predict such friction-driven forward whirl behaviors. A set of constraint equations are derived that relate a circular whirl motion of arbitrary orbital speed to the frequency response functions for the rotor-housing structure. This model is coupled with an evaluation of Coulomb friction associated with slip between the rotor and the supporting end-face of a thrust bearing. The resulting equations can be used to compute a set of possible whirl motions via a root-finding procedure. A case study is undertaken for a 140 kW energy storage flywheel. Model-based predictions are compared with measured data from spin-down tests and show a good level of agreement. The study confirms the role of friction-related forces in driving forward-whirl response behaviors. It also highlights the key role of housing and machine support characteristics in response behavior. This influence is shown to be complex and not open to simple physical interpretation. Therefore, the proposed analytical method is seen as a useful tool to investigate this influence while avoiding the need for time consuming numerical simulations.

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