Numerical Analysis of an Air Spring With Two Tanks Connected by a Long Pipe: Effect of Orifice Installed in the Pipe

2016 ◽  
Author(s):  
Masatoshi Toji ◽  
Toshihiko Asami ◽  
Tomohiko Ise
Keyword(s):  
Numerical Analysis ◽  
Nonlinear Partial Differential Equation ◽  
Inertia Force ◽  
Governing Equations ◽  
Air Spring ◽  
Vibratory System ◽  
Nonlinear Characteristics ◽  
Air Stream ◽  
Single Mass ◽  
Amplitude Dependency

This paper deals with the numerical analysis of an air spring that consists of two tanks connected by a long pipe. Two resonance points may appear in the frequency response of a vibratory system supported by this type of air spring despite the fact that the system has an apparent single mass. This phenomenon is caused by the presence of a secondary mass as reported in our previous paper. It was found that the secondary mass is the mass of air contained in the pipe. The magnitude of this mass is extremely small, but the acceleration of the air in the pipe — and therefore the inertia force generated from it — becomes very large. The generated force is further amplified by the Pascal’s principle and is transmitted to the supported mass. There are obvious nonlinear characteristics in this type of air spring; whereas the previous studies were based on linear assumptions. In this study, the governing equations for the air stream expressed by a nonlinear partial differential equation were solved by using the finite difference method. In particular, the pressure loss is evaluated due to air vortex being generated behind the orifice installed in the pipe. As a result of this study, it was found that the orifice is effective in suppressing the height of the secondary resonance point. Of course, it has become possible to accurately estimate the amplitude dependency of the dynamic characteristics of the air spring supported system by this non-linear analysis.

An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Toshihiko Asami ◽  
Yasutaka Yokota ◽  
Tomohiko Ise ◽  
Itsuro Honda ◽  
Hiroya Sakamoto
Keyword(s):  
Frequency Response ◽  
Simple Expression ◽  
Air Spring ◽  
Response Curves ◽  
Vibration Isolators ◽  
Input Amplitude ◽  
Calculation Results ◽  
Single Mass ◽  
Experimental Values ◽  
Amplitude Dependency

This paper proposes a simple expression for calculating the restoring and damping forces of an air spring equipped with a small pipe. Air springs are commonly used in railway vehicles, automobiles, and various vibration isolators. The air spring discussed in this study consists of two tanks connected by a long pipe. Using a pipe instead of an orifice enables flexibility in the arrangement of the two tanks. In addition, this makes it possible to manufacture a thin air spring. A vertical translational oscillating system, which consists of a single mass supported by this type of air spring, looks like a single-degree-of-freedom (SDOF) system. However, it may have two resonance points. In this paper, we propose a vibratory model of a system supported by the air spring. With the proposed model it is possible to correctly reproduce the two resonance points of a system consisting of a single mass supported by this type of air spring. In our analysis, assuming that the vibration amplitude is small and the flow through the pipe is laminar, we derive the spring constant and damping coefficient of an air spring subjected to a simple harmonic motion. Then, we calculate the frequency response curves for the system and compare the calculated results with the experimental values. According to the experiment, there is a remarkable amplitude dependency in this type of air spring, so the frequency response curves for the system change with the magnitude of the input amplitude. It becomes clear that the calculation results are in agreement with the limit case when the input amplitude approaches zero. We use a commercially available air spring in this experiment. Our study is useful in the design of thin air spring vibration isolators for isolating small vibrations.

Validation of the Accuracy of Approximation in a Design Formula for an Air Spring by Using Numerical Analysis

2013 ◽  
Author(s):  
Toshihiko Asami ◽  
Yasutaka Yokota ◽  
Masahito Okura ◽  
Tomohiko Ise ◽  
Itsuro Honda ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Amplitude Ratio ◽  
Major Influence ◽  
Approximation Formula ◽  
Air Spring ◽  
Response Curves ◽  
Sinusoidal Vibration ◽  
Input Amplitude ◽  
Inner Diameter ◽  
Amplitude Dependency

