from months to days - mark allen€¦ · the goal was to develop a path planning algorithm that...

A C y b e r n e t G r o u p C o m p a n y

A collection of Maplesoft customer application storiesDiscover how engineers and researchers are using Maplesoft solutions to rapidly accelerate their design projects.

From Months to Days

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A Word From Maplesoft’s President

Welcome to “From Months to Days,” a collection of Maplesoft customer application stories.

Engineers from around the world use Maplesoft technology to solve extremely difficult problems in a diverse range of industries and technical disciplines: Cleveland Golf uses Maplesoft technology to improve their driver performance; researchers at the University of Waterloo, in cooperation with the Canadian Space Agency, use Maplesoft technology to model a robotic space rover; the Shanghai Maglev Development Transportation Company uses Maplesoft technology to investigate the physics and control of the popular Maglev high-speed train technology. In this collection of customer application stories, you’ll find these and many other exciting examples of how Maplesoft technology is used in advanced engineering projects.

In engineering research and design, detail is vital. Design engineers and researchers must not only develop models quickly, but they also require in-depth analytical tools to help them understand on a fundamental level the intricacies of their models and the system-level behavior. Fortunately, MapleSimTM and MapleTM are available to researchers to aid in their model development and analysis.

The application stories in this collection demonstrate how the use of technical computing software, physical modeling and simulation technology, and real-time simulation solutions have allowed engineers to reduce design and prototyping costs significantly while fulfilling the demands of governments and markets. They illustrate how engineers and researchers use Maplesoft solutions to rapidly accelerate their design projects, reducing their model development time from months to days.

Please enjoy this collection of Maplesoft customer application stories, with our thanks. To learn more, please visit www.maplesoft.com/demo.

Sincerely,

Jim CooperPresident and CEOMaplesoft

Planetary Rovers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

NASA’s Jet Propulsion Laboratory . . . . . . . . . . . . . . . . . . . 6

Solar Panel Foil Systems. . . . . . . . . . . . . . . . . . . . . . . . . 7

Unmanned Aerial Vehicles . . . . . . . . . . . . . . . . . . . . . . . . 8

High-speed Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Hockey Sticks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Hybrid and Electric Vehicle Batteries . . . . . . . . . . . . . . . . . . 12

Golf Clubs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Engine Noise and Vibration . . . . . . . . . . . . . . . . . . . . . . . 16

Engine Seizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Maglev Trains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Chain Drive System Resonance . . . . . . . . . . . . . . . . . . . . . 19

Electric Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Walking Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Automation, Robotics, and Mechatronics. . . . . . . . . . . . . . . . 22

Efficient Washing Machines . . . . . . . . . . . . . . . . . . . . . . . 23

Home Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Watches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Broadcast Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Vehicle Driving Simulators . . . . . . . . . . . . . . . . . . . . . . . . 27

Contents

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MapleSim Breaks New Ground in Hardware-in-the-Loop Real-Time Simulation for Planetary Rovers

In the space industry, the design, building, and testing of rover prototypes is extremely expensive. System testing typically does not occur until late in the design/testing process, when it is more difficult and time consuming to make changes. In response to this situation, Dr. Amir Khajepour, Canada Research Chair in Mechatronic Vehicle Systems and Professor of Engineering in the Mechanical and Mechatronics Engineering department at the University of Waterloo (UW), and his team worked with the Canadian Space Agency (CSA) and Maplesoft to develop a hardware-in-the-loop (HIL) test platform for solar powered planetary rovers.

Their approach allows component testing within a simulation loop before a full rover prototype is available. It essentially creates a virtual testing environment for the component under test, “tricking” it into thinking it is operating within a full prototype. Using MapleSim, the modeling and simulation tool from Maplesoft, high-fidelity and computationally efficient models were created for this real-time application.

Using this test platform, scenarios that are hard to replicate in a lab setup, such as the Martian environment or components that are not yet available, can be modeled in software. Hardware components can then communicate with these software models for real-time simulations. The goal is to progressively add hardware components to the simulation loop as they become available. In this way, system testing takes place even without all the hardware components, bridging the gap between the design and testing phases.

The main advantage of this approach is that it significantly reduces the overall development time in the project. It also allows for component testing under dangerous scenarios without the risk of damaging a full rover prototype.

Rover KinematicsIn addition to simulating the rover dynamics, the MapleSim modeling environment was used to automatically generate the kinematic equations of the rover.

These equations then formed the basis for other tasks in the project such as HIL simulations, path planning, and power optimization. The modular system setup enables users to quickly change the rover configuration and explore different approaches in a short time.

Hardware-in-the-Loop FrameworkFigure 2 shows an overview of the test platform. Information regarding the rover’s position, orientation, tilt, speed, and power consumption (obtained from dynamic models of the rover)

is used as input to the software models. A library of rover components was developed within MapleSim and imported within LabVIEWTM Real-Time where the HIL program and interface were developed. The program was then uploaded to the embedded computer within National Instruments PXI where communication between the hardware components and the software models was established and the real-time simulation was run.

“Due to the multidomain nature of the system (mechanical, electrical, and thermal), it was desirable to model all the components within one modeling environment such that critical relationships can be easily discovered. In addition, computational efficiency is crucial in real-time simulations,” said Dr. Khajepour. “MapleSim was found to be the ideal environment for this application due to its multidomain abilities, use of symbolic simplification for higher computational efficiency, and ease of connectivity to LabVIEW.”

In addition to making use of MapleSim’s built-in component library, custom components were also easily developed. A model to estimate the solar radiation that a tilted surface would receive

on Mars was implemented using MapleSim’s Custom Component Block. This model took into account the sun’s position and the rover’s latitudinal and longitudinal position, orientation, and tilt as it traveled from point A to point B. This was used together with a solar array model to estimate the power generation of a rover throughout the day.

“The intuitive nature of MapleSim allowed my team to create high fidelity models in a short period of time,” said Dr. Khajepour. “This played a key role in the success of this modular HIL test platform, which allowed for component testing, power level estimation, as well as the validation of power management and path planning algorithms.”

The team also used MapleSim as a key tool in an earlier part of the project to develop a full solution for the power management system of autonomous rovers. They used MapleSim to rapidly develop high fidelity, multidomain models of the rover subsystems. The goal was to develop a path planning algorithm that took rover power demands and generation into account. Using the models, the path planner found the optimum path between point A and point B such that the rover maintained the highest level of internal energy storage while avoiding obstacles and high risk sections of the terrain.

