Wen-Bin Shangguan

Measurement and modelling of the fatigue life of rubber mounts for an automotive powertrain at high temperatures

A fatigue experiment is carried out on filled natural rubber specimens with two different Shore hardnesses (45 and 50) and three different temperatures (23 °C, 60 °C and 90 °C) under uniaxial tension loads. The measured fatigue life data obtained under different displacement loads are used to formulate fatigue life prediction models corresponding to different operating temperatures for the two hardnesses using the peak engineering strain as the damage parameter. The influences of the temperature, the stress softening at high temperatures and the hardness on the fatigue life of rubbers are measured and discussed. The proposed models are used to predict the fatigue life of a rubber mount for a powertrain mounting system. The validity of the prediction model is demonstrated by comparisons with the measured fatigue life data of the rubber mount at 90 °C. A method for determining the damage parameters required for predicting the fatigue life is presented on the basis of the finite element model of the rubber mount. The Mooney–Rivlin constitutive constants of the hyperelastic rubber material are identified on the basis of the measured data on the specimens. Comparisons of the measured and the estimated fatigue lives of the rubber mount at 90 °C revealed reasonably good agreement. The ratio of the predicted fatigue life to the measured fatigue life was within a factor of 2 under the range of loading conditions considered.

Prediction of fatigue life of rubber mounts using stress-based damage indexes

Prediction of fatigue lives of a rubber mount necessitate formulation of models for estimating fatigue life of the rubber materials used in the mount. Moreover, the prediction accuracy of the model is strongly dependent upon the choice of damage index that are based on different strain, energy or stress measures in the vicinity of critical locations of the rubber mount. In this study, relative performance of models employing different damage indices are evaluated for prediction of fatigue lives of rubber material and a drive-train rubber mount. A combined stress and an effective stress function are proposed as a damage index for predicting fatigue lives of rubber materials and the mounts. Different damage indices, identified from the finite element models of the rubber dumbbell cylindrical specimen are applied for formulations of fatigue life prediction models. The model parameters are identified from the measured data acquired for the rubber dumbbell cylindrical specimen under 31 different uniaxial displacement loads, using least squared error minimization technique. The identified models employing different damage indices are subsequently applied for predicting fatigue lives of rubber mounts under different magnitudes of loads applied along two different directions. The correlations of the predicted lives of the rubber mount from the models employing different damage indices with measured fatigue life data were subsequently investigated for the rubber mount subject to different load conditions. It is shown that the models identified for the rubber material could be effectively used for predicting fatigue lives of the mounts, which are made of same material. The fatigue lives predicted by the models considering either effective stress or combined stress as the damage index correlated with the measured data within a factor of two for the two, suggesting that stress-based damage indices could yield more accurate predictions of fatigue lives of typical mounts.

A study on optimization method of a powertrain mounting system with a three-cylinder engine

Compared with unbalance forces and moments of four- and six-cylinder engines, forces and moments applied to the engine block from a three-cylinder engine are large and the mechanism for balancing the unbalance forces are complex. So design of a mounting system for the powertrain with a three-cylinder engine is more challenging. This paper presents the analytical methods for obtaining the unbalance forces and moments applied to the engine block for a three-cylinder engine with or without balance measures, and develops a design methodology for the Powertrain Mounting System with a three-cylinder engine. The unbalance forces and moments generated by cylinders, crank and connecting rod mechanisms and applied to the engine block are analyzed firstly. Then, three balance methods for reducing the forces and moments applied to the engine block are proposed and discussed. Three balance measures are described and analyzed. The methods for estimating forces and moments applied to the engine block under the three balance measures are developed and compared. Thirdly, an optimization method is proposed to estimate mount stiffness based on minimization of mount forces transmitted to the car body or sub-frame, along with meeting requirements for placing natural frequencies of the powertrain in prescribed ranges and those for maximizing modal energy distributions of the powertrain in six directions. An example is given to validate the calculation methods and design philosophy for the mounting system of a powertrain with a three-cylinder engine.

