Leonardo da Vinci and the Force of Friction

Prof Rob Dwyer-Joyce, Head of Department  and Director of the Leonardo Centre for Tribology, Department of Mechanical Engineering, University of Sheffield

Leonardo da Vinci is well known for he paintings, sketches of the human form, anatomy, detailed designs for machines and weapons of war, and his beautifully illustrated notebooks - the Codices.

But perhaps it is less well known that Leonardo was the first to establish the laws that govern one of the most important and wide-ranging physical phenomenon. A phenomenon that is so central to our daily lives that it normally goes unnoticed, and that is the force of friction.

Friction is the force that resists motion.  When we try to pick up a pencil it is the friction force that allows us to hold on to it.  When we walk, it is the force of friction that allows us to propel ourselves along; and when we try to walk on ice, it is lack of friction that makes us to slip over.

Friction is a fundamental part of all moving machines, and engineers take great efforts in making sure friction is high enough when it is needed; for example, in brakes, tyres, clutches and shoes, but low enough when it needs to be overcome; in for example, bearings, gears, and engines.

So where does the mysterious force of friction come from?  Friction originates, for the most part, from adhesion. Molecules attract or adhere like tiny magnets.  The molecules on the surface of a book are attracted to the molecules in the surface of a table and, if you want to slide the book across the table, you have to break those attraction bonds. The force required to do this is the friction force.

Friction has a curious property that Leonardo studied and wrote about in his notebooks. It turns out that that friction is independent of the area between the two bodies in contact.  So, if the book is turned onto its edge, it takes the same force to push it across the table. In other words, if you are pushing something along the road, it does not help if you tip it on its side. This seems counter-intuitive.  If there is a bigger area to contact, then there should be more molecules attracting each other, and so more little magnets that have to be separated. It is this property of friction that has baffled engineers and scientists for centuries.

Leonardo was certainly interested in friction.  The sketches from the Codex Atlanticus, from the turn of the 15^th century, clearly show the experiments he performed pulling blocks along a surface in different orientations.  He wrote in the Codex Forster:

"The friction made by the same weight will be of equal resistance at the beginning of its movement, although the contact may be of different breadths and heights".

From these simple experiments, he deduced that the friction force was independent of area.  He also stated: "Friction produces double the amount of effort if the weight be doubled."

Nowadays, we would mathematically express these two observations by the equation, F=mP, where F is the friction force, P the normal load (the weight of the object), and m is the friction coefficient. Nowhere does the area of in contact appear in this simple equation. We usually refer to this as Coulomb friction after Charles-Augustin de Coulomb who carried out very similar experiments to Leonardo in 1785, some 300 years later.

The reason why friction is independent of area lies in how we define the area. In fact, when the book rests on the table, there is not complete contact.  The paper surface and the wood surface are both microscopically rough and it is only the peaks of this roughness, known as asperities, that contact.  So, the real area of contact between the book and table is much less than the 5" by 8" area of the cover.  If the book is now turned on its side, then the load is supported on less asperity contacts. This means they have a greater pressure acting on them. So they deform, flatten out, and grow.  It turns out that they grow in direct proportionality to the load.  So, it does not matter whether the book is face down or on its side, the real area of contact and, hence, the friction force, is virtually the same.

In the modern world, the amount of energy used up in overcoming friction is colossal.  Take, for example, the pistons in a car engine. The force required to slide a piston inside the cylinder is about 40 Newtons, equivalent to lifting 3 bags of sugar. This means that in a typical engine around one kilowatt of power is lost just to make the pistons slide up and down. Multiply this by the 600 million cars on the planet, and assuming that 10% are driving at any one time, this means that 60 GW of energy is being used up; equivalent to the output from 60 medium sized power stations. Remember that this is not the power required to drive the car it is just the power to overcome the friction between the piston and cylinder.

There are two ways to reduce friction. One is by separating the surfaces with a layer of lubricant, and making sure that layer is thicker than the roughness on the surfaces; Leonardo tells us:

"Thus let there be two bodies with different surfaces, one soft and polished, well greased or soaped, and let it be moved over a surface similar in kind, it will move much more easily than one that is roughened by lime or a rasping file."

