Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks

2003 ◽  
Vol 125 (2) ◽  
pp. 364-371 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Stiffness Matrix ◽  
Normal Force ◽  
Contact Forces ◽  
Contact Interface ◽  
Bladed Disks ◽  
Interface Elements ◽  
Friction Forces ◽  
Analytical Formulation ◽  
Harmonic Vibrations ◽  
Speed Accuracy

An analytical formulation for the vectors of contact forces and the stiffness matrix of the nonlinear friction contact interface is developed for the analysis of multi-harmonic vibrations in the frequency domain. The contact interface elements provided here an exact description of friction and unilateral contact forces at the interacting surfaces, taking into account the influence of the variable normal load on the friction forces, including the extreme cases of separation of the two surfaces. Initial gaps and interferences at the contact nodes, which affect the normal force, as well as the unilateral action of the normal force at the contact surface, are all included in the model. The accurate calculation of the force vector and the tangent stiffness matrix provides a very reliable and fast convergence of the iteration process used in the search for the amplitudes of nonlinear vibrations of bladed disks. Numerical investigations demonstrate excellent performance with respect to speed, accuracy and stability of computation.

Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Discs

2002 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Stiffness Matrix ◽  
Normal Force ◽  
Iteration Process ◽  
Contact Forces ◽  
Contact Interface ◽  
Interface Elements ◽  
Friction Forces ◽  
Analytical Formulation ◽  
Harmonic Vibrations ◽  
Speed Accuracy

An analytical formulation for the vectors of contact forces and the stiffness matrix of the non-linear friction contact interface is developed for the analysis of multi-harmonic vibrations in the frequency domain. The contact interface elements provided here an exact description of friction and unilateral contact forces at the interacting surfaces, taking into account the influence of the variable normal load on the friction forces, including the extreme cases of separation of the two surfaces. Initial gaps and interferences at the contact nodes, which affect the normal force, as well as the unilateral action of the normal force at the contact surface, are all included in the model. The accurate calculation of the force vector and the tangent stiffness matrix provides a very reliable and fast convergence of the iteration process used in the search for the amplitudes of nonlinear vibrations of bladed discs. Numerical investigations demonstrate excellent performance with respect to speed, accuracy and stability of computation.

Multiharmonic Analysis of Nonlinear Whole Engine Dynamics With Bladed Disc-Casing Rubbing Contacts

2012 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Gas Turbine ◽  
Frequency Domain Analysis ◽  
Forced Response ◽  
Contact Forces ◽  
Turbine Engines ◽  
Test Cases ◽  
Gas Turbine Engines ◽  
Interface Elements ◽  
Friction Forces ◽  
Engine Components

A method has been developed for frequency domain analysis of steady state forced response in gas turbine engines in the presence of rubbing and snubbing contacts between bladed discs and casing and between other rotor and stator engine components. The multiharmonic contact interface elements have been derived for modelling the nonlinear contact interactions: (i) at bearings and (ii) bladed disc-casing rubbing contacts with using flexible models for rotor and stator structures. The elements allow for the asymmetry of the casing, the discrete blade contacts with casing, individual blade-casing gap values, nonlinear dependency of the contact forces on rotor-stator incursion and friction forces, intermittent contacts between blades and the casing. High accuracy and computational efficiency of the methods and models developed has been demonstrated on a set of test cases and on an example of analysis of a realistic gas turbine structure.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

Dynamics of Rolling-Element Bearings—Part I: Cylindrical Roller Bearing Analysis

1979 ◽  
Vol 101 (3) ◽  
pp. 293-302 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Normal Force ◽  
Equations Of Motion ◽  
Roller Bearing ◽  
Rolling Element Bearings ◽  
Analytical Formulation ◽  
Rolling Element ◽  
Cylindrical Roller Bearing ◽  
Cylindrical Roller ◽  
Bearing Analysis

An analytical formulation for the roller motion in a cylindrical roller bearing is presented in terms of the classical differential equations of motion. Roller-race interaction is analyzed in detail and the resulting normal force and moment vectors are determined. Elastohydrodynamic traction models are considered in determining the roller-race tractive forces and moments. Formulation for the roller end and race flange interaction during skewing of the roller is also considered. Roller-cage interactions are assumed to be either hydrodynamic or fully metallic. Simple relationships are used to determine the churning and drag losses.

