Contact Kinematics Research Articles

Friction-induced noise of gear system with lead screw and nut: Mode-coupling instability

The mode-coupling instability in the gear system with a lead screw and nut is investigated. The actual gear geometry and the contact kinematics are developed in analytical the model. The complete set of vibration modes including axial, torsion and transverse displacements is applied to seek the solution of the linearized gear system. From the linear stability analysis, the bending mode pair as well as the torsion and axial mode pair have the strong tendency towards the mode-coupling instability. It points out that squeak noise in the lead screw system can occur even for a constant friction coefficient without the negative-friction velocity slope. The closed-form solution and numerical calculation also show that the rotating direction can drastically change the onset of mode-coupling instability.

Abnormal tibiofemoral contact mechanics in subjects with medial and lateral compartment articular cartilage lesions

s / Osteoarthritis and Cartilage 23 (2015) A82eA416 A306 481 ABNORMAL TIBIOFEMORAL CONTACT MECHANICS IN SUBJECTS WITH MEDIAL AND LATERAL COMPARTMENT ARTICULAR CARTILAGE LESIONS S.Y. Segev, D. Kumar, L. Nardo, V. Pedoia, T.M. Link, S. Majumdar, R.B. Souza. Univ. of California San Francisco, San Francisco, CA, USA Purpose: To evaluate the changes in cartilage-on-cartilage contact areas and medial and lateral contact area centroid movement in the tibiofemoral joint during knee flexion and extension using MRI in subjects with and without tibiofemoral cartilage lesion. Methods: Subjects from an observational study on knee Osteoarthritis (OA), including both subjects with andwithout radiographic OA, (n1⁄4 94 Mean age 1⁄4 54.1±10.5 years; Mean BMI 1⁄4: 24.4±3.4 kg/m2; Men:Women 1⁄4 35:59) underwent 2D fast-spin echo (FSE) MR imaging at 0 and 30 of knee flexion under axial loading (25% bodyweight). For subjects with radiographic OA, the more severe knee was enrolled. For subjects without radiographic OA, the enrolled knee was randomly selected. A fluid sensitive-fat-saturated 3D fast spin-echo sequence with variable flip angle (CUBE) was acquired in order to grade cartilage lesions using a semi-quantitative score. Subjects were then stratified into those with and without cartilage lesions at the tibiofemoral joint. Tibiofemoral contact area was defined on FSE images as the area of contact between the tibial and femoral articular cartilage, excluding meniscus contact area and joint fluid. This region of contact was semiautomatically segmented separately in the medial and lateral knee compartment using Bezier-splines created with in-house software written in Matlab. Contact area centroid position was determined by evaluation of the contact area on a defined anatomic coordinate system embedded within the tibia. Differences in medial and lateral contact area at flexed and extended conditions, and medial and lateral contact area centroid translations were compared between subjects with and without cartilage lesions using analysis of co-variance (ANCOVA), adjusted for age, gender, knee alignment, and BMI. Results: Subjects with medial compartment cartilage lesions (n1⁄428) had greater contact area in the affected compartment during extension (Figure 1, 361 vs. 270 mm2; p1⁄40.025), but not flexion (Figure 1, 287 vs. 219mm2; p1⁄40.146) when compared to subjects without lesions (n1⁄466). No differences in contact area in the lateral compartment were observed between subjects with and without medial compartment lesions. In contrast, subjects with lesions in the lateral compartment (n1⁄418) were found to have greater contact area than subjects without lesions (n1⁄476) in both extension (Figure 2, 366 vs. 271 mm2; p1⁄40.009) and flexion (Figure 2, 326 vs. 224 mm2; p1⁄40.002) as well as in the contralateral compartment while in full extension (Figure 2, 374 vs. 279 mm2; p1⁄40.012). With regard to contact kinematics, subjects with medial compartment lesions had greater anterior-posterior translation of the medial contact centroid when moving from extension to flexion (Figure 3, Figure 4, p1⁄40.047). No differences in anterior-posterior centroid translations were observed in either the medial or lateral compartment of subjects with lateral compartment lesions. Conclusions: Contact mechanics in subjects with cartilage lesions are significantly different compared to those without lesions. The higher contact area in subjects with cartilage lesions is likely due to the changes in the ability of the cartilage to adapt to loading, expanding the contact surface as the cartilage adjacent to the lesion gives way to the load. This phenomenon is coupled with abnormal contact kinematics in persons with cartilage lesions. While the normal kinematics of knee flexion requires the femur to slide back on the tibial plateau, our data suggests that the movement in the affected compartment is greater in knees with medial compartment cartilage lesions. This finding could be related to knee instability, an extremely common symptom in patients with OA. Taken together, these differences may be responsible for more rapid cartilage degeneration in individuals with OA. Abstracts / Osteoarthritis and Cartilage 23 (2015) A82eA416 A307s / Osteoarthritis and Cartilage 23 (2015) A82eA416 A307 482 SERUM LEVELS OF RESISTIN AND INTERLEUKIN-17 ARE ASSOCIATED WITH INCREASED CARTILAGE DEFECTS AND BONE MARROW LESIONS IN PATIENTS WITH KNEE SYMPTOMATIC OSTEOARTHRITIS K. Wang y, J. Xu y, J. Cai y, S. Zheng y, X. Yang y, C. Ding zy. yDept. of Rheumatology and Immunology, First Affiliated Hosp. of Anhui Med. Univ., Hefei, China; zMenzies Inst. of Med. Res., Univ. of Tasmania,

