Contact Stiffness Measurements Research Articles

A lubrication contact stiffness model considering asperity interactions

In practical engineering applications, most connection interfaces require lubrication. The contact stiffness of the lubrication interface can affect the static and dynamic characteristics of the interface, thus affecting the performance of the mechanical system, such as vibration, fatigue, and wear characteristics. Therefore, the measurement of lubrication contact stiffness is very important for the analysis and optimization of mechanical system performance. However, measuring the stiffness of the lubrication interface is a significant challenge. In this paper, a mixed lubrication contact stiffness model considering asperity interactions is proposed, which assumes the lubrication rough interface as an equivalent thin layer. The proposed model was compared with the lubrication contact model that does not consider the asperity interactions. Based on the microscopic contact behavior of the contact interface, the relationship between the mechanical parameters of the virtual thin layer and the contact pressure was analyzed. Finally, the predicted results of interface stiffness are verified by published theoretical and experimental results. The results show that the proposed model can more reasonably describe the actual contact behavior of the rough lubrication interface and give the variation law of the mechanical parameters of the virtual thin layer.

Study on gear contact stiffness and backlash of harmonic drive based on fractal theory

Contact stiffness and backlash in the harmonic drive significantly impact a robot's positioning accuracy and vibration characteristics. The height of the harmonic drive tooth pair is typically less than 1 mm, making the measurement and modeling of backlash and contact stiffness inherently complex. This paper proposes a contact stiffness and backlash model by establishing a correlation between fractal parameters and tooth contact load. To obtain the fractal roughness parameters of the real machined tooth surface, a combination of a noncontact optical profiler and the RMS method is employed. Subsequently, the study explores the influence of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash. The results demonstrate the substantial impact of surface topography parameters and contact force on contact stiffness and backlash. Specifically, an increase in the fractal dimension correlates with a reduction in gear backlash and contact stiffness. Conversely, the fractal roughness parameter exhibits the opposite effect. Notably, an increase in contact force enhances contact stiffness.

An improved acoustic model for mixed lubrication contact interface

Mixed lubrication interfaces are widespread in engineering. The measurement of contact stiffness is a challenge for device performance evaluation. The ultrasonic reflection method is an effective method, but the difficulty of accurate construction of the acoustic model limits the measurement accuracy. In this study, an improved acoustic model is proposed to analyze the contact stiffness of the mixed lubrication interface. The model is constructed using a quasi-static spring model, virtual material model, statistical microcontact model, and multilayer acoustic model. The mixed lubrication interface is equivalent to a homogeneous and isotropic virtual material layer. Then, the mechanical, geometric, and acoustic parameters of the virtual layer are determined by introducing thickness coefficients. The contact stiffness is obtained with the proposed model and compared with the quasi-static spring model and the virtual material layer model. The reflection coefficient of the interface can also be calculated using a multilayer acoustic model based on the calculated parameters. The proposed model is verified by comparing the predicted reflection coefficients with the published experimental results.

Microstructures and mechanical properties of Sb-doped ZnO thin films deposited on a-plane sapphire substrates

The structural features and nanomechanical properties of ZnO and Sb-doped (1.0 at%) ZnO (SbZO) thin films deposited on a-plane sapphire substrates by radio-frequency (RF) magnetron sputtering are comparatively investigated in this study. The X-ray diffraction and atomic force microscopy analyses indicated that both ZnO and SbZO thin films were highly (002)-oriented albeit with somewhat different grain structure and surface morphologies. Nanoindentation results of both films exhibited apparent discontinuities (so-called pop-ins) in the load-displacement curves (P-h curves), while no discontinuity was observed in the unloading segment of the P-h curves. By using a Berkovich nanoindenter operating with the continuous contact stiffness measurement mode, the obtained hardness and Young's modulus of ZnO (SbZO) thin films are 7.3 ± 0.2 (8.5 ± 0.4) GPa and 259.6 ± 17.8 (327.4 ± 13.9) GPa, respectively. Furthermore, the facture toughness and fracture energy of ZnO and SbZO thin films obtained by Vickers indentation were also compared.

The Microstructures and Characteristics of NiO Films: Effects of Substrate Temperature.