A Study on Calculation Method of Natural Frequency for Rubber Damped Torsional Vibration Absorbers

The natural frequency is the key performance parameters of a rubber materials damper, and it is determined by the static and dynamic shear properties of the rubber materials (rubber ring) and the moment of inertia of the inertia ring. The rubber ring is usually in compression state, and its static and dynamic shear properties are dependent on its sizes, compression ratio and chemical ingredients. A special fixture is designed and used for measuring static and dynamic shear performance of a rubber ring under different compression ratios in the study. To characterize the shear static and dynamic performances of rubbers, three constructive models (Kelvin-Voigt, the Maxwell and the fractional derivative constitutive model) are presented and the method for obtaining the model parameters in the fractional derivative constructive models are developed using the measured dynamic performance of a rubber shear specimen. The natural frequency of a rubber materials damper is calculated using the fractional derivative to characterize the rubber ring of the damper, and the calculated frequencies are compared with the measurements.Copyright

A universal approach to squeal analysis of the disc brakes involving various types of uncertainty

On the basis of fuzzy random variables, a universal approach to squeal analysis of the disc brakes involving various types of uncertainty is proposed in this paper. In the proposed approach, first, the brake stability analysis function related to reliability is constructed with fuzzy random variables. Next, the fuzziness represented by fuzzy random variables is decomposed into interval uncertainties by using a level-cut strategy. Then, the expectations and the variances of the brake stability analysis function are approximately solved by the random moment method at different cut levels, and the lower bounds and the upper bounds of the expectations and the variances are calculated by using a first-order Taylor expansion and a subinterval analysis. Finally, by combining the different interval solutions with the corresponding cut levels, the fuzzy solutions of the brake stability analysis function are obtained, which can be employed to evaluate the brake squeal instability. The proposed approach provides a universal framework for dealing with various types of uncertainty that may exist in automotive brakes. The universality, the accuracy and the efficiency of the proposed approach to the squeal instability analysis of the brakes involving various types of uncertainty are verified by the analysis results from nine different numerical examples.

Modeling and dynamic analysis of accessory drive systems with integrated starter generator for micro-hybrid vehicles

Belt-driven integrated starter generator system is a hybrid transmission that resembles the conventional serpentine belt-driven system. The system contains an integrated starter generator that performs a “start-stop” function on the engine. A two-pulley tensioner mechanism is attached to the integrated starter generator to maintain belt tension. The objectives of this paper are to develop modeling and calculation methods for estimating the performances of the belt-driven integrated starter generator system and to investigate the influence of damping of the two-pulley tensioner on vibration and shock. A systematic modeling and analysis method is proposed. The modeling method for the two-pulley tensioner is distinguished from any existing studies, which are generic for modeling the tensioner in belt-driven integrated starter generator systems with different layouts. A typical belt-driven integrated starter generator system is presented and a model is established to predict the dynamic response of rotational vibrations of pulleys, tensioner motions, and tension fluctuations. A parametric analysis is conducted to evaluate the two-pulley tensioner parameters with respect to their impact on the performances of the belt-driven integrated starter generator system.

Modelling of the rotational vibrations of the engine front-end accessory drive system: a generic method:

To investigate the rotation vibration dynamics of the pulleys and the tension arms, and to estimate the vibrations of the belts and the slip ratio between the belt and the pulleys in the engine front-end accessory drive systems, a systematic modelling and analytical method is proposed for engine front-end accessory drive systems; this can be used for modelling engine front-end accessory drive systems with different layouts and different numbers of tensioners, including automatic and fixed tensioners. In the modelling, the rotational pulleys are classified as fixed-axis pulleys and moveable-axis pulleys (such as the pulley in the tensioner). Moreover, the belt spans are classified as the belt spans between the two fixed pulleys, and the belt spans adjacent to the pulley of a tensioner. The equations of motion for each type of pulley and the tension calculation equations for each type of belt span are developed. In this way, the equations of motion for all the pulleys and the tensioner arms can be obtained easily, irrespective of the layout of the tensioners. To obtain the dynamic rotational vibration responses of an engine front-end accessory drive system by the conventional Runge–Kutta method, high-efficiency algorithms or methods are also proposed for calculating the tangent-point coordinates between a belt and the adjacent pulleys and the belt length of the contact arc on one pulley. The proposed modelling and analysis methods are validated by modelling different layouts of the engine front-end accessory drive systems with different types and numbers of tensioners, and also by comparisons between the calculated dynamic vibration responses of the pulleys and the belts and the real experimental data.