Affiliations: Wolfson School of Mechanical and Manufacturing
Engineering, Loughborough University, Leicestershire LE11 3TU, UK | Acoustics and Dynamics Laboratory, Mechanical
Engineering Department, The Ohio State University, Columbus, OH, USA
Abstract: Nonlinear torsional models are used to analyze automotive
transmission rattle problems and find solutions to reduce noise, vibration and
dynamic loads. The torsional stiffness and inertial distribution of such
systems show that the underlying mathematical problem is numerically stiff. In
addition, the clearance nonlinearities in the gear meshes introduce
discontinuous functions. Both factors affect the efficacy of time domain
integration and smoothening functions are widely used to overcome computational
difficulties and improve the simulation. In this paper, alternate smoothening
functions are studied for their influence on the numerical solutions and their
impact on global convergence and computation times. In particular, four
smoothening functions (arctan, hyperbolic-cosine, hyperbolic-tan and
quintic-spline) are applied to a five-degree-of-freedom generic torsional
system with two backlash (clearance) elements. Each function is assessed via a
global convergence metric across an excitation map (a design of experiment).
Regions of the excitation map, along with multiple solutions, are studied and
the implications to assessing convergence are critically examined.~ It is
observed that smoothening functions do not lead to better convergence in many
cases. The smoothening parameter needs to be carefully selected, or
over-smoothened solutions may be found. The system studied is representative of
a typical automotive rattle problem and it was found that benefits were limited
from applying such smoothening functions.
