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In order to analyze and predict the performance of mechanical structure and system, the tangential contact of solid-liquid interface under normal and tangential loads is studied, and the tangential stiffness model of rough surfaces is established by analyzing various contact states of the asperity under normal elastic-plastic deformation and tangential stick-slip. Based on the contact model of closed oil pits based on the influence of rough surfaces, on the basis of fully considering the influence of gradual application of load on the number of closed oil pit, and then changing the load distribution of solid-liquid interface, a liquid tangential stiffness model is established. The tangential stiffness of solid-liquid interface is obtained by two parts in parallel. Through simulation and experimental analysis, the effects of normal load, deformation and lubricant viscosity on the tangential stiffness of solid-liquid interface are revealed, and the tangential stiffness with or without lubricating medium is compared and analyzed. The results show that the tangential stiffness of solid-liquid interface and solid-solid interface increases nonlinearly with the increase of normal load and deformation. Due to the contribution of liquid stiffness, the tangential stiffness of solid-liquid interface is always slightly higher than that of solid-solid interface. The greater the viscosity of the lubricating medium, the greater the tangential stiffness of the solid-liquid interface. At low load, liquid contact is dominant, and the tangential stiffness of solid-liquid interface is low. Under moderate and heavy loads, the solid contact is dominant, and the tangential stiffness of the solid-liquid interface increases rapidly. Therefore, the tangential contact stiffness of the solid-liquid interface in mixed lubrication can be effectively improved by increasing the normal load and increasing the viscosity of the lubricating medium.

An experimental method that can quantify relative slip was developed using digital image correlation (DIC) in order to evaluate the sliding portion. The bridge-type test setup was designed to establish the fretting contact condition. The relative displacements between the contact surfaces were determined by DIC methods. Based on the evolution and distribution of relative slip, the transitions from gross slip to partial slip on the contact surface were found throughout all tests. This result indicated that the fretting scar was closely correlated to relative slip. The variation of relative slip corresponding to the stick-slip state was consistent with the tangential force coefficient. Besides, the load amplitude was an important factor for fretting fatigue damage, which can affect the stick-slip state. [ABSTRACT FROM AUTHOR]

This paper proposes a modified tangential contact stiffness model considering friction's effect, which is the first key step to establish the dynamic model of the fixture-workpiece system, and this is the foundation of vibration suppression for the manufacturing process of aerospace blades. According to Love's elastic deformation, the model's derivation process starts with the potential function in each coordinate axis's direction respectively. The generalized Hertz contact theory is employed to calculate the contact forces in this model. The symmetrical characteristic of the contact area has simplified the derivation process to obtain the eventual tangential contact stiffness model. A validation experiment focusing on a tangential stiffness measuring is achieved by putting two spherical objects in contact together to get the tangential contact stiffness. Based on the data collected in this experiment, a comparison with a most similar existed model is carried out, and the result shows that the relative error of this modified model are all less than 10%, while the original model's (the most similar model) relative error exceeding 50% captures more than 3/4 of the 30 data sets randomly selected in each experiment group, and that means the modification of this paper brings great improvement to the contact stiffness model. [ABSTRACT FROM AUTHOR]

An experimental method that can quantify relative slip was developed using digital image correlation (DIC) in order to evaluate the sliding portion. The bridge-type test setup was designed to establish the fretting contact condition. The relative displacements between the contact surfaces were determined by DIC methods. Based on the evolution and distribution of relative slip, the transitions from gross slip to partial slip on the contact surface were found throughout all tests. This result indicated that the fretting scar was closely correlated to relative slip. The variation of relative slip corresponding to the stick-slip state was consistent with the tangential force coefficient. Besides, the load amplitude was an important factor for fretting fatigue damage, which can affect the stick-slip state.

This paper proposes a modified tangential contact stiffness model considering friction’s effect, which is the first key step to establish the dynamic model of the fixture-workpiece system, and this is the foundation of vibration suppression for the manufacturing process of aerospace blades. According to Love’s elastic deformation, the model’s derivation process starts with the potential function in each coordinate axis’s direction respectively. The generalized Hertz contact theory is employed to calculate the contact forces in this model. The symmetrical characteristic of the contact area has simplified the derivation process to obtain the eventual tangential contact stiffness model. A validation experiment focusing on a tangential stiffness measuring is achieved by putting two spherical objects in contact together to get the tangential contact stiffness. Based on the data collected in this experiment, a comparison with a most similar existed model is carried out, and the result shows that the relative error of this modified model are all less than 10%, while the original model’s (the most similar model) relative error exceeding 50% captures more than 3/4 of the 30 data sets randomly selected in each experiment group, and that means the modification of this paper brings great improvement to the contact stiffness model.

On the basis of the M-B fractal model,and combining with distribution formula of two cylinders contact area,a calculation model of tangential contact stiffness for gear joint surface is set up by using anisotropic fractal geometric theory.The influence of the main parameters in the model on the gear fractal contact model is obtained through emulation of MATLAB.The results indicate that the joint surface tangential contact stiffness increases with increasing material property or gear teeth,but decreases with increasing fractal roughness or ratio of total tangential load to total normal load.When fractal dimension is smaller（D < 1.7）,the gear joint surface tangential contact stiffness increases as fractal dimension increases.However,when fractal dimension becomes larger（D≥1.7）,the gear joint surface tangential contact stiffness decreases as fractal dimension increases.

