Normal Contact Stress Research Articles

Axisymmetric contact analysis of piezoelectric materials with surface effect

Based on the surface piezoelectricity theory, this article predicts the axisymmetric smooth contact of a piezoelectric half-space indented by a rigid insulated punch. In this theory, the surface effect is characterized with four material parameters: the surface elastic constant, surface residual stress, surface piezoelectric constant and surface dielectric constant. By applying Hankel integral transform, the fundamental solution for this axisymmetric contact problem is derived with the surface effect. Then, the normal contact stress, radial electric displacement and radial stress of the contact surface are solved numerically. Finally, the surface effects on the normal contact stress, radial electric displacement and radial stress are analyzed. It is found that the surface effect is a significant influencing factor on the axisymmetric contact behaviors of micro-/nano-scale piezoelectric materials.

Rate Effect in Frictional Contact on Porous Rocks

The rate-dependent mechanism is analyzed for frictional contact between a blunt tool and a fluid-infiltrated porous rock under pressurized condition. The dimensional analysis is adopted to derive a dimensionless number $$\lambda$$ that predominantly governs the rate-dependent mechanism from pore pressure diffusion. The governing nature of $$\lambda$$ is analyzed by finite element modeling using the software ABAQUS for an idealized plane strain frictional contact problem. After validating the finite element model against analytical solutions for special cases, the rate-dependent frictional contact is analyzed for poroelastic, poroelastoplastic, rigid-poroplastic, and elasto-visco-plastic rocks, respectively. Three pore pressure regimes exist depending on $$\lambda$$ : low speed (0 < $$\lambda$$ ≲ 10–1), transient (10–1 ≲ $$\lambda$$ ≲ 103), and high speed ( $$\lambda$$ ≳ 103). The pore pressure generally increases, and the average effective contact stress decreases with increasing $$\lambda$$ for a poroelastic rock and a typical poroelastoplastic rock. The average effective contact stress generally decreases with increasing $$\lambda$$ for a rigid-poroplastic rock at a small dilatancy angle due to compactive weakening, but increases with $$\lambda$$ at a large dilatancy angle due to dilatant strengthening. A transition occurs from compactive weakening to dilatant strengthening with increasing the dilatancy angle. The average effective contact stress increases with decreasing the interface friction angle for a rigid-poroplastic rock. It is inferred from numerical results that the high-speed regime dominates with cavitation for frictional contact on shales in deep drilling, and that the strain rate effect is negligible in typical experiments on dry rocks at ambient pressure.

Research on Gear Flank Twist Compensation of Continuous Generating Grinding Gear Based on Flexible Electronic Gearbox

Gear flank twist occurs when threaded wheel grinds crowning lead modified helical gears, which reduces gear machining accuracy. To overcome this problem, a flank twist compensation method based on flexible electronic gearbox is proposed in this paper, the method can reduce the degree of twist and improve gear machining accuracy. Firstly, flank equations of gear and threaded wheel are established, coordinates and normal vectors of gear flank are used to represent twist. Secondly, coordinate transformation matrix between workpiece and tool coordinate system is established based on multi-body system theory and homogeneous coordinate transformation, and relationship between coordinates and normal vectors of gear flank and master-slave axis (B-axis, C-axis, X-axis, Y-axis, Z-axis) movement amount is obtained by inverse kinematics and electronic gearbox, then master-slave axis movement compensation amount between crowning lead modified flank and twisted flank is obtained. Finally, twist is compensated by compensating for master-slave axis movement amount, and flank contact analysis based on KISSsoft is carried out to observe normal force and contact stress of flanks. This paper uses inverse kinematics and electronic gearbox to realize flank twist compensation, which makes up for long period and high cost of traditional flank twist compensation by changing shape of threaded wheel. Simulation results show that this method can effectively compensate for flank twist and improve accuracy and efficiency when threaded wheel grinds crowning lead modified helical gears.

