Simple Method for Dynamic Interaction between Two Rigid Foundations

2011 ◽  
Vol 250-253 ◽  
pp. 2225-2228
Author(s):  
Bin Yan ◽  
Ying Hui Lv ◽  
Ping Hu

In the past many researchers studied dynamic stiffness and damping coefficients of surface and embedded rigid foundations of arbitrary shapes in the elastic homogenous half space. Dynamic stiffness and damping coefficients were obtained by using regularly shaped foundations instead of arbitrarily shaped ones. Obviously, the calculating methods were not perfect. In addition, the two parameters mentioned above were calculated only in the case of a single foundation. But the cases of two or more foundations were not presented because the interactions between foundations were not considered in all present papers. This paper eliminates two faults named above by using the assumption of the plane strain and of dynamic foundation-soil interaction factors. The calculating method of dynamic impedances presented by the paper proved to be accurate and practical.

1997 ◽  
Vol 119 (1) ◽  
pp. 57-63 ◽  
Author(s):  
M. J. Goodwin ◽  
P. J. Ogrodnik ◽  
M. P. Roach ◽  
Y. Fang

This paper describes a combined theoretical and experimental investigation of the eight oil film stiffness and damping coefficients for a novel low impedance hydrodynamic bearing. The novel design incorporates a recess in the bearing surface which is connected to a standard commercial gas bag accumulator; this arrangement reduces the oil film dynamic stiffness and leads to improved machine response and stability. A finite difference method was used to solve Reynolds equation and yield the pressure distribution in the bearing oil film. Integration of the pressure profile then enabled the fluid film forces to be evaluated. A perturbation technique was used to determine the dynamic pressure components, and hence to determine the eight oil film stiffness and damping coefficients. Experimental data was obtained from a laboratory test rig in which a test bearing, floating on a rotating shaft, was excited by a multi-frequency force signal. Measurements of the resulting relative movement between bearing and journal enabled the oil film coefficients to be measured. The results of the work show good agreement between theoretical and experimental data, and indicate that the oil film impedance of the novel design is considerably lower than that of a conventional bearing.


Author(s):  
Ahmad W. Yacout

This study has theoretically analyzed the surface roughness, centripetal inertia and recess volume fluid compressibility effects on the dynamic behavior of a restrictor compensated hydrostatic thrust spherical clearance type of bearing. The stochastic Reynolds equation, with centripetal inertia effect, and the recess flow continuity equation with recess volume fluid compressibility effect have been derived to take into account the presence of roughness on the bearing surfaces. On the basis of a small perturbations method, the dynamic stiffness and damping coefficients have been evaluated. In addition to the usual bearing design parameters the results for the dynamic stiffness and damping coefficients have been calculated for various frequencies of vibrations or squeeze parameter (frequency parameter) and recess volume fluid compressibility parameter. The study shows that both of the surface roughness and the centripetal inertia have slight effects on the stiffness coefficient and remarkable effects on the damping coefficient while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics. The cross dynamic stiffness showed the bearing self-aligning property and the ability to oppose whirl movements. The orifice restrictor showed better dynamic performance than that of the capillary tube.


Author(s):  
V. H. Saran ◽  
V. K. Goel

In this paper, a laboratory technique for determination of rolling dynamic stiffness and damping coefficients of small-sized, bias-ply tyres has been discussed. The effect of normal load, inflation pressure and speed on four different tyres has been reported. The results show similar trends to those reported by other investigators.