A contact layer element for large deformations

In many contact situations the material behavior of one contact member strongly influences the force acting between the two bodies. Unfortunately standard friction models cannot reproduce all of these material effects at the contact layer and often continuum interface elements are used instead. These elements are intrinsically tied to the fixed grid and hence cannot be used in large sliding simulations. Due to the shortcomings of the standard contact formulations and of the interface elements a new type of a contact layer element is developed in this work. The advantages of this element are the direct implementation of continuum models into the contact formulation and the application to arbitrary large deformations. Showing a relation between continuum and contact kinematics based on the solid-shell concept the new contact element is at the end a natural extension of the standard contact formulations into 3D. Two examples show that the continuum behavior can be exactly reproduced at the contact surface even in large sliding situations using this contact layer element. For the discretization of the new contact element the Mortar method is chosen exemplary, but it can be combined with all kinds of contact formulations.

Ankle Dorsiflexion Displacement During Landing is Associated With Initial Contact Kinematics but not Joint Displacement.

The ankle, knee, and hip joints work together in the sagittal plane to absorb landing forces. Reduced sagittal plane motion at the ankle may alter landing strategies at the knee and hip, potentially increasing injury risk; however, no studies have examined the kinematic relationships between the joints during jump landings. Healthy adults (N = 30; 15 male, 15 female) performed jump landings onto a force plate while three-dimensional kinematic data were collected. Joint displacement values were calculated during the loading phase as the difference between peak and initial contact angles. No relationship existed between ankle dorsiflexion displacement during landing and three-dimensional knee and hip displacements. However, less ankle dorsiflexion displacement was associated with landing at initial ground contact with larger hip flexion, hip internal rotation, knee flexion, knee varus, and smaller plantar flexion angles. Findings of the current study suggest that restrictions in ankle motion during landing may contribute to contacting the ground in a more flexed position but continuing through little additional motion to absorb the landing. Transverse plane hip and frontal plane knee positioning may also occur, which are known to increase the risk of lower extremity injury.

Stribeck and Traction Curves Under Moderate Contact Pressure: From Friction to Interfacial Rheology

Friction in the full-fluid-film regime is generally attributed to the shear response of the lubricated interface under pressure. However, the associated rheological law remains under debate. Stribeck and traction experiments were carried out for model fluids and complex aged fully formulated fluids using the IRIS tribometer, which allows simultaneous measurement of film thickness and friction force under controlled contact kinematics. This leads to the establishment of rheograms that collapse over a wide range of shear rate for moderate contact pressure. A theoretical methodology is then proposed to determine the rheology of the confined interfacial film in a unique way, the latter being discussed in terms of the Eyring and Cross physical non-Newtonian models.

