• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.816-821
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• 2005

The cycloid reducer has very high efficiency, high ratios, high stiffness and small size, in comparison with a conventional gear mechanism, which makes it an attractive candidate for limited space and precision application such as industrial robot. There are several publications on analysis and design of the cycloid reducer, however, it was assumed that the contact stiffness of pin rollers and cycloid disk is constant regardless of their contact geometry. Moreover, the torsional stiffness of the cycloid reducer couldn't be calculated due to the assumption. In this paper, we present a new procedure of calculating torsional stiffness of the cycloid reducer using Hertz contact theory. First, conventional force analysis of the cycloid reducer is briefly reviewed. Then, iterative numerical calculation procedure of the contact stiffness is proposed based on the Hertz contact theory where the contact stiffness depends on the contact force. In addition, total torsional stiffness of the cycloid reducer is estimated considering its rolling element bearing stiffness. The torsional stiffness of the cycloid reducer is dominated by the rolling element bearing stiffness since the contact stiffness of the cycloid disk is too large.

• Structural Engineering and Mechanics
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• v.83 no.3
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• pp.341-351
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• 2022

During bolted flange assembly, the contact stiffness of some areas of the joint surface may be low due to the elastic interaction. In order to improve the contact stiffness at the lowest position of bolted flange, the correlation model between the initial bolt pre-tightening force and the contact stiffness of bolted flange is established in this paper. According to the stress distribution model of a single bolt, an assumption of uniform local contact stiffness of bolted flange is made. Moreover, the joint surface is divided into the compressive stress region and the elastic interaction region. Based on the fractal contact theory, the relationship model of contact stiffness and contact force of the joint surface is proposed. Considering the elastic interaction coefficient method, the correlation model of the initial bolt pre-tightening force and the contact stiffness of bolted flange is established. This model can be employed to reverse determine the tightening strategy of the bolt group according to working conditions. As a result, this provides a new idea for the digital design of tightening strategy of bolt group for contact stiffness of bolted flange. The tightening strategy of the bolted flange is optimized by using the correlation model of initial bolt pre-tightening force and the contact stiffness of bolted flange. After optimization, the average contact stiffness of the joint surface increased by 5%, and the minimum contact stiffness increased by 6%.

• Tribology and Lubricants
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• v.34 no.1
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• pp.23-32
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• 2018

Coupling is a mechanical component that transmits rotational force by connecting two shafts. Curvic coupling is widely used in high-performance systems because of its excellent power transmission efficiency and easy machining. However, coupling applications change dynamic behavior by reducing the stiffness of an entire system. Contact surface stiffness is an important parameter that determines the dynamic behavior of a system. In addition, the roughness profile of a contact surface is the most important parameter for obtaining contact stiffness. In this study, we theoretically establish the process of contact and bending stiffness analysis by considering the rough surface contact at Curvic coupling. Surface roughness parameters are obtained from Nayak's random process, and the normal contact stiffness of a contact surface is calculated using the Greenwood and Williamson model in the elastic region and the Jackson and Green model in the elastic-plastic region. The shape of the Curvic coupling contact surface is obtained by modeling a machined shape through an actual machining tool. Based on this modeling, we find the maximum number of gear teeth that can be machined according to the contact angle. Curvic coupling stiffness is calculated by considering the contact angle, and the calculation process is divided into stick and slip conditions. Based on this process, we investigate the stiffness characteristics according to the contact angle.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.10
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• pp.749-755
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• 2014

The analytical-finite element(FE) squeal model is applied to investigate the squeal propensity associated with contact stiffness of the disc brake system. The system contact stiffness is incorporated into the perturbed equations of motion in the analytical manner where the brake components are modeled by FE method. The results show that the contact stiffness of the friction material and the contact stiffness between the pads and caliper are the influential factors on the squeal propensity. Particularly, the modal instability of the 3200 Hz squeal mode drastically changes with respect to the contact stiffness between the pads and caliper.

• Journal of the Korean Society for Nondestructive Testing
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• v.33 no.3
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• pp.276-282
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• 2013

This paper proposes an ultrasonic method for measurement of linear and hysteretic interfacial stiffness of contacting surfaces between two steel plates subjected to nominal compression pressure. Interfacial stiffness was evaluated by the reflection and transmission coefficients obtained from three consecutive reflection waves from solid-solid surface using the shear wave. A nonlinear hysteretic spring model was proposed and used to define the quantitative interfacial stiffness of interface with the reflection and transmission coefficients. Acoustic model for 1-D wave propagation across interfaces is developed to formulate the reflection and transmission waves and to determine the linear and nonlinear hysteretic interfacial stiffness. Two identical plates are put together to form a contacting surface and pressed by bolt-fastening to measure interfacial stiffness at different states of contact pressure. It is found from experiment that the linear and hysteretic interfacial stiffness are successfully determined by the reflection and transmission coefficient at the contact surfaces through ultrasonic pulse-echo measurement.