Dr. Khajepour and his team were able to create the mathematical model of the 6-wheeled rover without writing down a single equation. “MapleSim was able to generate an optimum set of equations for the rover system automatically, which was essential in the optimization phase,” he said. Dr. Khajepour was also impressed with MapleSim’s graphical interface. “In MapleSim, you can simply re-create the system diagram on your screen using components that represent the physical model. The ability to see the model, to see the moving parts, is very important to a model developer,” he concluded.

Figure 1 - Automatic generation of kinematic equations

Figure 3 - Solar array model in MapleSim

Figure 2 - Hardware-in-the-loop framework

University of Waterloo • Canadian Space Agency

The intuitive nature of MapleSim allowed my team to create high fidelity models in a short period of time. - Dr. Amir Khajepour, University of Waterloo

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Maple and MapleNet Streamline the Development of Solar Panel Foil Systems

As a technology consultant, Dr. Peter Waegli works with a wide range of companies to bring the latest and most efficient technology to his clients. His firm, Dr. P. Waegli-Research, provides technology-based strategies and solutions to clients.

Dr. Waegli recently advocated the use of Maple in a project related to solar panels. Solar panels are composed of a collection of connected photovoltaic cells, and the type of cell interconnection technology affects the performance of the solar panel. Eppstein Technologies, a subsidiary of EppsteinFOILS, is a developer of innovative foil systems for interconnecting and encapsulating photovoltaic cells. In a recent project with Eppstein Technologies, Dr. Waegli used Maple and MapleNet to help the company streamline the development process of their foil systems.

A simulation model for a module tester, which illuminates the test modules to measure their power conversion performance, was built in Maple. This model simulates the light distribution and intensity for various arrangements and specifications of the LED-sources. These results were then used to optimize LED positions, properties of the LEDs, and the collimation optics and distance of the LED assembly from the measuring plane. Based on the results of this optimization during the modeling phase, the tester light source was built and performed correctly on the very first try. Maple was then used to create simulation models of the modules. With virtual models of both the modules and the test platform, the company was able to optimize their designs early in the process, reducing the number of expensive physical prototypes they need to create and test.

The model and the results were fully described in interactive Maple documents and shared using MapleNet. As a result, every design engineer on the project has access to the information and can run simulations with their own parameters online.

Dr. Waegli feels that Maple has significant advantages over its competition, “Maple is much easier to use compared to other, similar products. Its intuitive user interface makes it simple to manipulate parameters, and it has excellent compatibility with other tools. In addition, its document interface is very useful as it provides ample opportunities to document my work.”

Being a consultant, Dr. Waegli needs a software tool that provides him the flexibility to share his work with different teams, located in different places, without his clients having to invest in new software. MapleNet provides him that facility because of its internet-based delivery. “Using MapleNet, I feel more in control of the data I share. Unlike other tools, MapleNet doesn’t need a player, which makes it very easy and convenient to use.”

Figure 1 - Light engine seen under an angle from the measuring plane, where the module is placed

Eppstein Technologies • Dr. P. Waegli-Research

NASA’s Jet Propulsion Laboratory Begins Widespread Adoption of Maplesoft Technology

Maplesoft announced a major adoption of its products by NASA’s Jet Propulsion Laboratory (JPL). JPL is implementing Maple, MapleSim, and MapleNet in its various projects. Whether creating America’s first satellite, Explorer 1, sending the first robotic craft to the moon, or exploring the edges of the solar system, JPL has been at the forefront of pushing the limits of exploration.

Curiosity, JPL’s latest space rover, which launched in 2012, aims to explore Mars to investigate whether the planet could have ever supported microbial life. Other JPL projects include spacecraft missions to comets, asteroids, and the edge of the solar system, as well as satellites that monitor the land, oceans, and atmosphere of our own planet.

Maplesoft products are expected to help JPL save time and reduce cost by providing more efficient and smarter methods for mathematical analysis, modeling, and simulation. Maplesoft solutions are built within a natively symbolic framework, avoiding some of the worst sources of error and computational

inefficiencies generated by traditional, numeric-based tools, thus providing great tools for precision-rich projects such as those of JPL.

In addition to using Maple for advanced mathematical analysis, JPL will use MapleSim, Maplesoft’s high-performance physical modeling and simulation platform, as a key tool in its engineering workflow. MapleSim works in combination with Maple. It accesses Maple’s symbolic computation technology to efficiently handle all of the complex mathematics involved in the development of engineering models, including multi-domain systems, multibody systems, plant modeling, and control design.

“Maplesoft products will allow JPL to unify their approach to mathematics, modeling, and simulation,” says Paul Goossens, Vice President, Applications Engineering, Maplesoft. “MapleSim’s intimate connection to the underlying physics of the system models, combined with the knowledge capture and analysis capabilities inherent in Maple, will make project design and development faster and more accountable. JPL scientists will arrive at optimal solutions much faster, and their models will be much more reusable.”

NASA’s Jet Propulsion Laboratory

Jet Propulsion Laboratory

Using MapleNet, I feel more in control of the data I share. - Dr. Peter Waegli, Dr. P. Waegli-Research

Figure 3 - PV-Module Evaluator user interface

Figure 2 - Typical light distribution in the measuring plane over the area of an individual photo-voltaic cell


Using MapleSim in Unmanned Aerial Vehicle Models Provides Insights Not Possible with Traditional Tools

High-speed Robot, DeltaBotTM, Designed using Maplesoft Technology

Unmanned aerial vehicles (UAV) are an increasingly important tool in situations where it is dangerous or extremely difficult for humans to enter. In addition to military applications, UAVs are used in environmental surveys, agriculture, and disaster relief

efforts, and are one of the most active areas of contemporary engineering research. In order to help researchers develop new algorithms for controlling UAVs under a variety of different conditions, Quanser Inc. developed the QBall-X4, a UAV experiment platform for research in UAV control and design.

MapleSim, Maplesoft’s modeling and simulation product, is a key tool for Quanser design engineers in developing the QBall. The QBall-X4 is a quadrotor helicopter design with four motors and speed controllers

fitted with 10-inch propellers. The entire mechanism is enclosed within a protective carbon fiber cage. The first step in its development was to create high-fidelity 3-D dynamics models of the system and its flying characteristics. The results and insights gained through using MapleSim were then transferred to the remaining toolchain to complete the development.