Previously, the authors proposed an approximation formula for designing an air spring that consists of two air tanks connected by a long pipe. The analysis was based on a linear approximation, so there is no amplitude dependency in the amplitude ratio for the sinusoidal vibration of a system with an the air spring. However, according to the experiment, it was found that there is remarkable amplitude dependency in a system with this type of air spring, so the frequency response curves for the system change with the magnitude of the input amplitude. It became clear that the approximation formula is in agreement with the limit value when the input amplitude approaches zero. We consider that the deviation between the approximation formula and the experimental results are caused by the various assumptions which used in the analysis. As we remove these assumptions one by one, we perform the numerical analysis based on the finite difference method for this air spring. As a result, it was found that the effects of the turbulent flow in the pipe and the pressure loss at the inlet and outlet of the pipe are very small. A major influence is attributed in the connector that connects the pipe to the air chamber. The flow is throttled and disturbed at the connector whose inner diameter is smaller than the inner diameter of the pipe.

Theoretical and Experimental Analysis of the Nonlinear Characteristics of an Air Spring With an Orifice

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Toshihiko Asami ◽  
Yasutaka Yokota ◽  
Tomohiko Ise ◽  
Itsuro Honda ◽  
Hiroya Sakamoto
Keyword(s):  
Vibration Isolation ◽  
Dynamic Properties ◽  
Flow Characteristics ◽  
Accurate Method ◽  
The Body ◽  
Nonlinear Flow ◽  
Air Spring ◽  
Damping Force ◽  
Nonlinear Characteristics ◽  
Amplitude Dependency

We herein propose a simple but accurate method for calculating the dynamic properties of an air spring that uses an orifice to produce a damping force. Air springs are commonly used in rail, automotive, and vibration isolation applications. However, because this type of air spring has nonlinear flow characteristics, accurate approaches have not yet been proposed. The restoring and damping forces in an air spring with an orifice damper vary with the amplitude of the body. This amplitude dependency has not been considered in previous studies. We herein propose a simple model for calculating the air spring constant and damping coefficient. However, this requires iterative calculation due to the nonlinearity of the air spring. The theoretical and experimental results are found to agree well with each other. The theoretical equations provide an effective tool for air spring design.

Post-Buckling of Piezoelectric Thin Plates

2015 ◽  
Vol 15 (07) ◽  
pp. 1540020 ◽  
Author(s):  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Nonlinear Behavior ◽  
Dirichlet Boundary Conditions ◽  
Thin Plates ◽  
Governing Equations ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Single Term ◽  
Post Buckling ◽  
Special Case

In the present paper, the geometrically nonlinear behavior of piezoelastic thin plates is studied. First, the governing equations for the electromechanically coupled problem are derived based on the von Karman–Tsien kinematic assumption. Here, the Berger approximation is extended to the coupled piezoelastic problem. The general equations are then reduced to a single nonlinear partial differential equation for the special case of simply supported polygonal edges. The nonlinear equations are approximated by using a problem-oriented Ritz Ansatz in combination with a Galerkin procedure. Based on the resulting equations the buckling and post-buckling behavior of a polygonal simply supported plate is studied in a nondimensional form, where the special geometry of the polygonal plate enters via the eigenvalues of a Helmholtz problem with Dirichlet boundary conditions. Single term as well as multi-term solutions are discussed including the effects of piezoelectric actuation and transverse force loadings upon the solution. Novel results concerning the buckling, snap through and snap buckling behavior are presented.

scholarly journals Detection and alleviation of the abnormal vibration of the monorail based on experiment and simulation

2019 ◽  
Vol 38 (2) ◽  
pp. 282-295 ◽  
Author(s):  
Yongzhi Jiang ◽  
Pingbo Wu ◽  
Jing Zeng ◽  
Lai Wei ◽  
Kaikai Lv ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Ride Comfort ◽  
Detection Method ◽  
Dominant Frequency ◽  
Experimental Results ◽  
Indirect Detection ◽  
Prominent Feature ◽  
Air Spring ◽  
Vertical Stiffness ◽  
Vehicle Acceleration

Wheel out of round, which has a significant influence on the ride comfort of vehicles, is very difficult to detect, especially for vehicles with rubber tires like a monorail. The prominent feature of wheel eccentricity caused by wheel out of round is that there will be a dominant frequency of the vehicle acceleration that varies with the speed of the vehicle, while the wavelengthes are all equal to the wheel circumference. By studying the experimental results of Chongqing straddle monorail, an indirect detection method of the wheel out of round is put forward. Then a simulation model of the monorail vehicle under the influence of the wheel out of round is established. The numerical analysis and experimental results lead to that the main reason for the abnormal vibration of the vehicle is the wheel out of round. Through the analysis of the vertical dynamic equation of the monorail system, all other factors that may affect the dominant frequency of vehicle vibration are analyzed. Finally, it is concluded this abnormal vibration caused by wheel out of round can only be reduced by increasing the vertical stiffness of the air spring and car body mass other than changing wheels.

