Increase In Contact Stiffness Research Articles

A Side Contact Model of Joint Considering the Horizontal Distance Distribution Between Asperities

Abstract A side contact model of joint is proposed, which considers the horizontal distance distribution and side contact between the asperities on the contact surfaces. The Leica DCM3D microscope is applied to collect the profile data of the grinding surfaces. After analyzing the profile data by the statistical method, it is found that the horizontal distance distributions between asperities on the contact surfaces show an approximate normal distribution. Based on the discovery, a contact model of joint considering the horizontal distance distribution and side contact between asperities is established by statistical theory. The simulation results of the model show that the dimensionless tangential contact stiffness of joint is always lower than that of the GZQ model under the condition of the same dimensionless average distance of contact surfaces and P/T. When the standard deviation of horizontal distance between asperities decreases, both the dimensionless tangential contact stiffness of joint and the dimensionless normal contact stiffness increase. The finite element analysis and the modal experiment based on the contact model are carried out. It is found that the first three modal frequencies and modal shapes obtained from finite element analysis are in good agreement with those from the modal experiment, and compared with the modal frequencies from experiment, the modal frequencies from finite element analysis based on the model proposed in this paper show less error than those of finite element analysis based on the GZQ model. Therefore, this model proposed in this paper can more accurately predict the dynamic characteristics of joint.

Relationship between the contact force strength and numerical inaccuracies in piecewise-smooth systems

This work studies the different types of behavior and inaccuracies that can occur when contact is not adequately accounted for in a dynamical system with freeplay, as the strength of the contact stiffness increases. The MATLAB® ode45 time integration solver, with the built-in Event Location capability, is first validated using past experimental data from a forced Duffing oscillator with freeplay. Next, numerical results utilizing event location are compared to results neglecting event location in order to highlight possible numerical errors and effects on multistable dynamical responses. Inaccuracies tend to occur in two different ways. First, neglecting event location can affect the boundaries between basins of attraction. Second, neglecting event location has little effect on the behaviors of the attractor solutions themselves besides merely resembling poorly converged solutions. Errors are less pronounced at the limits of soft or hard contact stiffness. This study shows the importance of accurately solving piecewise-smooth systems and the existing correlation between the strength of the contact force and possible numerical inaccuracies.

Dynamic response analysis of shrouded blades under impact-friction considering the influence of passive blade vibration

A new dynamic model of shrouded blades with elastic support and variable cross-section is derived based on the Timoshenko beam theory, in which factors to be considered include centrifugal stiffening, spin softening, Coriolis force, blade stagger angle, and twist angle. The proposed model (PM) is verified by comparing the dynamic frequency results of the finite element model (FEM) and the PM. An impact-friction model of shrouded blades is established which can take into account the inertia effects of two passive blades. By comparing the vibration response of the two models (PM and FEM), the established impact-friction model is verified. Finally, the influences of normal contact stiffness, blade root support stiffness, and shroud position on the vibration response of the system are analyzed. Meanwhile, bifurcation diagrams, time-domain waveforms, phase diagrams, Poincaré maps, and frequency spectrum are utilized to analyze the nonlinear vibration characteristics of shrouded blades. The results show that the impact and friction between adjacent shrouds will cause the complex nonlinear vibration of the blades. Under small initial gaps, hard nonlinear phenomena can be observed in the vibration response of the shrouded blade. While under small initial preloads, it shows an obvious soft nonlinear phenomenon. Furthermore, with the increase of normal contact stiffness and blade root support stiffness, the resonance peak of the blade-tip flexural displacement decreases. When the shroud is closer to the blade-tip of the blade, the vibration reduction effect of the shrouded blade is better. The active blade experiences the chaos, period-one motion due to the nonlinear behavior of the impact-friction coupling at the adjacent shroud contact interfaces.

Research on comprehensive stiffness characteristics of angular contact ball bearings under multi-factor coupling condition

In order to research the dynamic performance of angular contact ball bearings of high-speed motorized spindles in detail, based on Hertz contact theory and bearing quasi-static model, considering the influence of centrifugal force, gyroscope moment and thermal effect on bearing operation, the modified quasi-static model is established to calculate the bearing contact stiffness. Then, considering the influence of temperature on the dynamic viscosity of lubricating oil, film stiffness model of bearing is also presented. On the basis, the bearing comprehensive stiffness model is proposed, and the influences of combined load and rotational speed on the bearing stiffness are investigated. The results show that as the speed increases, the radial contact stiffness increases, while the axial and angular contact stiffness decrease, the dynamic viscosity of the lubricating oil decreases, the film stiffness decreases and the comprehensive radial, axial and angular stiffness decrease. With the increase of axial load, the radial, axial and angular contact stiffness increase, the comprehensive stiffness increases. When the radial load increases, the radial, axial and angular contact stiffness decreases, while the comprehensive stiffness increases. It is found that the comprehensive stiffness considering the temperature is larger than without consideration of the temperature.

