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This paper represents a mathematically rigorous and technically realistic effort of describing the idle rattle phenomenon. The two-degree-of-freedom model constitutes a relatively simple, analytical tool suitable for design and application purposes. It also introduces a new and more practical formulation of the rattle threshold. The model describes elastic-plastic collisions of meshing gears and splines, and allows for multi-harmonic excitation. The mathematical model not only consists of differential equations of gear and spline oscillations, but also equations of collisions and separations of meshing elements. When the impacts occur, a special algorithm is used for determining energy of collisions. The model is based on the fact that impact energy levels directly correspond to idle rattle noise levels. The computer simulation presented in this paper is to meet the pressing need for an analytical and computer design methodology for drivelines and their components.

During the starting of the vehicle, the friction clutch engagement sometimes generates judder. Judder prevents vehicles from starting smoothly, harms the ride comfort, and may produce damage to the drivetrain components. This unpleasant phenomenon, which often manifests in the form of noisy torsional vibrations of the drivetrain or a violent surging of starting vehicles, is an example of the many annoying problems that automotive engineers have been experiencing since the car was invented. Engineers and scientists have identified some causes of transient torsional oscillations connected to judder. Vibrations generated by the clutch facings when a special type of relationship between the friction coefficient and sliding speed occurs account for the most important source of judder.

With synchronized transmissions, the problem of shift effort and corresponding shift time are complex ones. They deal with the proper function of both the clutch and transmission within the total drivetrain system, cnd relate to the dynamic behavior of this system. The present paper represents an engineering effort of rigorously defining clutch and transmission compatibility with respect to shift quality. A technically realistic, analytical description of shiftability for synchronized transmissions and corresponding design limitations for the clutch-transmission system are the specijic objectives of this paper. Design recommendations based on the modeling introduced in this paper point out a significant clutch contribution to shifting problems and the importance of the system approach itself. The mathematical model describing shift and synchronizing processes is analyzed to determine shift quality, clutch quality and transmission quality with respect to shifting.

The present research constitutes an engineering approach to the performance level prediction of starting a vehicle without use of a throttle. The study is based on a dynamic clutch engagement model. A computer simulation of engagement dynamics is used in order to study the lock-up mechanism and to develop proper prediction procedures. In addition, the engagement model is used to develop guidelines and recommendations in order to optimize the engagement system including clutch components, clutch controls, and engine controls. The mathematical model presented in this paper incorporates important, new features in comparison to similar models from previous publications. Consisting of two inertias, it includes not only elastic properties of the clutch damper but also varying engine torque and clamping (pressure) force. Functions of engine torque and plate load simulate the actual control process, including human factors.

The present paper is a continuation of engineering efforts devoted mathematical modeling and computer simulation presented in [1]. The modeling and study is extended on starting a vehicle with use of a throttle. The basic mathematical model utilized in [1] has had to be modified because clutch engagement with throttle make investigators consider new human factors contributing strongly to starting conditions. In particular, not only the clutch release but also the accelerator pedal are controlled by a vehicle operator. This has made the authors modify the definition of an ideal engagement and incorporate both the throttle level and the throttle lead time to the mathematical model. Moreover, the model has been adjusted to consolidate dissimilar low range characteristics for diesel and gas engines.

It is common for difficult shifting to occur in synchronized transmissions. High shift effort is recognized as a basic performance malfunction that takes place during synchronization. This paper examines shift quality in vehicles with synchronized transmissions. The present study is working on three categories: a mathematical model and computer simulation of transmission shifts, an experimental verification of the model and program, and an engineering method for rating shift quality. The mathematical model in this study is a refinement of a model from an earlier paper [1]. With experience, this model has seen revisions that allow the results to be more accurate than the previous ones. The model takes into considerations many elements that affect the synchronizing process such as: synchronizing torque, inertia of both clutch disc(s) and transmission components, clutch drag, viscous drag in the transmission, shifting RPM's, etc.

A detailed methodology is presented in this paper for a complete assessment of various forces, torques, and kinematic effects due to universal joint angularities and shaft yoke phasing. A modular approach has been adopted wherein constitutive equations represent each of the key elements of a driveline namely the driveshaft, coupling shaft, universal joint, and the transmission/axle shafts. Concentrated loads are used wherever loads are being transferred between the elements of a driveline. Local matrices are developed for the equilibrium of the respective driveline members. The local matrices are then assembled into a global matrix and solved for the kinematic state of the complete driveline. A 6x15 matrix has been developed to represent a general shaft in the system and a 6x10 matrix has been developed for a universal joint cross. This gives us a complete picture of all the loads on all driveline members.

A novel computer simulation program entitled TORAN™ has been developed by the Spicer Clutch Division of Dana Corporation. TORAN™ has been developed for use as an engineering tool for quick and interactive, yet a complete torsional analysis of heavy duty truck drivetrains. This will allow the design and application engineers to examine and predict the behavior of these drivetrains throughout practical ranges of frequencies and torques. TORAN™ is more than just another modification of similar existing programs. The Program, which includes a database of confidential data furnished by drivetrain component and OEM manufacturers and algorithms proprietary to the Spicer Clutch Division. The algorithm accommodates some substantial nonlinearities, such as clutch damper hysteresis and universal joint disturbances. Also included are several new modeling features describing geometrical configuration of axles, torsional properties of tires, etc.

A major challenge in predicting driveline torsionals is the modeling of major energy dissipation mechanisms in the driveline. Primary candidates for such mechanisms are viscous dampers and dry friction (hysteresis) dampers which are specifically included by the designers to disperse the energy of torsional vibrations. The inherent structural and other internal damping in the components of the driveline is small as compared to those of viscous and dry friction dampers. Past attempts to model clutch hysteresis have repeatedly resorted to the classical approach of modeling that has been reported many years ago. However, such an approach is oversimplified and assumes, for instance, that the hysteretic effects are independent of the frequency. In addition, the motion of the damper is assumed to be purely harmonic. Also, such studies rely solely upon the static hysteresis characterization of the elements, particularly within the clutch.