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The advancement of Machine-learning (ML) methods enables data-driven creation of Reduced Order Models (ROMs) for automotive components and systems. For example, Gaussian Process Regression (GPR) has emerged as a powerful tool in recent years for building a static ROM as an alternative to a conventional parametric model or a multi-dimensional look-up table. GPR provides a mathematical framework for probabilistically representing complex non-linear behavior. Today, GPR is available in various programing tools and commercial CAE packages. However, the application of GPR is system dependent and often requires careful design considerations such as selection of input features and specification of kernel functions. Hence there is a need for GPR design optimization driven by application requirements. For example, a moving window size for training must be tuned to balance performance and computational efficiency for tracking changing system behavior.

Model-guided development of drivetrain control and calibration is a key enabler of robust and efficient vehicle design process. A number of CAE tools are available today for modeling hydro-mechanical systems. Automatic transmission behaviors are well understood to effectively tune the model parameters for targeted applications. Drivetrain models provide physical insight for understanding the effects of component interactions on system behaviors. They are also widely used in HIL/SIL environments to debug control strategies. Nonetheless, it is still a challenge to predict shift quality, especially during a sequence of multiple events, with enough accuracy to support model-guided control design and calibration. The inclusion of hydraulic circuits in simulation models often results in challenges for numerical simulation.

Automatic transmission (AT) upshift control performance in terms of shift duration and comfort can be improved during the inertia phase by coordinating the off-going clutch together with oncoming clutch and engine torque. The performance improvement is highest in low gear shifts (i.e., for high ratio steps), which are typically performed with open torque converter. In this paper, a discrete-time, linear quadratic regulation (LQR) is applied during the upshift inertia phase, as it provides an optimal multi-input/multi-output control action with respect to the prescribed cost function. The LQR law is based on a reduced-order drivetrain model, which is applicable to actual transmissions characterized by a limited number of available state measurements. The reduced-order model includes the linearized torque converter model. The shift duration is ensured by precise tracking of a linear-like oncoming clutch slip speed reference profile.

Innovations in mobility are built upon a management of complex interactions between sub-systems and components. A need for CAE tools that are capable of system simulations is well recognized, as evidenced by a growing number of commercial packages. However impressive they are, the predictability of such simulations still rests on the representation of the base components. Among them, a wet clutch actuator continues to play a critical role in the next generation propulsion systems. It converts hydraulic pressure to mechanical force to control torque transmitted through a clutch pack. The actuator is typically modeled as a hydraulic piston opposed by a mechanical spring. Because the piston slides over a seal, some models have a framework to account for seal friction. However, there are few contributions to the literature that describe the effects of seals on clutch actuator behaviors.

A wet clutch model is required in automotive propulsion system simulations for enabling robust design and control development. It commonly assumes Coulomb friction for simplicity, even though it does not represent the physics of hydrodynamic torque transfer. In practice, the Coulomb friction coefficient is treated as a tuning parameter in simulations to match vehicle data for targeted conditions. The simulations tend to deviate from actual behaviors for different drive conditions unless the friction coefficient is adjusted repeatedly. Alternatively, a complex hydrodynamic model, coupled with a surface contact model, is utilized to enhance the fidelity of system simulations for broader conditions. The theory of elastic asperity deformation is conventionally employed to model clutch surface contact. However, recent examination of friction material shows that the elastic modulus of surface fibers significantly exceeds the contact load, implying no deformation of fibers.

A step-ratio automatic transmission alters torque paths for gearshifting through engagement and disengagement of clutches. It enables torque sources to run efficiently while meeting driver demand. Yet, clutch thermal energy during gearshifting is one of the contributors to the overall fuel loss. In order to optimize drivetrain control strategy, including the frequency of shifts, it is important to understand the cost of shift itself. In a power-on upshift, clutch thermal energy is primarily dissipated during inertia phase. The interaction between multiple clutches, coupled with input torque truncation, makes the decomposition of overall energy loss less obvious. This paper systematically presents the mathematical analysis of clutch thermal energy during the inertia phase of a typical single-transition gearshift. In practice, a quicker shift is generally favored, partly because the amount of energy loss is considered smaller.

