Nonlinear Periodic Response of Engine Accessory Drives With Dry Friction Tensioners

1998 ◽  
Vol 120 (4) ◽  
pp. 909-916 ◽  
Author(s):  
M. J. Leamy ◽  
N. C. Perkins
Keyword(s):  
Dry Friction ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Incremental Harmonic Balance Method ◽  
Stick Slip ◽  
Automotive Engine ◽  
Wide Range ◽  
Serpentine Belt ◽  
Nonlinear Equations Of Motion

Belt drives have long been utilized in engine applications to power accessories such as alternators, pumps, compressors and fans. Drives employing a single, flat, “serpentine belt” tensioned by an “automatic tensioner” are now common in automotive engine applications. The automatic tensioner helps maintain constant belt tension and to dissipate unwanted belt drive vibration through dry friction. The objective of this study is to predict the periodic rotational response of the entire drive to harmonic excitation from the crankshaft. To this end, a multi-degree of freedom incremental harmonic balance method (IHB) is utilized to compute periodic solutions to the nonlinear equations of motion over a wide range of engine speeds. Computed results illustrate primary and secondary resonances of the accessory drive and tensioner stick-slip motions.

Periodic Response of Front End Accessory Drives With Dry Friction

1997 ◽  
Author(s):  
Michael J. Leamy ◽  
Noel C. Perkins
Keyword(s):  
Dry Friction ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Stick Slip ◽  
Automotive Engine ◽  
Belt Drives ◽  
Wide Range ◽  
Serpentine Belt ◽  
Incremental Harmonic Balance ◽  
Nonlinear Equations Of Motion

Abstract Belt drives have long been utilized in engine applications to power accessories such as alternators, pumps, compressors and fans. Drives employing a single, flat, ‘serpentine belt’ tensioned by an ‘automatic tensioner’ are now common in automotive engine applications. The automatic tensioner helps maintain constant belt tension and to dissipate unwanted belt drive vibration through dry friction. The objective of this study is to predict the periodic rotational response of the entire drive to harmonic excitation from the crankshaft. To this end, a multi-degree of freedom incremental harmonic balance (IHB) method is utilized to compute periodic solutions to the nonlinear equations of motion over a wide range of engine speeds. Computed results illustrate primary and secondary resonances of accessories and tensioner stick-slip motions.

A Study of Dynamic Instability of Plates by an Extended Incremental Harmonic Balance Method

1985 ◽  
Vol 52 (3) ◽  
pp. 693-697 ◽  
Author(s):  
C. Pierre ◽  
E. H. Dowell
Keyword(s):  
Harmonic Balance ◽  
Dynamic Instability ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Mathieu Equation ◽  
Equation System ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
Nonlinear Equations Of Motion

The dynamic instability of plates is investigated with geometric nonlinearities being included in the model, which allows one to determine the amplitude of the parametric vibrations. A modal analysis allowing one spatial mode is performed on the nonlinear equations of motion and the resulting nonlinear Mathieu equation is solved by the incremental harmonic balance method, which takes several temporal harmonics into account. When viscous damping is included, a new algorithm is proposed to solve the equation system obtained by the incremental method. For this purpose, a new characterization of the parametric vibration by its total amplitude—or Euclidian norm—is introduced. This algorithm is particularly simple and convenient for computer implementation. The instability regions are obtained with a high degree of accuracy.

Large Amplitude Forced Vibrations of Simply Supported Thin Cylindrical Shells

1973 ◽  
Vol 40 (2) ◽  
pp. 471-477 ◽  
Author(s):  
J. H. Ginsberg
Keyword(s):  
Nonlinear Response ◽  
Nonlinear Boundary ◽  
Circular Cylindrical Shell ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Inertia Effects ◽  
Modal Expansion ◽  
Wide Range ◽  
Nonlinear Equations Of Motion

The response of a thin circular cylindrical shell to resonant harmonic excitation is examined by a modal expansion approach. The nonlinear strain-displacement relations lead to a nonlinear boundary condition, as well as nonlinear equations of motion. The solution, which retains tangential inertia effects, is obtained by a perturbation technique that yields a consistent first approximation of the nonlinear response. The results are applicable for a wide range of parameters and to cases of excitation near any of the three lowest natural frequencies corresponding to given axial and circumferential wavelengths. For situations where shallow shell theory is valid, the results of previous studies, which were based upon such a theory, are in close agreement.

