29-12-2012, 06:57 PM
Non-Linear Contact Analysis of Meshing Gears
Non-Linear Contact Analysis of Meshing Gears.pdf (Size: 1.64 MB / Downloads: 278)
Abstract
Non-Linear Contact Analysis of Meshing Gears
Chun Hung Lee
Gear transmission systems are considered one of the critical aspects of vibration
analysis, and it contains various potential faults such as misalignment, cracks, and
noise. Therefore, it requires vibration monitoring to ensure the system is operating
properly. Case mounted accelerometers are frequently used to monitor frequencies in
a system. However, it is not a simple task to identify and interpret the acceleration
data since there are many gear mesh frequencies present. One of the approaches
utilized by researchers to perform gear diagnostic is Finite Element Modeling. This
study focuses on stiffness cycle and meshing stiffness of non-linear quasi-static finite
element modeling. The comparisons of meshing stiffness will concentrate on the
type of elements, the integration methods, the meshing quality, plane stress and plane
strain analysis, sensitivity of model tolerance, and crack modeling. The results show
that the FEA approach is extremely sensitive to tolerance, mesh density, and element
choice. Also, the results indicate that a complete sensitivity and convergence studies
should be carried out for a satisfactory stiffness match.
Introduction
Gears are one of the oldest of humanity’s inventions. Nearly all the devices we think
of as a machines utilize gearing of one type or another. Gear technology has been
developed and expanded throughout the centuries. In many cases, gear design is
considered as a specialty. Nevertheless, the design or specification of a gear is only
part of the overall system design picture. From industry’s standpoint, gear
transmission systems are considered one of the critical aspects of vibration analysis.
The understanding of the behavior when gears are in mesh is extremely important if
one wants to perform system monitoring and control of the gear transmission system.
Although there are large amount of research studies about various topics of gear
transmission, the basic understanding of gears in mesh still needs to be confirmed.
When a pair of gears mesh, localized Hertzian contact stress are produced along with
tooth bending and shearing. This is a non-linear problem, and it can be solved by
applying different types of contact elements and algorithms in finite element codes.
However, due to the complicated contact conditions, acquiring results in the meshing
cycle can be challenging since some solutions may not converge. In any case, using
quadrilateral elements seem to be useful in solving gear contact problems with finite
element analysis. Furthermore, meshing stiffness is often being discussed when a
pair of gears are in mesh. Meshing stiffness can be separated into Torsional Mesh
Stiffness and Linear Tooth Mesh Stiffness.
The torsional mesh stiffness is defined as the ratio between the input torque load and
the angular displacement of the input gear. Once in mesh, the gears’ pitch circles roll
on each other without slipping. With a constant torque load, the torsional mesh
stiffness changes through the rotation of the gears. These changes are due to the
contact ratio between the pinion and gear. Depending on the contact ratio; the
contact region would change and alternate from single tooth contact to double tooth
contact or even a higher number of contacting pairs. This change of contact regions
is referred to as a mesh cycle. Through the mesh cycle, the torsional mesh stiffness
can be utilized as a tool to investigate gear transmission errors. Furthermore, the
torsional mesh stiffness is related to the linear tooth mesh stiffness by the normal
contact force that acts along the line of action. Basically, the linear tooth mesh
stiffness of the gears is an easy approach to understand the coupling between the
torsional and transverse motions of the system. The linear tooth mesh stiffness has
been chosen as the primary parameter to be studied in this work.
Literature Review
Gears are a critical component in the rotating machinery industry. Various research
methods, such as theoretical, numerical, and experimental, have been done
throughout the years regarding gears. One of the reasons why theoretical and
numerical methods are preferred is because experimental testing can be particularly
expensive. Thus, numerous mathematical models of gears have been developed for
different purposes. This chapter presents a brief review of papers recently published
in the areas of gear design, transmission errors, vibration analysis, etc., also
including brief information about the models, approximations, and assumptions
made.
Gear Design and Calculations
Overview
The main purpose of gearing is to transmit motion from one shaft to another. If there
is any mistake or error on the gears, motion will not be transmitted correctly. Also, if
the errors on the gears are crucial, it may destroy or heavily damage the components
in a gearbox. Therefore, it becomes important to understand the subject of gearing.
In order to gain better understanding of gearing, one should get some knowledge
about the design of gear and the theory of gear tooth action.