This paper considers using linear quadratic regulation (LQR) for multi-input control of the Automatic Transmission (AT) upshift inertia phase. The considered control inputs include the transmission input/engine torque, oncoming clutch torque, and traditionally not used off-going clutch torque. Use of the off-going clutch has been motivated by discussed Control Trajectory Optimization (CTO) results demonstrating that employing the off-going clutch during the inertia phase along with the main, oncoming clutch can improve the upshift control performance in terms of the shift duration and/or comfort by trading off the transmission efficiency and control simplicity to some extent. The proposed LQR approach provides setting an optimal trade-off between the conflicting criteria related to driving comfort and clutches thermal energy loss.

A wet clutch continues to play a critical role for step-ratio automatic transmissions and finds new utilities in hybrid and electrified propulsion systems. A torque transfer function is often employed in practice for sophisticated clutch slip controls. It provides a simple, yet practical framework to represent clutch torque as a function of actuator force. An accurate transfer function is also increasingly desired in today's vehicle design process to enable upfront assessment of clutch controls through simulations. The most common approach is based on Coulomb's linear friction model, where the coefficients are adaptively identified based on vehicle data. However, it is generally difficult to tune Coulomb's model for hydrodynamic behaviors even if the reference vehicle data are available. It also remains a challenge to produce in-vehicle clutch behaviors on a component test bench to determine realistic transfer function before prototype vehicles are built.

Wet clutches are complex hydrodynamic devices used in both conventional and electrified drivetrain systems. They couple or de-couple powertrain components for applications such as automatic shifting, engine disconnect and torque vectoring. Clutch engagement behaviors vary greatly, depending on design parameters and operating conditions. Because of their direct impact on vehicle drivability and fuel economy, a predictive CAE model is desired for enabling analytical design verification processes. During engagement, a wet clutch transmits torque through viscous shear and asperity contact. A conventional Coulomb’s model, which is routinely utilized in shift simulations, is inadequate to capture non-linear hydrodynamic effects for higher fidelity analysis. Extensive research has been conducted over the years to derive hydrodynamic torque transfer models based on 1D squeeze film or 3D CFD. They are typically coupled with an elastic asperity contact model for mechanical torque transfer.

Simulations conducted on-board in a vehicle control module can offer valuable information to control strategies. Continued improvements to on-board computing hardware make online simulations of complex dynamic systems such as drivetrains within reach. This capability enables predictions of the system response to various control actions and disturbances. Implementation of online simulations requires model initialization that is consistent with the physical drivetrain state. However, sensor signals and estimated variables are susceptible to errors, compromising the accuracy of the initialization and any future state predictions as the simulation proceeds through the numerical integration process. This paper describes a drivetrain modeling and analysis method that accounts for initialization errors, thereby enabling accurate simulations of system behaviors.

A wet clutch couples or decouples gear elements to alter torque paths in an automatic transmission system. During the gear shifting event, the clutch torque is directly transmitted to the output shaft. Hence, clutch torque heavily influences the dynamics of the transmission. In order to evaluate the behavior of the transmission early and efficiently, the development process increasingly relies on high-fidelity transmission system simulations with added complexity. However, a wet clutch continues to be modeled using Coulomb’s friction in a typical shift simulation. Its linear framework does not physically represent non-linear hydrodynamic effects due to the presence of oil layer during clutch engagement. To make up the lack of physics, Coulomb’s clutch model often requires extensive tuning to match actual shift behaviors.