MapleSim gave Quanser engineers two significant advantages over traditional tools. The most important benefit to using MapleSim was its ability to fully capture the dynamics of the gyroscopic effects, the stabilizing effects of the spinning parts of the QBall. With traditional tools, gyroscopic effects are extremely difficult or impossible to treat, as developing sufficiently high fidelity models by hand is simply too difficult and too time consuming. Typically, design engineers resort to making various model simplifications or compromises for the model; ultimately, this reduces the accuracy and effectiveness of the simulation process. Since MapleSim automatically derives the system equations directly from the model diagram, the Quanser engineers developed a very high fidelity model with gyroscopic effects in very little time and with little effort.

Secondly, because it was so easy to make design changes in the MapleSim physical modeling environment, Quanser was able to test different designs for the rotors and choose the one that

worked the best for them. MapleSim let them efficiently consider and dismiss alternate UAV configurations,

such as single rotor, or coaxial counter rotating propeller configuration, before settling on

the quadricopter design.

Quanser was surprised by the speed with which the models were developed. Derry Crymble, lead engineer for the QBall-X4 project commented, “I was very impressed with how little time it took us to configure a high-fidelity

model using MapleSim.”

Dr. Jacob Apkarian, Founder and CTO of Quanser added, “MapleSim was an

eye-opener for us. It gave us insights that we otherwise would not have had. We discovered

behaviors in the system we hadn’t taken into account until we ran MapleSim simulations. We learned a lot about the system using MapleSim.”

Today, the Qball-X4 is one of Quanser’s premier products and is used by researchers in both academic research and industry. MapleSim continues to be a valuable tool in Quanser’s development initiatives.

Following the completion of the DeltaBot, a robot based on an innovative cable-actuated delta-style design, Dr. Amir Khajepour received a surprising number of requests from industry for its use. Based on this commercial demand, Dr. Khajepour established AEMK Systems, a company specializing in the design and distribution of high-speed, cable and vision-based robotics systems for use in a variety of industrial applications. The DeltaBot is capable of over 120 pick-and-place cycles per minute and handling up to 20 kg.

The AEMK DeltaBot robots use cables instead of rigid arms to reduce moving inertia and mechanical equipment costs. The simple design and scalability of the DeltaBot means that it can easily integrate into existing automation environments. The DeltaBot is capable of over 120 pick-and-place cycles per minute. One of the distinctive features of the DeltaBot over other delta robots is its high payload capacity. While other delta robots are limited to payloads under 3 kg, the DeltaBot is capable of handling up to 20 kg. Its high speed, low maintenance costs,

and high payload capacity make it a very attractive industry alternative in many automation applications.

Early in the initial research phase, Dr. Khajepour chose Maple, Maplesoft’s advanced technical computing software, as a key tool in the robot research project. All subsequent design improvements and enhancements to the Deltabot system were developed using Maple and MapleSim, Maplesoft’s high-performance physical modeling and simulation solution. Maple and MapleSim are built on a foundation of advanced symbolic computation technology, which lets users obtain highly accurate results about the system behavior.

“Maplesoft technology was an integral part of the design process of the DeltaBot system, and is now an integral part of the robot’s ongoing development,” says Dr. Khajepour, President and Founder of AEMK Systems, and University of Waterloo Professor of Mechanical Engineering. “With the use of Maplesoft technology, the initial development time for the robot was significantly reduced, and we continue to benefit from shorter development cycles as we make enhancements to our products.”

AEMK Systems is currently using MapleSim to model and simulate the DeltaBot system for use in real-time hardware-in-the-loop (HIL) testing, as part of its ongoing research and development program. When converting the concise model equations to real-time source code, the code generation tools in MapleSim apply additional optimization steps, further improving simulation speed so the results can be used in real-time systems.

“By using MapleSim and Maple, we will be able to design and test enhancements to the DeltaBot much more quickly than with other design tools,” says Dr. Khajepour. “These products make it possible for us to be very responsive to the needs of our customers and the changing demands of industry.”

Quanser Inc. AEMK Systems

I was very impressed with how little time it took us to configure a high-fidelity model using MapleSim. - Derry Crymble, Quanser Inc.

These products make it possible for us to be very responsive to the needs of our customers and the changing demands of industry.

- Dr. Amir Khajepour, AEMK Systems

MapleSim was used to fully capture the dynamics of the gyroscopic effects for a quadrotor helicopter.

Maplesoft products are used to design and test innovative, high-speed robots capable of over 120 pick-and-place cycles per minute.


Game-Changing Hockey Sticks with Help from MapleSim

With the widespread adoption of composite ice hockey sticks over the past decade, the frequent breakage of these sticks is all too common. Not only do these breaks drastically change the game at the professional level, they also lead to exorbitant costs for players. Reliable and durable hockey sticks can have a large impact on the game itself, on professional and recreational players, and of course on the wallets of parents whose children aim to be hockey stars one day!

Hockey Robotics is a company that has pioneered the concept of robotic testing for the hockey industry. It specializes in hockey stick design, performance, and durability testing using an advanced hockey stick testing robot. Hockey sticks most often break during a slap shot; therefore the company’s goal was to produce a robot capable of properly mimicking the professional hockey slap shot. The Hockey Robotics team, with support from industry partnerships, manufactured the SlapShot XT, a dynamic hockey stick robot capable of delivering a slap shot at speeds up to 110 mph. Hockey stick manufacturers are now using the robot to test their designs in a highly repeatable and controlled manner, providing evaluation data never before available.

The SlapShot XT is the first ever robot capable of executing a slap shot like a professional hockey player. The robot’s integrated

advanced electronics and software allows the gathering of data never seen before, enabling even more detailed analysis of the results to support further refinements in hockey stick design. The SlapShot XT is bringing about revolutionary changes in the way hockey sticks are developed.

In hockey sticks, breaking may occur when the stick is subject to very large three-point bending loads during a slap shot.

The first step in creating the robot was to fully understand the motion of the hockey stick during a slapshot using advanced motion tracking techniques, and then create a virtual model of the robot to reproduce that motion. During slap shots by highly proficient hockey players, the trajectory of the stick was tracked at important locations using high-speed cameras. By analyzing this data, the SlapShot XT robot was designed and developed to accurately re-create the loading to which a stick is subjected during a slapshot. The SlapShot XT is capable of shooting a puck at over 100 mph with either a left- or right-handed stick.