Model of the Ultimate Stress State of the Coated Tool Cutter Material

The article proposes a model of the ultimate stress state of the material of the coated tool cutter. It is found that with an increase in the fracture toughness of a tool in connection with the material ductility the machining accuracy deteriorates due to arising elastic-plastic vibrations of the tool cutter. In case when no ultimate stress state is reached, that is, a tool operates in the elastic region, then an alternating stress distribution diagram is realized for the tool cutter at the beam approximation. Therefore, in addition to the frictional vibrations, arising from the interaction between the tool cutter and a workpiece, the elastic vibrations can arise, which affects the machining accuracy and the service life of the coated tool cutter. The use of coatings makes it possible not only to increase the wear resistance of cutting tools, but also to transform the stress distribution diagrams of the normal σN and tangential τγ contact stresses acting on the rake face of the cutting tool. In particular, it is possible to control the length of the total contact area between the chips and the tool rake face.

Subloading-friction surface model with decrease of friction-coefficient by increase of normal contact stress

Subloading-friction surface model with decrease of friction-coefficient by increase of normal contact stress

Characterization of a novel aerostatic lubrication system for deep drawing processes

For economic and ecological aspects, use of lubricants containing mineral oil in sheet metal forming is sought to be reduced or avoided. Here, the application of gaseous N2 or liquid CO2 as volatile media acting as an aerostatic lubrication system represents a new approach for dry metal forming processes. In this paper, friction mechanisms occurring in this lubrication system and main factors influencing friction conditions had been identified by extended research work. An empirical friction model is presented, allowing the prediction of resulting friction coefficients as a function of the contact normal stresses acting between sheet metal and tool surface.

Analytical method for calculating the strength limit of rock specimens of wedge form of destruction at linear distributing of contact normal tensions

Abstract. An analytical method for calculating the parameters of the “stress – deformation” diagrams of prismatic samples with their wedge-shaped destruction is presented based on the distribution of the L. Prandtl contact stresses with using experimental values of four indicators of rock properties: shear resistance limit, internal and external friction coefficients, elastic modulus, which can be determined experimentally by simple methods in mining enterprises, where the calculation results can be promptly used. The method is based on the theory of local destruction of rocks along sliding lines developed by the authors. The theory makes it possible to determine the current values of the normal stresses at the crack tip during its development. As a strength criterion, the Coulomb strength criterion was adopted, supplemented by the authors by taking into account contact friction. The regularities of the distribution of normal stresses from contact friction were previously established by E.P. Unksov and L. Prandtl. The regularity of E.P. Unksov was used by the authors earlier to develop a method for calculating the strength limit of rock samples of the mentioned form of destruction. In this paper, the method is based on the method of L. Prandtl. To determine the strength limit, it was necessary to develop a method for calculating the parameters of “normal stress – longitudinal deformation” diagrams. The fact is confirmed that the stress at which the crack is formed is not the limit strength. The limit strength in the case of wedge-shaped destruction of the samples is the maximum value of the normal stress on the out-of-limit branch of the “stress- deformation” diagram. Some exorbitant curves have stress discharge, which are confirmed by experimental observations. At the moment of discharge, areas appear in the form of a so-called yield tooth, the formation of which we explain by the stresses discharge on the convex part of the slip line. In the middle part, the out-of-limit curves have stress jumps, which indicate the strengthening of the samples, which have not yet received any theoretical justification. We explain this phenomenon by the transition of the destruction process from the convex part of the slip line to the concave one. Comparison of the calculated strength limit of prismatic samples obtained according to the laws of distribution of contact normal stresses, exponential – by E.P. Unksov and linear – by L. Prandtl testifies to their practical identity. Keywords:rock, strength limit, destruction, crack, “stress – deformation” diagram.