The influence of the substrate temperature on the structural, surface morphological, optical and nanomechanical properties of NiO films deposited on glass substrates using radio-frequency magnetron sputtering was examined by X-ray diffraction (XRD), atomic force microscopy (AFM), UV-Visible spectroscopy and nanoindentation, respectively. The results indicate that the substrate temperature exhibits significant influences on both the grain texturing orientation and surface morphology of the films. Namely, the dominant crystallographic orientation of the films switches from (111) to (200) accompanied by progressively roughening of the surface when the substrate temperature is increased from 300 °C to 500 °C. The average transmittance of the NiO films was also found to vary in the range of 60-85% in the visible wavelength region, depending on the substrate temperature and wavelength. In addition, the optical band gap calculated from the Tauc plot showed an increasing trend from 3.18 eV to 3.56 eV with increasing substrate temperature. Both the hardness and Young's modulus of NiO films were obtained by means of the nanoindentation continuous contact stiffness measurements mode. Moreover, the contact angle between the water droplet and film surface also indicated an intimate correlation between the surface energy, hence the wettability, of the film and substrate temperature.

Finite Element Analysis of Nanoindentation Responses in Bi2Se3 Thin Films

In this study, the nanoindentation responses of Bi2Se3 thin film were quantitatively analyzed and simulated by using the finite element method (FEM). The hardness and Young’s modulus of Bi2Se3 thin films were experimentally determined using the continuous contact stiffness measurements option built into a Berkovich nanoindenter. Concurrently, FEM was conducted to establish a model describing the contact mechanics at the film/substrate interface, which was then used to reproduce the nanoindentation load-depth and hardness-depth curves. As such, the appropriate material parameters were obtained by correlating the FEM results with the corresponding experimental load-displacement curves. Moreover, the detailed nanoindentation-induced stress distribution in the vicinity around the interface of Bi2Se3 thin film and c-plane sapphires was mapped by FEM simulation for three different indenters, namely, the Berkovich, spherical and flat punch indenters. The results indicated that the nanoindentation-induced stress distribution at the film/substrate interface is indeed strongly dependent on the indenter’s geometric shape.

Effects of Substrate Temperature on Nanomechanical Properties of Pulsed Laser Deposited Bi2Te3 Films

The correlations among microstructure, surface morphology, hardness, and elastic modulus of Bi2Te3 thin films deposited on c-plane sapphire substrates by pulsed laser deposition are investigated. X-ray diffraction (XRD) and transmission electron microscopy are used to characterize the microstructures of the Bi2Te3 thin films. The XRD analyses revealed that the Bi2Te3 thin films were highly (00l)-oriented and exhibited progressively improved crystallinity when the substrate temperature (TS) increased. The hardness and elastic modulus of the Bi2Te3 thin films determined by nanoindentation operated with the continuous contact stiffness measurement (CSM) mode are both substantially larger than those reported for bulk samples, albeit both decrease monotonically with increasing crystallite size and follow the Hall—Petch relation closely. Moreover, the Berkovich nanoindentation-induced crack exhibited trans-granular cracking behaviors for all films investigated. The fracture toughness was significantly higher for films deposited at the lower TS; meanwhile, the fracture energy was almost the same when the crystallite size was suppressed, which indicated a prominent role of grain boundary in governing the deformation characteristics of the present Bi2Te3 films.

Contact stiffness of jointed interfaces: A comparison of dynamic substructuring techniques with frictional hysteresis measurements

The tangential contact stiffness is an important parameter used in non-linear dynamic analyses of jointed structures since it can strongly affect the prediction of resonance frequencies. Many experimental techniques are available for contact stiffness estimations, but the reliability of such estimations remains unknown due to a lack of comparative studies. This paper proposes a comparative study of contact stiffness measurements obtained with two experimental techniques: hysteresis loop measurements and Frequency Based Substructuring (FBS). Hysteresis loops are traditionally measured with dedicated friction test rigs to provide, amongst others, contact stiffness estimations through local interface measurements. The assumption with hysteresis measurements is that the measured parameters are independent of the dynamics of the test rig and can therefore be used as input for analyses of other structures, as long as loading conditions and contact interfaces are comparable. An alternative approach to identify the contact stiffness is FBS, which uses information from the overall system dynamics. FBS has the advantage that it can be applied to any structure, without the need of building ad-hoc test rigs, consequently giving a structure-specific information. Despite this advantage over hysteresis measurements, it is as of yet not well understood how accurately FBS can extract contact stiffness values. This paper presents FBS measurements and hysteresis loop measurements performed simultaneously on the same contact interface of a traditional high-frequency friction rig during vibration, thus enabling a cross-validation of the results of both techniques. This novel comparison validates FBS approaches against local hysteresis measurements and shows the strengths and limitations of both experimental methods, making it possible to improve the current understanding of the contact stiffness of jointed structures.