Author(s):  
Phuoc Vinh Dang ◽  
Steven Chatterton ◽  
Paolo Pennacchi ◽  
Andrea Vania ◽  
Filippo Cangioli

The use of tilting pad journal bearings (TPJBs) has increased in recent years due to their stabilizing effects on the rotor bearing system. Most of the studies addressing steady state and dynamic behaviors of TPJBs have been evaluated by means of thermo-hydrodynamic (THD) models, assuming nominal dimensions for the bearing, (i.e., the physical dimensions of all pads are identical and loads applied along the vertical direction). However machining errors could lead to actual bearing geometry and dimensions different from the nominal ones. In particular, for TPJB the asymmetry of the bearing geometry has not been well-investigated and can lead to an unexpected behavior of the bearing. The asymmetry of the bearing geometry can arise from large machining errors on only one or more pads, as a consequence of a pivot failure or after bad-mounting of the pads during assembly. These conditions can sometimes be detected by high values of the pad temperature, as measured by the temperature probes installed on the bearing pads, or by the abnormal vibration caused by pad-flutter phenomena. In this paper the authors investigate large machining errors on the pad thickness for a five-pad TPJB and analyze their effects on the bearing operating characteristics. Pad thickness errors correspond to a different preload factor or clearance for each pad. A sensitivity analysis was performed for several combinations of pad thickness using a THD model and the behavior of the bearing was analyzed, including dynamic stiffness and damping coefficients, clearance profile, shaft locus, minimum oil-film thickness, power loss, flow rate, and maximum pressure. The experimental case of a five pads TPJB with an intentional large machining error on the thickness of the pads is also described in the paper. The bearing has a nominal diameter of 100 mm, a diameter to length ratio (L/D) equal to 0.7 and can run at up to 3000 rpm. The experimental measurements are compared with the results obtained from the analytical model. The results show that the effects of asymmetry of the bearing geometry are more evident if the direction of the static load applied on the rotor bearing system, which is different from the vertical load, is also considered. For instance, the shape of shaft locus obtained by experimental tests changing the static load direction at a constant speed is an irregular pentagon if it is compared to the case of the nominal bearing. Based on our findings, we concludes that the machining error on the pads has a large influence on the shaft locus, minimum oil-film thickness and maximum pressure on pads, especially at high rotational speed, but has little effect on the flow rate and power loss. In addition, this error significantly affects the dynamic stiffness and damping coefficients, both in terms of rotational speed and load direction.


Author(s):  
R. N. Headifen ◽  
W. F. Weldon

In this paper a method is described that takes the nonlinear dynamic stiffness and damping coefficients for multiple hydrostatic bearings and incorporates them into a rotordynamic FEM model for a rotating machine. A Newton-Raphson iteration scheme is presented that uses updated bearing coefficients at every iteration to the solution. A non-linear computer program was written using the method described which models transient and synchronous response and calculates damped eigenvalues.


2015 ◽  
Vol 6 (5) ◽  
pp. 649-664
Author(s):  
Michael G. Papanikolaou ◽  
Michael G. Farmakopoulos ◽  
Chris A. Papadopoulos

Purpose – Wear in journal bearings occurs when the operating conditions (high load, high temperature, low angular velocity or low viscosity), downgrade the ability of the bearing to carry load. The wear depth increases because the rotor comes in contact with the bearing surface. Wear in journal bearings affects their characteristics because of its influence on the thickness of the fluid film. This influence can be detected in the dynamic behavior of the rotor and especially in the dynamic stiffness and damping coefficients. The paper aims to discuss these issues. Design/methodology/approach – In this paper, the effect of wear on the rotor dynamic stiffness and damping coefficients (K and C) of a short journal bearing is investigated. K and C in this work are estimated by using two methods a semi-analytical method and finite element (FE) analysis implemented in the ANSYS software. Findings – The main goal of this research is to make the identification of wear in journal bearings feasible by observing the alternation of their dynamic coefficients. Both of the methods implemented are proven to be useful, while FE analysis can provide more accurate results. Originality/value – This paper is original and has not been published elsewhere.


1978 ◽  
Vol 20 (5) ◽  
pp. 291-296 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar

A periodic (displacement) disturbance is imposed on an aerostatic, porous, journal bearing of finite length under steady-state conditions. The dynamic pressure distribution is obtained by a pressure perturbation analysis of Reynolds equation and a modified flow continuity equation in a porous medium. Dynamic stiffness and damping coefficients for different operating conditions are calculated numerically, using a digital computer, and presented in the form of design charts.


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