MapleSim played a critical role in the design and development of the SlapShot XT. MapleSim is a physical modeling and simulation tool from Maplesoft built on a foundation of symbolic computation technology. It efficiently handles all of the complex mathematics involved in the development of engineering models, including multi-domain systems, plant modeling, and control design. MapleSim allowed Hockey Robotics to efficiently and accurately simulate the coupled dynamic electrical and mechanical behavior of the equipment. MapleSim enabled the concurrent study of the flexible body deformation and rigid body motion of the machines, which is a very difficult, time-consuming, and error-prone task when done by hand. It also allowed them to quickly prototype the designs and investigate the coupled motion of the mechanisms very easily.

A four-bar mechanism was synthesized to match the hockey player’s motion, and subsequent dynamic and stress analyses were used to develop and confirm the performance of the resulting robot design. A flywheel maintained the stick’s momentum during contact with the ice, and the robotic hands allowed the stick to bend about two axes, storing and releasing strain energy throughout the shot. The final design was evaluated using NX 6 from Siemens PLM Software and finite element models of the components.

Hockey Robotics The result was definitive: The robot provides repeatable, unbiased test data on the performance and durability of hockey sticks, a first in the industry.

“MapleSim is the engine driving our development,” said Dr. John McPhee, Chief Scientist at Hockey Robotics. “It has been crucial in our development and testing, resulting in tremendous savings in design and prototyping. In addition, MapleSim allows us to perform engineering analysis that was previously too challenging

and computationally intensive for our industry to undertake.”

Future projects at Hockey Robotics involve using MapleSim to develop a rapid prototyping tool that they believe has the potential to permanently change the way that hockey sticks are designed and evaluated. They expect that their new solution will provide much shorter development cycles and substantial reductions in development costs for hockey equipment manufacturers.

MapleSim is the engine driving our development. - Dr. John McPhee, Hockey Robotics


MapleSim Used to Create High Fidelity Physical Models of Hybrid and Electric Vehicle Batteries MapleSim Helps Improve Your Golf Game

In recent years, the demand for hybrid-electric and fully electric vehicles has increased enormously. The development of such vehicles is a significantly more complex task than designing conventional cars because they incorporate many different engineering domains into a single system. At the same time, competitive pressures are forcing auto manufacturers to come up with new designs faster than ever before. The industry is turning to math-based physical modeling techniques, which allow engineers to accurately describe the behavior of the components that comprise the system and the physical constraints on the system. These model equations are then used to develop, test, and refine designs very quickly, and without the expense and time required to build physical prototypes.

One of the most important components of a hybrid-electric or fully electric vehicle is the battery itself. Having a good virtual model of the battery is essential so that both battery behavior and the physical interaction of the battery with all the other components are properly reflected in the model. Because the battery plays such a vital role in the vehicle, capturing these interactions is essential to designing an efficient, effective electric vehicle.

Dr. Thanh-Son Dao and Mr. Aden Seaman worked with Dr. John McPhee, the NSERC/Toyota/Maplesoft Industrial Research Chair for Mathematics-based Modeling and Design, to develop high-fidelity models of hybrid-electric and electric vehicles, including the batteries. The research was done at the University of Waterloo. They chose MapleSim because they have found the symbolic approach in MapleSim to be an effective way to develop simulation models that have fast real-time speeds for hardware in the loop (HIL) testing and very high fidelity compared to models created in conventional modeling tools.

Battery Electric Vehicle (BEV) ModelUsing MapleSim, Dr. McPhee and Mr. Seaman designed a math-based model of a complete battery pack, and then developed simple power controller, motor/generator, terrain, and drive-cycle models. The resulting differential equations were simplified symbolically and then simulated numerically. A variety of driving conditions were simulated, such as hard and gentle acceleration and driving up and down hills. The results were physically consistent and clearly demonstrated the tight coupling between the battery and the movement of the vehicle. This model will form the basis for a more comprehensive vehicle model, which will include a more sophisticated power controller and more complex motor, terrain, and drive-cycle models.

Hybrid-Electric Vehicle (HEV) ModelDr. McPhee, Dr. Dao, and Mr. Seaman used MapleSim to develop a multi-domain model of a series HEV, including an automatically

generated optimized set of governing equations. The HEV model consists of a mean-value internal combustion engine (ICE), DC motors driven by a chemistry-based NiMH battery pack, and a multibody vehicle model. Simulations were then used to demonstrate the performance of the developed HEV system. Simulation results showed that the model is viable and, as a result of MapleSim’s lossless symbolic techniques for automatically producing an optimal set of equations, the number of governing equations was significantly reduced, resulting in a computationally efficient system. This HEV model can be used for design, control, and prediction of vehicle handling performance under different driving scenarios. The model can also be used for sensitivity analysis, model reduction, and real-time applications such as hardware-in-the-loop (HIL) simulations.

“With the use of MapleSim, the development time of these models is significantly reduced, and the system representations are much closer to the physics of the actual systems,” said Dr. John McPhee. “We firmly believe that a math-based approach is the best and quite possibly the only feasible approach for tackling the design problems associated with complex systems such as electric and hybrid-electric vehicles.”

In the world of golf, players are always looking for ways to improve their game, and equipment manufacturers are always looking for ways to give their customers an edge. Cleveland Golf / Srixon, an internationally recognized maker of golf clubs with a strong tradition of innovation, wanted to explore ways to increase the performance of their drivers. Their engineers turned to MapleSim, a physical modeling and simulation tool from Maplesoft, to help them in this project.

In particular, Cleveland Golf / Srixon wanted to investigate and understand the effect of different club weights and club lengths on the performance of the driver. A key focus for them was to understand how the flexibility of the shaft in both bending and torsion needed to be optimized for different club weights and lengths. The engineers were looking for a good, efficient model which would allow them to explore the effects of different shaft designs on club performance.

With the help of Dr. John McPhee, NSERC Industrial Research Chair and Professor of Systems Design Engineering at the University of Waterloo, and his colleagues Dr. Matt Millard and Mr. Sukhpreet Sandhu, they used MapleSim to create a model of a driver. The shaft itself was modeled using MapleSim’s built-in flexible beam component. The driver head model was carefully designed to include the exact characteristics of the Cleveland Golf / Srixon driver head, including factors such as its mass and moments of inertia. To simulate a variety of swings from different players, experimental measurements were taken from varsity players

on the university golf team. This information was input into the model as the 6 degree-of-freedom motion of the grip, which in turn determined the movement of the shaft. Different versions of this base model were created by modifying model parameters to match the properties of the different club designs.

When the models were validated against the experimental data, good to very good agreement was found between the simulation and the experimental data for club head speed and the dynamic loft and droop at the instant of contact with the ball. In addition, the MapleSim models were found to run significantly faster than similar models based on finite-element techniques.

