Mathematics software, Maple, is used by Renault to estimate the risk of an engine seizing - User Case Studies - Maplesoft
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# User Case Study: Mathematics software, Maple, is used by Renault to estimate the risk of an engine seizing

Renault’s Mechanical Engineering Department has developed a Maple model that describes the general behaviour of a lubricated mechanical system, to predict engine seizure. This type of modelling, known as 0D-1D modelling, concentrates on describing physical behaviour over time. In this way, the manufacturer is able to avoid the additional costs, estimated at between 1 and 2 million euros, which arise when the first prototype of an engine exhibits a tendency to seize.

The problem of seizing can occur in many complex mechanical systems. It is the result of a high thermal imbalance between supplied and dissipated energy, and can take a number of different forms, including for example a sudden increase in the friction coefficient, heating and destruction of mechanical parts in contact, and/or the jamming of movement in the mechanical system. Avoiding this kind of failure is a major issue for thermal engine designers, particularly among car manufacturers. When the first prototype exhibits a tendency to seize, this can lead to delays and considerable additional costs, not to mention the additional costs resulting from the delay in the project, which rise significantly as the production launch approaches.

There can be many causes behind the seizure of a system: Too little or too much clearance, rough surfaces, pollution, etc. One thing is certain: a model which makes it possible to predict seizure and helps formulate design recommendations is a critical asset to the designer.

The purpose of the Maple model is to describe the general physical behaviour of a lubricated mechanical system, by calculating the behaviour of the system at a limited number of points and for the physical quantities necessary to predict seizure. Unlike detailed models, such as finite elements, 0D-1D models allow a good physical interpretation of the results, and also offer much more powerful and much faster possibilities for optimization.

The model developed by Renault consists of two parts. The first part is used to build up data tables from a pre-existing lubrication model. The second part deals with thermics-related aspects, based on the tables mentioned above. Physically, the modelling as a whole considers two cylindrical mechanical surfaces in a mixed lubrication situation.

The physical phenomena in play here are very complex:

• Lubrication (Equations involving thin viscous rough films with a low Reynolds number)
• Cavitation (Phase change in a film of oil)
• Non-Newtonian fluids (piezoviscosity and the effect of shear rate)
• Wall elasticity coupling
• Oil shear (heating)
• Microcontact causing friction (heating by microcontact)
• Forced convection and conduction (Thermo-fluid)

The model is constructed by describing the combined effect of these phenomena by putting their equations into the Maple software. Some of the equations used to describe thermics in this process are illustrated in below. The writing of equations is significantly simplified by the Maple technical document interface, enabling mathematical expressions to be written in a natural way.

The parametric model constructed with Maple makes it possible to predict the risk of seizure and to understand how it works. “Overheating” and the seizure which follows take place over a very short period of time, but it is also important to fully understand the conditions leading to the “overheating”, sometimes over long periods of time. The 0D/1D model constructed with Maple makes it possible to map the seizure according to many different parameters. More generally, it makes it possible to predict seizure behaviour according to a given set of parameters.

“The parameterised model constructed with Maple allows us to apply more physics to the modelling of phenomena and so to generate answers where classic systems cannot help us,” says Mr Ligier, R&D Manager at Renault’s Mechanical Engineering Department. “This approach means that rapid iterations are possible, building up sensitivity analyses or mappings, and responding in super-quick time to the new challenges that any competitive industrial development is capable of throwing up.”

The Maple software is currently being used within Renault’s Mechanical Engineering Department for the physical 0D/1D modelling of systems. Using this approach, relevant technical recommendations can be made in a very short period of time over a wide range of applications.