Non-conformal Contact Research Articles

Modeling and test verification of variable cross-section contact behavior for spherical rollers during lapping process

Curved surface contact is widely used in the industry of bearing roller machining and shaft-hole connection, but there is no universal model to describe it. In order to study the contact problem between the spherical roller and the lapping sleeve, the existing cylindrical contact models were firstly compared and applied to the contact problem using slicing method, and a hybrid contact model was established. Based on Winkler's elastic foundation theory, a variable cross-section contact model was established and its analytical expression was obtained. Since the new model has no elastic half-space assumption, it can be used to solve conformal contact and non-conformal contact problems. Finally, the finite-element simulation results and the lapping test results show that compared with the hybrid contact model, the variable cross-section contact model can more accurately describe the static contact characteristics between the spherical roller and the lapping sleeve, and can provide a theoretical reference for roller machining and coordinated deformation of shaft-hole.

Quasi-conformal versus Hertz superposition: a comparison for two-dimensional contact

Hertz contact theory results in a relation between the normal contact force and the rigid indentation of the contact surfaces, the force is proportional to the indentation to the power of 3/2, and a semi-ellipsoidal traction distribution. It is a valid theory for non-conformal contact between smooth surfaces (curves in 2D) of elastic bodies. This force model can be derived by considering the Taylor polynomials of degree 2 at the contact point as approximations for the surfaces/curves. In the 2D case, it depends only on the curvature radii of the curves and is undefined when they are equal, the equality of radii violates the non-conformality.The Hertzian force is usually applied to the contact of solid particles as a model compensating for the small local deformations that occur in the contact region. We consider the 2D contact of a rigid convex particle with a rigid concavity enforcing the contact constraint with a barrier method, an approach that prevents overlapping of the bodies, resulting in a force that acts on the contact point. The geometries and the motion are specially designed to show the coalescence of two contact points into one. It illustrates two possible issues with convex-concave contact, the non-uniqueness of contact points and the conformality. We compare the results with a deformable finite element model for equivalent bodies and motion showing that there is a transition between a Hertzian and a non-Hertzian behavior. We conclude that a criterion for the conformality of curves must include the ever-present gap when a barrier method is used to enforce the constraint and the Hertzian force is not suitable for the coalescence of contact points.

Investigation of Effect of Surface Modification by Electropolishing on Tribological Behaviour of Worm Gear Pairs

Electropolishing using a high-current density results in a pitting phenomenon, producing a surface texture distinguished by many pits. Apart from the change in surface topography, electropolishing forms an oxide surface layer characterized by beneficial tribological properties. This paper introduces surface texturing in worm gear pairs by electropolishing a 16MnCr5 steel worm surface. Electropolishing produces surface pits 1 μm to 5 μm deep and 20 to 100 μm in diameter. The material characterization of 16MnCr5 steel is compared against the electropolished 16MnCr5 steel based on microstructure, hardness, surface topography and chemical composition. Experimental tests with worm pairs employing electropolished worms are conducted, and the results are compared to conventional worm pairs with ground steel worms. Electropolished worms show up to 5.2% higher efficiency ratings than ground ones and contribute to better running-in of worm gear pairs. Moreover, electropolished worms can reliably support full contact patterns and prevent scuffing due to improved lubrication conditions resulting from the produced surface texture and oxide surface layer. Based on the obtained results, electropolishing presents a promising method for surface texturing and modification in machine elements characterized by highly loaded non-conformal contacts and complex geometry.

Meshing theory and contact analysis of double enveloping hourglass worm drive with planar generatrix

The meshing and limit equations of worm drive usually have strong nonlinearities such as multiple solutions, solution nonexistence and equation singularity. Meanwhile, the tooth surfaces of worm drive are in nonconforming line contact, which often requires mesh refinement of contact region for the loaded contact analysis. These two challenges cause that the modeling of worm drive heavily relies on manual adjustment and the loaded contact analysis of worm drive is still rare especially when edge contact and assembly error are concerned. Focusing on the double enveloping hourglass worm (DEHW) drive with planar generatrix, this work presents procedures to solve meshing and limit equations with global convergence. The instantaneous contact line, meshing limit line, curvature interference limit line and tooth surface grid discretization are adaptively generated, without manual trial or adjustment. On the basis of adaptive mesh refinement of tooth surface, the mortar virtual element method is adopted for loaded contact analysis of DEHW drive with edge contact and center distance error. Under sliding friction, the discrete system of governing equalities and inequalities is solved by semi-smooth Newton algorithm after constraint condensation. Numerical results for meshing theory and loaded contact analysis of DEHW drive with planar generatrix are discussed.

