Effect of Stiffness Ratio of Piecewise-Linear Spring on the Occurrence of Subharmonic Nonlinear Vibration in Automatic Transmission Powertrain

2015 ◽  
Vol 786 ◽  
pp. 156-160 ◽  
Author(s):  
Takahiro Ryu ◽  
S. Rosbi ◽  
K. Matsuzaki ◽  
T. Nakae ◽  
A. Sueoka ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Nonlinear Vibration ◽  
Forced Vibration ◽  
Piecewise Linear ◽  
Automatic Transmission ◽  
Torque Converter ◽  
Degree Of Freedom ◽  
Stiffness Ratio ◽  
Linear Spring ◽  
Subharmonic Vibration

In the torque converter, a damper with a piecewise-linear spring is used to reduce the forced vibration, and the subharmonic vibration occurs when the spring restoring torque characteristics approach the switching point. This research analyzed the effect of stiffness ratio between the neighboring piecewise-linear springs on the occurrence of the subharmonic nonlinear vibration in automatic transmission powertrain. The powertrain is modeled with multi degree-of-freedom nonlinear system as an actual vehicle. The result shows higher value of the stiffness ratio between the neighboring springs creates larger value of the subharmonic vibration.

scholarly journals Fundamental study on countermeasures against subharmonic vibration of order 1/2 in automatic transmissions for cars

2018 ◽  
Vol 211 ◽  
pp. 13004
Author(s):  
Fumiya Takino ◽  
Takahiro Ryu ◽  
Takashi Nakae ◽  
Kenichiro Matsuzaki ◽  
Risa Ueno
Keyword(s):  
Piecewise Linear ◽  
Vibration Reduction ◽  
System Model ◽  
Torsional Vibrations ◽  
Fundamental Study ◽  
Automatic Transmissions ◽  
Linear Spring ◽  
Low Stiffness ◽  
Subharmonic Vibration ◽  
The One

In automatic transmissions for cars, a damper is installed in the lock-up clutch to absorb torsional vibrations caused by combustion in the engine. Although a damper with low stiffness reduces the torsional vibration, low-stiffness springs are difficult to use because of space limitations. To address this problem, dampers have been designed using a piecewise-linear spring having three different stages of stiffness. However, a nonlinear subharmonic vibration of order 1/2 occurs because of the nonlinearity of the piecewise-linear spring in the damper. In this study, we experimentally and analytically examined a countermeasure against the subharmonic vibration by increasing the stages of the piecewise-linear spring using the one-degree-of-freedom system model. We found that the gap between the switching points of the piecewise-linear spring was the key to vibration reduction. The experimental results agreed with results of the numerical analyses.

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

Dynamic Temperature Testing and Modeling for an Automatic Transmission Clutch

2001 ◽  
Author(s):  
Thomas DeMurry ◽  
Yanying Wang
Keyword(s):  
Experimental Data ◽  
Real Time ◽  
Automatic Transmission ◽  
Thermal Characteristics ◽  
Torque Converter ◽  
Telemetry System ◽  
Temperature Model ◽  
And Control ◽  
Good Agreement ◽  
Dynamometer Test

Abstract The primary objectives of this study are (1) to validate the hardware design and control methodologies for preserving the thermo-mechanical integrity of a launch clutch emulating a torque converter and (2) to develop a simple, control oriented clutch-temperature model that may act as a virtual thermocouple in the processor of an automobile for real-time clutch-temperature predictions. In a dynamometer test cell, a Ford CD4E transaxle is instrumented with a thermocouple-based telemetry system to investigate clutch thermal characteristics during engagements, neutral idle, single and repeated launching, torsional isolation, and hill holding. A nonlinear, SIMULINK™-based model for estimating temperature is developed. The results from the simulations are in good agreement with the experimental data.

scholarly journals Feedback control for two-degree-of-freedom vibration system with fractional-order derivative damping

