Suspended Decoupler Design of Hydraulic Engine Mount

2011 ◽  
Author(s):  
Reza N. Jazar ◽  
M. Mahinfalah ◽  
J. Christopherson
Keyword(s):  
Steady State ◽  
Transient Response ◽  
Equations Of Motion ◽  
State Behavior ◽  
State Response ◽  
Nonlinear Finite Elements ◽  
Lumped Parameter ◽  
Start Up ◽  
Engine Mount ◽  
Static Conditions

A known problem in classical hydraulic engine mount is that because of the density mismatch between the decoupler and surrounding fluid, the decoupler might float, or stick to the cage bounds, assuming static conditions. The problem appears in the transient response of a bottomed up floating decoupler hydraulic engine mount. To overcome the bottomed up problem, a suspended decoupler design for improved decoupler control is introduced. The new design does not noticeably effect the mechanisms steady state behavior, but improves start up and transient response. Additionally, the decoupler mechanism is incorporated into a smaller, lighter, yet more tunable and hence more effective hydraulic mount design. Ususally the elastomechanical components in a hydraulic engine mount are assumed lumped and linear. To have a more realistic modeling, utilizing nonlinear finite elements in conjunction with a lumped parameter modeling approach, we evaluate the resorting characteristics of the components and implement them in the equations of motion. The steady state response of a dimensionless model of the mount is examined utilizing the averaging perturbation method applied to a set of second order nonlinear ordinary differential equations. It is shown that the frequency responses of the floating and suspended decoupled designs are similar and functional.

scholarly journals Suspended Decoupler: A New Design of Hydraulic Engine Mount

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. Christopherson ◽  
M. Mahinfalah ◽  
Reza N. Jazar
Keyword(s):  
Steady State ◽  
Transient Response ◽  
Equations Of Motion ◽  
State Behavior ◽  
Engine Mounts ◽  
Nonlinear Finite Elements ◽  
Lumped Parameter ◽  
Start Up ◽  
Engine Mount ◽  
Static Conditions

Because of the density mismatch between the decoupler and surrounding fluid, the decoupler of all hydraulic engine mounts (HEM) might float, sink, or stick to the cage bounds, assuming static conditions. The problem appears in the transient response of a bottomed-up floating decoupler hydraulic engine mount. To overcome the bottomed-up problem, a suspended decoupler design for improved decoupler control is introduced. The new design does not noticeably affect the mechanism's steady-state behavior, but improves start-up and transient response. Additionally, the decoupler mechanism is incorporated into a smaller, lighter, yet more tunable and hence more effective hydraulic mount design. The steady-state response of a dimensionless model of the mount is examined utilizing the averaging perturbation method applied to a set of second-order nonlinear ordinary differential equations. It is shown that the frequency responses of the floating and suspended decoupled designs are similar and functional. To have a more realistic modeling, utilizing nonlinear finite elements in conjunction with a lumped parameter modeling approach, we evaluate the nonlinear resorting characteristics of the components and implement them in the equations of motion.

Periodic Motions of a Two-Body System Subjected to Repetitive Impact

1969 ◽  
Vol 91 (4) ◽  
pp. 931-938 ◽  
Author(s):  
David L. Sikarskie ◽  
Burton Paul
Keyword(s):  
Steady State ◽  
High Speed ◽  
Equations Of Motion ◽  
Point Of View ◽  
State Behavior ◽  
State Response ◽  
Stability Of Solution ◽  
Straightforward Method ◽  
Parametric Studies ◽  
Repetitive Impact

The dynamics of a widely used class of hammer impact machines are investigated on the basis of a two-degree-of-freedom idealization. The difficulty in the problem is due to the repetitive impact which introduces a nonlinearity in the system. It is the purpose of the analysis to develop a solution for the steady-state behavior of the system. There are several ways this can be done. One of the most efficient ways, from the point of view of ease of parametric studies of the system, is to convert the problem to a “boundary” value problem. With this technique, the system is governed by the equations of motion between impacts, and further satisfies additional conditions at the beginning and end of each impact cycle. Since the solution is obtained in only one cycle, it thus represents a straightforward method of studying the effect of various system parameters. A fundamental assumption in the analysis is that the steady-state response of the system has a period equal to the forcing period. This is verified for one set of parameters through the use of high-speed movies of an actual machine. There are several other interesting features in the analysis, including multivaluedness of the solution, allowable solution domain, and stability of solution, which have not been completely resolved to date.

Development of a New Design Hydraulic Engine Mount

2005 ◽  
Author(s):  
G. Nakhaie Jazar ◽  
J. Christopherson
Keyword(s):  
Steady State ◽  
Nonlinear Model ◽  
State Behavior ◽  
Design Flexibility ◽  
Fluid Behavior ◽  
Start Up ◽  
Hysteretic Damping ◽  
Elastomeric Materials ◽  
Engine Mount ◽  
Steady State Behavior

In this paper a new design of the passive hydraulic engine mount is introduced. A means for improved decoupler control is introduced that does not noticeably affect the mechanisms steady state behavior, but improves start up and transient response. In addition, the decoupler mechanism is incorporated into a smaller, lighter, yet more tunable and hence more effective hydraulic mount design. The performance of the new hydraulic mount is discussed by means of a full nonlinear model. The increased design flexibility afforded by the redesigned support structure provides means by which to tune the engine mount to various engine support configurations. In addition, the proposed mount does not rely as heavily on hysteretic damping provided through elastomeric materials, which can be difficult to control, but more so on fluid behavior inside the engine mount; therefore, the damping of the system is much more tunable than previous hydraulic engine mount designs.