Design of Measure and Control System of the Ring Block Casing Wear Tester

2013 ◽  
Vol 423-426 ◽  
pp. 2414-2418
Author(s):  
Xiang Tong Yang ◽  
Xiao Zeng Wang ◽  
Yin Ping Cao ◽  
Yi Hua Dou
Keyword(s):  
Control System ◽  
Calibration Method ◽  
Contact Forces ◽  
Wear Depth ◽  
Friction Forces ◽  
Deep Wells ◽  
Geological Conditions ◽  
Casing Wear ◽  
Measure And Control System ◽  
And Control

In deep wells and ultra-deep wells the complex geological conditions often result in serious casing wear. In order to obtain the wear efficiency which is used to compute the wear depth of downhole casing, the ring block drillpipe casing wear tester is developed. The measure and control system which include the measure circuits of contact forces between casing and drillpipe samples, the measure circuits of the friction forces are main component of wear tester. It is very important to design the measure and control system of tester. The paper also develops the calibration method of the loads sensors used to measure the contact and friction force. The wear tester can accurately measure the wear efficiency and the friction coefficient needed by casing wear prediction.

On a Perturbation Method for the Analysis of Unsteady Belt-Drive Operation

2004 ◽  
Vol 72 (4) ◽  
pp. 570-580 ◽  
Author(s):  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Perturbation Method ◽  
Element Model ◽  
Contact Forces ◽  
Steady Solution ◽  
Belt Drive ◽  
Friction Forces ◽  
Direct Contrast ◽  
Validity Criteria

A perturbation method is presented for use in analyzing unsteady belt-drive operation. The method relies on the important assumption that for operating states close to steady operation, the friction state (i.e., whether the belt is creeping or sticking at any location on the pulley) is similar to that of the well-known steady solution in which a lone stick arc precedes a lone slip arc (Johnson, K. L., 1985, Contact Mechanics, Cambridge U.P., London, Chap. 8; Smith, D. P., 1999, Tribol. Int., 31(8), pp. 465–477). This assumption, however, is not used to determine the friction force distribution, and, in fact, the friction forces in the stick zone are found to be nonzero, in direct contrast to the steady solution. The perturbation analysis is used to derive expressions for the span tensions, the pulley tension distributions, the contact forces between the belt and the pulleys, and the angular velocity of the driven pulleys. Validity criteria are developed which determine bounds on the operation state for which the assumed friction state is upheld. Verification of response quantities from the perturbation solution is accomplished through comparison to quantities predicted by an in-house dynamic finite element model and excellent agreement is found. Additionally, the finite element model is used to verify the key assumption that a lone slip arc precedes a lone stick arc.

Measurements of Forces Between a Synchronous Belt and a Pulley

2000 ◽  
Author(s):  
Martin Distner ◽  
Tomas Johannesson
Keyword(s):  
Load Distribution ◽  
Contact Forces ◽  
Automotive Application ◽  
Friction Forces ◽  
Running Time ◽  
Application Range ◽  
Normal Forces ◽  
Belt Speed ◽  
Pitch Difference ◽  
Static Conditions

Abstract In modern belt profiles, power is transmitted by both normal forces and friction forces. To control the load distribution between a belt and a pulley, avoiding power circulation and local tooth load peaks, it is necessary to take into account both types of forces. An analytical model for the load distribution has previously been presented by the authors. This work also introduces the effective pitch difference, EPD, which is the actual pitch difference between a pulley and a loaded belt. To examine these matters and verify the model, a series of 270 experiments was carried out in a two-pulley test rig. Parameters investigated are: torque, tension, belt speed, pitch difference and running time. All of the measurements were conducted under quasi-static conditions. The equipment used included a specially designed measurement pulley that can measure four different engagement forces. Experiments show that belt speed within automotive application range has no effect on load distribution, apart from engagement and disengagement peaks. Tooth flank normal forces and land area friction forces often work against each other. Belts with dissimilar pitch difference give rise to great differences in load distributions. Even a short running time causes a redistribution of the friction forces, although their sum remains constant. The results show that it is possible to tailor the load distribution by adjusting the EPD. This offers an opportunity to avoid power circulation and unnecessary high contact forces. Changing the EPD for the correct load distribution at each interaction is easily achieved by individual adjustment of the pulley radius.