Molybdenum Disilicide (MoSi2) and Ferrophosphorus Particles (FemPn) Improve the Anti-Seizure Properties of Copper-Tin-Bismuth Composites under Conformal and Nonconformal Contacts

Seizure is a severe accident that can abruptly stop or even damage running equipment. Improving the anti-seizure properties of friction pair materials is also crucial as lubricating and wear resistance. While the tribological performances of molybdenum disilicide (MoSi2) and ferrophosphorus (FemPn) particle-doped copper-tin-bismuth (Cu-Sn-Bi) composites have been investigated in previous studies, the specific effects of MoSi2 and FemPn particles on the anti-seizure property of Cu-Sn-Bi materials remain unclear. This study explores the seizure resistance of Cu-Sn-Bi composites containing MoSi2 and/or FemPn under conformal and nonconformal contact conditions. The materials were prepared using powder sintering technology, and the metallographic structures of four types of self-lubricating copper composites were observed. Seizure resistance under starved lubrication conditions was investigated, and the worn surfaces under different contact types were discussed and analyzed. The results indicate that the addition of MoSi2 and/or FemPn particles effectively refines the grain size, and these particles exhibit different distribution trends after powder sintering. The MoSi2 and FemPn particles improved the maximum seizure load of copper-based composite samples by 66.67% and 84.62%, respectively. The seizure forms under different contact types were also discussed.

A Novel Non-Contact Method for Monitoring the Acoustic Emission From Mixed Elastohydrodynamic Lubrication Contacts

Abstract Lubricated non-conformal contacts, such as between gear teeth, operate with high levels of mixed lubrication, where the amount of direct asperity contact depends on operating parameters that influence the film thickness. Understanding of the levels of surface interaction is key to optimizing component life, and there is considerable interest in sensitive monitoring methods such as Acoustic Emission (AE). Researchers have shown that AE can detect subtle changes in lubrication conditions, using sensors mounted directly on the rotating gears. However, the use of such sensors is complex and unsuitable for implementation in real gearboxes. The alternative, of using sensors placed on housings, is hampered by signal attenuation and noise. This paper presents a novel, non-contact stationary sensor, coupled by an oil film to the rotating gear, which is shown to be capable of detecting important changes in lubrication conditions with significantly higher consistency and precision than housing-mounted sensors, whilst avoiding the complexities of gear-mounted sensors.

Experimental investigation of the effects of debris on non-conforming contact stress

Debris widely exists in contact structures, affecting the reliability of structures. In this investigation, the effects of debris on the non-conforming contact stress are investigated through two-body and three-body contact experiments. According to the relationship between the contact length and debris length, debris is divided into long debris and short debris, which show different influences on the contact behaviors. The non-conforming contact stress is reconstructed based on full-field metrology and an inverse method. The evolution of contact stress induced by debris is analyzed with various parameters and contact surface profiles. Different factors, including debris material, debris length, debris thickness, plate material, and load amplitude, are considered in experiments. Their influence rules are discussed and summarized. The plate materials and short debris materials have coupling effects on the contact stress, which is associated with the deformation characteristics of the contact surface. The results provide an experimental reference for the research of non-conforming contact problems.

Element differential method for contact problems with non-conforming contact discretization

Element differential method for contact problems with non-conforming contact discretization

Low-impedance tissue-device interface using homogeneously conductive hydrogels chemically bonded to stretchable bioelectronics.

Stretchable bioelectronics has notably contributed to the advancement of continuous health monitoring and point-of-care type health care. However, microscale nonconformal contact and locally dehydrated interface limit performance, especially in dynamic environments. Therefore, hydrogels can be a promising interfacial material for the stretchable bioelectronics due to their unique advantages including tissue-like softness, water-rich property, and biocompatibility. However, there are still practical challenges in terms of their electrical performance, material homogeneity, and monolithic integration with stretchable devices. Here, we report the synthesis of a homogeneously conductive polyacrylamide hydrogel with an exceptionally low impedance (~21 ohms) and a reasonably high conductivity (~24 S/cm) by incorporating polyaniline-decorated poly(3,4-ethylenedioxythiophene:polystyrene). We also establish robust adhesion (interfacial toughness: ~296.7 J/m2) and reliable integration between the conductive hydrogel and the stretchable device through on-device polymerization as well as covalent and hydrogen bonding. These strategies enable the fabrication of a stretchable multichannel sensor array for the high-quality on-skin impedance and pH measurements under in vitro and in vivo circumstances.

