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

2012 ◽  
Author(s):  
Toshihiko Asami ◽  
Yasutaka Yokota ◽  
Tomohiko Ise ◽  
Itsuro Honda ◽  
Hiroya Sakamoto
Keyword(s):  
Frequency Response ◽  
Simple Expression ◽  
Air Spring ◽  
Response Curves ◽  
Vibration Isolators ◽  
Sdof System ◽  
Input Amplitude ◽  
Limit Value ◽  
Small Tube ◽  
Amplitude Dependency

This paper proposes a simple expression for calculating the restoring and damping forces of an air spring equipped with a small tube. Air springs are commonly used in railway vehicles, automobiles, and various vibration isolators. The air spring used in this study consists of two tanks connected by a long tube. Using a tube 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. The oscillating system, which consists of a single mass supported by this type of air spring, is a single-degree-of-freedom (SDOF) system. However, it has two resonance points for a reason that had been unknown for a long period of time. In this paper, we explain why the SDOF system has two resonance points. After that, assuming that the vibration is small and the flow through the tube 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 value when the input amplitude approaches zero.

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.

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.

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Magnification curves of electromagnetic seismographs

1964 ◽  
Vol 54 (5A) ◽  
pp. 1459-1471
Author(s):  
S. K. Chakrabarty ◽  
G. C. Choudhury ◽  
S. N. Roy Choudhury
Keyword(s):  
General Solution ◽  
Frequency Response ◽  
Experimental Method ◽  
Phase Shifts ◽  
Response Curves ◽  
Operating Condition ◽  
Coil Inductance ◽  
The World ◽  
Electromagnetic Seismograph ◽  
Proper Design

Abstract The general solution of the equations connecting the motion of the two coupled components in an electromagnetic seismograph has been obtained in another paper and it shows that the magnification of a seismograph depend on seven instrumental constants. Using these results, equations and curves have been derived in the present paper from which the Magnification as well as Phase shifts in the response of a seismograph and their variations with damping and coil inductance can be easily obtained. Based on these curves a number of magnification curves for different combinations, which are in operation at the different seismological stations of the world, have been derived. Suitable equations and curves have also been obtained which can be used for estimating the absolute Magnification of a Seismograph. An experimental method of obtaining the frequency response curves of seismographs in their operating condition has been described and the results obtained by this method has been given. It has been indicated how the results incorporated in the present paper can be used in the proper design of seismographs required for the different purposes.

scholarly journals Optimization of Transformer Winding Deformation Assessment Criterion Considering Insulation Aging and Moisture Content

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6491
Author(s):  
Qian Wu ◽  
Yizhuo Hu ◽  
Ming Dong ◽  
Bo Song ◽  
Changjie Xia ◽  
...  
Keyword(s):  
Moisture Content ◽  
Frequency Response ◽  
High Sensitivity ◽  
Response Analysis ◽  
Frequency Response Analysis ◽  
Response Curves ◽  
Insulation Aging ◽  
Transformer Winding ◽  
Winding Deformation ◽  
Paper Insulation

Frequency response analysis is widely used to diagnose transformer winding deformation faults due to its high sensitivity, strong anti-interference capability, and equipment portability, but the results of frequency response analysis can be affected by insulation aging and moisture in the transformer, leading to errors in the diagnosis of winding deformation faults. Currently, there is no effective method to prevent such errors. This paper focuses on optimizing the criterion for diagnosing winding deformations when insulation aging and moisture are present. First, the winding frequency response curves of oil-paper insulation were determined by combining insulation aging and moisture tests of the oil-paper insulation with frequency response simulations of the transformer winding. Next, the winding deformation criterion predicting the likelihood and extent of errors diagnosing transformer winding deformations due to the insulation aging and moisture content is discussed. Finally, the corresponding criterion optimization method is proposed. The corresponding results show that insulation aging and moisture can lead to errors when using the correlation coefficient R criterion to diagnose the transformer winding deformations. Moreover, the possibility of winding deformation errors caused by the change of insulation state can be reduced by introducing the corresponding auxiliary criterion through comparing the capacitance change rate based on the frequency response method and that based on the dielectric spectrum method.

scholarly journals Vibration Parameters Estimation by Blade Tip-Timing in Mistuned Bladed Disks in Presence of Close Resonances

2020 ◽  
Vol 10 (17) ◽  
pp. 5930
Author(s):  
Saeed Bornassi ◽  
Christian Maria Firrone ◽  
Teresa Maria Berruti
Keyword(s):  
Frequency Response ◽  
Optimization Technique ◽  
Numerical Test ◽  
Parameters Estimation ◽  
Least Square ◽  
Response Curves ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Resonance Frequencies ◽  
Blade Tip

The present paper is focused on the post processing of the data coming from the Blade Tip-Timing (BTT) sensors in the case where two very close peaks are present in the frequency response of the vibrating system. This type of dynamic response with two very close peaks can occur quite often in bladed disks. It is related to the fact that the bladed disk is not perfectly cyclic symmetric and the so called “mistuning” is present. A method based on the fitting of the BTT sensors data by means of a 2 degrees of freedom (2DOF) dynamic model is proposed. Nonlinear least square optimization technique is employed for identification of the vibration characteristics. A numerical test case based on a lump parameter model of a bladed disk assembly is used to simulate different response curves and the corresponding sensors signals. The Frequency Response Function (FRF) constructed at the resonance region is compared with the traditional Sine fitting results, the resonance frequencies and damping values estimated by the fitting procedure are also reported. Accurate predictions are achieved and the results demonstrate the considerable capacity of the 2DOF method to be used as a standalone or as a complement to the standard Sine fitting method.

Atrioventricular responses of canine heart following chronic unilateral vagotomy

1987 ◽  
Vol 253 (2) ◽  
pp. H394-H401 ◽  
Author(s):  
D. V. Priola ◽  
C. Anagnostelis ◽  
C. Sanchez-Wilson ◽  
T. M. Blomquist
Keyword(s):  
Frequency Response ◽  
Control Mechanisms ◽  
Canine Heart ◽  
Response Curves ◽  
Group Iii ◽  
Group I ◽  
Group Ii ◽  
The Right ◽  
Inotropic Responses ◽  
Intrinsic Cardiac Nerves

The intrinsic cardiac nerves (ICN) have been shown to develop supersensitivity to nicotine (NIC) following complete extrinsic cardiac denervation. The present experiments were performed to delineate the pattern of ICN distribution in the heart by examining the pattern of NIC supersensitivity after unilateral vagotomy (VGX). Thirty-eight dogs were placed on cardiopulmonary bypass and inotropy evaluated by means of isovolumic pressures from fluid-filled balloons placed in the atria and ventricles. The animals were divided into three groups: group I, sham-operated controls; group II, animals studied 1–2 wk after VGX; and group III, animals studied 8–12 wk after VGX. Chronotropic and inotropic responses were evaluated in terms of NIC and acetylcholine (ACh) dose-response curves as well as frequency-response curves to stimulation of the intact vagus nerve (0.5–30 Hz). No change in NIC sensitivity was observed in group II, and vagal frequency-response curves were identical to group I. In group III dogs, both the right atrium and right ventricle showed significant increases in NIC sensitivity after left vagotomy. All group III animals showed right-shifted frequency-response curves. We conclude that nicotinic supersensitivity of the ICN and inotropic unresponsiveness to vagal stimulation occur but are slow in developing (70–130 days); and preganglionic sprouting does not appear to play a functional role in the adjustment of cardiac control mechanisms to unilateral vagotomy.

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