Cleveland Golf / Srixon was impressed with both the accuracy of the model and the flexibility and performance MapleSim gave them. “The MapleSim models we’re running allow us to predict head delivery conditions with more variables, higher

precision, and faster run times”, said John Rae, Vice President, R&D, of Cleveland Golf / Srixon.

“Using MapleSim’s simulation tools we can generate custom swing calculations based on every equipment variable, leaving nothing to speculation.”

With efficient, validated dynamic models of a golf driver, Cleveland Golf / Srixon was able to quickly

explore different designs and “what if” scenarios allowing them to identify the ideal combinations for their newest product offering, the Launcher Ultralight Series, which consists of 3 distinct drivers with unique weight, length, and shaft combinations. MapleSim allowed Cleveland Golf to minimize the need for expensive prototypes and shortened the necessary time to identify the ideal combinations, helping get the product to market at the right time with the best possible performance.

Toyota Cleveland Golf / Srixon

Using MapleSim’s simulation tools, we can generate custom swing calculations based on every equipment variable, leaving nothing to speculation. - John Rae, Cleveland Golf / Srixon

A high-fidelity battery model is essential to the development of electric and hybrid-electric vehicles.


From Months to Days...

Electro-Hydraulic Clutch Actuator1 month to 3 daysA highly realistic clutch actuation system incorporating effects from seven different domains in one model.

Power-Split Hybrid Electric Vehicle

3 months to 15 daysA complex, multi-domain model that covers all aspects of a hybrid electric vehicle, including a mean-value internal combustion engine.

Solar Array1 month to 3 daysA full solar array model that simulates power generation of both stationary and tracking solar panels.

Wind Turbine1 month to 4 daysA full wind turbine model that simulates stabilized power output using controlled wind blades.

Vibration Analysis for Marine Driveline Systems 24 months to 20 daysA full model of the vibrational modes found in a marine driveline system.

Planetary Rover 3 months to 10 days A complex multidomain model that simulates planetary rover motion, wheel/soil interaction, energy consumption, and more.

Unmanned Aerial Vehicle 1 month to 4 daysAn aerial vehicle model that provides behavior insights not possible with traditional tools.

Biomechanical Walking Robot1 month to 5 daysA dynamic model of a walking robot which incorporates both kinematic behavior and ground contact interactions.

Do you want to develop complex system-level models quickly?

Request a live technical demonstration of MapleSim: www.maplesoft.com/demo


Leading Car Manufacturer Renault Solves Unwanted Engine Noise and Vibration Using Maple

When an engine stops, several engine components take part in the process. Components can produce unwanted noise and vibrations when the engine slows down, which can lead to their deterioration. Jean-Louis Ligier, a Research and Development manager at Renault, and his team were tasked with determining the sources of these noises and vibrations in a 2.2 liter 4-cylinder

turbo diesel engine. They found Maple to be the most efficient tool to model the engine and determine the source of the unwanted noise. More importantly, they also used Maple to determine a solution to the problem.

Ligier, who has a Ph.D. in Mechanical Engineering, has been using Maple for over 20 years. He has used the software in several applied research projects, such as time-varying thermal analysis in gearbox components, engine friction optimization, and vibration analysis. He has been with Renault for many years, managing thermal behaviors and mechanic fatigue on engine components, as well as determining new simulation methodology. His primary goal in using Maple was to write equations that control the engine components very easily.

When creating mathematical models of various components, different software can be implemented. Ligier has found through his experiences that Maple is the easiest and fastest software for his tasks. “In comparison with others, Maple can do in a couple of hours what other software can take days to compute,” he said. “The natural math notation allows me to enter the equations as if I were writing them by hand. The fact that I can do symbolic calculations allows me to do optimizations that are virtually impossible with other software. What’s more, the results are extremely accurate.”

When speed decreases in an engine, several mechanical resonances are generated. If there is too much movement within the engine, not only do the components create noises disturbing to the driver, but they also begin to wear out prematurely. The goal of the study was to model and understand the cause for the vibrations. The modeled engine was a 4-cylinder from Renault’s

Laguna line of cars. The model of the engine was a system of five differential equations and focused primarily on the crankshaft, the dual mass flywheel (DMF), as well as the whole power train. From these equations, Ligier could estimate the level of vibration created during the deceleration of the engine. After plotting the results of the simulation, it became apparent that the vibrations were primarily occurring from shocks inside the DMF. To rectify the problem, a rather simple solution was implemented, which involved modifying the air intake while decelerating.

Discovering the exact cause of the problem led to a substantial cost-saving benefit to Renault because it meant that the problem was fixed with a simple solution—only a slight modification of the engine was required.

By analyzing the simulation results, Ligier reduced the noise by as much as 30%. Modeling the engine in Maple allowed him to analyze the symbolic equations, which enabled a more in-depth understanding of the system. The numeric results were plotted and the location of the unwanted vibrations was discovered. By using Maple, he was able to create and run his model in one day, which was a substantial time saver in comparison to other software, which took over a week for the same task. “I have always liked how easy Maple is to use, and how powerful it is. The ability to perform both symbolic and numeric computations is a huge time saver for me, allowing me to get results in a day, instead of weeks with other software,” concluded Ligier.

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 modeling, known as 0D-1D modeling, 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 modeling 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. 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 behavior according to a given set of parameters.

“The parameterized model constructed with Maple allows us to apply more physics to the modeling 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 modeling of systems. Using this approach, relevant technical recommendations can be made in a very short period of time over a wide range of applications.

Mathematics Software, Maple, is Used by Renault to Estimate the Risk of an Engine Seizing

Renault Renault

In comparison with others, Maple can do in a couple of hours what other software can take days to compute. - Jean-Louis Ligier, Renault


Maple Helps Ford Motor Company with Analytical Predictions of Chain Drive System Resonances

Shanghai Maglev Development Transportation Company uses MapleSim in their Modeling Projects

Like other automotive manufacturers, Ford Motor Company wrestled with a common concern – incessant noise and vibration in chain drive systems. Chain drives have been widely used for power transmission in automotive systems for decades. While chain drives are effective, undesirable noise and vibrations have always been a problem. This was particularly the case when Ford detected a severe 1800 – 1900 Hz chain noise in a new transmission prototype. Sound pressure levels were 10 -15 dB over nominal values and the cause was unknown.

At Ford, Jack S.P. Liu, Das Ramnath, and Rajesh Adhikari set out to understand the source of the noise and develop simple, analytical models for quick computation of the chain drive system resonances.