Another way of overcoming friction is to change the sliding motion to rolling.  In the Codex Madrid, Leonardo designed many bearings that used a rolling motion, rather than sliding.

"Their movement will be facilitated by interposing between them balls and rollers.  But if the balls or rollers touch each other in their motion, they will make movement more difficult than if there were not contact between them, because their touching is by contrary motions and this friction causes contrariwise movements."

This describes beautifully the design of a ball bearing and cage which are in common use today.

Nowadays, the study of friction and the related aspects of lubrication and wear is known as the science of tribology. The UK is proud to be a world leader in Tribology. The word was coined in 1966 with the formation of a Committee on Tribology by the then Minister of Technology, Tony Benn, to explore its economic impact. Tribology research at the British universities is flourishing. In 2009 a new research centre called the Leonardo Centre for Tribology and Surface Engineering was established.  Their mission is to understand the fundamentals of friction, lubrication and wear, and to apply them to industrial applications.

Overcoming and harnessing friction was a great challenge to Leonardo; and some 500 years later, friction still plays a crucial part in the economic viability of the modern world.

For further information, contact the author of this article, Prof Rob Dwyer-Joyce, Head of Department  and Director of the Leonardo Centre for Tribology, Department of Mechanical Engineering, University of Sheffield.

New hybrid linear bearing combines rolling and sliding

Linear technology expert igus has developed a completely new breed of hybrid linear bearing that both rolls and slides. Called DryLin® WJRM, this innovative bearing system reduces driving force significantly and is particularly well-suited to applications that combine sliding and rolling movements, such as manually adjustable doors, guards, partitions and locks, as well as for light handling tasks.

The lubricant-free plastic sliding plain bearings ensure the hybrid linear system is robust, insensitive to dirt and humidity, as well as being lightweight and cost-competitive. The polymer rollers, which are also maintenance-free, allow for easy manual adjustment of heavy machine doors and protective doors that can weigh up to 50kg. At a defined installation position, the roller bearing, which carries the main load, reduces the overall driving force by a factor of between four and five - this eases manual operation considerably.

The principle of the installation position for the new hybrid bearing is such that the main load is on the roller bearing which reduces the driving momentum required. The plastic sliders compensate any lateral forces.

The igus DryLin W is a flexible modular system made of hard anodized aluminium profiles, diecast zinc housings, stainless steel or aluminium and plastic plain bearings. The wide variety of options within this easy-to-install system allows engineers to optimise the available design space. Combined with different carriage lengths, the rail widths permit many combinations. The four design sizes range from 6mm to a shaft diameter of 20mm.

The innovative hybrid linear bearing DryLin® WJRM from igus UK combines rolling and sliding. It was developed for the manual adjustment of machine and guard doors up to 50 kg.

All the DryLin W guide systems work without lubricants as 'dry-running systems', which means that they do not have to be serviced during operation. The linear bearings are offered with the polymer sliding bearings iglidur® J or iglidur J200. Both of these materials offer low wear and low friction values. In addition, they are resistant to chemicals, help dampen vibrations and are impervious to moisture that might accumulate in humid environments.

The hybrid linear bearing design is based around the field proven DryLin W linear guide family. igus has modelled the new DryLin WJRM system in such a way that the roller fits inside without increasing the overall design width, which remains at 18mm. Standard economic guide profiles can be used, which are available in three styles for 10mm diameter shafts - as individual rails for a flexible guiding distance or as double rails with centre spacing of 40mm or 80mm, which allow self-aligning for speedy installation. The hybrid bearing housing is of blue-chromed diecast zinc.

Igus in profile
Based in Northampton in the UK, and with global headquarters in Cologne, Germany, igus is the largest producer of injection moulded polymer bearings and reinforced plastic cable carriers in the world. Product lines include industry-leading E-Chain cable carriers, Chainflex continuous-flex cables, iglidur plastic plain bearings, igubal spherical bearings, DryLin linear bearings and guide systems.The company has 26 subsidiaries across 31 countries and employs approximately 1,800 people worldwide.

With plastic bearing experience since 1964, cable carrier experience since 1971 and continuous-flex cable since 1989, igus provides the right solution based on 80,000 products available from stock with between 1,500 and 2,500 new products introduction each year. For further information, view website: www.igus.co.uk

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