In this work, the role of the contact stiffness in the measurement of principal variables in fretting wear tests is assessed. Several fretting wear tribometers found in the literature, including one developed by the authors, are analysed and modelled using numerical methods. The results show the importance of the tribosystem stiffness and tangential contact stiffness in the displacement sensor calibration and in the correct numerical modelling of fretting wear tests, especially for flat-to-flat contact configuration. The study highlights that, in most cases, direct comparisons between fretting results with severe wear obtained with different tribometers cannot be performed if the contact stiffness is not properly considered during the development of the experiments.

Vibration of a blade couple damped by a dry friction contact in the shroud is investigated by means of hysteresis loops and response curves analysis. The studied system is excited by one harmonic external force in a frequency range near to the lowest eigenfrequency of real blades. Blades are connected by means of a damping element consisting of dry friction part linked in series with linear spring. This "stick-slip" damping element is supposed to be either weightless or of a very small mass which models the mass of elastically deformed parts of contacting bodies near the friction surface. Two approximate mathematical models of "stick-slip" dry friction elements are suggested and analysed. The response curves of blade couple connected by stick-slip damping element are presented for different values of slip friction forces and two values of mass of elastically deformed parts.

This study demonstrates optical measurements of a real contact area and tangential contact stiffness in a rough contact interface between a soft adhesive elastomer and a glass plate. A friction tester developed in this study employs a rough contact interface between a rough rubber plate that is made of cross-linked poly-dimethyl siloxane (PDMS) and a smooth optical glass (BK7) hemisphere. This friction tester also equips a transmission optical system that is composed of a white light-emitting diodes (LED) light source, an objective lens system, and a charge coupled device (CCD) camera, for the in situ observation of the space distribution of the real contact area in the apparent contact region. Based on a simplified analysis, in accordance to the measurements of the transmitted light intensity, the amount of the real contact area was determined without any complicated calibrations. As a result, it was found that the amount of the real contact area linearly increased with normal load. Furthermore, using the digital image correlation (DIC) method, the time changes in the surface displacement field within the apparent contact region were visualized from the onset of the sliding motion to the onset of the steady sliding. These results provided a direct estimation of the tangential contact stiffness that resulted from the tangential deformation at the contacting asperity layer.

Vibration of a blade couple damped by a dry friction contact in the shroud is investigated by means of hysteresis loops and response curves analysis. The studied system is excited by one harmonic external force in a frequency range near to the lowest eigenfrequency of real blades. Blades are connected by means of a damping element consisting of dry friction part linked in series with linear spring. This ''stick-slip'' damping element is supposed to be either weightless or of a very small mass which models the mass of elastically deformed parts of contacting bodies near the friction surface. Two approximate mathematical models of ''stick-slip'' dry friction elements are suggested and analysed. The response curves of blade couple connected by stick-slip damping element are presented for different values of slip friction forces and two values of mass of elastically deformed parts. [ABSTRACT FROM AUTHOR]

Digital image correlation (DIC) is a full field three dimensional measurement technique that can quantify displacements and strains of a surface. In this paper, digital image correlation is used as a slip measurement technique during coupon scale fretting fatigue experiments. Slip measured with the novel DIC technique is compared to conventional slip measurement techniques as clip gauges and modified clip gauge measurements proposed by Wittkowsky et al. Slip measurements with the DIC system show lower slip values and higher tangential contact stiffness's compared to (modified) clip gauge measurements. Slip measured with DIC is obtained closer to the contact compared to clip gauges, eliminating the influence of elastic deformations or fitting parameters. During the fretting fatigue experiments are two equal contacts simultaneously tested. However, the slip of both contacts is not identical with outliers of more than 10% difference in slip amplitude. [ABSTRACT FROM AUTHOR]

The dynamic analysis model of axial piston pump was established; both the kinematics and dynamics simulation analysis were conducted by virtual prototyping approach. The displacement, velocity, acceleration and stress curves of the piston under different working conditions were investigated. In addition, a ball-in-socket contact model was established, and the effects of hydraulic pressure, piston radius and radial clearance on normal displacement, contact radius, maximum contact pressure, normal contact stiffness and tangential contact stiffness were analyzed comprehensively. The results indicate that the normal displacement, maximum contact pressure, contact radius, normal contact stiffness and tangential contact stiffness can be improved by enlarging the piston radius and decreasing the radial clearance. [ABSTRACT FROM AUTHOR]

In this work, the role of the contact stiffness in the measurement of principal variables in fretting wear tests is assessed. Several fretting wear tribometers found in the literature, including one developed by the authors, are analysed and modelled using numerical methods. The results show the importance of the tribosystem stiffness and tangential contact stiffness in the displacement sensor calibration and in the correct numerical modelling of fretting wear tests, especially for flat-to-flat contact configuration. The study highlights that, in most cases, direct comparisons between fretting results with severe wear obtained with different tribometers cannot be performed if the contact stiffness is not properly considered during the development of the experiments. [ABSTRACT FROM AUTHOR]