Earlier experimental research identified chain-sprocket meshing noise as the most significant noise source, and suggested that chain drive system dynamic parameters such as speed, tension, mass and pitch of the chain, sprocket inertia, and the natural frequencies of the chain sprocket system are closely related to the meshing noise. The Ford team took on the challenge of analytically predicting chain drive system resonance based on the assumption that existence of chain resonances can amplify the radiated chain meshing noise.

The team started with the analysis of the chain noise test data and compared this with the theoretical mathematical model. Their results indicated that three types of chain resonance existed: the transverse strand resonance, the longitudinal chain sprocket coupled resonance, and the longitudinal chain stress wave type resonance.

To help deal with the complex calculations and analysis involved in developing these advanced models, Ford used the mathematical software Maple. Its extensive symbolic and numeric math solvers were used in modeling the physical system to gain an understanding of the vibrational behavior. The partial differential equations used in the model were solved quickly and easily using Maple’s world-leading differential equation features. When describing results, such as the eigenfunctions that represent the unique mode shapes of the natural resonant frequencies, Maple’s extensive plotting capabilities were indispensable. In addition, the unique documentation capability of Maple enabled Ford to publish integrated worksheets and reports for easy and convenient dissemination across the organization.

By using Maple, Ford could validate mathematical model predictions against both an ABAQUS CAE model and the experimental test results. Also, Ford created a predictive design tool to develop analytical models and predict chain drive dynamics using Maple’s embedded components, including features such as variable slider inputs to modify design variables. This design tool will enable other technical staff to perform

future predictions of chain-drive resonances in a quick and easy manner.

“We were amazed at the power of Maple. Its analytical power and modeling capabilities enabled us to get the accuracy we were aiming for,” said Jack S.P. Liu, a CAE engineer at Ford

Motor Company. “I especially appreciate embedded components and their role in GUI design. Maple’s symbolic math capability exceeds that of other CAE tools in areas where we used it.”

The Ford team was able to accurately determine the exact locations of the 1800 Hz noise source and the problematic noise peak. By combining transverse and longitudinal natural frequencies, both the analytical and CAE models predicted the 1800-1900 Hz longitudinal chain resonance as observed in chain test data. The team concluded that a thorough understanding of all types of chain resonances is critical for powertrain engineers to design a quiet and smooth chain drive system.

Ford Motor Company

We were amazed at the power of Maple. Its analytical power and modeling capabilities enabled us to get the accuracy we were aiming for.

- Jack S.P. Liu, Ford Motor Company

In 2004, Shanghai introduced the world’s only commercially operating magnetically levitated (maglev) train service. Maglev technology is growing in popularity because it emits fewer harmful pollutants and is more efficient at higher speeds than conventional forms of mass transport. Additionally, increasing crude oil prices and the maglev’s inherently quieter operation have propelled maglev technology forward as a viable green alternative to air travel between large urban population centers.

Engineers at the Shanghai Maglev Transportation Development Co., Ltd. (SMTD) recently chose MapleSim, Maplesoft’s multi-domain modeling and simulation software, as a core part of a new commercially funded controls research laboratory. MapleSim is the leading physical modeling tool that helps engineers meet

the challenges of complex physical modeling projects. It is the ideal software package for developing models for multi-domain engineering systems, including sophisticated plant models for control systems development. SMTD is using MapleSim to investigate the physics and control of the increasingly popular maglev technology.

Maplesoft’s full service partner in China, CCA Technology, introduced SMTD to MapleSim, and they immediately recognized MapleSim’s potential in control design applications. “With MapleSim’s analytical tools for signal processing and controller development, and its multibody and custom component functionality, there are a number of benefits that MapleSim can bring to our research. As a result, we chose to integrate MapleSim into our toolchain,” says Mr. Bo, Maglev Control System engineer, SMTD.

Shanghai Maglev Transportation Development Co., Ltd.


GM and Maplesoft to Collaborate on Electric Vehicle Technologies at the University of Waterloo

A five-year, $10.5-million partnership between General Motors of Canada, Waterloo-based Maplesoft, and a multidisciplinary research team at the University of Waterloo is tackling the challenges of next generation electric vehicles. Through model-based design and prototype testing, the team will investigate crucial technologies for achieving more widespread use of electric vehicles.

“Vehicle electrification is a key pillar of our energy diversification strategy,” said Kevin Williams, president and managing director of GM of Canada. “Building on our leading R&D commitments in Canada, this project better positions us to exceed customers’ expectations with respect to the performance, safety, and sustainability of our electric vehicle technologies.”

The research is being supported by the Automotive Partnership Canada (APC) with the Natural Sciences and Engineering Research Council of Canada (NSERC) as the lead agency. APC is contributing $3.6 million, in addition to $2.5 million from the Ontario Research Fund.

The development and validation of key enabling technologies such as vehicle stability control, power management systems, and battery monitoring and charging devices will be important focus areas for the research team, led by Dr. Amir Khajepour from the University of Waterloo.

Importantly, the technologies originating from Waterloo will also be tested by GM vehicle development teams. Engaging the research team in the vehicle development process will provide them with a unique opportunity to gain insight into bringing new technology concepts to market, and help transform the research findings into a truly integrated technological solution.

“Electrification of automotive systems presents complex challenges for a vehicle’s powertrain, control systems, battery health monitoring, thermal management, and safety,” added Dr. Khajepour. “With the APC funding and the support of General Motors, we plan to tackle these challenges to develop the next generation of key electric vehicle technologies.”

Learning to Walk Faster with High Performance Modeling

The ability for robots to mimic humans is one of science’s most talked about issues. The rewards for reproducing human movement and actions go far beyond engineering, having applications and ramifications for medical treatment, computer technology, defence, exploration, and much more.

A project using MapleSim physical modeling software at the University of Manchester is helping to perfect the process of humanoid walking in robots. The new centre at Manchester, the Centre for Interdisciplinary Computational and Dynamic Analysis (CICADA), has been working with Professor Darwin Caldwell at the Italian Institute of Technology, Genova, who has been developing a novel compliant humanoid robot (CCub) based on the previously developed humanoid robot iCub at IIT.

Part of CICADA’s work looks at walking characteristics and other locomotive actions using a hybrid model. The model uses spring/dampers to simulate ground reaction force, actuator dynamics, and compliant elements to capture the robot’s full dynamic response.

