• Proceedings of the KSR Conference
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• 1998.05a
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• pp.315-322
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• 1998

A two dimensional elasto-plastic finite element program taking into account contact between crack surfaces if developed in order to analyze subsurface cracking in rolling contact. But the friction between upper and lower surface of the crack is not considered. Under the assumptions of small deformation and small displacement, the incremental theory of plasticity is used to describe plastic deformation. J-integral is computed as the applied Hertzian load slides over the surface with friction. J-integral is correlated with wear rate of the rail. The propagation rate of the right tip of the surface crack is fast by 45% than that of the left side.

• Transactions of Materials Processing
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• v.24 no.3
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• pp.212-217
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• 2015

SmartCrown is a system to control the plate crown by shifting the sine-shaped work rolls in the axial direction. The control range of the plate crown depends on a depth of sine-shaped roll profile because the roll radius varies continuously along the axial direction. When the roll profile is changed to improve the control range, the contact stress between the work roll and the back-up roll also changes. In the current study, the contact stress for various profiles and rolling conditions were analyzed using the finite element method and compared with results from Hertzian contact theory. A submodel method is used to increase the accuracy of the finite element analysis. The analysis results showed that the maximum increase in the contact stress was only 53MPa, so it is anticipated that no back-up roll spalling will occur.

• Wind and Structures
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• v.32 no.5
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• pp.487-499
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• 2021

The wind-blown sand effect on the high-speed train is investigated. Unsteady RANS equation and the SST k-ω turbulent model coupled with the discrete phase model (DPM) are utilized to simulate the two-phase of air-sand. Sand impact force is calculated based on the Hertzian impact theory. The different cases, including various wind velocity, train speed, sand particle diameter, were simulated. The train's flow field characteristics and the sand impact force were analyzed. The results show that the sand environment makes the pressure increase under different wind velocity and train speed situations. Sand impact force increases with the increasing train speed and sand particle diameter under the same particle mass flow rate. The train aerodynamic force connected with sand impact force when the train running in the wind-sand environment were compared with the aerodynamic force when the train running in the pure wind environment. The results show that the head car longitudinal force increase with wind speed increasing. When the crosswind speed is larger than 35m/s, the effect of the wind- sand environment on the train increases obviously. The longitudinal force of head car increases 23% and lateral force of tail increases 12% comparing to the pure wind environment. The sand concentration in air is the most important factor which influences the sand impact force on the train.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2636-2646
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• 2002

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modeled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian con tact theory is applied to calculate the elastic deflection and nonlinear contact force while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the nonlinear governing equations of the rotor, which are solved by using the Runge-Kutta-Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e. the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing but also between those of two or more ball bearings constrained by the rotor.

• Journal of KSNVE
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• v.8 no.4
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• pp.616-622
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• 1998

An analytical method has been developed to estimate the dynamic contact force between wheel and rail when trains are running on rail with vertical irregularities. In this method, the effect of Hertzian deformation at the contact point is considered as a linearized spring and the wheel is considered as an sprung mass. The rail is modelled as a discretely-supported Timoshenko beam, and the periodic structure theory was adopted to obtain the driving-point receptance. As an example, the dynamic contact force for a typical wheel/rail system was analysed by the method developed in this research and the dynamic characteristics of the system was also discussed. It is revealed that discretely-supported Timoshenko beam model should be used instead of the previously used continuously-supported model or discretelysupported Euler beam model, for the frequency range above several hundred hertz.

• Journal of Advanced Marine Engineering and Technology
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• v.12 no.3
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• pp.29-42
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• 1988

With the Hertzian contact theory, it is possible to determine the bearing load distributing pattern among the balls and rollers and also variations of the load-displacement relationships for rolling elements contacting raceways according to bearing clearance, load distribution, contact forces and dimensions of bearing components (i.e diameter of raceway and rolling elements), etc. In this paper the calculation theories of contact load and normal approach between two raceways under radial load are reviewed, and compared these calculation results with those of experimental results. A new calculation theory for elastic displacement of outer-race of ball bearing under radial load is developed by authors by application of energy method, which is independent on the effects of roughness, bending or eccentricity of bearing with driving shaft, and is effective in measuring the location of its defect.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.411-412
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• 2006

It is very difficult to analyze the dynamic characteristic because railway vehicle is a very complex system which are connected various mass element with railway vehicle system. To realize and analyze actual phenomenon has restriction that usual commercial software calculates creep force under creep theory about wheel-rail contact mechanism as basic analyzing, and approach about contact point are based on two dimensional non-linear contact theory and simplified Hertzian contact which considers just displacement change on the YZ plain. Therefore, to solve these problems there should be a new approach difference with existing one. In this research, a new algorithm for finding wheel-rail contact position, calculation method of contact force and applied force will be presented.

• Proceedings of the KSR Conference
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• 2005.11a
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• pp.131-139
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• 2005

It is very difficult to analyze the dynamic characteristic because tilting vehicle is a very complex system which are connected various mass element with tilting system. To realize and analyze actual phenomenon has restriction that usual commercial software calculates creep force under creep theory about wheel -rail contact mechanism as basic analyzing, and approach about contact point are based on two dimensional non-linear contact theory and simplified Hertzian contact which considers just displacement change on the YZ plain. Therefore, to solve these problems there should be a new approach difference with existing one. In this research, a new algorithm for finding wheel-rail contact position, calculation method of contact force and applied force will be presented.

• Tribology and Lubricants
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• v.4 no.2
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• pp.28-35
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• 1988

A general and efficient algorithm is proposed for the analysis of the frictionless elastic contact problems. It utilizes a simplex-type algorithm with a modified entry rule and incoporates finite element method to obtain flexibility matrices. The algorithmic solution is compared with the Hertzian solution for the contact problem between two cylinders to prove its accuracy and the contact problem between pin and piston rod is solved and compared with the numerical results of Frankavilla and Zienkiewicz to demonstrate the generality and effectiveness of the suggested algorithm. The contact problem between mating involute gear teeth at the worst load position is considered. The computed contact stress is smaller than the result of Hertz's theory applied to the contact between two kinematically equivalent discs and the contact area is larger than that of Hertz's theory.

• Journal of the Korean Society for Railway
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• v.16 no.3
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• pp.175-182
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• 2013

Rolling noise is an important source of noise from railways; it is caused by wheel and rail vibrations induced by acoustic roughness at the wheel/rail contact. To reduce rolling noise, it is necessary to have a reliable prediction model that can be used to investigate the effects of various parameters related to the rolling noise. This paper deals with modeling rolling noise from wheel and rail vibrations. In this study, the track is modeled as a discretely supported beam by regarding concrete slab tracks, and the wheel vibration is simulated by using the finite element method. The vertical and lateral wheel/rail contact forces are modeled using the linearized Hertzian contact theory, and then the vibration responses of the wheel and rail are calculated to predict the radiated noise. To validate the proposed model, a field measurement was carried out for a test vehicle. It was found that the predicted result agrees well with the measured one, showing similar behavior in the frequency range between 200 and 4000 Hz where the rolling noise is prominent.