Modeling and Analysis of the Composite Stiffness for Angular Contact Ball Bearings

As a core component of the motorized spindle, the dynamic stiffness of the angular contact ball bearing directly affects the dynamic characteristics of machinery. A modified quasistatic model of the ball bearing is established considering the influences of thermal deformation, centrifugal deformation, and elastohydrodynamic lubrication (EHL). Then, the film stiffness model considering spin motion is constructed. On this basis, the composite stiffness model of the ball bearing is proposed, and the effects of different factors on dynamic characteristic parameters are investigated. The results show that different factors have different effects on the dynamic parameters. With the increase in preload, the contact stiffness and composite stiffness increase. Considering EHL, the radial contact stiffness and composite stiffness increase while the axial and angular contact stiffness and composite stiffness decrease. Considering the thermal effect and centrifugal effect, the radial contact stiffness and composite stiffness increase while the axial and angular contact stiffness and composite stiffness decrease. The film stiffness and composite stiffness increase with the consideration of the spinning motion.

Statistical Analysis of Contact Stiffness for Shaft-Bearing Assembly with Tolerancing and Fit

Abstract Tolerance and fit (T&F) are crucial as it affects the performance of mechanical system. Fitting condition between shaft and bearing is the most typical one that affects the pressure distribution between the them that, in turn, determines its contact stiffness. This paper is aimed to explore a method to analyze the statistical distribution of the contact pressure and stiffness between the shaft and the bearing based on the size distribution of the T&F specification. We analyzed the pressure distribution corresponding to the T&F specifications of the shaft and the bearing by the probability density function and convolution. Contact pressures and stiffness of the mating surface are analyzed according to the amount of interference. A roller bearing with diameter 50 mm is taken as an example to illustrate this analysis. The contact pressure and stiffness are analyzed under a transition fitting condition o50H6/k5, as recommended by many bearing makers and design handbooks. The results showed that there is a high possibility to become clearance fit in this case and the expectation is a gap of 0.5μm, which implies loss of the contact stiffness thus far from the original design intention. Two approaches, either using tighter tolerance of bearing inner ring or higher dimensional deviation of the shaft diameter, are further investigated to overcome this problem. The results showed that probability and expectation of contact stiffness increase by employing either approach. The main contribution of this paper is to develop a methodology for analyzing statistical distribution of contact stiffness between the shaft-bearing assembly based on the T&F specification. It also shows tighter tolerance for the bearing inner ring or higher dimensional deviation of the shaft diameter will improve contact stiffness, if the T&F specification does not meet stiffness requirement.

A modelling approach for the nonlinear dynamics of assembled structures undergoing fretting wear.

Assembled structures tend to exhibit nonlinear dynamic behaviour at high excitation levels due to the presence of contact interfaces. The possibility of building predictive models relies on the ability of the modelling strategy to capture the complex nonlinear phenomena occurring at the interface. One of these phenomena, normally neglected, is the fretting wear occurring at the frictional interface. In this paper, a computationally efficient modelling approach which enables considerations of the effect of fretting wear on the nonlinear dynamics is presented. A multi-scale strategy is proposed, in which two different time scales and space scales are used for the contact analysis and dynamic analysis. Thanks to the de-coupling of the contact and dynamic analysis, a more realistic representation of the contact interface, which includes surface roughness, is possible. The proposed approach is applied to a single bolted joint resonator with a simulated rough contact interface. A tendency towards an increase of real contact area and contact stiffness at the interface is clearly observed. The dynamic response of the system is shown to evolve over time, with a slight decrease of damping and an increase of resonance frequency, highlighting the impact of fretting wear on the system dynamics.

