Nonlinear Dynamics of One-Way Clutches in Belt-Pulley Systems

2003 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Second Primary ◽  
Arc Length ◽  
The One

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modeled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modeled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom (DOF). The harmonic balance method (HBM) combined with arc-length continuation is employed to illustrate the nonlinear dynamic behavior of the one-way clutch. HBM with arc-length continuation yields the stable and unstable periodic solutions for given parameters. These solutions are examined across a range of excitation frequencies. The results are confirmed by numerical integration and the widely used bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening nonlinearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on system parameters such as clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the nonlinear dynamics across a range of conditions.

Electromechanical modelling of piezoelectric vibration energy harvester with a novel dynamic magnifier

2020 ◽  
Vol 87 (9) ◽  
pp. 575-585
Author(s):  
Suresh Kote ◽  
Shankar Krishnapillai ◽  
Sujatha Chandramohan
Keyword(s):  
Output Power ◽  
Output Voltage ◽  
Degrees Of Freedom ◽  
Energy Harvester ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Base Excitation ◽  
Vibration Energy Harvester ◽  
Piezoelectric Energy ◽  
Energy Harvesting Devices

AbstractIn piezoelectric energy harvesting devices, the relative displacement between the two ends of the harvester beam decides the output power from the piezoelectric patch. A novel four bar mechanism with a helical spring is used as a dynamic magnifier to improve the relative displacement and thereby the output power from the harvester. This dynamic magnifier is placed between the base excitation location and the composite harvester beam to form two degrees of freedom (2DOF) piezoelectric energy harvester. Electromechanical coupled analytical equations for the voltage and output power are derived using a lumped electromechanical model. The model is developed assuming linear transverse vibrations of the harvester. A dynamic magnifier is fabricated for the required frequency range and the suitable dimensions of the harvester beam are estimated using commercially available software. Experiments are conducted for base excitation amplitude of 0.05 mm and the performance of the proposed 2DOF harvester is studied for the output voltage and power. The proposed 2DOF harvester has shown 110 % improvement in output power in first mode and 270 % improvement in second mode compared to the conventional single degree of freedom (SDOF) cantilevered harvester for given identical input conditions. The measured frequencies and output power are validated with analytical solutions and are found to be in good agreement. Further, the effect of mass ratio, stiffness ratio and base excitation amplitude on the output voltage and power is investigated using analytical expressions.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

Modeling and Experimental Validations of a Piezoelectric Energy Harvester Under Combined Galloping and Base Excitations

2014 ◽  
Author(s):  
Amin Bibo ◽  
Abdessattar Abdelkefi ◽  
Mohammed F. Daqaq
Keyword(s):  
Bluff Body ◽  
Energy Harvester ◽  
Constitutive Relations ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Beam Theory ◽  
Excitation Amplitude ◽  
The Body ◽  
Base Excitation ◽  
Piezoelectric Energy

This paper develops an experimentally validated model of a piezoelectric energy harvester under combined aeroelastic-galloping and base excitations. To that end, an energy harvester consisting of a thin piezoelectric cantilever beam subjected to vibratory base excitation is considered. To permit galloping excitation, a bluff body is rigidly attached at the free end such that a net aerodynamic lift is generated as the incoming airflow separates on both sides of the body giving rise to limit cycle oscillations when the flow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitation is derived using the energy approach and by adopting the nonlinear Euler-Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The partial differential equations of the system are discretized and a reduced-order-model is obtained. The mathematical model is validated by conducting a series of experiments with different loading conditions represented by wind speed, base excitation amplitude, and excitation frequency around the primary resonance.

Shape Synthesis and Optimization Using Intrinsic Geometry

1990 ◽  
Author(s):  
Shahriar Tavakkoli ◽  
Sanjay G. Dhande
Keyword(s):  
Optimization Problems ◽  
Piecewise Linear ◽  
Shape Design ◽  
Arc Length ◽  
Intrinsic Geometry ◽  
Shape Model ◽  
Design Variables ◽  
Dimensional Shape ◽  
Variable Geometry Truss ◽  
Arc Lengths

Abstract The present paper outlines a method of shape synthesis using intrinsic geometry to be used for two-dimensional shape optimization problems. It is observed that the shape of a curve can be defined in terms of intrinsic parameters such as the curvature as a function of the arc length. The method of shape synthesis, proposed here, consists of selecting a shape model, defining a set of shape design variables and then evaluating Cartesian coordinates of a curve. A shape model is conceived as a set of continuous piecewise linear segments of the curvature; each segment defined as a function of the arc length. The shape design variables are the values of curvature and/or arc lengths at some of the end-points of the linear segments. The proposed method of shape synthesis and optimization is general in nature. It has been shown how the proposed method can be used to find the optimal shape of a planar Variable Geometry Truss (VGT) manipulator for a pre-specified position and orientation of the end-effector. In conclusion, it can be said that the proposed approach requires fewer design variables as compared to the methods where shape is represented using spline-like functions.