Indentation Modulus, Indentation Work and Creep of Metals and Alloys at the Macro-Scale Level: Experimental Insights into the Use of a Primary Vickers Hardness Standard Machine.

In this work, the experimental method and the calculation model for the determination of indentation moduli, indentation work, and indentation creep of metallic materials, by means of macroscale-level forces provided by a primary hardness standard machine at the National Institute of Metrological Research (INRIM) at the at room temperature were described. Indentation moduli were accurately determined from measurements of indentation load, displacement, contact stiffness and hardness indentation imaging and from the slope of the indentation unloading curve by applying the Doerner-Nix linear model; indentation work, representing the mechanical work spent during the force application of the indentation procedure, was determined by calculating the areas under the loading–unloading indentation curve, through fitting experimental data with a polynomial law. Measurements were performed with a pyramidal indenter (Vickers test). The applied force was provided by a deadweight machine, and the related displacement was measured by a laser interferometric system. Applied forces and the occurring indentation depths were simultaneously measured: the resulting loading–unloading indentation curve was achieved. Illustrative tests were performed on metals and alloy samples. Discussion and comments on the suitability of the proposed method and analysis were reported.

Contact Stiffness Measurements with an Atomic Force Microscope

We propose a method for improving accuracy of nanomechanical measurements by an atomic force microscope. We describe the contact interaction of the cantilever with the sample using an analytic model taking into account different mechanisms of the cantilever probe operation (it can be clamped or can slide over the sample surface), the geometrical and mechanical characteristics of the sample and the cantilever, and their mutual arrangement. For the case of sliding, a filter is developed for correcting signals of contact stiffness and deformation measured on a sample with a developed relief. The application of the filter is illustrated by images obtained with an atomic force microscope in the visualization regime based on point-by-point recording of the forced quasi-static interaction of the cantilever probe with the sample.

The Indentation-Induced Pop-in Phenomenon and Fracture Behaviors of GaP(100) Single-Crystal

The deformation behaviors and fracture features of GaP(100) single-crystal are investigated by using nano- and micro-scale indentation techniques. The hardness and Young’s modulus were measured by nanoindentation using a Berkovich diamond indenter with continuous contact stiffness measurements (CSM) mode and the values obtained were 12.5 ± 1.2 GPa and 152.6 ± 12.8 GPa, respectively. In addition, the characteristic “pop-in” was observed in the loading portion of load-displacement curve, which was caused by the nucleation and/or propagation of dislocations. An energetic estimation methodology on the associated nanoindentation-induced dislocation numbers resulting from the pop-in events was discussed. Furthermore, the Vickers indentation induced fracture patterns of GaP(100) single-crystal were observed and analyzed using optical microscopy. The obtained fracture toughness KC of GaP(100) single-crystal was ~1.7 ± 0.1 MPa·m1/2, which is substantially higher than the KIC values of 0.8 MPa·m1/2 and 1.0 MPa·m1/2 previously reported for of single-crystal and polycrystalline GaP, respectively.

Indentation modulus at macro-scale level measured from Brinell and Vickers indenters by using the primary hardness standard machine at INRiM

In this paper, the experimental procedure and calculation model for the measurement of the indentation modulus by using the primary hardness standard machine at INRiM in the macro-scale range at room temperature is described. The indentation modulus is calculated based on the Doerner-Nix linear model and from accurate measurements of indentation load, displacement, contact stiffness, and hardness indentation imaging. Measurements are performed with both pyramidal (Vickers test) and spherical indenters (Brinell test). Test force is provided by a dead-weight machine, and the occurring displacement is measured by a laser-interferometric system. The geometrical dimensions of both the Vickers and Brinell indentations are measured by means of a micro-mechanical system and optical microscopy imaging techniques. Applied force and indentation depth are measured simultaneously, at a 16 Hz sampling rate, and the resultant loading-unloading indentation curve is obtained. Preliminary tests are performed on metal and alloy samples. Considerations and comments on the accuracy of the proposed method and analysis are discussed.

