• Korean Journal of Applied Biomechanics
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• v.27 no.2
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• pp.109-116
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• 2017

Objective: This study aimed to investigate the relationship between leg stiffness and kinematic variables according to load while running. Method: Participants included eight healthy men (mean age, $22.75{\pm}1.16years$; mean height: $1.73{\pm}0.01m$; mean body weight, $71.37{\pm}5.50kg$) who ran with no load or a backpack loaded with 14.08% or 28.17% of their body weight. The analyzed variables included leg stiffness, ground contact time, center of gravity (COG) displacement and Y-axis velocity, lower-extremity joint angle (hip, knee, ankle), peak vertical force (PVF), and change in stance phase leg length. Results: Dimensionless leg stiffness increased significantly with increasing load during running, which was the result of increased PVF and contact time due to decreased leg lengths and COG displacement and velocity. Leg length and leg stiffness showed a negative correlation (r = -.902, $R^2=0.814$). COG velocity showed a similar correlation with COG displacement (r = .408, $R^2=.166$) and contact time (r = -.455, $R^2=.207$). Conclusion: Dimensionless leg stiffness increased during running with a load. In this investigation, leg stiffness due to load increased was most closely related to the PVF, knee joint angle, and change in stance phase leg length. However, leg stiffness was unaffected by change in contact time, COG velocity, and COG displacement.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.8
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• pp.849-855
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• 2008

An experimental method based on contact resonance is developed to extract the contact parameters of mechanical joints under various clamped conditions. Mechanical joint parameters of shear contact stiffness and damping were extracted for different physical joint parameters such as surface finish of the mating surfaces, the presence of lubrication, the effect of the clamping pressure, and shear load. It was found that the shear contact stiffness values decreased with increasing clamping load and increased with increasing shear loading. Contact damping ratio values were almost constant with clamping load, but decreased with increasing shear load. Moreover, rough surfaces exhibited the highest shear stiffness and contact damping compared to smooth surfaces.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.3 s.96
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• pp.259-265
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• 2005

A two-degree-of-freedom out-of-plane model with contact stiffness is presented to describe dynamical interaction between the pad and disc of a disc brake system. It is assumed that the out-of-plane motion of the system depends on the friction force acting along the in-plane direction. Dynamic friction coefficient is modelled as a function of both in-plane relative velocity and out-of-plane normal force. When the friction coefficient depends only on the relative velocity, the contact stiffness has the role of negative stiffness. The results of stability analysis show that the stiffness of both pad and disc is equally important. Complex eigen value analysis is conducted for the case that the friction coefficient is also dependent on the normal force. The results further verify the importance of the stiffness. It has also been found that increasing the gradient of friction coefficient with respect to the normal force makes the system more unstable.

• Tribology and Lubricants
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• v.23 no.1
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• pp.9-13
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• 2007

Despite numerous researches on atomic-scale friction have been carried out for understanding the origin of friction, lots of questions about sliding friction still remain. It is known that friction at atomic-scale always shows unique phenomena called 'stick-slips' which reflect atomic lattice of a scanned surface. In this work, experimental study on the effects of system stiffnesses and load on the atomic-scale stick-slip friction of graphite was performed by using an Atomic Force Microscope and various cantilevers/tips. The objective of this research is to figure out the dependency of atomic-scale friction on the nanomechanical properties in sliding contact such as load, stiffness and contact materials systematically. From this work, the experimental observation of transitions in atomic-scale friction from smooth sliding to multiple stick-slips in air was first made, according to the lateral cantilever stiffness and applied normal load. The superlubricity of graphite could be verified from friction vs. load experiments. Based on the results, the relationship between the stickslip behaviors and contact stiffness was carefully discussed in this work. The results or this work indicate that the atomic-scale stick-slip behaviors can be controlled by adjusting the system stiffnesses and contact materials.