СОВЕРШЕНСТВОВАНИЕ МЕТОДА РАСЧЕТА ПРЕДЕЛА ПРОЧНОСТИ ОБРАЗЦОВ ГОРНЫХ ПОРОД ПРИ СЖАТИИ

The paper describes a procedure for improving the approach to determining the ultimate strength of rock samples, the basic method is L. Prandtl’s method. In earlier works of the authors of this paper, the L. Prandtl’s method was improved in relation to rocks, using a general algebraic equation for calculating horizontal normal stresses depending on the vertical component and mechanical characteristics of the rock. Here, the authors reject the assumption that the tangent contact stresses resulting from L. Prandtl's solution do not depend on the abscissa x and on the variable vertical stresses, in contrast to the well-known Coulomb–Amonton law, according to which the tangent stresses are directly proportional to the vertical pressure. The regularities of contact normal and tangential stresses distribution at failure of prismatic samples are clarified. As result, the method was developed for calculating the tensile strength of samples with three characteristic values of mechanical properties: kп, yield strength of material in shear; ρ, angle of internal friction; fс, coefficient of contact friction. These characteristics can be established experimentally by simple experimental studies. The proposed approach is effective for constructing ultimate curves and diagrams of “stress — longitudinal strain” of rocks in the case of contact friction. A comparative evaluation is given for the proposed method for calculating the tensile strength of samples during their destruction with experimental data. Comparison of the calculated tensile strength with experimental data shows that the relative error of calculations according to the proposed method is significantly lower than the relative error of calculations performed using the E. Unksov’s method. The proposed method can be recommended for practical application.

Simulation of contact voltages in two-roll modules

Mathematical models of the regularities of the distribution of contact stresses in the generalized two-roll module are obtained. These models take into account all the main parameters of two-roll modules and describe the distribution diagrams of contact stresses for all special cases of interaction of the processed material with pairs of rolls in two-roll modules. New data on the regularities of the distribution of contact stresses are revealed: normal contact stresses change from zero at the beginning and at the end of the contact zone of the rolls to a maximum at a point lying to the left of the center line (towards the beginning of the contact of the rolls); the tangential contact stresses change their signs at the neutral point, which in the driven roll is located towards the entrance of the material layer into the contact zone of the rolls, and in the free one - towards the exit.

Accurate Arthroscopic Cam Resection Normalizes Contact Stresses in Patients With Femoroacetabular Impingement

Background: Femoroacetabular impingement (FAI) is increasingly recognized as a cause of hip pain in young adults. The condition leads to chondrolabral separation and chondral delamination and eventually predisposes to osteoarthritis of the hip. FAI that inflicts cartilage damage has been observed in hips with abnormal morphological characteristics and is related to a long-term evolution toward osteoarthritis. Arthroscopic surgery, which allows for correction of morphological characteristics and restores impingement-free motions, is the current standard of treatment. Hypothesis: Arthroscopic cam resection can restore the normal mechanical environment of the hip joint in cam-type FAI. Study Design: Descriptive laboratory study. Methods: Patient-specific discrete element models from 10 patients with cam-type FAI (all male; age, 18-40 years) were defined based on preoperative computed tomography scans and postoperative magnetic resonance imaging (MRI) scans. Complete cam resection postoperatively on MRI was confirmed with alpha angles <55°. The preoperative and postoperative peak contact stress findings during impingement testing were compared against a matched control group. Results: Peak contact stress was significantly elevated in patients with cam-type FAI during impingement testing, with increasing amounts of internal hip rotation (26.6 ± 11.64 MPa in cam patients preoperatively, 12.1 ± 4.62 MPa in those same patients postoperatively, and 11.4 ± 1.72 MPa in the virtual control group during impingement testing at 20° of internal hip rotation; P < .01). This effect was normalized after arthroscopic cam resection and loading patterns matched those of the control group. Conclusion: Accurate arthroscopic cam resection restored the normal peak joint contact stresses in the hip joint. This highlights the importance of early and complete cam resections in the face of a positive diagnosis of cam-type FAI. Clinical Relevance: Treatment of cam-type FAI effectively normalizes hip joint contact mechanics.

Comparison of the contact stress between the sensor and real polyethylene insert in total knee arthroplasty: a finite element analysis.