Experiments on Laminar Flow about a Rotating Sphere in an Air Stream

1987 ◽  
Vol 201 (6) ◽  
pp. 427-438 ◽  
Author(s):  
M A I El-Shaarawi ◽  
M M Kemry ◽  
S A El-Bedeawi
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Separation Angle ◽  
Governing Equations ◽  
Rotating Sphere ◽  
Axis Of Rotation ◽  
Air Stream ◽  
Uniform Stream

Laminar flow about a rotating sphere which is subjected to a uniform stream of air in the direction of the axis of rotation is investigated experimentally. Measurements of the velocity components within the boundary layer and the separation angle were performed at a Reynolds number, Re, of 10 000 and Ta/Re 2 of 0, 1 and 5. These measurements are compared with the numerical solutions of the same problem where either theoretical potential or actual experimental boundary conditions are imposed on the governing equations.

Numerical analysis of the air spring which two air tanks were connected to a pipe

2017 ◽  
Vol 2017.92 (0) ◽  
pp. M303
Author(s):  
Masatoshi TOJI ◽  
Toshihiko ASAMI ◽  
Itsuro Honda ◽  
Tomohiko Ise
Keyword(s):  
Numerical Analysis ◽  
Air Spring

Three-Dimensional Flow Optimization of a Nozzle with a Continuous Adjoint

2015 ◽  
Vol 16 (3-4) ◽  
pp. 151-156
Author(s):  
Krzysztof J. Wolosz ◽  
Jacek Wernik
Keyword(s):  
Objective Function ◽  
Three Dimensional ◽  
Flow In Porous Media ◽  
Material Structure ◽  
Governing Equations ◽  
Global Extremum ◽  
Air Stream ◽  
Continuous Adjoint Method ◽  
Air Nozzle ◽  
Continuous Adjoint

AbstractThe article presents results of multi-criteria optimization of air nozzle topology. The optimization in the CFD has been recently developed since equations of flow in porous media were applied among others governing equations. Optimization is a seeking for extremum of an objective function with respect to the function constraints. With this definition in mind, the optimization by using a continuous adjoint for the current cases is a finding such channel topology which minimizes for example pressure or energy loss when the constraints of objective function are in the form of flow governing equations of momentum and continuity. This methodology of optimization makes a design process faster comparing to the methods related to Design of Experiments (DoE). However, for the sake of flow governing equations nonlinearity, the continuous adjoint method can be successfully applied only in relatively simply and steady-state cases. The reason is of possibility of finding the global extremum of the objective function only for that kind of cases. The results of optimization of two selected cases are presented in the article and show advantages and limitations of the method applied. The continuous adjoint simulation results indicate the nozzles design directions and can be applied in industry with limited reliability. The object of research reported in the article is the nozzle which is augmented equipment used with a pneumatic pulsator. The pulsators are devices that utilize an air stream to destruct vaults created in loose material structure. The pulsator productivity equipped with a nozzle depends on outlet pressure. Therefore, the optimization problem was stated so that pressure loss is to be as low as possible.

Mechanical Vibration Filters With Nonlinear Characteristics

1960 ◽  
Vol 82 (4) ◽  
pp. 369-375
Author(s):  
Will J. Worley
Keyword(s):  
Steady State ◽  
Mechanical Vibration ◽  
Nonlinear Characteristics ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Nonlinear Springs ◽  
Sinusoidal Oscillations ◽  
Single Mass ◽  
Linear And Nonlinear ◽  
Differential Analyzer

The behavior of a single degree of freedom system consisting of a single mass mounted on a spring and damper attached to an oscillating base is investigated. Steady-state and transient sinusoidal oscillations are applied to the base to which the suspension is attached. The response of the mass is recorded for various combinations of linear and nonlinear springs and dampers. Solutions are obtained with a differential analyzer.

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