Numerical Investigation of the Influence of Friction Coefficient on Brake Groan

2010 ◽  
Vol 44-47 ◽  
pp. 1923-1927 ◽  
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Equilibrium Points ◽  
Static Friction ◽  
Kinetic Friction ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model ◽  
The Stability

A two degrees of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction of brake disk and pads is built firstly, the stability of vibration system at the equilibrium points is analyzed using the nonlinear dynamics theory. Finally the numerical method is taken to study the impacts of friction coefficient on brake groan. The calculation result shows that with the increase of kinetic friction coefficient /or the decrease of difference value between static friction coefficient and kinetic friction coefficient can prevent or restrain self-excited vibration from happening.

Analysis of Subharmonic Resonance Response of the Time-Delayed System

2010 ◽  
Vol 163-167 ◽  
pp. 2910-2915 ◽  
Author(s):  
Hong Zhang ◽  
Xiao Hong Wu ◽  
Lei Zhang
Keyword(s):  
Amplitude Ratio ◽  
Harmonic Balance Method ◽  
Subharmonic Resonance ◽  
Feedback Gain ◽  
Incremental Harmonic Balance Method ◽  
Third Harmonic ◽  
System Parameters ◽  
Resonance Response ◽  
Exciting Frequency ◽  
The One

The subharmonic resonance response of the strongly nonlinear delay differential equation is solved using the incremental harmonic balance method. The value of the exciting frequency when the subharmonic resonance occurs is discussed. The influences of the time delay and the feedback gain on the system subharmonic resonance response are studied. The variation of the subharmonic resonance response with the system parameters is obtained. The results show that the value of the exciting frequency when the subharmonic resonance occurs is affected by the system parameters. The proportion of the one third harmonic in the amplitude increases rapidly with the increase of the exciting frequency. The variation of the amplitude ratio of the one third harmonic and the first harmonic is wavy type. The proportion of the one third harmonic in the amplitude decreases with increasing the displacement feedback gain and increases with increasing the velocity feedback gain. The proportion of the one third harmonic in the amplitude occupies a dominant position in the subharmonic resonance response.

Shock isolation characteristics of a bistable vibration isolator with tunable magnetic controlled stiffness

2021 ◽  
pp. 1-28
Author(s):  
Bo Yan ◽  
Peng Ling ◽  
Yanlin Zhou ◽  
Chuan-yu Wu ◽  
Wen-Ming Zhang
Keyword(s):  
Damping Ratio ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Vibration Isolator ◽  
Maximum Acceleration ◽  
Vibration Isolators ◽  
Displacement Ratio ◽  
Shock Isolation ◽  
Maximum Relative Displacement ◽  
Isolation Performance

Abstract This paper investigates the shock isolation characteristics of an electromagnetic bistable vibration isolator (BVI) with tunable magnetic controlled stiffness. The theoretical model of the BVI is established. The maximum acceleration ratio (MAR), maximum absolute displacement ratio (MADR) and maximum relative displacement ratio (MRDR) are introduced to evaluate the shock isolation performance of the BVI. The kinetic and potential energy are observed to further explore the performance of the BVI. The effects of the potential barrier, shape of potential well, damping ratio on the BVI are discussed compared to the linear vibration isolators (LVI). The results demonstrate that the intrawell oscillations and snap-through oscillations are determined by the excitation amplitude and duration time of main pulse. MADR and MRDR of the BVI are smaller than those of the LVI. The maximum acceleration peak amplitude of the BVI is far below that of the LVI, especially when the snap-through oscillation occurs. In brief, the proposed BVI has a better shock isolation performance than the LVI and has the potential to suppress the shock of space structures during the launch and on-orbit deploying process.

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