**Tom Shelley reports on a radicall approach to
computer-aided machine design and how it is expected to lead to
cheaper bearings
**

A new method of designing machines, based on Morphological Analysis, considers all possible configurations in 3D graphical form.

The software has been developed by Julian Allwood, a lecturer at the Institute for Manufacturing at Cambridge University. In an article published in Eureka in March 2005 about Dr Allwood's NC incremental sheet forming process, we mentioned that he was moving onto NC incremental ring rolling to improve the manufacture of rings used in bearings and automotive and aerospace components. He has since moved onto the problem of designing a ring rolling - or for that matter, any other machine - starting from first principles and using this new computer software.

When applied to rolling metal rings, the software generated a kind of 'periodic table' of all possible configurations. This has led to the development of a bench top experimental machine that can be reconfigured to try out the most promising forming processes - much faster than is possible using finite element modelling.

The basic configuration of present day ring rolling machines
is to use four rolls: one inside, one outside and two on the
front and rear surfaces. The process was invented in 1850 and the
first machine built in 1851. In order to be turned into products,
30 per cent of the rolled ring material must typically be
machined away to make a bearing ring. For many aerospace
components, this is closer to 90 per cent. However, there is no
fundamental reason why two pairs of orthogonal rollers should be
an ideal configuration. Why could the inner and outer rollers not
be conical, Dr Allwood asked himself, in order to produce angled
profiles? Need they be orthogonal to the ring axis? And why need
they be smaller than the ring? There is no reason why the ring
should not be formed inside a larger diameter circular die,
provided the bulk of the deformation is still made by a smaller
diameter roll on the inside.

Dr Allwood proposed starting from first principles by assuming
only that the ring remains circular throughout the process, is
initially of square cross section, and its axis does not move. It
is further assumed that the tools are solid rolls, each with a
point of no-slip with the ring, and may be located anywhere
around the ring - but in such a way as to maintain continuous
contact. Basic tools could be cylinders, narrow cones or wide
angled cones, and have profiles that are flat or profiled.

Applying only these constraints leads to a vast number or
options. However, many are impractical and the number can be cut
further by applying additional constraints. For example, the ring
must be kept circular. This effectively rules out configurations
where there might be two rolls on opposite sides on the inside,
with none on the outside. This would have the effect of making
the rings oval, bending them back and forth as they go round,
leading to cyclic fatigue failure. Another constraint, therefore,
must be a set of tools whose forces balance each other acting at
each single location.

There are five ways in which a tool may act: on a corner at a
shallow or steep angle; pressing in a profile; on an entire
surface; or with the surface of the ring engaging with a groove
in the roller. Each of these can also be applied where the ring
sits in or against a die with contact around the circumference.
There may be two, three or four tools around the cross section,
but candidate machines in which the tools may intersect must be
rejected. In addition, the forces applied to the ring by the
tools must lead to force and moment equilibrium for the ring.

The force applied to the ring by the tool must have a positive
normal component - adhesion is not possible, but the tangential
component of the force may or may not be limited by friction. The
selection process to find all possible machine combinations is
written in Matlab. This leads to a 'periodic table' of 102
machines in 12 groups, according to the number of flat faces and
corners of the ring that are deformed.

This has led to a practical project to find the best way of
manufacturing trapezoidal rings for tapered roller bearings -
generally regarded as a "hard" problem to solve. A
laboratory machine that makes rings made of 'Plasticine' has been
built using six stepper motors under open loop control that can
be configured in all the ways considered. A laser transducer
measures the position of the outside of the ring. The controller,
made by Trinamic Motion Control in Hamburg, is linked by RS232 to
Matlab and Simulink running on a PC. The machine can be
reconfigured to try different geometries several times during the
three-week period required for a single, full finite element
analysis. According to graduate student Alistair Willoughby, the
machine is being used to investigate what shapes can be made and
which methods are viable. In future, he said, the machine could
include feedback control and extra axes, while the energy
consumed could also be measured.

The new process design methodology is a step beyond
computer-based design aids such as TRIZ and Invention Machine,
which call up known solutions to problems that may be relevant to
solving a problem. Using the new methodology, it is possible to
consider all possible designs including those nobody has ever
tried before.

Following publication of the periodic table of ring rolling, Dr
Allwood received an award from the Royal Academy of Engineering
allowing him to take a one-year sabbatical. He will use the time
to apply the same approach to a much broader class of processes,
including extrusion, forging and sheet forming. The method could
potentially be applied to investigating all possible ways of
achieving any particular mechanical motion.

Julian
Allwood's web page

Trinamic Motion Control

mailto:jma42@cam.ac.uk Email
Dr Julian Allwood</a>

**History of Morphological Analysis**

Morphological Analysis is the invention of Swiss-American
Professor Fritz Zwicky at Caltech who developed his approach as a
method for structuring and investigating the total set of
relationships contained in multi-dimensional, usually
non-quantifiable, problem complexes. He applied this method to
the classification of astrophysical objects, the development of
jet and rocket propulsion systems, and the legal aspects of space
travel and colonization. He founded the Society for Morphological
Research in the 1930s and ran it until his death in 1974. More
information from the Swedish Morphological Society
www.swemorph.com .

**Pointers**

* Method allows the systematic examination of all possible ways
of building a machine

* Constraints reduce the number of possibilities

* Practical tests are then required to determine which of the
practicable possibilities works best

For more technical
developments see www.eurekamagazine.co.uk