EUREKA JULY 2006 COVER FEATURE STORY

Configuring to find the ultimate machine

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

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