Energy Balancing Method to Identify Nonlinear Damping of Bolted-Joint Interface

2016 ◽  
Vol 693 ◽  
pp. 318-323 ◽  
Author(s):  
Xin Liao ◽  
Jian Run Zhang
Keyword(s):  
Dry Friction ◽  
Harmonic Excitation ◽  
Joint Interface ◽  
Damping Factor ◽  
Viscous Damping ◽  
Bolted Joint ◽  
Energy Balancing ◽  
Stick Slip ◽  
Non Linear ◽  
Linear Damping

The interface of bolted joint commonly focuses on the research of non-linear damping and stiffness, which affect structural response. In the article, the non-linear damping model of bolted-joint interface is built, consisting of viscous damping and Coulomb friction. Energy balancing method is developed to identify the dry-friction parameter and viscous damping factor. The corresponding estimation equations are acquired when the input is harmonic excitation. Then, the vibration experiments with different bolted preloads are conducted, from which amplitudes in various input levels are used to work out the interface parameters. Also, the fitting curves of dry-friction parameters are also obtained. Finally, the results illustrate that the most interface of bolted joint in lower excitation levels occurs stick-slip motion, and the feasibility of the identification approach is demonstrated.

Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method

1985 ◽  
Vol 52 (4) ◽  
pp. 958-964 ◽  
Author(s):  
C. Pierre ◽  
A. A. Ferri ◽  
E. H. Dowell
Keyword(s):  
Time Domain ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Frequency Domain Analysis ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
The Time Domain ◽  
Damped Systems

A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.

Nonlinear Truck Ride Analysis

1974 ◽  
Vol 96 (2) ◽  
pp. 597-602 ◽  
Author(s):  
G. R. Potts ◽  
H. S. Walker
Keyword(s):  
Numerical Integration ◽  
Nonlinear Equations ◽  
Digital Computer ◽  
Dry Friction ◽  
Shock Absorber ◽  
Equations Of Motion ◽  
Deflection Curve ◽  
Force Velocity ◽  
Nonlinear Equations Of Motion ◽  
Dry Friction Damping

The nonlinear vibratory motions of a three-axle semitrailer truck were investigated via the use of a digital computer. The nonlinear equations of motion are presented and a method of numerical integration is discussed. The analysis allows any shape of suspension force-deflection curve (including wheel hop, suspension stops, and dry friction damping) and a similar liberality of shock absorber force-velocity characteristics. An experimental vibration study, performed on a model truck, is described and the results compare favorably with the calculated results of the numerical integration.

The Forced Oscillation of the Centrifugal Pendulum With Wide Angles

1953 ◽  
Vol 20 (1) ◽  
pp. 41-47
Author(s):  
F. R. E. Crossley
Keyword(s):  
Forced Oscillation ◽  
Torsional Oscillation ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Harmonic Order ◽  
Pendulum Motion ◽  
Type Curves ◽  
Effective Dynamic ◽  
Nonlinear Equations Of Motion ◽  
Effective Resonance

Abstract The simple pendulum mounted to a rotor suffering torsional oscillation is used as an effective dynamic damper which may be tuned to any one harmonic order of vibration. The nonlinear equations of motion are here developed to investigate whether wider angles of swing, or whether larger or smaller sizes of pendulum relative to its carrier, are more effective. Resonance-type curves are drawn by assuming a single harmonic excitation and hyperelliptic pendulum motion without damping; it is shown that theoretically oscillations up to 90 deg may be used which are predictable, and that in all cases the tuning must be higher than that indicated by small-angle theory.

