Research Papers: Elastohydrodynamic Lubrication

Fast Solution of Transient Elastohydrodynamic Line Contact Problems Using the Trajectory Piecewise Linear Approach

[+] Author and Article Information
Daniel Maier

Department of Future Mechanical
and Fluid Components,
Corporate Sector Research
and Advanced Engineering,
Robert Bosch GmbH,
Gerlingen-Schillerhöhe 70049, Germany
e-mail: daniel.maier6@de.bosch.com

Corinna Hager

Department of Future Mechanical
and Fluid Components,
Corporate Sector Research
and Advanced Engineering,
Robert Bosch GmbH,
Gerlingen-Schillerhöhe 70049, Germany

Hartmut Hetzler, Wolfgang Seemann

Institute of Engineering Mechanics (ITM),
Karlsruhe Institute of Technology (KIT),
Karlsruhe 76131, Germany

Nicolas Fillot, Philippe Vergne, David Dureisseix

Villeurbanne F-69621, France

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received November 8, 2014; final manuscript received June 30, 2015; published online August 14, 2015. Assoc. Editor: Dong Zhu.

J. Tribol 138(1), 011502 (Aug 14, 2015) (9 pages) Paper No: TRIB-14-1273; doi: 10.1115/1.4031064 History: Received November 08, 2014

In order to obtain a fast solution scheme, the trajectory piecewise linear (TPWL) method is applied to the transient elastohydrodynamic (EHD) line contact problem for the first time. TPWL approximates the nonlinearity of a dynamical system by a weighted superposition of reduced linearized systems along specified trajectories. The method is compared to another reduced order model (ROM), based on Galerkin projection, Newton–Raphson scheme and an approximation of the nonlinear reduced system functions. The TPWL model provides further speed-up compared to the Newton–Raphson based method at a high accuracy.

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Grahic Jump Location
Fig. 1

Training trajectories (1) and (2) with m = 11 selected operating points and test trajectories (3) and (4) within a two-dimensional state space

Grahic Jump Location
Fig. 2

Extract of dimensionless pressure and film thickness profile at time τ = 1 for case 1 (left) and case 2 (right)

Grahic Jump Location
Fig. 3

Influence of the number of operating points on the TPWL model in comparison to RNSA for a relative tolerance of ɛ=0.001

Grahic Jump Location
Fig. 4

Central pressure and central film thickness over time of full and reduced Newton–Raphson method and of the TPWL model for set 2 with excitations T = 1 (left) and T = 1/3 (right)

Grahic Jump Location
Fig. 5

Input signal of test trajectories

Grahic Jump Location
Fig. 6

Central pressure and central film thickness over time of full and reduced Newton–Raphson method and of the TPWL model



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