A new generation of a planetary-gear-based automatic transmission system is designed with an increasing number of ratio steps. It requires synchronous operation of one or more wet clutches, to achieve a complex shift event. A missed synchronization results in drive torque disturbance which may be perceived by vehicle occupants as an undesirable shift shock. Accurate knowledge of clutch behaviors in an actual vehicle environment is indispensable for achieving precise clutch controls and reducing shift calibration effort. Wet clutches are routinely evaluated on an industry-standard SAE#2 tester during the clutch design process. While it is a valuable tool for screening relative frictional behaviors, clutch engagement data from a SAE#2 tester do not correlate well with vehicle shift behaviors due to the limited reproducibility of realistic slip, actuator force profiles, and lubrication conditions.

Wet clutch packs are widely used in today’s automatic transmission systems for gear-ratio shifting. The frictional interfaces between the clutch plates are continuously lubricated with transmission fluid for both thermal and friction management. The open clutch packs shear transmission fluid across the rotating plates, contributing to measurable energy losses. A typical multi-speed transmission includes as many as 5 clutch packs. Of those, two to three clutches are open at any time during a typical drive cycle, presenting an opportunity for fuel economy gain. However, reducing open clutch drag is very challenging, while meeting cooling requirements and shift quality targets. In practice, clutch design adjustment is performed through trial-and-error evaluation of hardware on a test bench. The use of analytical methodologies is limited for optimizing clutch design features due to the complexity of fluid-structure interactions under rotating conditions.

A transmission system model is developed at various complexities in order to capture the transient behaviors in drivability and fuel economy simulations. A large number of model parameters bring more degree of freedom to correlate with vehicular test data. However, in practice, it requires extensive time and effort to tune the parameters to satisfy the model performance requirements. Among the transmission model, a hydraulic clutch actuator plays a critical role in transient shift simulations. It is particularly difficult to tune the actuator model when it is over-parameterized. Therefore, it is of great importance to develop a hydraulic actuator model that is easy to adjust while retaining sufficient complexity for replicating realistic transient behaviors. This paper describes a systematic approach for reducing the hydraulic actuator model into a piecewise 1st order representation based on piston movement.

This paper presents the characterization of the random noise in driveline output shaft torque measurements that is commonly induced by road disturbances. To investigate the interaction between the shaft torque and road side excitation, torque signals are measured using a magnetoelastic torque sensor, as well as a conventional strain gauge sensor, under various types of road surfaces and conditions such as unevenness. A generalized de-trending method for producing a stationary random signal is first conducted. Statistical methods, in particular the probability density function and transform technique, are utilized to provide an evident signature for identifying the road excitation effect on the vehicle output shaft torque. Analysis results show how the road surface can act as a disturbance input to the vehicle shaft torque.

An oil-lubricated wet clutch has a direct impact on the drivability and fuel economy of a vehicle equipped with an automatic transmission system. However, a reliable analysis of clutch behavior still remains a challenge. The purpose of this study is to advance the state-of the-art in CFD methodology for modeling transient clutch behavior. First, a new iterative scheme is developed, in combination with commercial CFD software, which is capable of simulating the squeeze film process in a wet clutch. The numerical results are then validated using analytical solutions of the Reynolds equation for simplified clutch geometry and various boundary conditions. It is found that the choice of boundary conditions has a strong influence on squeeze film simulation. The iterative scheme is further validated by comparison to clutch engagement experiments.

In a step-ratio automatic transmission system, wet friction components are widely utilized to alter planetary gear configurations for automatic shifting. Thus, their engagement characteristics have a direct impact on shift quality or drivetrain NVH. A vehicle design process can benefit from predictive friction component models that allow analytical shift quality evaluation, leading to reduced development time. However, their practical application to shift analysis is seldom discussed in the literature although there are many references available for friction component modeling itself. A successful shift analysis requires a balance of model complexity, predictability and computational efficiency for a given objective. This paper reviews three types of friction component models found in today's open literature, namely, first principle based, algebraic, and empirical models. Model structure, assumptions, computational efficiency, and utilities are discussed.