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.2
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• pp.160-167
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• 2004

A two degree-of-freedom mathematical model is presented to investigate the friction mechanism of a disc brake system. A contact parameter is introduced to describe the coupling between the in-plane and the out-of-plane motions. The model with the contact parameter is considered under the assumption that the out-of-plane motion depends on the friction force along the in-plane motion. In order to describe the relationship between the friction force and the out-of plane motion, the dynamic friction coefficient is considered as a function of both relative velocity and normal farce. Using this friction law, a contact stiffness matrix along the normal direction can be obtained. The out-of-plane motion is then investigated by both the stability analysis and the numerical analysis for various parametric conditions. The results show that the stiffness parameters of the pad and the disc must be controlled at the same time. Also, the numerical analysis shows the existence of limit cycle caused by the effect of intermittent contact stiffness.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.11
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• pp.1217-1224
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• 2009

This paper presents a finite element (FE) analysis of the torsional rigidity of a two-stage cycloid drive. The cycloid disk makes contact with a number of pin-rollers simultaneously and eccentric shafts transmit not only torque of the spur gear stage to the cycloid disk, but also that of the cycloid disk to the output disk. Contacts between the disk and pin-rollers are simplified as linear spring elements, and the bearing of eccentric shaft is modeled as a rigid ring that has frictional contact to the disk and an elastic support. FE analysis for an ideal solid cycloid drive was performed and verified by a theoretical calculation. Accurate contact forces were then estimated by iterating between FE analysis for contact forces and Hertz theory calculations for nonlinear contact stiffness. In addition, torsional rigidity of the cycloid drive is analyzed to show that the bearing and nonlinear Hertz contact theory should be considered in analysis and design of a cycloid drive, which was verified with experiments. Finally, the effects of contact stiffness, bearing stiffness and cycloid disk structural stiffness according to the cycloid disk rotation on the torsional rigidity were investigated.

• Tribology and Lubricants
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• v.30 no.4
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• pp.205-211
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• 2014

Recent studies emphasize the importance of pivot stiffness in the analysis of tilting pad bearings (TPBs). The present paper develops a finite element model of the pad pivot and compares the predicted pivot stiffness to the results of Hertzian contact model calculations. Specifically, a finite element analysis generates tetrahedral mesh models with ~40,000 nodes for a ball-socket pivot and ~50,000 nodes for a rocker-back pivot. These models assume a frictionless boundary condition in the contact area. Increasing the applied loads on the pad in conjunction with increasing time steps ensures rapid convergence during the nonlinear numerical analysis. Predictions are performed using the developed finite element model for increasing the differential diameters between the pad pivot (or ball) and the bearing housing (or socket). The predictions show that the pivot contact area increases with decreasing differential diameters and increasing applied loads. Further, the maximum deformation occurring at the pivot center increases with increasing differential diameters and increasing applied loads. The pivot stiffness increases nonlinearly with decreasing differential diameters and increasing applied loads. Comparisons of results of the developed finite element model to those of Hertzian contact model calculations assuming a small contact area show that the latter model underestimates the pivot stiffnesses predicted by the finite element models of the ball-socket and rocker-back pivots, particularly for small differential diameters. This result implies the need for cautionduring the design of pivot stiffness by the Hertzian contact model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.597-600
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• 2004

A two-degree-of-freedom out-of-plane model with contact stiffness is presented to describe dynamical interaction between the pad and disc of a disc brake system. It is assumed that the out-of-plane motion of the system depends on the friction force acting along the in-plane direction. Dynamic friction coefficient is modelled as a function of both in-plane relative velocity and out-of-plane normal force. When the friction coefficient depends only on the relative velocity, the contact stiffness has the role of negative stiffness. The results of stability analysis show that the stiffness of both pad and disc are equally important. Complex eigenvalue analysis is conducted for the case that the friction coefficient is also dependent on the normal force. The results further verify the importance of the stiffness. It has also been found that increasing the gradient of friction coefficient with respect to the normal force makes the system more unstable. Nonlinear analysis is also performed to demonstrate various responses. Comparing the responses with experimental data has shown that the proposed model may qualitatively well represent a certain type of brake noise.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.11a
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• pp.523-524
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• 2010

• Transactions of the Korean Society of Automotive Engineers
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• v.18 no.3
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• pp.127-132
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• 2010

Eigensolutions associated with self-excited vibration of disc brake system can be obtained by complex eigenvalue analysis. The eigenvalue sensitivity to change in contact stiffness can be used to demonstrate stability criteria and eigenvalue veering. Dynamic instability on eigenvalue loci with respect to the variation of contact stiffness is found to be related to mode interaction between two adjacent modes. This modal interaction can be effectively shown by mode shape visualization. This paper presents the methodology to construct the mode shape of disc brake system where a disc and two brake pads are coupled with contact stiffness.