Articular contact kinematics of the knee before and after a cruciate retaining total knee arthroplasty.

Accurate knowledge of tibiofemoral articular contact kinematics of the knee after total knee arthroplasty (TKA) is important for understanding the intrinsic knee biomechanics and improving the longevity of the components. The objective of this study was to compare the in vivo articular contact kinematics of the knees with end-stage medial osteoarthritis (OA) during a weight-bearing, single leg lunge activity before and after a posterior cruciate retaining TKA (CR-TKA) using a dual fluoroscopic imaging technique. We found that the CR-TKA resulted in more posterior contact positions on the tibial surface and a reduced range of motion in the medial and lateral compartments. The distances between medial and lateral contact locations in the CR-TKA knees were statistically larger than the OA knees. The articular contact centers have shifted from medial side of the tibial plateau pre-operatively to the lateral side after operation. This study indicated that the CR-TKA resulted in significant changes in contact kinematics of the knees in both anteroposterior and mediolateral directions. Further studies are needed to determine the influence of the altered in vivo contact kinematics on the longevity of polyethylene liner and long term clinical outcomes of the TKA.

On some aspects for contact with rigid surfaces: Surface-to-rigid surface and curves-to-rigid surface algorithms

Special algorithms allowing a simplified description of contact between deformable body and rigid surfaces are developed based on the geometrically exact covariant description of contact. A special attention is given to various geometric combinations where the contact can be represented as (a) contact between surfaces and (b) contact between a curve and a surface. For contact between surfaces, leading to the Segment-To-Analytical Surface (STAS) approach, two algorithms can be distinguished based on the selection of a coordinate system for the Closest Point Projection (CPP) procedure: (a) Rigid Surface is a “Slave” surface and (b) Rigid Surface is a “Master” surface. A special combination of both contact kinematics for the surface-to-surface and for the curve-to-curve approaches is employed for the contact between a curve and a surface leading to the Curve-To-Rigid Surface (CTRS) approach. The last algorithm is verified with the well known Euler formula for the rope–cylinder interaction as well as with a new derived generalization into a 3D spiral rope on a cylinder. The developed algorithms can be straightforwardly implemented within an iso-geometric approach as well as within the conventional finite elements where rigid surfaces are given by CAD patches. Any type of elements can be employed for the contacting deformable surface/curve because the algorithms are formulated in a covariant form.

Finite element modeling for stick-slip pattern of squeal modes in disc brake

This paper provides the finite element modeling for describing the nonlinear stick-slip response of squealing modes in a disc brake system. The analytical nonlinear contact kinematics is applied to each contact node of the finite element disc and pads. Numerical results show that a portion of the contact area can undergo the stick-slip oscillation. Depending on the size of the stick-slip zone, the corresponding squeal vibration can be either the pure harmonic or periodic oscillation. Particularly, the squeal mode arising from the pad rigid mode generates the periodic stick-slip limit cycle in its steady-squealing response, as opposed that the disc squeal modes become the pure harmonic response.

A direct experimental–numerical method for investigations of a laboratory under-platform damper behavior