2017 ◽  
Vol 37 (3) ◽  
pp. 554-564
Author(s):  
Canchang Liu ◽  
Chicheng Ma ◽  
Jilei Zhou ◽  
Lu Liu ◽  
Shuchang Yue ◽  
...  
Keyword(s):  
Feedback Control ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Suspension System ◽  
Degree Of Freedom ◽  
Vehicle Suspension ◽  
Vibration System ◽  
Fractional Order Derivative ◽  
Vehicle Suspension System ◽  
Two Degree Of Freedom

A two-degree-of-freedom nonlinear vibration system of a quarter vehicle suspension system is studied by using the feedback control method considered the fractional-order derivative damping. The nonlinear dynamic model of two-degree-of-freedom vehicle suspension system is built and linear velocity and displacement controllers are used to control the nonlinear vibration of the vehicle suspension system. A case of the 1:1 internal resonance is considered. The amplitude–frequency response is obtained with the multiscale method. The asymptotic stability conditions of the nonlinear system can be gotten by using the Routh–Hurwitz criterion and the ranges of control parameters are gained in the condition of stable solutions to the system. The simulation results show that the feedback control can effectively reduce the amplitude of primary resonance, weaken or even eliminate the nonlinear vibration characteristics of the suspension system. Fractional orders have an impact on control performance, which should be considered in the control problem. The study will provide a theoretical basis and reference for the optimal design of the vehicle suspension system.

scholarly journals Experimental feedback linearisation of a non-smooth nonlinear system by the method of receptances

2018 ◽  
Vol 24 (2) ◽  
pp. 465-482 ◽  
Author(s):  
Domenico Lisitano ◽  
Shakir Jiffri ◽  
Elvio Bonisoli ◽  
John E Mottershead
Keyword(s):  
Nonlinear System ◽  
Dynamic Behaviour ◽  
Complete System ◽  
Degree Of Freedom ◽  
System Matrix ◽  
The Third ◽  
Partial Feedback ◽  
Lumped Masses ◽  
First Time ◽  
Experimental Rig

Input–output partial feedback linearisation is experimentally implemented on a non-smooth nonlinear system without the necessity of a conventional system matrix model for the first time. The experimental rig consists of three lumped masses connected and supported by springs with low damping. The input and output are at the first degree of freedom with a non-smooth clearance-type nonlinearity at the third degree of freedom. Feedback linearisation has the effect of separating the system into two parts: one linear and controllable and the other nonlinear and uncontrollable. When control is applied to the former, the latter must be shown to be stable if the complete system is to be stable with the desired dynamic behaviour.

Forced Vibration of Systems With Nonlinear, Nonsymmetrical Characteristics

1957 ◽  
Vol 24 (3) ◽  
pp. 435-439
Author(s):  
S. Mahalingam
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Nonlinear Vibration ◽  
Forced Vibration ◽  
Free Vibrations ◽  
Frequency Function ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Nonlinear Vibration Absorber ◽  
Single Degree

Abstract A one-term approximate solution is given for the amplitudes of steady forced vibration of a single-degree-of-freedom system with a nonlinear (nonsymmetrical) spring characteristic. The method is similar to that of Martienssen (1), but the construction uses a modified curve (or “frequency function”) in place of the actual spring characteristic, the curve being so chosen that it gives the correct frequency for free vibrations. The method is extended to deal with a nonlinear vibration absorber fitted to a linear system.

Uniformly Bounded Input Gives Ultimately Bounded Output: On the Dynamics of a Piecewise Linear Beam System

1999 ◽  
Author(s):  
Marcel F. Heertjes ◽  
Marinus J. G. van de Molengraft ◽  
Jan J. Kok
Keyword(s):  
Periodic Solution ◽  
Piecewise Linear ◽  
Wave Force ◽  
Degree Of Freedom ◽  
Harmonic Force ◽  
Periodic Force ◽  
Beam System ◽  
Bounded Input ◽  
Uniformly Bounded

Abstract A periodically excited piecewise linear beam system is studied. The beam system consists of a supported multi-degree-of-freedom beam with one-sided spring. This system is proved to have a 1-periodic solution to any uniformly bounded periodic force applied along the beam. The existence of a 1-periodic solution will be shown numerically and experimentally for both a harmonic force and a block-wave force.

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