A computational methodology for analysis of spatial flexible multibody systems, considering the effects of the clearances and lubrication in the system spherical joints, is presented. The dry contact forces are evaluated through a Hertzian-based contact law, which includes a damping term representing the energy dissipation. The frictional forces are evaluated using a modified Coulomb's friction law. In the case of lubricated joints, the resulting lubricant forces are derived from the corresponding Reynolds' equation. An absolute nodal formulation is utilized in flexible body formulation. The generalized-α method is used to solve the resulting equations of motion. The effectiveness of the methodology is demonstrated by two numerical examples.

Modeling of clearance joints plays an important role in the analysis and design of multibody mechanical systems. Based on the absolute nodal coordinate formulation (ANCF), a new computational methodology for modeling and analysis of planar flexible multibody systems with clearance and lubricated revolute joints is presented. A planar absolute nodal coordinate formulation based on the lockingfree shear deformable beam element is implemented to discretize the flexible bodies. A continuous contactimpact model is used to evaluate the contact force, in which energy dissipation in the form of hysteresis damping is considered. A force transition model from hydrodynamic lubrication forces to dry contact forces is introduced to ensure continuity in the joint reaction force. A comprehensive study with different lubrication force models has also been carried out. The generalized-α method is used to solve the equations of motion and several efficient methods are incorporated in the proposed model. Finally, the methodology is validated by two numerical examples.

A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960's. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links' flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.

A new approach to model and analyze flexible spatial multibody systems with clearance of cylindrical joints is presented in this work. The flexible parts are modeled by using absolute nodal coordinate formulation (ANCF)-based elements, while the rigid parts are described by employing the natural coordinate formulation (NCF), which can lead to a constant system mass matrix for the derived system equations of motion. In a simple way, a cylindrical joint with clearance is composed of two main elements, that is, a journal inside a bearing. Additionally, a lubricant fluid can exist between these two mechanical elements to reduce the friction and wear and increase the system's life. For the case in which the joint is modeled as a dry contact pair, a technique using a continuous approach for the evaluation of the contact force is applied, where the energy dissipation in the form of hysteresis damping is considered. Furthermore, the frictional forces developed in those contacts are evaluated by using a modified Coulomb's friction law. For the lubricated case, the hydrodynamic theory for dynamically loaded journal bearings is used to compute the forces generated by lubrication actions. The lubricated model is based on the Reynolds equation developed for the case of journal bearings with length-todiameter ratios up to 1. Using this approach, the misalignment of the journal inside the bearing can be studied. Finally, two demonstrative examples of application are used to provide results that support the discussion and show the validity of the proposed methodologies.

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time emergency medical service vehicle response system that uses real-time travel time information and that assists the emergency vehicle dispatchers in assigning response vehicles and guiding those vehicles through noncongested routes is developed. Different response strategies are evaluated with this simulation model. These include the first-called, first-served strategy, the nearestorigin assignment strategy, and the flexible assignment strategy that uses real-time travel time information to assign and dispatch response vehicles. Different assumptions and conditions are used to test the sensitivity of the flexible assignment strategy.

An efficient method of model order reduction is proposed for the dynamic computation of a flexible multibody system undergoing both large overall motions and large deformations. The system is initially modeled by using the nonlinear finite elements of absolute nodal coordinate formulation and then locally linearized at a series of quasi-static equilibrium configurations according to the given accuracy in dynamic computation. By using the Craig-Bampton method, the reduced model is established by projecting the incremental displacements of the locally linearized system onto a set of local modal bases at the quasi-static equilibrium configuration accordingly. Afterwards, the initial conditions for the dynamic computation for the reduced model via the generalized-α integrator can be determined from the modal bases. The analysis of computation complexity is also performed. Hence, the proposed method gives time-varying and dimension-varying modal bases to elaborate the efficient model reduction. Finally, three examples are presented to validate the accuracy and efficiency of the proposed method. KEYWORDSabsolute nodal coordinate formulation, Craig-Bampton method, flexible multibody dynamics, model order reduction Nomenclature: C, vector of constraints; d, vector of augmented external forces; e, vector of generalized coordinates; E, Young's modulus; I, moment of inertia; h, time step; K, global stiffness matrix;K, augmented global stiffness matrix; M, global mass matrix;M, augmented global mass matrix; n, total number of degrees of freedom; n c , number of constraint equations; n e , number of finite elements; n m , number of dynamic equations; n p , number of degrees of freedom per node; n s , revolution per minute; n t , number of truncated modes; n t 1 , initial number of truncated modes; n t max , maximal number of truncated modes; q, vector of augmented modal coordinates; Q, vector of external forces; r, vector of global position; t, time; t N , moment of the Nth local linearization; T, transformation matrix;ũ, vector of augmented coordinates; U, strain energy; XYZ, global frame of coordinates; X i Y i Z i , the ith body frame of coordinates; C , matrix of constrained modes; V , matrix of vibration modes; , vector of modal coordinates of internal part; , vector of Lagrange multipliers; j , the jth eigenvalue; , diagonal matrix of eigenvalues; Ω, configuration region; , vector of augmented acceleration-like variables; s , rotation angle; s , angular velocity; Δ max , threshold of local linearization; , specified value of mode selection; Δ RMS , root of mean squared error. Superscripts and subscripts: () B , symbol related to boundary part; () I , symbol related to internal part; () BI , () IB , symbol related to coupling parts; () e , the Jacobian with respect to vector e; () N , symbol corresponding to the Nth local linearization;() k , symbol corresponding to the kth time step; () d , reserved quantity; () r , residual quantity. Overbar: (^), quantity in the reduced model; (˜), quantity in the non-reduced model; (...

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