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Research Papers

# Modeling, Analysis, and Optimal Design of the Automotive Transmission Ball Capsule System

[+] Author and Article Information
Xingyong Song, Mohd Azrin Mohd Zulkefli, Zongxuan Sun

Department of Mechanical Engineering, University of Minnesota, Twin Cities Campus, Minneapolis, MN 55455

Hsu-Chiang Miao

Research and Development Center, General Motors Corporation, Warren, MI 48090

J. Dyn. Sys., Meas., Control 132(2), 021003 (Feb 02, 2010) (12 pages) doi:10.1115/1.4000662 History: Received December 21, 2008; Revised October 12, 2009; Published February 02, 2010; Online February 02, 2010

## Abstract

Clutch shift control is critical for the performance and fuel economy of automotive transmissions, including both automatic and hybrid transmissions. Among all the factors that influence clutch shift control, clutch fill and clutch engagement are crucial to realize a fast and smooth clutch shift. When the clutch is not engaged, the fluid held by the centrifugal force inside of the clutch chamber, which introduces additional pressure that will affect the subsequent clutch fill and engagement processes, should be released. To realize this function, a ball capsule system is introduced and mounted on the clutch chamber. When the clutch chamber is ready to be filled for engagement, the ball capsule needs to close quickly and remain closed until the clutch is disengaged. It is also desirable to have an appropriate closing velocity for the ball capsule to minimize noise and wear. In this paper, the ball capsule dynamics is modeled, in which the derivation of the ball capsule throttling area is considered novel and critical because of its asymmetrical nature. Through this, the ball capsule’s intrinsic positive feedback structure is also revealed, which is considered to be the key to realize a fast response. Moreover, through the system dynamics analysis, the slope angle of the capsule is found to be an effective control parameter for system performance and robustness. To this end, the optimal shape of the capsule is designed using dynamic programming to achieve the desired performance.

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## Figures

Figure 1

Automotive transmission clutch control and ball capsule system

Figure 2

Schematic diagram of the ball capsule system

Figure 3

Schematic diagram of the ball capsule system

Figure 4

Fluid centrifugal pressure

Figure 5

Geometric representation of the ball capsule system. (a) Capsule and ball geometries. (b) Integration of the minimum distance. (c) β and φ relationship.

Figure 6

Theoretical and PROE Ath values’ comparisons

Figure 7

Simulation result comparison between the second and fourth order models

Figure 8

System dynamics of the ball capsule system

Figure 9

Region for U

Figure 10

Ball capsule system with multiple slope angles. (a) A capsule system with two different slope angles. (b) Coordinates of the state space and the state transit portrait.

Figure 11

Geometry of the discrete capsule system

Figure 12

State space quantization for dynamic programming

Figure 13

Ball capsule design

Figure 14

Angular velocity of the ball

Figure 15

The trajectory of the ball center rc

Figure 16

Actuation torque on the ball

Figure 17

The throttling area Ath

Figure 18

The closing and holding input pressures

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