Thermal mixed elastohydrodynamic lubrication modeling and analysis of the lubricated non-conformal contacts with non-Gaussian surface roughness and coating

The lubricated non-conformal contact generally works under the mixed-EHL regime. Optimizing the surface topography or selecting the right coating is an effective way to improve its performance. This paper presented an improved mixed-TEHL model for the lubricated non-conformal contacts with the effects of roughness and coating in consideration. The effect of coating was solved analytically by employing the Papkovich–Neuber potentials. It was found that the properties of coatings, especially their elastic modulus, significantly affect the pressure and stress distribution. In comparison to other roughness parameters, standard deviation and kurtosis have a significant impact. As expected, the present model can provide an efficient analysis of the tribological behavior and the stress distribution of the lubricated non-conformal contacts.

Tribological Properties of a Sliding Joint with an a-C:H:W Coating under Lubrication Conditions with PAO8 Oil and the Addition of 2% MoS2 Nanoparticles.

One of the promising methods for improving the durability and reliability of friction joints in combustion engines is the use of thin and hard coatings, including coatings based on amorphous DLC. The a-C:H:W coating was produced using the commercial PVD method. The tested tribological joints were made of AISI 4337 steel and SAE-48 bearing alloy (conformal contact) and AISI 4337 steel and valve shims (non-conformal contact). The contact area was lubricated with SAE 5W40 engine oil and PAO8 oil + 2 wt.% MoS2 nanoparticles. The objective of this work is to explore the influence of PAO8 + MoS2 on the tribological properties of a sliding joint with an a-C:H:W coating and the change in the properties of the oils. In the conformal contact, the lubrication of the a-C:H:W coating with PAO8 + MoS2 caused a significant increase in the friction resistance (than in) as compared to the joints with a quenching and tempering surface layer and lubricated SAE 5W40, while in the non-conformal contact, the lubrication of the a-C:H:W coating with PAO8 + MoS2 caused a decrease in the friction resistance and temperature of the contact area. The joints with the a-C:H:W coating were characterized by higher wear of the SAE-48 bearing alloy, as compared to the joints with the surface layer without coating (lubricated with SAE 5W40 oil-11-fold increase, PAO8 + MoS2-46-fold increase). The wear of valve shims with the a-C:H:W coating was significantly lower as compared to the wear of the commercial version of the valve shims (the difference between joints lubricated with SAE 5W40 oil and PAO8 + MoS2 was 12%, 36% and 29% for unit pressures of 10, 15 and 20 MPa). Lubrication of the a-C:H:W coating with PAO8 oil + MoS2 protected the sliding joints against seizing in non-conformal contact.

Wear and Friction Behaviour of Additive Manufactured PEEK under Non-conformal Contact

Tribological properties of laser sintered polyether-ether-ketone (EOS PEEK HP3) were investigated using a rolling-sliding test rig. This investigation aimed to study the wear and friction failure mechanism of EOS PEEK HP3. The main objectives included to conduct wear and friction tests under non-conformal contact, to monitor surface temperature, to carry out surface characterization with microscopy. With this rolling-sliding test rig, tests were carried out on an EOS PEEK HP3 specimen running against a steel disc unlubricated, with various slip-ratios under a contact pressure of 56 MPa, 48 MPa and 39 MPa respectively. Both wear and friction were measured. The results have shown that both friction and wear were increased with an increase of either slip-ratios or the contact pressures, exacerbated by high surface temperatures. It has also been observed that both friction and wear failures were associated with the degradation of the non-conformal contact surfaces due to crystallinity changes that correlated well with working conditions. Using microscopy it was found that such failures as pitting, fatigue and surface cracking were affected by the surfaces in contact, including the degree of melting of the surface. Based on the observation on the contact surfaces, the failure mechanisms of EOS PEEK HP3 include surface melting and contact fatigue failures with the high slip-ratio and the high contact pressure conditions. The findings of this investigation have the potential to help to design & develop additive manufacturing PEEK products. Typically, these results can be used in a design process for a more effective polymeric gear system.

