UWE Bristol Engineering showcase 2015

James Hook
MEng Mechanical Engineering
Project Supervisor
Dr Benjamin Drew
Designing non-circular gears for use in power transmission
Introduction
Discretisation
Figure 1: Steve Caplin, 2014
Project summary
Non-circular gears represent a potential point of improvement for any drive
train with a non-constant cycling torque profile. The gears can be used to
smooth the input torque profile to improve efficiency and reduce vibration.
However there is also design limitations involved in producing these gears.
Theory
When non-circular gears are applied to torque bearing applications they can
be used to change the shape of the output torque profile for a cycle-based
system, such as a 2-stroke engine. This is done through the varying gear ratio
across the course of the rotation of the gear. To do this a simple gear ratio
formula is used.
rr ii = TT ii
× rr
TT oo
oo
Where TT oo = torque output TT ii = torque input
rr oo = radius of output gear rr ii = radius of output gear
MATLAB model
MATLAB was used to apply the gear theory across a discretised model of the
gear. This allows complex gear shapes to be designed quickly. To apply the
above formula the following code was used. where a “for” loop has been
used to apply the formula at all the discretised node points of the gear
shape.
Where mp = matrix position irm = input radius matrix ogr = output gear ratio
Itm = input torque matrix dotm = desired output torque matrix
References
Steve Caplin, (2014). Nautilus gears [image]. Available at: http://www.3dgeni.us/nautilusgears/[Accessed
10 November 14].
The model uses a finite number of data points to represent the shapes of the
gears. At each data point there is a radius value so as to define the shape of
the gear at that point. So this can give an approximation to the shapes of the
gears. This has the disadvantage that in the space between the node points
is unknown so assumptions have to be made.
Example
Here is the gear shape for a system with a sinusoidal input torque profile.
Below shows the effect of the above gear profile on the output torque
profile.
This project involved producing a general MATLAB
model to design non-circular gear pairs. The model is
applicable to both chain/belt driven gear pairs and
directly meshing gear pairs. Additional factors
including applying limiters and determining the
chain/belt stretch where also considered.
Project Objectives
The aims of this project where to produce a MATLAB
model that could determine the extent of the benefit
of non-circular gear pairs, and determine the
potential applications.
Project Conclusion
Across the development of the MATLAB model the
effectiveness of the gears has been assessed to a
certain extent. It is also clear from the theory that
each gear type is applicable to different applications.
So to a certain extent some of the limitations have
been recognised. Without testing, the gains cannot
be easily quantified. So at this stage of the project the
aim has been met.