BackgroundIn implants, sensors are made of an acrylic-like plastic, while polyethylene (PE) inserts are made of ultra-high-molecular-weight PE (UHMPE). Thus, the stress distribution on the sensor may be different from that on the PE insert due to variations in material properties. The present study sought to analyze and compare the stress distribution profile between the sensor and PE insert after total knee arthroplasty (TKA).MethodsFinite element analysis was performed to estimate contact stress between the sensor and PE insert after TKA. The materials of the femoral component, sensor, and PE insert were determined as cobalt-chrome-molybdenum, acryl plastic, and UHMWPE, respectively. The stiffness levels of medial and lateral soft tissue were set at 28.8 N/mm and 18.8 N/mm at knee flexion and 24.7 N/mm and 17.2 N/mm at knee extension, respectively. The average and peak contact stress levels on the sensor and PE were analyzed in knee flexion and extension.ResultsThe average amount of contact stress in the medial compartment was 43.4 MPa on the sensor and 31.9 MPa on the PE insert at knee extension. Meanwhile, the medial compartmental peak contact stress levels were 55.2 MPa on the sensor and 48.8 MPa on the PE insert at knee extension. The other values of average and peak contact stress among the two materials were less than 5 MPa.ConclusionsThere was a difference in the contact stress distribution between the sensor and PE insert due to material properties, especially in the medial compartment at knee extension. The development of a sensor composed of a material with properties similar to a PE insert would be useful in the prediction of femorotibial contact stress in real implants.

Load Transfer from an Infinite Inhomogeneous Stringer to a Prestressed Elastic Strip Clamped at One Edge*

The plane contact problem of the transfer of a horizontal load from a weakly inhomogeneous infinite stringer to a prestressed elastic strip clamped at one edge is solved using the linearized theory of elasticity. The solution has a general form for the theory of large initial deformations and different theories of small initial deformations for an arbitrary elastic potential. The problem for the normal and tangential contact stresses is reduced to a governing system of recurrent systems of integro-differential equations, which is solved in powers of a small parameter. The zero-order approximation of the inhomogeneous problem is derived using the Fourier transform. The contact stresses are represented by Fourier integrals.

Assessment of experimental friction parameters and contact property of pipe string for the estimation and verification of a solution for pipe stuck in the China's first rock pipe jacking

The first rock pipe jacking project of China in Chongqing Guanjingkou encountered a pipe sticking problem soon following the abrupt increase of jacking force. It was essential for the direct shear test results and stresses acting normal to the outer periphery of the pipe strings to be relevant in the understanding of jacking forces for the pipe stuck. In this paper, direct shear tests were performed on the frictional characteristic between a dolomite and concrete specimen using the same test method in the earlier companion paper. The normal stresses of the pipe string were obtained through plane strain finite element modeling of the pipe-jacking under different engineering geological conditions, contact characteristics, overburden and contact areas, the threshold values of the normal contact stresses increased dramatically have also been achieved, simultaneously. Then the jacking force needed for stuck pipe strings has been predicted based on the frictional test results and the normal stress simulation in order to determine where the temporary intermediate jacking stations (TIJSs) should be installed. Finally, the pipe stuck problem is solved successfully using the TIJS method, this result provides excellent reference data for the similar engineering problems in the future.

RESEARCH DEVELOPMENT OF CONTACT DEFORMATION STRESSES WHILE ROLLING

The method of determination of contact normal and tangential stresses during rolling is considered, taking into account the development of deformation over time. There are many methods for determining the contact normal and tangential stresses, but they all consider the distribution along the strain boundary. This approach to solving problems does not allow to take into account the uneven deformation in the transverse direction and the influence of lateral non-contact zones adjacent to the actual deformation center. These factors should be taken into account when determining the tangent and normal stresses when rolling in calibers with different ratios of geometric shapes and rolling billet. Also, existing methods of determining contact normal and tangential stresses do not take into account the development of deformation over time. Deriving the equations that determine the deformation force of the friction force and pressure, it was assumed that the normal to the plane would not coincide with any of the axes of the coordinate system, and the inclined platform was considered as an inclined section in the parallelepiped voltage across the edges of the volume, which is distributed uniformly. The obtained formulas for determining the normal and tangent contact stresses in the deformation zone take into account rolling in calibers with different ratio of geometric shapes and rolling billet, characterize the dynamics of change of the deformation cell in time. The paper deals with rolling of AK6 alloy workpieces having Ø25x150 mm dimensions in oval caliber, with a height of 13 mm and a width of 29 mm and calculated normal and contact stresses. The plots of normal and tangent stresses show a change in the value of stress with increasing contact area and deformation time. The results of studies of normal and tangent stresses show a change in their values with increasing contact area and deformation time. When checking the proposed method, the discrepancy between the results of the theoretical calculation and the experimental data is not more than 4%, which confirms the possibility of using the method to determine the contact normal and tangential stresses during rolling.