An assessment of the effect of surface topography on coefficient of friction for lubricated non-conformal contacts

Determining an accurate state of lubrication is of utmost importance for the precise functionality of machine elements and to achieve elongated life and durability. In this work, a homogenized mixed-lubrication model is developed to study the effect of surface topographies on the coefficient of friction. Various measured real surface topographies are integrated in the model using the roughness homogenization method. The shear-thinning behavior of the lubricant is incorporated by employing the Eyring constitutive relation. Several Stribeck curves are generated to analyze the effect of roughness lays and root mean square (RMS) roughness on the coefficient of friction. The homogenized mixed lubrication model is validated against experimental rolling/sliding ball-on-disc results, and a good agreement between simulated and experimental coefficient of friction is found.

Tribological Performance of Laser‐Based Surface Textured Nonconformal Contacts

The benefits of surface textures on rolling and sliding tribological contacts have been an exciting field of study over the last three decades. Laser surface texturing (LST) is a comparatively newer texturing methodology that yields repeatable precise microtextures. A detailed overview of the available literature on the various works in this field is consolidated in this review. The main focus is on the effect of surface textures (with focus on laser ablation) for nonconformal contacts with elastohydrodynamic lubrication (EHL), as in rolling element bearings. A review of literature on textured contacts for the EHL regime, emphasizing its effect on friction, wear, rolling contact fatigue, vibration, texture geometry, and numerical simulation studies, is carried out with possibilities of future works. Basic details on LST processes and various parameters of the laser beam that determine the texture geometry are discussed. Being a field of continuing research, the review paper will aid in understanding the present developments and future directions in laser‐based surface texturing for nonconformal tribological contacts.

An Ultrasoft and Flexible PDMS-Based Balloon-Type Implantable Device for Controlled Drug Delivery.

Non-biodegradable implants have undergone extensive investigation as drug delivery devices to enable advanced healthcare toward personalized medicine. However, fibroblast encapsulation is one of the major challenges in all non-biodegradable implants, besides other challenges such as high initial burst, risk of membrane rupture, high onset time, non-conformal contact with tissues, and tissue damage. To tackle such challenges, we propose a novel ultrasoft and flexible balloon-type drug delivery device for unidirectional and long-term controlled release. The ultrasoft balloon-type device (USBD) was fabricated by using selective bonding between 2 polydimethylsiloxane (PDMS) membranes and injecting a fluid into the non-bonded area between them. The balloon acted as a reservoir containing a liquid drug, and at the same time, the membrane of the balloon itself acted as the pathway for release based on diffusion. The release was modulated by tuning the thickness and composition of the PDMS membrane. Regardless of the thickness and composition, all devices exhibited zero-order release behavior. The longest zero-order release and nearly zero-order release were achieved for 30 days and 58 days at a release rate of 1.16 μg/day and 1.68 μg/day, respectively. Invivo evaluation was performed for 35 days in living rats, where the USBD maintained zero-order and nearly zero-order release for 28 days and 35 days, respectively. Thanks to the employment of ultrasoft and flexible membranes and device design, the USBD could achieve minimal tissue damage and foreign body responses. It is expected that the proposed device may provide a novel approach for long-term drug delivery with new therapeutic modalities.

Tailoring the Coefficient of Friction by Direct Laser Writing Surface Texturing.

The modification of the surface topography at the micro- and nanoscale is a widely established as one of the best ways to engineering the surface of materials, to improve the tribological performances of materials in terms of load capacity and friction. The present paper reviews the state of the art on laser surface texturing by exploiting the technique of direct laser writing for tailoring the coefficient of friction, highlighting the effect of the textures' arrangement on the lubricated conformal and non-conformal contact behavior.

