Model-Based Energy Path Analysis of Tip-In Event in a 2WD Vehicle with Range-Extender Electric Powertrain Architecture

Vehicle driveability is one of the important attributes in range-extender electric vehicles due to the electric motor torque characteristics at low-speed events. Physical vehicle prototypes are typically used to validate and rectify vehicle driveability attributes. However, this can be expensive and require several design iterations. In this paper, a model-based energy method to assess vehicle driveability is presented based on high-fidelity 49 degree-of-freedom powertrain and vehicle systems. Multibody dynamic components were built according to their true centre of gravity relative to the vehicle datum to provide an accurate system interaction. The work covered a frequency of less than 20 Hz. The results consist of the components’ frequency domination, which was structured and examined to identify the low-frequency resonances sensitivity based on different operating parameters such as road surface coefficients. An energy path method was also implemented on the dominant component by decoupling its compliances to study the effect on the vehicle driveability and low-frequency resonances. The outcomes of the research provided a good understanding of the interaction across the sub-systems levels. The powertrain rubber mounts were the dominant component that controlled the low-frequency resonances (<15.33 Hz) and can change the vehicle driveability quality.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

A Universal Nonlinear Analyzer for Rigid Multibody Systems Based on the Efficient Galerkin Averaging-Incremental Harmonic Balance Method

The bridge between the multibody dynamic modeling theory and nonlinear dynamic analysis theory is built for the first time in this work by introducing an efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method for steady-state nonlinear dynamic analysis of index-3 differential algebraic equations (DAEs) for general rigid multibody systems. The multibody dynamic modeling theory has made significant advances in generality and simplicity, and multibody systems are usually governed by DAEs. Since the fast Fourier transform and EGA are used, the EGA-IHB method has excellent robustness and computational efficiency. Since the Floquet theory cannot be directly used for stability analysis of periodic responses of DAEs, a new stability analysis procedure is developed, where perturbed, linearized DAEs are reduced to ordinary differential equations with use of independent generalized coordinates. A modified arc-length continuation method with a scaling strategy is used for calculating response curves and conducting parameter studies. Three examples are used to show the performance and capability of the current method. Periodic solutions of DAEs from the EGA-IHB method show excellent agreement with those from numerical integration methods. Amplitude-frequency and amplitude-parameter response curves are generated, and stability and period-doubling bifurcations are analyzed. The EGA-IHB method can be used as a universal solver and nonlinear analyzer for obtaining steady-state periodic responses of DAEs for general multibody systems.

Finite Element Modeling of Geometrically Exact Shell With Large Deformation and Rotation

This paper developed a new geometrically exact shell element to model the relatively thin structures with large deformations and arbitrary rigid motions. The deformations were well decoupled from rigid motions by using the direct modeling approach. The rotation-free Green-Lagrange strain tensor described the large deformations together with geometrical nonlinearities. Meanwhile, the Wiener-Milenković parameter was applied to vectorial parameterize the arbitrary rotations of the fiber avoiding the singularities usually occurred in the classical shell formula. This paper also designed a new interpolating algorithm without losing objectivity to discretize the vectorial parameters, which improves the robustness of new shell element. The application of Mixed Interpolation of Tensorial Components with 9 nodes (MITC9) makes the shell element shear-locking free and with second-order accuracy. Each node contains five degrees of freedom, three for translations and two for rotations, achieving a minimal set representation of arbitrary motions. These innovations contribute to a new shell formula featuring high computational efficiency with good accuracy. Finally, two flexible multibody dynamic models are discretized by this new shell element. The numerical simulation results of the new shell element have been verified to demonstrate the capability of new shell element dealing with large deformations and arbitrary motions of thin structures.

A multibody dynamic model for predicting operational load spectra of dual clutch transmissions

In this paper, a generalized nonlinear time-varying multibody dynamic model of dual clutch transmissions (DCT) is presented. The model consists of clutches, shafts, gears and synchronizers, and can be used to model any DCT architecture. A nonlinear clutch model is used to determine the transmitted power to the transmission at any speed and clutch temperature. The clutch can be a single- or multi-plate clutch and can operate in a wet or dry-clutch configuration. A combined kinematic and powerflow simulation enables calculation of gear, shaft, bearing and clutch quasi-static loads as well as gear mesh frequencies following a duty cycle as the input. For the corresponding Linear-Time-Invariant (LTI) system model, natural frequencies and mode shapes are obtained by solving the eigenvalue problem. The modal summation technique is used to determine the steady state forced vibration response of the system. For the corresponding NTV system, Newmark's time-step marching based integration is used to determine both the steady state and transient forced vibration response of the system. The DCT model is exercised using a common transmission architecture operating at several different operating conditions. The resulting impact of changing operational conditions on gear and bearing loads as well as dynamic transmission error spectra are demonstrated.