Experimental studies of the “foundation-soil” system operation with sudden loading

The experimental studies’ results of the foundations with a soil base interaction are presented. The relevance of the research is associated with increased accidents of buildings and structures in recent decades. The reasons for the occurrence and features of sudden foundations loading are considered. The experimental research methodology, the characteristic models of foundations are presented. The preliminary experimental studies’ results of the foundations with sudden loading are presented and analyzed. Some features of the “foundation-soil” system are determined. A decrease in the bearing capacity of the foundations during sudden loading, depending on the level and prestressing type, was revealed. It is established that the main reason for the decrease in the foundations’ bearing capacity is a change in the normal contact stresses diagram. The necessity and directions of further research in this area are substantiated.

INFLUENCE OF FRICTION REGIMES ON THE TRIBOTECHNICAL PROPERTIES OF COMPOSITES BASED ON PTFE AND CARBON FIBERS

The paper presents the results of tribotechnical tests of polymer composite materials based on polytetrafluoroethylene (PTFE) and carbon fibrous activated material UVIS-AK-P (SPC UVIKOM LLC) depending on the contact pressure in dry and boundary friction modes in various oils. I-20A industrial oil, Siboil TAD-17u transmission oil, and Rosneft Gidrotec HLP 46 hydraulic oil were used as liquid lubricants for the friction of polymeric materials. For tribotesting, a polymer composite with a content of 5 % wt. UVIS-AK-P, obtained using sequential mixing of filler with PTFE and the technology of joint activation of components in a planetary mill, is the most wear-resistant material according to the results of previous studies. It has been established that despite the heavy wear at increased bearing pressure during dry friction, unfilled PTFE does not undergo plastic deformation and maintains a low coefficient of friction practically unchanged. It has been found that the friction coefficient passes through a minimum during dry friction of a composite with CF at a load of 350 N. It is associated with the transition of the elastic contact of the interacting elements of the surfaces of the metal-polymer tribosystem to the plastic one with increasing load. During friction of PTFE in a lubricating oil environment, a significant decrease in mass wear, friction coefficient and temperature in the contact zone are observed due to the formation of secondary structures on the friction surfaces and the significant flexibility of PTFE. This increases the actual area of the tribocontact, which reduces the value of real normal contact stresses. During friction of polymer composite materials in the environment of lubricating oils, a decrease in the friction coefficient and the area of the friction track by 1.7-2.7 times was recorded as well. Deformations, groove formation and mass wear were not observed. It has been revealed that the greatest effect of increasing the wear resistance and permissible friction load and lowering the temperature in the friction zone of PTFE and composite is observed when using Siboil TAD-17u transmission oil. This is due to the presence of special antifriction additives in this oil brand and a decrease in the actual contact of the working surface of the polymer material with the lubricant, which helps to reduce the intensity of the destructive process in the surface layer while contacting with the lubricant.