Interfacial mechanical properties of graphene on randomly rough PET substrate surface: A molecular dynamics study

In this work, molecular dynamics (MD) simulations are performed to create a series of polyethylene terephthalate (PET) substrates with random roughness, and the morphological characteristics and interfacial bonding of graphene on the real rough PET surface are first simulated. The results show that the interfacial mechanical behavior of graphene freely adhered to the PET roughness is influenced by the surface profile. Besides causing the non-conformal contact, the rough surface hinders the propagation of bending waves from the graphene corner regions during the adhesion and weakens their overlap. The increased surface roughness weakens interfacial adhesion and inhibits interfacial sliding, leading to the formation of larger morphological defects such as wrinkles. Furthermore, the measurement of the interfacial adhesion energy of graphene/PET substrate is achieved by the shaft loaded blister test (SLBT), which for the first time is used to simulate the interfacial debonding of graphene on rough PET surfaces. For low surface roughness, interfacial adhesion dominates the debonding behavior and the blister boundary preferentially extends along the interfacial defect area. For high surface roughness, the increasingly serious non-conformal contact makes the blister more likely to instability and enter the stage where normal and shear interactions are coupled.

Conformal Theoretical Modeling of Arbitrary Shape Flexible Electronic Sensors Mounted Onto General Curved Surface Substrates

Abstract Stretchable and flexible electronic sensors have been attracted to novel applications due to their conformal integration onto complex curved surfaces, whereas the mounting strains generated by the geometric mismatch of substrate surface and electronic sensors may cause non-conformal contact at the interface, thus would induce non-negligible effects on the performance of sensors. To investigate the influence rules of the shape of electronic sensors and their geometric parameters on conformal contacts, this paper presents a novel conformal model to study the arbitrary shaped films as flexible sensors mounted onto general curved-surface substrates. The energy minimization principle and the integral summation method play vital roles during the modeling, and three types of films with various shapes including rectangular, oval, and hexagonal mounted onto a bicurvature substrate are investigated. The influences of three dimensionless shape parameters of oval and hexagonal film/substrate contacts are analyzed for the dimensionless strain energy of conformal mounting. The strain and critical dimensionless strain energy of three films/bicurvature substrate contacts are calculated and compared under the same conformal area. The results demonstrated that the contour shape of electronic sensor has a considerable effect on conformal mounting and strain. Thus, the developed conformal model would have great significance in guiding the design of flexible electronic devices and sensors when applied to general curved surfaces.

A fast version of ‘CONTACT’ for normal problem calculations

In its different versions, the CONTACT method developed by Prof. Kalker is the primary reference in wheel-rail contact mechanics. Despite adopting simplifications associated with the elastic behaviour of the solids and being a non-conformal contact theory, CONTACT provides precise solutions for most wheel-rail contact conditions, with lower computational and modelling costs than other numerical methods such as Finite Elements. Nevertheless, the computational cost of CONTACT is still too high for its implementation in dynamic simulation.The present work proposes a fast and accurate wheel-rail contact method for normal problems based on Kalker's CONTACT algorithm. Dissimilarly to CONTACT, the new method formulates the normal traction distribution through a suitable basis, which reduces the dimension of the problem. This method is able to faithfully reproduce the contact patch and the normal traction distribution, even when the yaw angle of the wheelset is non-zero. Results obtained with this method are compared with the ones calculated with CONTACT, and errors about 0.05% are obtained in normal contact forces, with a reduction on the computation cost between 30 and 60 times.

The Effect of Steel Electropolishing on the Tribological Behavior of a Steel–Bronze Pair in the Mixed and Boundary Lubrication Regimes

Electropolishing at high current densities without agitation of the electrolyte results in a pitting phenomenon that produces dimple-like surface features. Although pitting is unfavorable in the electropolishing process, its effect on surface modification, such as surface texturing, has not been thoroughly investigated. Surface topography and chemical composition analyses of electropolished steel revealed surface pits and an oxide surface layer, indicating the presence of surface texture and coating. The resulting surface is characterized by negative skewness and high kurtosis values. The tribological behavior of the electropolished steel-bronze pair is investigated by evaluating coefficients of friction and bronze wear using sliding tests conducted in mixed and boundary lubrication regimes. The results are compared to those of the ground steel-bronze pair. In the mixed and upper range of the boundary lubrication regime, coefficients of friction reduction up to 30% and shorter running-in phases are observed for electropolished steel (electropolished steel μavg = 0.019 vs. ground steel μavg = 0.028). In contrast, the coefficient of friction increased in the lower range of boundary lubrication regime by 50% (electropolished steel μavg = 0.098 vs. ground steel μavg = 0.065). Electropolishing, as a cost- and time-effective method applicable to complex geometries, presents an alternative method for achieving surface modifications aimed at friction reduction and improved tribological behavior for non-conformal contacts in the boundary and mixed lubrication regimes.