Under-platform dampers are commonly adopted in order to mitigate resonant vibration of turbine blades. The need for reliable models for the design of under-platform dampers has led to a considerable amount of technical literature on under-platform damper modeling in the last three decades.Although much effort has been devoted to the under-platform damper modeling in order to avail of a predictive tool for new damper designs, experimental validation of the modeling is still necessary. This is due to the complexity caused by the interaction of the contacts at the two damper-platform interfaces with the additional complication of the variablity of physical contact parameters (in particularly friction) and their nonlinearity. The traditional experimental configuration for evaluating under-platform damper behavior is measuring the blade tip response by incorporating the damper between two adjacent blades (representing a cyclic segment of the bladed disk) under controlled excitation. The effectiveness of the damper is revealed by the difference in blade tip response depending on whether the damper is applied or not. With this approach one cannot investigate the damper behavior directly and no measurements of the contact parameters can be undertake. Consequently, tentative values for the contact parameters are assigned from previous experience and then case-by-case finely tuned until the numerical predictions are consistent with the experimental evidence. In this method the physical determination of the contact parameters is obtained using test rigs designed to produce single contact tests which simulate the local damper-platfom contact geometry. However, the significant limitation of single contact test results is that they do not reveal the dependence of contact parameters on the real damper contact conditions. The method proposed in this paper overcomes this problem.In this new approach a purposely developed test rig allows the in-plane forces transferred through the damper between the two simulated platforms to be measured, while at the same time monitoring in-plane relative displacements of the platforms. The in-plane damper kinematics are reconstructed from the experimental data using the contact constraints and two damper motion measurements, one translational and one rotational. The measurement procedures provide reliable results, which allow very fine details of contact kinematics to be revealed. It is demonstrated that the highly satisfactory performance of the test rig and the related procedures allows fine tuning of the contact parameters (local friction coefficients and contact stiffness), which can be safely fed into a direct time integration numerical model.The numerical model is, in turn, cross-checked against the experimental results, and then used to acquire deeper understanding of the damper behavior (e.g. contact state, slipping and sticking displacement at all contact points), giving an insight into those features which the measurements alone are not capable of producing. The numerical model of the system is based on one key assumption: the contact model does not take into account the microslip effect that exists in the experiments.Although there is room for improvement of both experimental configuration and numerical modeling, which future work will consider, the results obtained with this approach demonstrate that the optimization of dampers can be less a matter of trial and error development and more a matter of knowledge of damper dynamics.

Fast interpolation and time-optimization with contact

This paper presents a method for generating dynamically feasible, keyframe-interpolating motions for robots undergoing contact, such as in legged locomotion and manipulation. The first stage generates a twice-differentiable interpolating path that obeys kinematic contact constraints up to a user-specified tolerance. The second stage optimizes speeds along the path to minimize time while satisfying dynamic constraints. The method supports velocity, acceleration, and torque constraints, and polyhedral contact friction constraints at an arbitrary number of contact points. The method is numerically stable, and empirical running time is weakly linear in the number of degrees of freedom and polynomial in the time-domain grid resolution. Experiments demonstrate that full-body motions for robots with 100 degrees of freedom and dozens of contact points are calculated in seconds.

A level set enhanced natural kernel contact algorithm for impact and penetration modeling

SummaryA natural kernel contact (NKC) algorithm under the framework of the semi‐Lagrangian reproducing kernel particle method (semi‐Lagrangian RKPM) is proposed to model multi‐body contact with specific consideration for impact and penetration modeling. The NKC algorithm utilizes the interaction of the semi‐Lagrangian kernel functions associated with contacting bodies to serve as the non‐penetration condition. The effects of friction are represented by introducing a layer of the friction‐like elasto‐plasticity material between contacting bodies. This approach allows the frictional contact conditions and the associated kinematics to be naturally embedded in the semi‐Lagrangian RKPM inter‐particle force calculation. The equivalence in the Karush–Kuhn–Tucker conditions between the proposed NKC algorithm and the conventional contact kinematic constraints as well as the associated state variable relationships are identified. A level set method is further introduced in the NKC algorithm to represent the contact surfaces without pre‐defined potential contact surfaces. The stability analysis performed in this work shows that temporal stability in the semi‐Lagrangian RKPM with NKC algorithms is related to the velocity gradient between contacting bodies. The proposed methods have been verified by several benchmark problems and applied to the simulation of impact and penetration processes. Copyright © 2014 John Wiley & Sons, Ltd.