Mechanical Performance of Prefabricated External Wall Panel under Horizontal Displacement

In this paper, experiment and Finite Element Method (FEM) approaches are employed to study the mechanical performance of prefabricated external wall panel under lateral displacement. Tensile bond strength test and Z-shaped specimen direct shear test of the bonding interface of mortar to ceramsite concrete are performed, the normal and shear mechanical property of the interface is studied respectively. Scaled model test of prefabricated external wall panel under lateral displacement is then performed to obtain load-displacement curve, and mechanical behavior of prefabricated external wall panel in different stages is studied. Moreover, ABAQUS finite element analysis model for scaled model test panel is established based on previous study about bond interface and the results from experiment and FEM analysis are relatively consistent with each other. It is found that with the gradual increase in tangential contact stiffness of joint interfaces, the overall lateral stiffness of wall panels will approach complete joint consolidation conditions before the peak load. However, when the tangential contact stiffness of joint interfaces increases to a certain extent, there will be little change in initial lateral stiffness.

Correlation between cavitation erosion resistance and cyclic mechanical properties of different metallic materials

Machine components in contact with flowing fluids are especially prone to cavitation erosion, where plastic deformation and material loss occur due to the repeated implosion of cavitation bubbles in the vicinity of a solid surface. Identifying a correlation between experimentally derivable material properties and resistance against cavitation erosion could help improve the lifetime of cavitation-affected components. Cavitation erosion is a predominantly fatigue-driven phenomenon. In this investigation, we conducted nanoindentation experiments to examine cyclic micromechanical material properties in response to an increasing number of cycles. The experiments were performed on pure iron and different steel grades, i.e., austenitic stainless CrMnCN steels, interstitially alloyed with carbon and nitrogen. We confirmed the view, also proposed in literature, that indentation hardness is inappropriate for ordering the investigated materials by incubation period or maximum erosion rate. We found that the percentage increase of nanoindentation contact stiffness, after an increasing number of cycles, is a promising indicator in terms of the overall ranking of cavitation erosion resistance among the considered materials. Although a single cavitation impact is associated with a significantly higher strain rate than nanoindentation experiments, it is shown that the plastically deformed area around each indent exhibits indications of deformation, such as the formation of slip lines that are also observable after cavitation-induced impacts.

Production and characterization of a novel carbon nanotube/titanium nitride nanocomposite

A novel titanium nitride (TiN)/carbon nanotube (CNT) nanocomposite is produced with the purpose to mechanically, structurally and chemically stabilize a ‘felt-like’ CNT growth structure. The CNTs are grown on stainless steel (SS) 304 by chemical vapor deposition using the direct growth method previously developed, which does not require the use of an additional catalyst precursor. The TiN coating is achieved by physical vapor deposition and is shown here to generate a nanocomposite with a porous three-dimensional architecture. The contact stiffness is evaluated using nanoindentation, and wetting properties of the TiN/CNT nanocomposites are determined from contact angle measurements. An increase in contact stiffness and effective elastic modulus with TiN coating time was observed. The TiN coating on the non-wetting CNT felt results in a wetting nanocomposite surface. The wetting property is found to be a function of the TiN coating thickness on the CNT structure.

Identification of contact parameters from elastic-plastic impact of hard sphere and elastic half space

The theoretical and experimental analysis described in this paper demonstrate a simple systematic procedure to determine the contact parameters between a spherical impactor and an elastic half space via impact tests. Two main contact parameters were measured at different velocities of impact, that is the time duration of contact and the maximum normal contact force. A general nonlinear contact model based on power law is used to extract the contact stiffness and frequency of contact resonance from these two main contact parameters. Experimental results were obtained and compared for three steel samples with different hardness numbers and impacted by different sphere diameters of 2.0, 2.5 and 3.5mm to investigate the limits of elastic deformation. Effect of the used sphere diameter on the contact parameters are shown. The test results show that the adopted model using independently measured material data can predict the contact parameters due to hard sphere impact with elastic half space. The general trend shows the increase of contact stiffness with the sphere diameter but the limits of elastic regime decrease.

Analysis of a retrieved squeaking ceramic-on-ceramic hip arthroplasty bearing

Ceramic-on-ceramic bearings in total hip replacements have shown superior wear performance compared to other material couples. However, 1–10% of patients have reported squeaking with the use of ceramic-on-ceramic bearings. A ceramic-on-ceramic bearing was retrieved from a patient after 4.5 years in service secondary to squeaking. The explant was analyzed to investigate the possible factors attributing to the hip squeak utilizing acoustic analysis, visual inspection, modal analysis, random vibration analysis, and mathematical modeling. Random vibration analysis of the parts of the implant showed that boundary conditions along the metallic shell play an important role in squeal occurrence. The implant also showed the evidence of material transfer. Using the results of modal analysis, a 2-degree of freedom friction model demonstrated the influence of third body material transfer on the stability of the system to be an important factor in squeaking. The mathematical parametric analysis showed that a larger mass creates more instability, and hence more noise and vibration. Increased stiffness of the shell proved to stabilize the system for most loading conditions. Limit-cycle plots showed a definite change in the system behavior but stability was maintained through a significant increase in contact stiffness.

