Manfred Zehn

Finite element formulations for effective computations of geometrically nonlinear deformations

The paper presents finite element formulations aimed at efficient computation of large geometrically nonlinear flexible body deformations. The formulations are primarily developed for applications in the field of virtual reality technology, but applications in other fields requiring high computational efficiency are also possible. Many applications in the field of virtual reality require real-time or nearly real-time simulation of behaviour of deformable objects, quite often with deformations involving large local rotations. The well-known simplified approach based on mass-spring systems is shortly discussed with advantages and disadvantages pointed out. This is followed by a co-rotational 3D-FEM approach based on rigid-body rotations performed on element level. The approach accounts for large local rotations and yields reasonable accuracy combined with high numerical efficiency. Examples are provided to demonstrate features of proposed formulations.

Study on clutch engagement judder during launch process for dual clutch transmissions

Clutch engagement judder, as part of vehicle noise, vibration and harshness (NVH), is an important vehicle attribute in the design of dual clutch transmissions (DCTs). This paper presents a system analytical model for clutch engagement judder during launch for DCT vehicles. Influencing factors on clutch judder, including internal factors (friction characteristic, damping, backlash) and external factors (engine torque fluctuation, applied oil pressure fluctuation), are studied analytically and numerically through system stability analysis and free vibration analysis. The results of the simulations show that clutch judder is dependent on the slope of the friction coefficient, static friction coefficient, system damping, applied oil pressure and engine torque fluctuation. Sensitivity analysis and sensitivity functions are presented to find the most sensitive elements in mass matrix and stiffness matrix to shift the undesirable system natural frequencies. The research provides a basis for refinement and optimisation of vehicle design.

Selecting boundary conditions in physiological strain analysis of the femur: Balanced loads, inertia relief method and follower load

Selection of boundary constraints may influence amount and distribution of loads. The purpose of this study is to analyze the potential of inertia relief and follower load to maintain the effects of musculoskeletal loads even under large deflections in patient specific finite element models of intact or fractured bone compared to empiric boundary constraints which have been shown to lead to physiological displacements and surface strains. The goal is to elucidate the use of boundary conditions in strain analyses of bones. Finite element models of the intact femur and a model of clinically relevant fracture stabilization by locking plate fixation were analyzed with normal walking loading conditions for different boundary conditions, specifically re-balanced loading, inertia relief and follower load. Peak principal cortex surface strains for different boundary conditions are consistent (maximum deviation 13.7%) except for inertia relief without force balancing (maximum deviation 108.4%). Influence of follower load on displacements increases with higher deflection in fracture model (from 3% to 7% for force balanced model). For load balanced models, follower load had only minor influence, though the effect increases strongly with higher deflection. Conventional constraints of fixed nodes in space should be carefully reconsidered because their type and position are challenging to justify and for their potential to introduce relevant non-physiological reaction forces. Inertia relief provides an alternative method which yields physiological strain results.

Study on shift dynamics and shift quality of dual clutch transmissions

Dual clutch transmissions (DCTs) offer full shift comfort, and significantly improved fuel efficiency and performance. This paper presents a model for the simulation and analysis of shift dynamics for DCT vehicles. A DCT structure for heavy duty trucks was proposed and the simulation model was built with the software Matlab/Simulink. System dynamic equations were derived according to the detailed analysis of upshifts and downshifts. The importance of engine throttle control, clutch apply timing and clutch pressure characteristics were quantitatively analysed and explained. Simulation results show that better shift quality can be achieved with proper throttle control. The release signal of off-going clutch should be initiated at the same time as the engaging signal of on-coming clutch in upshifts. Optimised clutch pressure can be achieved for smooth shifts by modifying the clutch pressure characteristics interactively based on the simulation results.

Application of the Craig-Bampton model order reduction method to a composite structure: MACco, COMAC, COMAC-S and eCOMAC

The Craig-Bampton model order reduction (CBMOR) method based on the Rayleigh-Ritz approach was applied in a previous work to simulate dynamic behavior of a composite structure (CFRP) using the modal assurance criteria (MAC) and cross orthogonality (XOR) to validate the correlation. Different coordinatemodal assurance criteria are applied to complement and verify the eigenfrequencies and eigenvectors obtained of the full and reduced models using substructures (super-elements). An improvement is observed per pairedmode-sensor with the MAC per coordinates criterion (MACco) in a CFRP once the stiffness parameters are updated in the full model applying a mix-numerical experimental technique (MNET) using a design of experiments (DOE). The coordinate modal assurance criteria (COMAC) and the scale COMAC (COMACS) results of the full models display the best results respect to the reduced model. Furthermore, slight improvement of the enhanced COMAC (eCOMAC) results are observed in the reduced model despite having lower MAC performance. This approach complements the results of the previous work using several COMAC techniques, and demostrates the feasibility to achieve low COMACs results in the reduced finite element model once the stiffness parameters of the full elementmodel are updated. The example was prepared and solved with MSC/NASTRAN SOL103 and SDTools-MATLAB for comparative purposes.