Finite element incremental contact analysis with various frictional conditions

Okamoto, Noriaki; Nakazawa, Masaru

doi:10.1002/nme.1620140304

Cited by 155 publications

(25 citation statements)

References 17 publications

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“…The graph of Coulomb's friction law is a quadratic cone [22,23]. In order to obtain the LCP formulation, a piecewise linearization of Coulomb's friction law is introduced…”

Section: The Linear Complementarity Problem (Lcp) Formulationmentioning

confidence: 99%

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Numerical simulation of contact problems in vane machinery by a parametric quadratic programming method

Zhang

Liao

2006

Arch Appl Mech

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Interference fits are widely used for connecting impeller and shaft assembly that are forced together slowly by pressing. The interference fit design ensures stable balance behavior and allows for positive contact between the impeller and shaft assembly throughout the range of operating speeds. In addition to maintaining radial contact, sufficient net radial interface pressure must remain in order to transmit torque when the rotational speed is very high. Therefore, the interference fit between the impeller and the shaft assembly is one of the most important factors influencing the performance of the turbo unit in the design of turbocharger compressor. A suitable fit tolerance needs to be considered in the structural design.A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference fit loading is used for the analysis. The finite-element (FE) parametric quadratic programming (PQP) method developed based on the parametric variational principle (PVP) is used for the analysis of the stress distribution in the three-dimensional (3D) contact problem of impeller. The advantages of the parametric programming method compared with conventional approaches are that the penalty factors can be canceled and that solutions can be obtained directly without tedious iterative procedures such as the general incremental iterative method. To save time in the computation, a multi-substructure technique is adopted for structural modeling. This not only simplifies the calculation, but also provides a convenient service for process computer-aided design (CAD) by means of FE simulation. The effects of the fit tolerance, coefficient of friction and rotational speed (centrifugal force), wall thickness of the shaft sleeve and the contact stress on the interference-fitting surfaces are studied in detail in the numerical computation. It is found that a nonuniform initial amount of interference in the structural design avoids the relative displacement generated and ensures uniformity of the contact stress. To assure quality of press-fitting, the amount of interference between the shaft sleeve and shaft should be strictly controlled to avoid the rapid increase of the contact stress. The numerical results demonstrate the high accuracy and good convergence of the algorithm presented here, which provides an effective approach that achieves more-reliable interference-fitted connections and more-precise assembly accuracy with lower manufacturing cost in the structural design.

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“…The graph of Coulomb's friction law is a quadratic cone [22,23]. In order to obtain the LCP formulation, a piecewise linearization of Coulomb's friction law is introduced…”

Section: The Linear Complementarity Problem (Lcp) Formulationmentioning

confidence: 99%

“…(22) and (24) is called a parametric quadratic programming problem, which can be converted to the following standard LCP formulations:…”

Section: Finite-element Discretizationmentioning

confidence: 99%

Numerical simulation of contact problems in vane machinery by a parametric quadratic programming method

Zhang

Liao

2006

Arch Appl Mech

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“…The displacements and structures must satisfy different equilibrium equations and continuity conditions for different contact constraints as indicated above. For one pair of double-nodes, for example, 1 and 9, both conditions can be written as where I is the identity mixed and Supposing nodes (1,9) are in the state of slip, double nodes (2, 10) are in the mixed state with sliding in direction s, double nodes (3, 1 1 ) are in the free state and other double nodes are in the fixed state. In this case, matrices L!…”

Section: Constraint Conditions On Contact Surfacementioning

confidence: 99%

Simulation of arch dam – foundation interaction with a new friction interface element

Swoboda

Lei

1994

Num Anal Meth Geomechanics

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SUMMARYA new model for three-dimensional non-linear contact problems with irreversible friction is presented here for the interaction between the rock foundation and an arch dam structure. Based on the finite element method and load incremental theory, a constraint contact element with displacements and contact stresses as node parameters is developed. In this approach, four contact conditions are considered, i.e. fixed, slip, free and mixed. This model can simulate frictional slippage, decoupling and re-bonding of two bodies initially mating at a common interface or with any initial gaps. Furthermore boundary conditions for this element are discussed and treatment measures proposed. This method is shown to be effective and to have the advantage of being easily implemented into standard finite element programs. Solutions are obtained for a centrally loaded, simply supported composite beam and for an end-loaded elastica with initial gaps in regional contact with a rigid surface. The results obtained for these examples are compared to the plane stress solutions by contact friction analysis. As an application example, Quanshui arch dam located in Ruyuan County of Guangdong Province in southern China is simulated with the new element.

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“…Taking the first variation of the functional in equation (7) and integrating by parts the variations of derivatives yields…”

Section: Application To the Contact Problemmentioning

confidence: 99%

The mixed finite element method applied to two‐dimensional elastic contact problems

Tseng

Olson

1981

Numerical Meth Engineering

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SUMMARYThe application of the mixed finite element method to two-dimensional elastic contact problems is investigated. Since in the mixed method, both displacements and stresses are retained as variables, it is found that all the contact conditions-displacement as well as stress-can be approximated directly. A significant novelty is that some of the displacement variables are treated as natural boundary conditions in the contact region. In cases where the contact region is independent of the applied loading, an iterative procedure is used to establish the sliding and adhering portions of the contact region. In cases where the contact region is a function of the applied loading, for example progressive contact, an incremental formulation is employed to describe the discretized contact stages before invoking the former iterations. Several numerical examples are presented and the results are compared with those from the conventional potential energy or displacement finite element method.

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Finite element incremental contact analysis with various frictional conditions

Cited by 155 publications

References 17 publications

Numerical simulation of contact problems in vane machinery by a parametric quadratic programming method

Numerical simulation of contact problems in vane machinery by a parametric quadratic programming method

Simulation of arch dam – foundation interaction with a new friction interface element

The mixed finite element method applied to two‐dimensional elastic contact problems

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