Estimation of distinctive mechanical properties of spark plasma sintered titanium–titanium boride composites through nano-indentation technique

Abstract In this paper, two titanium–titanium boride composites aiming at 20 % and 40 % (by volume) of titanium boride reinforcement were processed through spark plasma sintering. The mechanical properties such as fracture toughness, indentation creep, contact stiffness, indentation hardness and Young's modulus of the processed composites were evaluated by means of nano-indentation. The Young's modulus, indentation hardness and contact stiffness increase with the increase in volume fraction of titanium boride, while the fracture toughness and indentation creep decrease. The titanium composite with 38.5 % (by volume) titanium boride showed improved mechanical properties compared to the composite with 24 % (by volume) titanium boride reinforcement. The morphological influence of TiB reinforcement on the mechanical properties was also discussed.

Mechanical characteristics of graphene nanoribbons encapsulated in single-walled carbon nanotubes using molecular dynamics simulations

We perform molecular dynamics (MD) simulations of nanoindentation to study the mechanical properties of a graphene nanoribbon encapsulated in a single-walled carbon nanotube (GNR@SWCNT). The effects of different temperatures, nanotube diameters, and slenderness ratios on the properties of the GNR@SWCNT are examined. Results show that the maximum load and contact stiffness increase with an increase of temperature. But the adhesion force and ratio of springback are low at a high temperature of 1200K. The maximum load and contact stiffness are high for the nanoindentation of the GNR@SWCNT with a low slenderness ratio. In addition, the GNR@SWCNT has a more than 15% rate of springback exhibiting a superelastic nanocomposite behavior. The results are useful for engineering applications of nanocomposites composed of carbon nanotubes and graphene materials.

Ultrasonic measurement of contact stiffness and pressure distribution on spindle–holder taper interfaces

The measurement of contact characteristics of the spindle–holder taper interface is critical for the evaluation of the performance of a machine tool spindle system. In this study, an ultrasonic method was proposed to measure the contact stiffness and pressure distribution on the taper interface. The taper interface was scanned by an ultrasound transducer, and the nominal contact area was directly estimated from the resulting ultrasonic reflection coefficient. The normal stiffness distribution was determined by the spring-damper model from the reflection coefficient. On this basis, the distributed and global radial stiffness of the taper interface was calculated by the presented theoretical formulas. Meanwhile, a calibration curve was established to convert the ultrasonic reflection to contact pressure. Based on the proposed ultrasonic method, the effects of angle fitting error and clamping force were studied. The results show that the contact area, contact pressure and contact stiffness increase with the clamping force. As the angle fitting error increases, the contact area decreases, while the pressure and stiffness at the big end of the taper interface become much larger than these at the small end. In the meantime, the global radial stiffness increases first and then decreases. This result suggests that a larger angle fit error within the permissible range is better for the global radial stiffness. Moreover, the measured results confirm that a taper joint with an angle fit error larger than +36" is not suitable for practical application, because the contact pressure at the small end is too small. To compare with the ultrasonic method, the geometrical shape profiles of the contact surfaces were constructed, and FE models were also established for contact pressure predictions. The comparison shows that the ultrasound results are consistent with the surface shape profiles and the numerical predictions. Besides, one of the taper interfaces was measured three times with the same clamping force, and the results indicate that the repeatability of the proposed method is good.

Normal contact stiffness of the elliptic area between two asperities

A new expression for contact deformation is given, and the normal contact stiffness between single asperities is derived according to Hooke's law. A contact model between two ellipsoidal asperities is simulated by the FE method, the result compared with the theoretical solution. It is found that the curves of the normal contact stiffness versus the included angle in the principal curvature direction show similar trends and evolve as a cosine feature. The effects of the parameters on normal contact stiffness are found to show that normal contact stiffness increases and reaches the upper limit gradually with an increase in these parameters.