One of the challenges facing the Manchester team, lead by Dr. Martin Brown and Dr. Gustavo Medrano-Cerda, is visualising experiments quickly and effectively, to avoid slowing down the process and to ensure that experimentation is valid and relevant. “The ability to visualise in MapleSim, without having to write our own programs, has been invaluable,” says PhD student Houman Dallali. “What’s more, we can directly generate C++ code to interface with the hardware and speed up the controller implementation/debugging process.”

With a comprehensive and advanced library of models online – in one place

– Mr. Dallali has been able to construct complex simulations easily using the ‘drag and drop’ modeling environment and then edit existing models with little effort due to MapleSim’s intuitive interface. The inclusion of linearization techniques in the MapleSim offering is also important for robotic modeling.

“We are building models faster and completing experiments with better data thanks to MapleSim’s accuracy and kinematics capabilities,” Mr. Dallali continues.

The speed and success of the MapleSim-aided research means that the CICADA team will quickly move on to projects for dynamic walking with full body control and extended range of gaits. Dr. Martin Brown and his PhD student Onder Tutsoy are working on ‘reinforcement learning’ for humanoid robots as well as ‘iterative learning’ techniques. “In the future, we will be adding logic and learning approaches to our code and looking to develop applications from the research, such as better prosthetics and walking aids,” says Mr. Dallali.

General Motors of Canada • University of Waterloo University of Manchester • Italian Institute of Technology

The ability to visualize in MapleSim, without having to write our own programs, has been invaluable. - Houman Dallali, University of Manchester


MapleSim and Maple Used in Advanced Research Projects at the ARM Lab at SUNY Buffalo

The Automation, Robotics and Mechatronics (ARM) Lab is a research laboratory in the Department of Mechanical & Aerospace Engineering at the School of Engineering & Applied Sciences in The State University of New York (SUNY) at Buffalo. The lab combines an in-depth understanding of mathematical theory with experimental validation to develop a new generation of smart mechanical and mechatronic systems. Their work includes projects in haptic devices for surgical simulations, musculoskeletal simulation to refine human-machine interactions, cooperative payload transport by robot collectives, and omnidirectional wheeled robots. Several of their research projects have directly resulted in the creation of commercially available devices that are then used by labs around the world for education and further research.

Since most of their projects start with an in-depth analysis of the underlying mathematics of the system, the ARM Lab requires tools for developing and analyzing mathematical equations. They have chosen Maple and MapleSim as key tools to complete these tasks. Dr. Venkat Krovi, director of the ARM Lab, finds using a symbolic approach invaluable to their work. “Performing these calculations symbolically allows for the development of exact, closed form expressions. We don’t need to worry about accumulating errors from numerical calculations. Perhaps even more importantly, with the exact mathematical equations, we can identify singularities, perform parametric design refinements, and improve the real-time model-based control strategies.”

One of the ARM Lab’s research projects involved the study of kinematic and dynamic simulations of 6 degree of freedom

6-Prismatic-Universal-Spherical (6-P-U-S) type manipulators. This type of manipulator combines a platform that moves and a fixed base, interconnected by several legs. In his research, Dr. Krovi and his research team analyzed a general 6 DOF 6-P-U-S manipulator. They used Maple and MapleSim to automatically generate the governing equations, and conducted a kinematic analysis of those equations with Maple. Starting with these general equations, specialized equations were extracted from the general system that correspond to a specific architecture with desirable properties – superior structural design with minimal interior singularities within its workspace. They were then able to analyze the workspace of such parallel-architecture manipulators, with the primary goal of optimizing the link geometries and parameters to enhance overall workspace and other selected geometric workspace-based performance-measures.

Dr. Krovi and his team then worked with Quanser Consulting Inc., a world leader in the design and manufacture of advanced systems for real-time control design and implementation, to create a physical prototype of the parallel arm manipulator corresponding to the design developed from the specialized kinematic and dynamic equations. Quanser also used MapleSim’s modeling and simulation capabilities during the final design and development process. The 6 DOF motion platform, termed the Hexapod, is now part of Quanser’s mechatronic controls collection and can be used in various applications, including vibration studies, earthquake simulations, and flight simulations. Dr. Krovi continues to use the Hexapod in his research and teaching and MapleSim and Maple in ongoing research projects at the ARM Lab.

3-D Hall Sensor Algorithm Developed in Maple Produces a More Efficient Washing Machine Design

Dr. Frank Allmendinger leads a research and development project team at Marquardt GmbH, a German company that develops and manufactures switches and switching systems. His team designed an innovative three-dimensional load and imbalance sensor, which is used in a new washing machine model from a well-known company in the “white goods” sector.

In industry, the trend is to move from washing machines with a drum capacity for 5 kg of laundry to larger ones with a capacity of 7 or 8 kg. However, these large drums are still being placed in the standard washing machine housing with a width of 60 cm, which means there is a much smaller space left between the drum and the housing. This means collisions are more probable. It is therefore necessary to measure the position of the drum relative to the housing, use this signal to identify impacts of the drum against the housing in advance, and react accordingly. Marquardt’s sensor was developed to detect the relative position, in three dimensions, of the washing machine drum to the housing.

Having the ability to measure the drum position gives several other advantages; for instance, it is possible to sense imbalances and detect resonant frequencies of the mechanical system during the machine’s spin cycle. These imbalances can be reduced by slowing the rotation speed and distributing the weight more evenly. It even becomes possible to measure a load of clothing as it is placed into the machine and give a recommendation of how much detergent to use!

The Marquardt team, in close collaboration with the Fraunhofer Institute for Integrated Circuits, developed a new 3-D Hall sensor application-specific integrated circuit (ASIC) that measures the three vector components of a dipole magnetic field. The complete measurement system consists of a magnet affixed to the drum in the washing machine and the 3-D Hall sensor ASIC

attached to the unit housing. The Hall sensor measures both the direction and strength of the magnetic field, determining the relative movement of the magnet simultaneously in all three dimensions. This information is then communicated to the onboard microcontroller, which uses a proprietary algorithm to determine how to control the movement of the drum.

To develop the algorithm, the Marquardt group used Maple. Dr. Allmendinger found Maple to be an invaluable tool, allowing him to work on complex problems such as modeling the magnetic fields, estimating the allowed tolerances for the magnet, and determining whether the tilt of the 3-D Hall sensor module was within a very small tolerance of approximately two degrees. The resulting algorithm was translated to C code to run on the controller.