Effects of Cu doping on the structural and nanomechanical properties of ZnO thin films

The effects of Cu doping on the microstructures, surface morphological and nanomechanical properties of Cu-doped ZnO (CZO) thin films deposited on glass substrates by radio frequency magnetron sputtering method are investigated. The microstructural properties and surface morphological features of CZO thin films are characterized using X-ray diffraction (XRD) and atomic force microscopy (AFM), respectively. The XRD results indicated that CZO thin films exhibited (002)-preferred orientation. From AFM observations, an increase in surface roughness of CZO thin films was observed when the Cu-doping concentration was increased from 2 at% up to 6 at%. Moreover, the nanoindentation tests performed with the continuous contact stiffness measurements (CSM) mode revealed that both the hardness and Young’s modulus of CZO thin films are increased with increasing the Cu-doping concentration, with the maximum value being obtained at 6 at%. Further increasing the Cu concentration up to 8 at% appeared to result in reduced microstructure texturing and nanomechanical performances, indicating that grain boundary effect might have played an important role.

An improved virtual material based acoustic model for contact stiffness measurement of rough interface using ultrasound technique

In this work, an improved acoustic model based on virtual material is proposed to provide an accurate measurement of interfacial contact stiffness using ultrasound. The rough interface is assumed to be a thin layer of virtual material to incorporate the effect of ultrasound attenuation at the interface. The derived acoustic model shows that the developed contact stiffness expression is a refinement of the general spring model by considering the interfacial property and is related to the material properties of the virtual material thin layer. The analytical solutions of the material parameters for the virtual material are further deduced based on the statistical micro-contact theory. It reveals that the surface roughness parameters of the contact interface and the material property of the contact body are other information required to improve the measurement accuracy of contact stiffness, in addition to the ultrasonic measurement parameters in the original spring model. The accuracy of the developed acoustic model for contact stiffness measurement is verified by comparison with the spring model and the statistical contact models.

The deformation behavior and fracture toughness of single crystal YSZ(111) by indentation

The nano-scale deformation behaviors and indentation-induced fracture features of the (111)-oriented yttrium-stabilized zirconia single crystal (YSZ(111)) were investigated by Berkovich and micro-Vicker indentations, respectively. The load-displacement curves in the Berkovich nano-indentation experiments evidently exhibited indentation-induced single “pop-in” phenomenon during loading, indicating that the nano-scale deformation in the YSZ(111) crystals is due primarily to the activities of dislocation nucleation and propagation. Based on this scenario, the number of nanoindentation-induced dislocation loops giving rise to the pop-in event was estimated to be around 2 × 105 with a critical radius of ∼2 nm. The hardness and Young's modulus of YSZ(111) single crystal obtained by the continuous contact stiffness measurements (CSM) mode were 22.3 ± 1.1 GPa and 270.6 ± 8.5 GPa, consistent with those reported previously in the literature. In addition, the fracture toughness of YSZ(111) single crystal was estimated to be about 1.4–1.6 MPa m1/2.

Effects of annealing temperature on nanomechanical and microstructural properties of Cu-doped In2O3 thin films

In this study, the effects of post-annealing on the microstructural, surface morphological and nanomechanical properties of Cu-doped In2O3 (CIO) thin films were investigated using X-ray diffraction, scanning electron microscopy and nanoindentation techniques, respectively. The CIO thin films were deposited on the c-plane sapphire substrates at room temperature using the radio frequency magnetron sputtering system. Post-annealing was carried out at the temperatures of 750–950 °C, and resulted in progressive increase in the average grain size and improved crystallinity of CIO thin films. In addition, the hardness and Young’s modulus of CIO thin films were measured by a nanoindenter equipped with a Berkovich diamond tip and operated with the continuous contact stiffness measurements mode. Results indicated that the values of hardness and Young’s modulus of CIO thin films increased when the annealing temperature increased from 750 to 950 °C.