Influence Factors Comparison and Analysis of Axial Contact Stiffness between Single-Nut and Double-Nut Ball Screws

Axial contact stiffness increase of ball screws can reduce the vibration and enhance machining precision of CNC machine tool during machining process. On the basis of Hertz contact theory, calculation formula of axial contact stiffness was deduced with consideration of helix angle for 5010 single-nut and double-nut ball screws, influence factors comparison and analysis was carried out, and contrast curve was obtained. The result shows that the axial contact stiffness of preloaded double-nut ball screws is higher than that of single-nut ball screws. Ball number, contact angle and curvature ratio has obvious influence on the axial contact stiffness of double-nut ball screws: ball number increase can enhance the axial contact stiffness; increase of contact angle and curvature ratio can lower the axial contact stiffness. The axial contact stiffness of single-nut and double-nut ball screws does almost not vary with axial force and helix angle. The conclusion provides certain theoretical basis for design and selection of ball screws.

Non-linear Behavior of Normal Contact Stiffness of Tunnel Surface and Supporting System of Tunnel Boring Machines

The interfacial contact stiffness between the supporting system of tunnel boring machines(TBM) and the tunnel surfaces is closely related to the mechanical behavior of rocks and the morphology of tunnel surfaces. The mathematical model based on the fractal theory is employed to study the relation between the roughness and fractal parameters of three dimensional tunnel surfaces. The coarse surfaces are established by using the projecting method according to the characteristics of tunnel surfaces. Many parameters such as the roughness of the tunnel surfaces, the mechanical behavior of rocks, the number of the supporting boots and composite geologic structures are taken into consideration to obtain the correlation between the normal contact stiffness and the loads. The results show that the increases of the fractal dimension, the elastic modulus, the normal loads and the number of support boots cause the increase of the interfacial contact stiffness. The contact stiffness of the double supporting systems is twice of that of the single one subjected to the same load. The normal stiffness is minimal when the ratios of the soft and hard rocks in the composite geologic structures are approximately identical. The increasing of the ratio of soft rocks in the contacting area causes the increase of the contact stiffness. However, the variation of the contact stiffness is not obvious when the proportions of two kinds of rocks on the contacting area are changed.

Multibody modelling of a TB31 and a TB32 crash test with vertical portable concrete barriers: Model verification and sensitivity analysis

In this article the multibody simulation software package MADYMO for analysing and optimizing occupant safety design was used to model crash tests for Normal Containment barriers in accordance with EN 1317. The verification process was carried out by simulating a TB31 and a TB32 crash test performed on vertical portable concrete barriers and by comparing the numerical results to those obtained experimentally. The same modelling approach was applied to both tests to evaluate the predictive capacity of the modelling at two different impact speeds. A sensitivity analysis of the vehicle stiffness was also carried out. The capacity to predict all of the principal EN1317 criteria was assessed for the first time: the acceleration severity index, the theoretical head impact velocity, the barrier working width and the vehicle exit box. Results showed a maximum error of 6% for the acceleration severity index and 21% for theoretical head impact velocity for the numerical simulation in comparison to the recorded data. The exit box position was predicted with a maximum error of 4°. For the working width, a large percentage difference was observed for test TB31 due to the small absolute value of the barrier deflection but the results were well within the limit value from the standard for both tests. The sensitivity analysis showed the robustness of the modelling with respect to contact stiffness increase of ±20% and ±40%. This is the first multibody model of portable concrete barriers that can reproduce not only the acceleration severity index but all the test criteria of EN 1317 and is therefore a valuable tool for new product development and for injury biomechanics research.

An experimental method for tangential contact stiffness evaluation of contact interfaces with controlled contact asperities

An experimental method for estimating the tangential contact stiffness of contact interface with controlled contact asperities is discussed. The tangential contact stiffness is analyzed from the shift of certain eigenmode frequency of the system resulting from the changes in the density of contact asperities and the application of normal force. The results show that for the case of contact combination with 189 contact asperities, the corresponding eigenmode frequency shifted from 1.01 kHz at normal force of 19 N to 1.64 kHz at normal force of 148 N. This shift corresponds to the increase of tangential contact stiffness from 34.08 MN/m at normal force of 19 N to 67.44 MN/m at normal force of 148 N. It is found that the corresponding eigenmode frequency and its shift were affected by the density of contact asperities as well as the normal force. In the case of contact combination with 397 contact asperities, the corresponding eigenmode frequency shifted from 2.36 kHz at normal force of 49 N to 3.9 kHz at normal force of 153 N, indicating the increase of the tangential contact stiffness from 93.91 to 140.73 MN/m. A simple power relationship is proposed to explain the quantitative relationship between the eigenmode frequency shift and the tangential contact stiffness value.