Realization of foot rotation by breaking the kinematic contact constraint

SUMMARYPrevious research has revealed that foot rotation of the supporting foot in a single support phase could increase walking speed. This paper presents a method for force-controlled bipeds to realize foot rotation by breaking the kinematic contact constraint between the supporting foot and the ground. An inverse dynamics controller is proposed to make the biped model controllable even when the constraint is broken. In addition, a linear inverted pendulum model is extended to make its ZMP adjustable so that the ZMP can be predefined as required. When the planned ZMP is in the toe, the kinematic contact constraint will be broken and foot rotation can be achieved. A walking simulation demonstrates the effectiveness of the proposed method.

MACRO-MICRO ANALYSIS FOR ANTI-PENETRATING POSTBUCKLING OF FIBER REINFORCED, DEBONED LAMINATES WITH CONTACT EFFECTS

This paper presents a close-form solution for the anti-penetrating postbuckling problem of fiber reinforced, rectangular laminates. The laminate has a through-width debonded region buried at the center position and is simply supported at its four edges subjected to the in-plane compressive load. Based on the previous analysis of the contact kinematics from micro mechanics of composite material, the nonlinear contact effects at the interfaces of the debonded region are considered and characterized by a contact factor. Governing equations are established and are solved using the perturbation approach. Asymptotic solutions from perturbation analysis are presented. It is found that for fiber reinforced, debonded laminates the postbuckling deformation involves global deflection and local buckling with amplitude of the global one 104 times larger than the local one. The global deflection is induced by the postbuckling load and the local buckling is caused by the anti-penetrating contact effects. Due to the contact effects, the load carry capacity of the delaminated laminate is tremendously enhanced. Further examination indicates that both the buckling load and the contact performances are intrinsic properties of the laminates. Parametric analyses show that (i) the buckling load decreases with the increasing of the delamination length and the delamination depth and is very sensitive to the changing of the aspect ratio, (ii) the contact performances, including the location and size of the contact areas, rely only on the geometries of the debonded region and the material properties but are hardly affected by the aspect ratio. The analysis is in effect by comparing with the well established results.

Description of sub‐ and superharmonic motion in rotor‐stator contact using Fourier series

AbstractThis paper deals with the description of steady‐state sub‐ and superharmonic motion in rotor‐stator contact using truncated complex Fourier series. Two different approaches are presented with different stages of simplification. In particular, a kinematic contact condition describing continuous contact is used. The multi‐harmonic balance method is applied to solve the differential algebraic system of equations. A further simplification is implemented which uses the triangular inequality to approximate the nonlinear term in the kinematic contact condition. The Fourier coefficients of the nonlinear term are calculated using an integral expression. Reasonable initial values of the Fourier coefficients for the numerical solution are obtained by a hybrid approach. Results show good agreement with calculations by direct numerical integration using a pseudo‐linear viscoelastic contact model.

Variable Singularity Power Wedge Element for Multilayered Composites

Multilayered composites can be weakened by local failures, which can give rise to singular stress fields. Singularities can be removed or integrated to obtain bounded quantities which may be used for the analysis. In any case, the participation of singular stresses should be identified. Serving this purpose, a new mixed singular wedge element based on interpolation functions with a variable singularity power is developed, which can adapt to the problem and can represent the non-singular fields as a particular case. The displacements and the interlaminar stresses are assumed as nodal d.o.f. to a priori fulfill the kinematic and stress contact conditions at the material interfaces and the stress boundary conditions in point form. The application to sample cases taken from literature shows that the element can be successfully employed for the analysis of singular fields. The variable singular representation and the mixed formulation give more accurate results than their displacement-based, non-singular, or singular counterparts with a fixed singularity. The failure loads of initially delaminated specimens are accurately predicted either using the virtual crack closure technique or a mesoscale model by running in a reasonable time on a personal laptop computer.

