Chinar R. Aphale Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48105 e-mail: caphale@umich.edu Jinhyun Cho Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48105 e-mail: jinhyunc@umich.edu William W. Schultz Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48105 e-mail: schultz@umich.edu Steven L. Ceccio Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48105 e-mail: ceccio@umich.edu Takao Yoshioka Dynax Corporation, Hokkaido, Japan e-mail: yoshioka-t@mail.dxj.co.jp Henry Hiraki Dynax Corporation, Hokkaido, Japan e-mail: hiraki-h@mail.dxj.co.jp Modeling and Parametric Study of Torque in Open Clutch Plates The relative motion of the friction and separator plates in wet clutches during the disen- gaged mode causes viscous shear stresses in the fluid passing through the 100 microns gap. This results in a drag torque on both the disks that wastes energy and decreases fuel economy. The objective of the study is to develop an accurate mathematical model for the above problem with verification using FLUENT and experiments. Initially we two consider flat disks. The mathematical model calculates the drag torque on the disks and the 2D axisymmetric solver verifies the solution. The surface pressure distribution on the plates is also verified. Then, 3D models of one grooved and one flat disk are tested using CFD, experiments and an approximate 3D mathematical model. The number of grooves, depth of groove and clearance between the disks are studied to understand their effect on the torque. The study determines the pressure field that eventually affects aeration incipience (not studied here). The results of the model, computations and experiments corroborate well in the single-phase regime. DOI: 10.1115/1.2162553 1 Introduction The fluid motion over a single rotating plate has been studied extensively. Von Karman 1 studied the problem of an infinite disk rotating in quiescent fluid revealing the swirling flow patterns over the disk. He reduced the equations of motion to a nonlinear differential equation using the assumption of axisymmetry and similarity. His work and the subsequent solution to those equa- tions by Cochran 2 determined the nature of flow field over the rotating disk. Fluid entrains axially and exits the disk surface ra- dially. This problem has many similarities to rotating turbo ma- chinery such as compressors and centrifugal pumps. Here, our primary interest is in the open clutch system where two disks rotate at different speeds. Some early work with two co-rotating disks is attributed to Batchelor 3 and Stewartson 4. Batchelor proposed that the core of fluid between the two plates away from the boundary layer on the disks rotates with constant angular ve- locity while Stewartson suggested that boundary layer forms only on the rotating disk and that the remaining fluid will not rotate if one disk is stationary or counter-rotating. Further, we study the case where the plate separation is small and lubrication scaling is appropriate. Recent work by Kitamura 5 highlights this asymptotic treatment of the Navier-Stokes equations. Since the gap between the two disks is very small compared to their radii, the equations can be scaled accordingly. The relative effects of inertial, gravitational and surface tension forces were assessed. These simplified equations are the basis of the mathematical model for the problem in this paper. The ease of pressure and shear stress distribution calculations using the model makes this tool very useful. This study focuses on reducing shear stress and hence conse- quently the drag on the disks. In an open clutch system, a rotating friction plate FP and a stationary separator plate SP are 100 microns apart. An oil film is maintained between the disks for lubrication when the clutch disks are brought together for engage- ment. However in the disengaged mode, the viscous shearing of this oil film causes unnecessary torque on both disks. This wastes energy that decreases fuel economy. Schade 6, Fish 7, and Lloyd 8 empirically determine trends regarding geometric parameters such as groove patterns, depths as well as clearance and flow rate. They also indicate the importance of disk waviness in reducing drag torque. This study is restricted to flat not wavy plates, with the exception of possible grooves 9–11. The most important aspect that reduces the torque is aeration. Air infiltration between the two disks reduces torque substantially since air has low viscosity. The analysis here will show where aeration is likely to occur. The flow rate is very important in determining the pressure distribution along the disks however its direct effect on drag torque for nonaerated lubrication is minimal. As a result, varying flow rates are not considered in these single- phase simulations. We leave aeration study to subsequent publica- tion. Yuan 12 also compares computations of grooved plates with experiments. Their results suggest that surface tension has an im- Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 25, 2004; final manuscript received September 19, 2005. Review conducted by Lyndon S. Stephens . 422 / Vol. 128, APRIL 2006 Copyright © 2006 by ASME Transactions of the ASME