Feature

Artistic Dreams, Engineering Limitations

An engineering team is scaling up flexible kinetic sculptures and finding that the artist's dreams have engineering limitations.

J. K. Raine, S.D. Gooch, E.A.Webb

University of Canterbury engineers have been working on how to scale up the moving metal sculptures of one of New Zealand's most well-regarded artists, encountering some interesting design problems that challenge the material and the model involved.

The sculpture Blade is one of a number of very flexible kinetic sculptures designed by the New Zealand artist Len Lye (1901-1980). While they have been built at a model scale, Lye conceived these sculptures as much larger works that could be erected in open spaces and create effects on a monumental scale in public places.

In 1989 cooperative work began between the Len Lye Foundation and the Department of Mechanical Engineering at the University of Canterbury to develop an understanding of the engineering behaviour and limitations of the sculpture Flip and Two Twisters (also called Trilogy), and a later project explored the scaling up of Universe.

Len Lye's original Blade consisted of a "blade" of cold rolled strip steel measuring 1,630 mm high by 200 mm wide by 1.85 mm thick. The base of the blade is fixed in a rigid clamp which is oscillated on linear bearings by a geared electric drive and crank system. At certain frequencies of oscillation of the clamp, Blade responds by vibrating to form various wave forms or mode shapes. In front of the blade stands a 500 mm-tall stainless steel wand carrying a 75 mm-diameter cork ball. As the amplitude of vibration increases, the cork ball hits the blade, causing a loud acoustic ringing and chaotic motion of both Blade and the ball on its wand. The whole sculpture rotates slowly on the mounting plinth that conceals its drive mechanism, and executes its performance under microprocessor control.

To date Blade has been an indoor work, exhibited in local and overseas galleries over the past 20 years. Late in 1995 a project to design and build a double-size Blade was begun, funded by a joint grant to the University of Canterbury from Creative New Zealand and the Len Lye Foundation.

Design Rules

The "big" Blade is intended to be an outdoor sculpture -- Len Lye had hoped that it might be built at least 10 metres high, around six times the model height.

The overriding design criteria were that the visual and acoustic qualities of the sculpture had to be preserved when it was scaled up. The surface of the larger Blade also had to have a shiny metallic appearance, and its drive mechanism had to be hidden below the ground or in a mounting plinth.

Lye's method of establishing the height for the original model Blade was to extend the blade material vertically, supported only at the base, until it buckled under its own weight. He then reduced this length until the material would stand vertically. This determined the final height for the sculpture.

An application of engineering design scaling laws, determined from beam-bending theory, showed that for a taller Blade of the same material to achieve the same deflected shapes as the model Blade, the thickness is required to increase as (scale ratio)^3/2. Because of this increase in blade thickness, stresses in the material would increase as the square root of the scale ratio, and the frequencies of oscillation would fall as the reciprocal of the square root of the scale ratio. For example, if the size of Blade were increased by a factor of four, stresses would double and the number of vibrations per second at each resonant condition would halve.

It was immediately obvious that, while the slower oscillations were no problem and would appear natural in the larger sculpture, the higher stresses would limit the life of the sculpture before metal fatigue caused Blade to fail. Even the best engineering materials that could be manufactured in a size to suit the sculpture would not permit a scale ratio much above 2:1 without seriously reducing the life of the sculpture. A nominal scale of 2:1 was chosen for the present project.

Design laws were used to develop a material performance index that could be used for selection of the best possible metal alloy for Blade. A survey of candidate blade materials revealed a titanium alloy (6Al-4V) as the best available material that could be supplied in the size needed. Acoustic tests were carried out on a sample of the titanium at the model Blade size. These showed that despite having theoretically poorer reverberation properties than spring steel, it produced excellent ringing tones. The available thickness of the titanium alloy material determined the final height of the big Blade to be 3,400 mm, a scale ratio of approximately 2.1:1.

Concurrent with the mechanical and electrical design of the new drive system, extensive theoretical analysis was done using plate theory to explore the resonant frequencies of the model sculpture. These were compared with experimental measurements on the model Blade. Very good agreement was found between the theoretical and measured values, with 1st, 2nd and 3rd order frequencies around 0.32 Hz, 3.5 Hz and 10.3 Hz. Blade executes a twisting resonance at around 9.4 Hz. These are the oscillation frequencies of the clamp at which Blade develops large amplitude vibrations.

By theoretically modelling the vibration frequencies for the smaller work and comparing these with experimental results we were able to confidently predict the vibration frequencies for the larger work and therefore know how it would appear to spectators.

Building it Bigger

The design of this sculpture is unusual because Blade vibrates at resonant frequencies. This condition is almost always avoided in mechanical engineering design due to the high loads, large deflections, and loud noises which result, and becuase it may lead to premature failure. The consequence of resonant vibrations on Blade are high fatigue stresses and a finite working life.

Experimental observations of the original sculpture were instructive in defining the design requirements for the drive mechanism of the larger work. The detailed design of the drive mechanism aimed for a quiet, reliable, simple and cost-effective solution. Two geared induction motor drives of 3 and 0.12 kilowatts respectively are used to drive the oscillating clamp and the turntable for the double-size Blade. The supporting structure and the concrete base foundation to which it will be mounted must be rugged, as side-to-side forces of over 8,500 Newtons (about 0.85 tonnes force) could be generated by a replacement spring steel blade at resonance. Provision must also be made to protect Blade and its drive system from wind and rain by means of some sort of enclosure and tethering system for use in bad weather.

Technical staff at Canterbury University are now working hard to ready the double size blade for an outdoor public display of sculptures in Christchurch over the summer. For the university engineering team, Shayne Gooch and John Raine, the project continues to be an exciting departure from the usual run of design and research projects, and the chance to work on a project with a purely aesthetic aim offers unusual freedom. And Evan Webb, director of the Len Lye Foundation, has the reassurance that this scaled-up realisation of one of Lye's many extraordinary works, has been through a rigorous engineering analysis and design process.

Shayne Gooch is in the University of Canterbury's Mechanical Engineering Department
John Raine is in the University of Canterbury's Mechanical Engineering Department
Evan Webb is director of the Len Lye Foundation.