Transient Tribo-Dynamics of Thermo-Elastic Compliant High-Performance Piston Skirts

Advanced piston technology for motorsport applications is driven through development of lightweight pistons with preferentially compliant short partial skirts. The preferential compliance is achieved through structural stiffening, such that a greater entrainment wedge is achieved at the skirt’s bottom edge through thermo-elastic deformation, whilst better conforming contact geometry at the top of the skirt. In practice, the combination of some of these conditions is intended to improve the load-carrying capacity and reduce friction. The approach is fundamental to the underlying ethos of race and high-performance engine technology. Contact loads of the order of 5 kN and contact kinematics in the range 0–35 m/s result in harsh transient tribological conditions. Therefore, piston design requires detailed transient analysis, which integrates piston dynamics, thermo-elastic distortion and transient elastohydrodynamics. The paper provides such a detailed analysis as well as verification of the same using non-invasive ultrasonic-assisted lubricant film thickness measurement from a fired engine under normal operating conditions, an approach not hitherto reported in literature. Good agreement is noted between measured film thickness and predictions.

Nonsmooth analysis of the impact between successive skew bridge-segments

Skew bridges with in-deck joints belong to the most common types of existing bridges worldwide. Empirical evidence from past earthquakes indicates that such, multi-segment, skew bridges often rotate in the horizontal plane, increasing the chances of deck unseating. The present paper studies the oblique in-deck impact between successive bridge segments, which triggers this peculiar rotation mechanism. The analysis employs a nonsmooth rigid body approach and utilizes set-valued force laws. A key feature of this approach is the linear complementarity problem (LCP) which encapsulates all physically feasible post-impact states. The LCP results in pertinent closed-form solutions which capture each of these states, and clarifies the conditions under which each post-impact state appears. In this context, a rational method to avoid the singularities arising from dependent constraints is coined. The results confirm theoretically the observed tendency of skew (bridge deck) segments to bind in their obtuse corners and rotate in such a way that the skew angle increases. Further, the study offers equations which describe the contact kinematics between two adjacent skew planar rigid bodies. The same equations can be used to treat successively as many pairs of skew bridge-segments as necessary.

Three‐dimensional numerical solution for wear prediction using a mortar contact algorithm

SUMMARYA finite element formulation to compute the wear between three‐dimensional flexible bodies that are in contact with each other is presented. The contact pressure and the bodies displacements are calculated using an augmented Lagrangian approach in combination with a mortar method, which defines the contact kinematics. The objective of this study is to characterize the wear rate coefficients for bimetallic pairs and to numerically predict the wear depths in new component designs. The proposed method is first validated with the classical pin‐on‐disc problem. Then, experimental results of wear for the metallic pairs used in internal combustion engine valves and inserts are presented and are taken as a reference solution. An example is provided that shows agreement of the numerical and experimental solution. Finally, the proposed algorithm is used to predict the wear in an application example: the wear in an internal combustion engine valve. Copyright © 2013 John Wiley & Sons, Ltd.

Tire grip identification based on strain information: Theory and simulations

A novel technique for the identification of the tire–road grip conditions is presented. This is based on the use of strain information inside the tire, from which relevant characteristics of the tire–road contact can be extracted also through a factor named area slip ratio. This process forms the basis of a technology for grip identification that requires a new model of the tire dynamics. The model permits to determine closed form analytical relationships between the measured strain and the area slip ratio. On this basis, a procedure that can extract the contact kinematic parameter from the time history of the internal strain of the rolling tire is presented. Numerical simulations offer the chance to validate the identification algorithm.

Fracture and fragmentation of thin shells using the combined finite–discrete element method

SUMMARYA model for fracture and fragmentation of multilayered thin shells has been developed and implemented into the combined finite–discrete element code. The proposed model incorporates an extension of the original combined single and smeared fracture approach to multilayered thin shells; it then combines these with an interaction algorithm that is based on the original distributed potential contact force approach. The developed contact kinematics preserves both energy and momentum balance, whereas the developed fracture model is capable of modelling complex fracture patterns such as fracture of laminated glass under impact. Copyright © 2013 John Wiley & Sons, Ltd.