Gear System Speed/Torque Analysis

Leveraging the power of math models in driveline development requires a deeper appreciation for the multi-disciplinary and wide ranging physical system dynamic behaviors involved. The models have to handle operational demands of multi-configurable systems brought on by hybrid powertrains in general and automatic/manual transmissions, specifically. As a first requirement, system models have to be broken down into physically compatible subsystems, not as the hardware looks but, as the interface dynamics suggest. Transient dynamics, brought on by subsystem power flow disturbances and attendant noise generation and controls challenges must be addressed up front. This paper delves into the levels of detail automotive propulsion system models must possess not only to offer insight to the inner dynamics of a product but, also, make such formulation compatible with modern control system techniques.

The motivation for this effort is to enable driveline systems to be modeled, understood, tuned to specific criteria and assembled into larger integrated systems that solve specific problems. Additionally, because the system's dynamics itself could be an object of control, simple “Lever Diagram” method of system analysis may not be sufficient. Gears and gear clusters must be given independent degrees of freedom wherein interface dynamics are formulated to facilitate stable power flow path- switching, as well as, inclusion of dry and wet friction device behaviors through which gear shifts are executed under driver or automatic control. From this vantage point a structured interaction between a pair of gears is analyzed, propagated to cover planetary gears and, by extension, be made to cover more intricate gear clusters like the Ravigneaux gear system. Equally, modeling techniques to handle complex behaviors of friction devices and the control strategies needed to manage them are brought to the fore into the modeling space. Formulating the math model this way enables the analyst to create a wider range of functional problem expression for which potential remedies may be explored to fix an existing design or, hopefully, before a proposed design is committed to hardware. A limited math model of a popular truck is exercised to demonstrate ideas outlined above.