• Journal of the Korean Society for Nondestructive Testing
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• v.28 no.6
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• pp.504-511
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• 2008

This paper proposes an ultrasonic measurement method for measurement of linear interfacial stiffness of contacting surface between two steel plates subjected to nominal compression pressures. Interfacial stiffness was evaluated by using shear waves reflected at contact interface of two identical solid plates. Three consecutive reflection waves from solid-solid surface are captured by pulse-echo method to evaluate the state of contact interface. A non-dimensional parameter defined as the ratio of their peak-to-peak amplitudes are formulated and used to calculate the quantitative stiffness of interface. Mathematical model for 1-D wave propagation across interfaces is developed to formulate the reflection and transmission waves across the interface and to determine the interfacial stiffness. Two identical plates are fabricated and assembled to form contacting surface and to measure interfacial stiffness at different states of contact pressure by means of bolt fastening. It is found from experiment that the amplitude of interfacial stiffness is dependent on the pressure and successfully determined by employing pulse-echo ultrasonic method without measuring through-transmission waves.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1350-1353
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• 2007

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.

• Journal of the Korean Society for Precision Engineering
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• v.32 no.5
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• pp.415-422
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• 2015

Ballscrews are important motion transfer and positioning units of industrial machinery and precision machines. Positioning accuracy of the feed drive system depends upon axial stiffness of ballscrew systems. As the nut stiffness depends upon preload and operating conditions, analytical modeling of the stiffness is performed through the contact and body deformation analysis. For accurate contact analysis, the contact angle variation between balls and grooves is incorporated in the developed model. To verify the developed mathematical stiffness model, experiments are conducted on the test-rig. Through the uncertainty analysis according to GUM (Guide to the expression of Uncertainty in Measurement), it is confirmed that the formulated stiffness model has over 85% estimation accuracy. After constructing the ballscrew DB, a quick turnaround system for the nut stiffness estimation has been developed in this research.

• Structural Engineering and Mechanics
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• v.82 no.5
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• pp.643-650
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• 2022

In this paper a novel mathematical model and its analytical solution of global buckling behaviour of slender elastic concrete-filled double-skin tubular (CFDST) columns with finite compliance between the steel tubes and a sandwiched concrete core is derived for the first time. The model is capable of investigating the influence of various basic parameters on critical buckling loads of CFDST columns. It is shown that the elastic buckling load of circular and slender CFDST columns is independent on longitudinal contact stiffness, but, on the other hand, it can be considerably dependent on circumferential contact stiffness. The increasing of the circumferential contact stiffness increases the critical buckling load. Furthermore, it is shown that analytical results can agree well with the experimental and numerical results if the calibrated values of circumferential contact stiffness are used in the calculations. Moreover, it is shown that the contact between the steel tubes and a sandwiched concrete core of tested large-scale CFDST columns used in the comparison is relatively weak. Finally, the proposed analytical results can be used as a benchmark solution.

• Journal of the Korean Society for Nondestructive Testing
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• v.30 no.6
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• pp.578-586
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• 2010

This paper describes a theoretical model and acoustic analysis of hysteresis of contacting surfaces subject to compression pressure. Contacting surfaces known to be nonlinear and hysteretic is considered as a simple spring that has a complex stiffness connecting discontinuous displacements between two solid contact boundaries. Mathematical formulation for 1-D interfacial wave propagation between two contacting solids is developed using the complex spring model to derive the dispersion relation between the interface wave speed and the complex interfacial stiffness. Existence of the interface wave propagating along the hysteretic interface is studied in theory and discussed by investigating the solution to the dispersion equation. Unlike the linear interface without hysteresis, there can exist only one distinct mode of interface waves for the hysteretic interface, which is anti-symmetric motion. The anti-symmetric mode of interface wave propagates with the velocity faster than the Rayleigh surface wave but less than the shear wave depending on the interfacial stiffness. If the contacting surfaces are compressed so much that the linear interfacial stiffness is very high, the hysteretic stiffness does not affect the interface wave velocity. However, it has an effect on the speed of interface wave for a loosely contact surfaces with a relatively low linear stiffness. It is also found that the phase velocity of anti-symmetric wave mode converges to the shear wave velocity in despite of the linear stiffness value if the hysteretic stiffness approaches 0.5.