Measuring and Understanding Contact Area at the Nanoscale: A Review

The size of the mechanical contact between nanoscale bodies that are pressed together under load has implications for adhesion, friction, and electrical and thermal transport at small scales. Yet, because the contact is buried between the two bodies, it is challenging to accurately measure the true contact area and to understand its dependence on load and material properties. Recent advancements in both experimental techniques and simulation methodologies have provided unprecedented insights into nanoscale contacts. This review provides a detailed look at the current understanding of nanocontacts. Experimental methods for determining contact area are discussed, including direct measurements using in situ electron microscopy, as well as indirect methods based on measurements of contact resistance, contact stiffness, lateral forces, and topography. Simulation techniques are also discussed, including the types of nanocontact modeling that have been performed and the various methods for extracting the magnitude of the contact area from a simulation. To describe and predict contact area, three different theories of nanoscale contact are reviewed: single-contact continuum mechanics, multiple-contact continuum mechanics, and atomistic accounting. Representative results from nanoscale experimental and simulation investigations are presented in the context of these theories. Finally, the critical challenges are described, as well as the opportunities, on the path to establishing a fundamental and actionable understanding of what it means to be “in contact” at the nanoscale.

Nanomechanical and wettability properties of Bi2Te3 thin films: Effects of post-annealing

In this study, Bi2Te3 thin films were deposited on SiO2/Si(100) substrates by pulsed laser deposition (PLD) at 250 °C. The films were then annealed in-situ in the deposition chamber at various annealing temperatures (Ta) ranging from 200 to 300 °C. The microstructural, morphological, and nanomechanical properties of the Bi2Te3 thin films were investigated by X-ray diffraction (XRD), scanning electron microscopy, and nanoindentation techniques, respectively. The XRD results indicated that all the Bi2Te3 thin films have high crystalline quality with predominant (0015) texture. Nano-indentation measurements performed with a Berkovich nanoindenter operating under the continuous contact stiffness measurement mode revealed that both the hardness and Young's modulus of the Bi2Te3 films decreased with increasing Ta. In addition, the water contact angle measurements were carried out to delineate the effects of annealing on the changes in the surface energy and wettability of the films.

Rough Surface Normal Nanocontact Stiffness: Experimental Measurements and Rough Surface Contact Model Predictions

This work presents experimental contact stiffness measurements for various thin films as well as homogenous materials through pressing a flat punch onto a nominally flat rough surface. These materials are typically used in micro/nano technological applications with thickness of the order of few nanometers. The experimental contact stiffness results are compared with predictions by different statistical rough surface contact models to assess their predictive accuracy for thin-film applications and, in addition, to get better insight to the physics of the contact. It is observed that rough surface contact models that account for asperity interaction show good agreement with the experimental results of the thin-layered specimens contact response. This indicates the importance of accounting for asperity interaction in surface roughness contact modeling of relatively smooth thin-film materials. It is verified that interfaces with compliant films on stiff substrates as well as homogeneous materials compare relatively well with statistical models accounting for asperity interactions.

Effects of post-annealing on the structural and nanomechanical properties of sputter-deposited FePd thin films

The effects of post-annealing on the microstructures, surface morphologies and nanomechanical characteristics of FePd thin films are investigated by means of X-ray diffraction (XRD), atomic force microscopy (AFM), transmission electron microscopy (TEM) and nanoindentation techniques. The FePd thin films were deposited on the glass substrates at room temperature by magnetron sputtering system. Post-annealing was carried out at 500, 600 and 700 °C, respectively, resulting in progressive increase of the average grain size and surface roughness of FePd thin films, as well as the improved film crystallinity. XRD results show that FePd thin films are predominantly (111)-oriented, indicating a well-ordered microstructure. The hardness and Young's modulus of FePd thin films measured by a Berkovich nanoindenter operated with the continuous contact stiffness measurements (CSM) option indicated that both mechanical properties are decreased with increasing the annealing temperature. Furthermore, the relationship between the hardness and films grain size appears to follow closely with the Hall–Petch equation.