Nonlinear Dynamics of Shrouded Turbine Blade System with Impact and Friction

2014 ◽  
Vol 706 ◽  
pp. 81-92 ◽  
Author(s):  
B. Santhosh ◽  
S. Narayanan ◽  
C. Padmanabhan
Keyword(s):  
Frequency Response ◽  
Turbine Blade ◽  
Dry Friction ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Tangential Direction ◽  
Stick Slip ◽  
Variable Friction ◽  
Blade System ◽  
Constant Normal Load

Dry friction dampers are passive devices used to reduce the resonant vibration amplitudes in turbine bladed systems. In shrouded turbine blade systems, in addition to the stick- slip motion induced by dry friction during the contact state in the tangential direction, the interface also undergoes intermittent separation in the normal direction. The problem can thus be treated as a combination of impact and friction. In this work, the dynamics of dry friction damped oscillators which are representative models of dry friction damped bladed system is investigated. A one dimensional contact model which is capable of modeling the interface under constant and variable normal load is used. The steady state periodic solutions are obtained by multi - harmonic balance method (MHBM). Frequency response plots are generated for different values of normal load using the arc length continuation procedure. The MHBM solutions are validated using numerical integration. A single degree of freedom (dof) model under constant normal load with constant and variable friction coefficients, a dry friction damped two dof system under constant normal load and a two dof system under variable normal load are investigated. In the presence of variable normal load, the system shows multivalued frequency response and jump phenomenon. The optimal value of the normal load which gives minimum resonant response is also obtained.

Influence of Tensioner Dry Friction on the Vibration of Belt Drives With Belt Bending Stiffness

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Dry Friction ◽  
Harmonic Balance ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Friction Torque ◽  
Stick Slip ◽  
Pulley System ◽  
Coulomb Damping ◽  
Belt Drives ◽  
Linear Subsystem

A model of dry friction tensioner in a belt-pulley system considering transverse belt vibration is developed, and the influence of the dry friction on the system dynamics is examined. The discretized formulation is divided into a linear subsystem including linear coordinates and a nonlinear subsystem addressing tensioner arm vibration, which reduces the dimension of the iteration matrices when employing the harmonic balance method. The Coulomb damping at the tensioner arm pivot mitigates the tensioner arm vibration but not necessarily the vibrations of other system components. The extent of the mitigation varies for different excitation frequency ranges. The critical amplitude of the dry friction torque beyond which the system operates with a locked arm is determined analytically. Superharmonic resonances are observed in the responses of the generalized span coordinates, but their amplitudes are small. The energy dissipation at the tensioner arm hub is discussed, and the stick-slip phenomena of the arm are reflected in the velocity reversals near the arm extreme location. Dependence of the span tension fluctuations on Coulomb torque is explored.

Influence of Nonlinear Wheel/Rail Contact Geometry on Stability of Rail Vehicles

1977 ◽  
Vol 99 (1) ◽  
pp. 172-185 ◽  
Author(s):  
R. Hull ◽  
N. K. Cooperrider
Keyword(s):  
Dry Friction ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Rail Vehicles ◽  
Freight Car ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Lateral Behavior ◽  
Hunting Stability

Nonlinear behavior caused by wheel flanges, worn wheel treads, and dry friction can have an important effect on rail-vehicle stability. In this paper the influence of such nonlinearities on the stability of rail freight vehicles is investigated using quasi-linearization techniques. Nonlinear equations of motion are presented that describe the lateral behavior of a 9-degree-of-freedom representation of a complete freight car with three-piece trucks. The nonlinear wheel/rail geometric constraint functions for the rolling radii, angle of wheel/rail contact, and wheelset roll angle are found by a numerical technique. The suspension description includes dry friction where appropriate. The hunting stability of the freight car is studied by employing describing-function techniques. Results are presented for a typical freight car with three different wheel profiles. The stability results illustrate the dependence of behavior on the amplitudes of vehicle motions. Application of the results in realistic situations and suggestions for future quasi-linear studies are discussed.

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