Sensitivity Analysis for the Steady-State Response of Damped Linear Elastodynamic Systems Subject to Periodic Loads

1990 ◽  
Author(s):  
Daniel A. Tortorelli
Keyword(s):  
Steady State ◽  
Vibration Amplitude ◽  
Equations Of Motion ◽  
Steady State Response ◽  
Analysis Techniques ◽  
Direct Differentiation ◽  
State Response ◽  
Need To Evaluate ◽  
The Time Domain ◽  
General Response

Abstract Adjoint and direct differentiation methods are used to formulate design sensitivities for the steady-state response of damped linear elastodynamic systems that are subject to periodic loads. Variations of a general response functional are expressed in explicit form with respect to design field perturbations. Modal analysis techniques which uncouple the equations of motion are used to perform the analyses. In this way, it is possible to obtain closed form relations for the sensitivity expressions. This eliminates the need to evaluate the adjoint response and psuedo response (these responses are associated with the adjoint and direct differentiation sensitivity problems) over the time domain. The sensitivities need not be numerically integrated over time, thus they are quickly computed. The methodology is valid for problems with proportional as well as non-proportional damping. In an example problem, sensitivities of steady-state vibration amplitude of a crankshaft subject to engine firing loads are evaluated with respect to the stiffness, inertial, and damping parameters which define the shaft. Both the adjoint and direct differentiation methods are used to compute the sensitivities. Finite difference sensitivity approximations are also calculated to validate the explicit sensitivity results.

Periodic Steady State Response and Fatigue Analysis of a Nonlinear City Bus Model

2009 ◽  
Author(s):  
George Valsamos ◽  
Christos Theodosiou ◽  
Sotirios Natsiavas
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
High Stress ◽  
Direct Determination ◽  
Accurate Information ◽  
Steady State Response ◽  
State Response ◽  
Periodic Steady State

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.

Transient Response of Inductrack Systems for Maglev Transport: Part II—Solution and Dynamic Analysis

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen Yang
Keyword(s):  
Steady State ◽  
Dynamic Analysis ◽  
Transient Response ◽  
Numerical Procedure ◽  
Steady State Response ◽  
Governing Equations ◽  
Transient Model ◽  
State Response ◽  
Proposed Model ◽  
Non Linear

Abstract In Part I of this two-part paper, a new benchmark transient model of Inductrack systems is developed. In this Part II, the proposed model, which is governed by a set of non-linear integro-differential governing equations, is used to predict the dynamic response of Inductrack systems. In the development, a state-space representation of the non-linear governing equations is established and a numerical procedure with a specific moving circuit window for transient solutions is designed. The dynamic analysis of Inductrack systems with the proposed model has two major tasks. First, the proposed model is validated through comparison with the noted steady-state results in the literature. Second, the transient response of an Inductrack system is simulated and analyzed in several typical dynamic scenarios. The steady-state response results predicted by the new model agree with those obtained in the previous studies. On the other hand, the transient response simulation results reveal that an ideal steady-state response can hardly exist in those investigated dynamic scenarios. It is believed that the newly developed transient model provides a useful tool for dynamic analysis of Inductrack systems and for in-depth understanding of the complicated electro-magneto-mechanical interactions in this type of dynamic systems.

Trigonometric Collocation for Computation of Steady State Responses of Cracked Structures

2012 ◽  
Author(s):  
Bakeer Bakeer ◽  
Oleg Shiryayev ◽  
Ammaar Tahir
Keyword(s):  
Steady State ◽  
Fatigue Cracks ◽  
Equations Of Motion ◽  
Dynamic Responses ◽  
Vibration Period ◽  
State Response ◽  
Trigonometric Collocation ◽  
Steady State Responses ◽  
Cracked Structures ◽  
State Responses

Development of vibration-based structural health monitoring techniques requires the use of various computational methods to predict dynamic responses of damaged structures. The method described in this work can be used for prediction of steady state harmonic responses for structures with fatigue cracks and may have several advantages over alternative techniques. The method appears to be relatively easy to implement and computationally inexpensive. The steady state response of the system at a given number of time points distributed over one vibration period is represented in terms of Fourier series containing higher frequency harmonics. Equations of motion are formulated in the form that allows for easy computation of Fourier coefficients for all terms in the series. Iterative procedure is used for determining the time of stiffness change in order to capture bilinear dynamic behavior. We present results of initial investigation by applying the method to a model of a cantilever beam with a crack.

scholarly journals Effects of Stator Stiffness, Gap Size, Unbalance, and Shaft’s Asymmetry on the Steady-State Response and Stability Range of an Asymmetric Rotor with Rub-Impact

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Zhaoli Zheng ◽  
Yonghui Xie ◽  
Di Zhang ◽  
Xiaolong Ye
Keyword(s):  
Steady State ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Impact Behavior ◽  
Gap Size ◽  
Steady State Response ◽  
Arc Length ◽  
State Response ◽  
Asymmetric Rotor ◽  
Nonlinear Equations Of Motion

The asymmetric rotor and the rub-impact behavior are important sources of instability and may cause severe vibrations. However, the dynamics of the rotor-bearing system simultaneously considering the two factors has not gained sufficient attention in available investigations. In this paper, the steady-state response and stability of an asymmetric rotor with rub-impact were evaluated. The asymmetric rotor was modeled by beam elements with asymmetric cross section, and the nonlinear equations of motion were established in the rotating frame. The multiharmonic balance (MHB) method was employed to obtain the linearized form of the nonlinear equations of motion. Either the asymmetry of rotor or rub-impact can result in instability and make the problem difficult to solve. Thus, the arc-length method was utilized to trace the branch of the solutions. In order to improve the calculation speed and accurately predict the solution, the alternating frequency/time domain (AFT) was adopted to calculate the iteration of the arc-length method. Based on the proposed method, the effects of stator stiffness, gap size, unbalance, and asymmetric in shaft on the steady-state response and stability were obtained.

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