As consumers deal with higher fuel costs and the effects of inflation and looming recession, they are beginning to scrutinise their buying decisions more and more carefully. It’s just not enough anymore to build the fastest and most reliable car on the road; it also has to be the most fuel-efficient and cost-effective. Competition is fierce and the buying public wants these new products now. The result is enormous pressure on the engineers tasked with producing new designs that will appeal to today’s consumers, says Laurent Bernadin
An industry expert at Toyota has confirmed that what limits a company’s growth is how quickly it can bring new products to market. Physical modelling and simulation techniques are key factors in reducing time-to-market. Testing and analysis of the model can be performed well before the physical prototyping phase, allowing designers to isolate problematic behaviour and develop solutions in the early stages of the process. This translates into both time and cost savings - crucial ingredients to a company’s success.
Many software tools are available to assist in generating virtual prototypes of systems. However, although these may have been revolutionary when they were introduced, they do not adequately address today’s demands. Based on a signal-flow concept, they do address the challenges of numeric simulation, but the modelling environment is not intuitive and is difficult to use. Signal-flow design works very well with control systems design but quickly reaches its limits when applied to physical modelling.
In order to use these traditional modelling tools, you must first manipulate the physical system into a form that the software recognises. This generally involves a great deal of time manually deriving mathematical equations to represent the system. Such derivations are time consuming, error prone, and require advanced mathematical knowledge. For example, even when working with something as simple as a spring-mass-damper system, manually deriving the system equations is a lengthy process.
Before you can simulate this simple system and extract valuable design information, you must first draw the free body diagram and extract from it mathematical relationships between the physical components. Then you derive the differential equations for the system, convert these to integral form, and finally break these equations down to represent blocks. In addition, the resultant block diagram looks nothing like the original system representation. Several pages of derivation are required just to go from a free body diagram to the simple differential equation.
Apply this to something more complicated - the design of a hybrid vehicle steering system, for example – and you are likely to spend an inordinate amount of time in the process. Not ideal when you are designing for a fast-paced market. The reality is that traditional signal-flow based simulation tools have not stood the test of time. The complexity of today’s engineering models continues to advance in orders of magnitude, and to stay competitive, change is clearly needed.
Mainstream engineers in Europe have begun to adopt next-generation modelling techniques, and engineers in North America are also beginning to consider how this new approach can help in their own physical modelling work. These techniques are based on a symbolic mathematical approach to physical modelling. Unlike purely numeric computation techniques, symbolic-based approaches automatically generate the equations representing the physical system, allowing you to extract meaning and insight about the model that would not be available otherwise.
This can make all the difference and help create better designs. In addition, symbolic simplification techniques are used to reduce the complexity of the resulting systems of equations in order to make even large systems tractable. Simulation speeds can increase by a factor of ten as a result.
Symbolic-based physical modelling tools, like the multi-domain simulation software MapleSim from Maplesoft, let you represent the system graphically, using intuitive components such as gears, moving joints, pneumatic tyres, or electric circuit representation, making them easier to build and understand. Engineering designs are described using components that represent their actual physical counterparts: electric circuits are built using resistors and inductors, and mechanical transmissions are built with gear sets and drive shafts.
A broad range of physical components across several physical domains is provided, including rotational and translational mechanics; analogue, digital, and multiphase electric circuits; multi-body mechanics; and thermodynamics. These discrete physical components contain information about which physical laws they must obey, and two connected components exchange information about what physical quantities (such as energy, voltage, torque, heat and mass flows) must be conserved. It is impossible to connect two components if it doesn’t make sense, since MapleSim ‘knows’ which domains and components make sense together. Traditional signal-flow blocks can, of course, be incorporated and simulated, allowing you to build the model for both controller and physical system in the same environment.
With these tools, the learning curve is much less steep; they are faster than traditional modelling tools and the design process is speeded up considerably. Next-generation physical modelling tools handle the grunt work and allow the engineer to focus on what they do best: be creative, design innovative products, and solve challenging problems.
Let’s consider how this affects the bottom line. How much time does a designer have to spend setting up his or her model before getting all the information needed for analysis and simulation? Because model equations are automatically generated from the graphical representation, the equations that define a component’s behaviour do not have to be derived or entered manually.
All of the necessary relational, physics, and mathematical information for complex systems is automatically captured and managed, making it easier to develop efficient, high-fidelity models. Since the system equations are generated symbolically, these complex models can be automatically simplified using sophisticated symbolic techniques such as automatic substitution, algebraic simplification, and differential elimination before they are solved numerically, yielding concise models and high-speed simulations of sophisticated systems. All of this adds up to substantial time saving, which can range from a few days to many months, depending on the project.
Toyota Motor Corporation, known for its innovative design philosophy (and its strong sales), is one company that is realising the benefits of these new technologies: producing better products and dramatically shortening the product development cycle. It has entered into a multi-year partnership with Maplesoft to produce advanced physical modelling tools that are built on top of the MapleSim modelling and simulation software.
By describing the complex, acausal relationships of a physical model in a clear and efficient way, MapleSim and related tools enable simplification and optimisation, taming the complexity of large models and reducing development and testing time. These tools will help Toyota redesign its Model-Based Development process. The intent of this new process is to improve time-to-market and reduce cost, while maintaining high quality and reliability standards.
Tools developed by Maplesoft will provide the fundamental mathematical framework for physical modelling within the new process. All areas of engineering development, such as engines, transmissions, suspensions, braking systems, climate control systems, and in-vehicle electronics, stand to gain from the use of the new set of modelling tools. Similar benefits are to be realised in other industries.
This is merely the beginning of a sea change in the engineering world, which will become more and more evident in the coming months. Those who are taking advantage of the new symbolic-based modelling technologies are already realising how much more efficient their work can become, with improvements in cycle times, cost optimisation, and smoother implementation of extremely complex systems.
So far, engineers in all industries have been very successful in their efforst to design and build outstanding products. However, this does not guarantee future accomplishments in a fast-paced environment where system complexity continues to increase. By making sure that your ‘pit crew’s’ toolkit is fully equipped with the latest technology, you stand a much better chance of staying in the race.
Laurent Bernardin is chief scientist and vice president of research and development at Maplesoft