Applications of the Static Condensation Technique to Nonlinear Structural Analysis of Floating Offshore Structures

2017 ◽  
Author(s):  
Min-Han Oh ◽  
Seung-Hwan Boo ◽  
Phill-Seung Lee ◽  
Jong-Min Kim ◽  
Joong-Soo Moon ◽  
...  
Keyword(s):  
Reduction Method ◽  
Cost Effective ◽  
Offshore Structures ◽  
Fe Model ◽  
Contact Interface ◽  
Friction Forces ◽  
Static Condensation ◽  
Load Carrying ◽  
Nonlinear Contact ◽  
Actual Design

A cost effective finite element (FE) procedure is proposed for analysis of load-carrying structures with nonlinear contact and frictional behaviors between large floating offshore structures. The key of the procedure is to use the static condensation technique developed from the Guyan model reduction method. The time for computing contact and friction forces on contact interface areas can be dramatically reduced compared to nonlinear analysis with a full FE model. Two representative applications to offshore projects are presented. One is a problem with nonlinear contact of independent tank support in FLNG hull structures and the second is a sea-fastening system used during offshore dry transportation. The reliability and computing efficiency of the proposed analysis procedure are investigated. It is conclusively confirmed that the proposed procedure is practical for application to actual design of offshore projects.

Effects of Contact Interface Parameters on Vibration of Turbine Bladed Disks With Underplatform Dampers

2011 ◽  
Author(s):  
C. W. Schwingshackl ◽  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Structural Integrity ◽  
Turbine Blades ◽  
Contact Interface ◽  
Bladed Disks ◽  
Normal Contact ◽  
Input Parameters ◽  
Software Codes ◽  
Model Setup ◽  
Interface Parameters ◽  
Underplatform Damper

The design of high cycle fatigue resistant bladed disks requires the ability to predict the expected damping of the structure in order to evaluate the dynamic behaviour and ensure structural integrity. Highly sophisticated software codes are available today for this nonlinear analysis but their correct use requires a good understanding of the correct model generation and the input parameters involved to ensure a reliable prediction of the blade behaviour. The aim of the work described in this paper is to determine the suitability of current modelling approaches and to enhance the quality of the nonlinear modelling of turbine blades with underplatform dampers. This includes an investigation of a choice of the required input parameters, an evaluation of their best use in nonlinear friction analysis, and an assessment of the sensitivity of the response to variations in these parameters. Part of the problem is that the input parameters come with varying degrees of uncertainty, since some are experimentally determined, others are derived from analysis and a final set are often based on estimates from previous experience. In this investigation the model of a commercial turbine bladed disc with an underplatform damper is studied and its first flap, first torsion and first edgewise modes are considered for 6EO and 36EO excitation. The influence of different contact interface meshes on the results is investigated, together with several distributions of the static normal contact loads to enhance the model setup and hence increase accuracy in the response predictions of the blade with an underplatform damper. A parametric analysis is carried out on the friction contact parameters and the correct setup of the nonlinear contact model to determine their influence on the dynamic response and to define the required accuracy of the input parameters.

Contact Force Distribution and Induced Anisotropy in Granular Materials under Biaxial Test

2012 ◽  
Vol 446-449 ◽  
pp. 1927-1934
Author(s):  
Min Yun Hu ◽  
Qiao Hao Chen ◽  
Ying Shen ◽  
Xiao Wu Tang
Keyword(s):  
Contact Force ◽  
Normal Force ◽  
Microscopic Analysis ◽  
Contact Forces ◽  
Force Chain ◽  
Particle Flow Code ◽  
Biaxial Compression ◽  
Biaxial Test ◽  
Induced Anisotropy ◽  
Structural Anisotropy

A 2-dimensional granular assembly, subjected to isotropic consolidation and biaxial compression, is simulated by applying discrete element method and the particle flow code of PFC2D. The contact force network and distribution are examined and compared to an analogous photoelastic experiment carried out by other studies. The current study shows that the assembly undergoes dilatation and strain-softening after peak strength, and the coordination number (average contact number of particles) increases a little in the initial stage of strain hardening followed by a sharp dropping before the onset of softening. This is correlated with the contact force chain establishment and the evolution of structural anisotropy. The distribution of the normal force and the ratio of tangential to normal force for both the isotropically compressed and sheared stages indicates that the strong normal contacts are crucial for the force chain transmitting stress through assembly. The angular distribution of the contact forces supported this point and could help visualizing the induced anisotropy. These issues are vital for gaining a deeper understanding of the macroscopic behavior of granular material from microscopic analysis.

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