Analytical solution of axisymmetric indentation of multi-layer coating on elastic substrate body

We consider the axisymmetric contact problem of a multi-elastic layer with various elastic constants bonded to an elastic semi-infinite substrate indented by rigid flat-ended cylindrical and spherical indenters. The transfer matrix method is applied to each elastic layer, and dual integral equations are reduced to an infinite system of simultaneous equations by expressing the normal contact stress at the surface elastic layer as an appropriate series with Chebyshev orthogonal polynomials. Numerical results demonstrate the effects of the elastic constant of each elastic layer and the semi-infinite elastic substrate on the radial distribution of the normal contact stress and normal displacement of the free surface of the elastic layer, stress singularity factor at the edge of the cylindrical indenter, and axial load of a rigid indenter which penetrates the multi-layer material to a constant depth. The results of axial load are in good agreement with previously reported results. The numerical results are given for several combinations of the shear modulus of each elastic layer and the substrate. These results will contribute to the establishment of indentation tests for composite materials and serve as guidelines for the design of appropriate mechanical properties of layered materials.

Frictional receding contact problem of a functionally graded layer resting on a homogeneous coated half-plane

This paper investigates the frictional receding contact problem between a functionally graded (FG) layer resting on a homogeneous coated half-plane when the system indented by a rigid cylindrical punch. The shear modulus of the upper graded layer is assumed to vary exponentially in the depth direction. Upon loading, the advancing contact and receding contact occur between the FG layer and rigid punch and between the FG layer and coating, respectively. Under the assumptions of sliding contact, the shear and normal contact stresses are related through Coulomb’s law of friction. The contact problem is converted analytically using Fourier integral transforms and the proper boundary conditions into a system of two singular integral equations. The unknowns of these integral equations consist of the contact stresses under the punch and between the FG layer and coating as well as the dimensions of the contact zones. The Gauss–Jacobi quadrature collocation method is then employed to transform the singular integral equations into a system of nonlinear equations which are solved using an appropriate iterative algorithm to compute the contact stresses and the dimensions of the contact areas. The main purpose of this paper is to examine the influence of several parameters on the upper and lower contact stresses, which include the material inhomogeneity parameter, friction coefficient, punch radius, applied load, thickness of homogeneous layer, shear modulus of homogeneous layer and shear modulus of homogeneous half-plane. One of the most important conclusions from this study is that the contact stresses and contact areas can be controlled with the addition of the homogeneous layer.

Improvement of the optical method for researching the contact stresses during the forging

Dobrov I. V., Semichev A. V. Improvement of the optical method for researching the contact stresses during the forging. Material working by pressure. 2020. № 1 (50). Р. 24-27.&#x0D; The analysis of the results of experimental resarch of contact normal stresses during the forging of a symmetrical workpiece under conditions of plane deformation performed by the tensometric method is carried out. It is shown that when comparing the combined graphs of the distribution of contact normal stresses along the symmetry axis of the workpiece, depending on the position of the considered section of the workpiece relative to the length (diameter) of the contact surface, presented in the technical literature, it is necessary to take into account the real change in the dimensions of the contact surface during forging of the initial workpiece with different degrees of deformation. An optical method for research of the distribution of contact normal stresses during forging under conditions of plane deformation of a symmetric workpiece made of a material with high plastic properties, which during forging, flows into holes of equal diameter, located along the axis of symmetry at an equal distance from each other in the diaphanous puncheon of new design. The results of experimental expand the physical understanding of the nature of the redistribution of normal contact stresses during forging and qualitatively coincide with the results of load cell measurements of normal contact stresses in real conditions presented in the scientific and technical literature.

Dynamics of a viscoelastic cylinder on a viscoelastic half-space

The deceleration of a viscoelastic cylinder rolling with slipping on a viscoelastic half-space of the same material without driving forces and torques is studied. The interaction of the cylinder and the half-space is described from the solution of the 2D quasistatic contact problem of viscoelasticity (Goryacheva in J Appl Math Mech 37(5):877–885, 1973, Contact mechanics in tribology, Kluwer, Dordrecht, 1998). This solution states that the contact region consists of the slip and stick zones, and it is shifted forward in the direction of motion. Contact normal and shear stresses and, therefore, the resultant force and torque depend on the values of the linear velocity of the cylinder and creep ratio, as well as the mechanical properties of contacting bodies and sliding friction coefficient. The Cauchy problem for dynamical equations of the cylinder’s deceleration was solved numerically. The analysis of the deceleration process and changes in the contact normal and shear stress distributions in time for various initial conditions is presented.