Charles M. Krousgrill

Finite element modeling of engagement of rough and grooved wet clutches

A finite element model has been developed to investigate the engagement of rough, grooved, paper-based permeable wet clutches. The finite element (Galerkin) approach was used to discretize the modified Reynolds and force balance equations, and the solution domain geometry was described using an isoparametric formulation. Surface roughness effects were modeled via the Patir and Cheng (1978) average flow model, while asperity load sharing was calculated using the Greenwood and Williamson (1966) approach. The finite element model developed was used to investigate the effects of applied load, friction material permeability, and groove size on the engagement characteristics of wet clutches (i.e., torque, pressure, engagement time, and film thickness). The results indicate that the applied load, friction material permeability, and groove width significantly influence the engagement characteristics. Higher facing pressures increase peak torque and decrease engagement time. Higher permeability of the friction material significantly decreases engagement time but dramatically increases peak torque. Wider grooves decrease the peak torque and increase the engagement time. Groove depth does not significantly affect engagement characteristics for this model.

Analytical and Numerical Modeling of Engagement of Rough, Permeable, Grooved Wet Clutches

A simple mathematical model for the engagement of rough, permeable, grooved wet clutches has been developed and used to determine the effect of various input parameters (applied load, grooved area, and friction material permeability) on engagement. The model includes the effects of surface roughness according to Patir and Cheng (1978), friction material permeability according to Natsumeda and Miyoshi (1994) and Beavars and Joseph (1967), and grooving in the friction material according to a new approximation. The approach reduces the system ofReynolds and force balance equations to a single, first-order differential equation in film thickness and time. A line searching algorithm, exploiting the low computational cost of function evaluations for the new model, is used to find the set of input parameter combinations yielding the same engagement characteristics. This set of design points is presented as an engagement isosurface in the parameter space (F app , Φ, A red ). The isosurface implicitly gives information about engagement time, and it shows regions in which the desired engagement characteristics cannot be achieved. The input parameters are classified as those affecting the transient portion of engagement and those affecting the steady-state portion.

Stability of Sliding in a System Excited by a Rough Moving Surface

A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.

Distance Education: New Technologies and New Directions

Distance education has been undergoing incremental change over the past decade or so since the advent of the commercial Internet and the World Wide Web. However, we are currently on the cusp of advances that will facilitate experiential learning at a distance, reduce the cost of distance education production, expand access to education, and closely integrate formal education into the fabric of everyday life. Following a review of distance education technology past and present, this paper presents the evolving technologies that will facilitate the most important advances in the field and reviews their early applications.

Torque transmission characteristics of automatic transmission wet clutches : Experimental results and numerical comparison

A test rig has been designed to quantify the torque transmission characteristics of wet clutches. This apparatus is presented and its features discussed. A comparison is made between the torque measurements from the test rig and simulations using a previously developed mathematical model. Results are given for a variety of operating conditions. The data presented here validate the computational model as an accurate tool for wet clutch design and analysis. Important results include accurate torque transfer prediction capabilities, with the limiting factor being precise knowledge of the sliding friction coefficient μc. Another important conclusion of the work is that torque transfer during a single engagement event can be adequately predicted using the isothermal model presented here. The simplicity of the isothermal model, along with its computational efficiency, makes it attractive for wet clutch torque transfer prediction and wet clutch design. Presented at the 52nd Annual Meeting in Kansas City, Missour...

A simplified approach to modeling thermal effects in wet clutch engagement : Analytical and experimental comparison

The simplified isothermal model for wet clutch engagement previously developed by Berger, Sadeghi, and Krousgrill (1997a) was extended to include fluid thermal effects. The modified Reynolds and thermal diffusion equations were simultaneously solved to obtain torque and temperature characteristics during wet clutch engagement. The modified Reynolds equation was integrated using the Adams-Gear scheme and the alternating direction implicit method (ADI) finite difference technique was used to solve the thermal diffusion equation. The model was used to study the effects of speed, temperature, and load on the torque transfer and lubricant temperature variation during wet clutch engagement. A comparison of thermal and isothermal results indicates that the thermal model generally predicts a longer engagement time and smaller peak torque than the isothermal model. Comparison of analytical and experimental results indicates that including fluid thermal effects in the model is critical for achieving good correlation between analytical and experimental results.

An Efficient Approach to Estimate Critical Value of Friction Coefficient in Brake Squeal Analysis

Automotive brake squeal generated during brake applications has become a major concern in automotive industry. Warranty costs for brake noise related complaints have been greatly increasing in recent years. Brake noise and vibration control are also important for the improvement of vehicle quietness and passenger comfort. In this work, the mode coupling instability mechanism is discussed and a method to estimate the critical value of friction coefficient identifying the onset of brake squeal is presented. This is achieved through a sequence of steps. In the first step, a modal expansion method is developed to calculate eigenvalue and eigenvector sensitivities. Different types of mode couplings and their relationships with possible onset of squeal are discussed. Then, a reduced-order characteristic equation method based on the elastically coupled system eigenvalues and their derivatives is presented to estimate the critical value of friction coefficient. The significance of this method is that the critical value of friction coefficient can be predicted accurately without the need for a full complex eigenvalue analysis, making it possible to determine the sensitivity of system stability with respect to design parameters directly.

Effect of Temperature on Thermoelastic Instability in Thin Disks

A model of a thin annular plate sliding against an elastic foundation was developed and used to study thermoelastic instability (TEI) in clutches. The analysis examines the stability of the quasi-steady state solution of the governing equations by considering non-axisymmetric perturbations. The results indicate that above critical values of temperature and sliding speed the response of the plate becomes unstable and exhibits large deformations. Two mechanisms account for this behavior: thermal buckling and bending. It is shown that a conservative approximation of the stability boundaries can be constructed by computing only two points on the stability curve. The boundary between stable and unstable behavior depends on the material properties, geometry, and boundary conditions. The model was used to conduct a parametric study which indicates that stability of the sliding system can be improved by reducing the sliding speed, decreasing the modulus of elasticity of the plate, increasing the thermal conductivity, or increasing the thickness. In addition, for a range of sliding speeds, increasing the stiffness of the friction material improves the stability of the system. For speeds outside this range, increasing the stiffness makes the system less stable.

Nonlinear dynamics in Tomlinson’s model for atomic-scale friction and friction force microscopy

Tomlinson’s model is often used to describe the friction of a single asperity or of a scanning force probe sliding over an atomic lattice. We present results on the complex dynamic behavior found in this model using a combination of continuation methods, perturbation techniques, and numerical simulations. Specifically, periodic stick-slip motions and their bifurcations and stability are investigated in the slow-sliding speed range and in higher speed ranges at which fundamental and parametric resonances set in. The results predict a complex range of bifurcations, superharmonic and subharmonic motions, and possibly chaotic dynamics which bear significant implications for understanding single-asperity friction or the dynamic response in friction force microscopy.

Combination parametric resonance leading to periodic and chaotic response in two-degree-of-freedom systems with quadratic non-linearities

The dynamic response of a parametrically excited non-linear system with two degrees of freedom is studied. The system of equations, which describes the compliant motion of a robotic manipulator, exhibits internal resonance and is excited at a frequency near a primary resonance. The effect of coupling is studied in detail. Non-zero periodic motions are observed to co-exist with a stable equilibrium state over a range of detuning near the resonant frequency. Loss of stability of the periodic response is observed at points of vertical tangency (corresponding to a jump in the response), while for some of the cases, Hopf bifurcation in the response corresponding to amplitude-modulated motions is observed. In the latter case, period-doubling of the amplitude of response is observed with a monotonic change in detuning, eventually leading to chaotic motion in the system. Near exact tuning to the parametric resonance, a quenching of the chaotic motion is found, leaving only the stable zero equilibrium state for the system over some detuning interval.