Dr. Allmendinger first worked with Maple while studying at university. He was impressed by Maple’s ability to work with symbolic mathematics, its powerful graphing tools, its technical document interface, and its export capabilities to other languages (such as C, MATLAB®, and Java). Dr. Allmendinger said, “It was very simple to work in Maple, even with the

complex mathematics involved. We found it quite easy to enter and modify equations, determine whether they had a solution, then go back and make necessary changes. I found Maple’s user interface very easy and smooth to work with, especially the export capabilities; interoperability with other technical programs have become much better, and it is now invaluable in rapid solution development.”

The new 3-D positioning algorithm in the Hall sensor yields several advantages.

First, assembly is simple because there is no mechanical

connection between the magnet and the sensor. As the measured values of the three

magnetic field components can be recorded simultaneously, the sensor system also offers the option of calculating speed. Overall, the design enables natural resources to be handled more responsibly. The use of mathematic field modeling makes it possible to discard traditional 3-D mapping techniques and use a smaller, more cost-effective microcontroller. Also, fewer resources are used by creating the considerably smaller magnet.

Marquardt GmbH SUNY Buffalo

I found Maple’s user interface very easy and smooth to work with. - Dr. Frank Allmendinger, Marquardt GmbH


Maple is Used by Ulysse Nardin to Lengthen the Running Time of New Watches

A Swiss watch manufacturer, Ulysse Nardin, is a pioneer in the innovative use of new technologies and materials in wristwatches. This company introduced the first silicon-diamond composite barrel spring in a wristwatch and continues to produce sophisticated new watches based on cutting-edge designs. Maple, the symbolic and mathematical calculation software from Maplesoft, is a key tool in the research process at Ulysse Nardin.

The architecture of mechanical pocket watches and wristwatches has long been based on the same principle. A leaf spring, which is the barrel spring or main spring, is wound inside a barrel drum. Because the dimensions of the spring and the drum are limited by the small volume available in watches, the mechanical energy stored in the barrel is also limited. The power reserve of the watch, that is, the running time of the watch at rest, without user interaction, depends on this stored energy. In most cases, the power reserve of a watch is about 48 hours. If the density of energy storage (the stored energy to volume ratio) can be maximized, the power reserve of the watch is also increased. This is why Ulysse Nardin initiated the development of a barrel spring made of composite materials giving an elastic limit and impact resistance far superior to the best steels known.

The watch designs require the production of several springs that are more than half a meter long on a silicon wafer that is limited to a diameter of 6 inches (15.4 cm). This limits the dimensions of the free spring, which means that a preform that is compatible with the tiling of the springs on the wafer must be selected, while imposing a varying thickness along the spring to obtain constant torque. To meet this challenge,

Ulysse Nardin called upon Claude Bourgeois, an engineering consultant and former Centre Suisse d’Electronique et de Microtechnique (CSEM) researcher.

Claude Bourgeois used Maple to model and optimize these new composite barrel springs. The application developed in Maple associates the anisotropy of silicon with the integration of the characteristic differential equations to describe the behavior of the springs under large displacements. Maple made it easy to identify the critical parameters related to the required function and the figures of merit of the system. It also helped to establish analytical macromodels, which are useful elements for analysis and for developing new concepts. The first watch to use the new barrel springs was the Ulysse Nardin Freak Caliber, which has a power reserve of more than seven days.

While employed at the CSEM, Claude Bourgeois developed many other simulation applications with Maple. These applications involved anisotropic elasticity, piezoelectricity and electromagnetism, as well as gaseous and liquid microfluidics, in particular, during the development of high-performance resonators made of quartz, then of silicon activated by AlN, and many types of MEMS sensors and actuators.

Ulysse Nardin

A Flight into the Future with MapleSim

Dr. Richard Gran is well placed to appreciate the benefits modern technology has brought to modeling and simulation. As a key member of the NASA team that designed the digital flight control system for the Apollo Lunar Module in the 1960s, he spent many months developing a FORTRAN simulation on an IBM 7090 to verify the design. Now the president and CEO of The Mathematical Analysis Company, he uses MapleSim to reduce the time it takes to develop physical models and prototype control systems.

His career has spanned five decades, and has included projects such as Princeton’s Tokamak Fusion Test Reactor, the X-29 Forward Swept Wing aircraft, and magnetically levitated trains for the US Department of Transportation. He has seen the growth of computing power from slide rules and mainframes in the 1960s to the powerful, yet very affordable, multiple-core PC workstations available today. This evolution now enables engineers, like Dr. Gran, to exploit software technology that automates the time-consuming processes of creating high-fidelity physical models, generate high-speed C-code for real-time applications, and document designs in a math-aware environment.

To try MapleSim, Dr. Gran developed a model of an eight-room house to investigate a new home heating system controller. MapleSim’s remarkably intuitive drag-and-drop physical modeling environment allowed him to rapidly develop the model while also learning to use MapleSim. The model uses a hierarchy of eight simple room subsystems as the building blocks. Each room subsystem consists of a thermal capacitance that accounts for the heat stored in the air volume of the room. Heat in the room is conducted to adjacent rooms, to the spaces above and below, and to the outside. In addition, convection and radiation elements model the heat flow from the room heaters. Eight of these building block subsystems create the house model.

Connections at this top level of the hierarchy provide the thermal sink to the outside air temperatures, the furnace heat inputs (from the

Heating Controller), and the PID controllers that regulate the temperature of each of the two heating zones in the house. This exercise shows that continuous heating controllers provide energy savings by circulating the heat from the heating source to the rooms at lower absolute temperatures. This reduces the conductive heat loss from the ducts or plumbing that circulates the heat to the rooms.

Dr. Gran had created a simpler version of this system for a book he wrote. This simpler model had only two rooms and two heat exchangers. The derivation and simulation of the equations for the book took over three days to create. This eight-room model, the control system design, and the simulation to verify the results took less than eight hours. He remarked, “The original model was about 1/10 the complexity of the MapleSim model but took me days to develop. MapleSim saved me many hours of work because the model maps onto the topology of the physical system and the dynamic equations do not have to be developed by hand. This also enables very complex multi-disciplinary system models to be built and analyzed by a single person. MapleSim converts a painstaking and laborious process into one that is simple and enjoyable.”

Mathematical Analysis Company

MapleSim saved me many hours of work because the model maps onto the topology of the physical system and the dynamic equations do not have to be developed by hand. - Dr. Richard Gran, Grumman (ret.)

The results of this MapleSim simulation demonstrate that a continuous form of heating control is more efficient than a

controller that uses a bi-metal thermostat.

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Broadcasting Benefits of Math and Analysis SoftwareMapleSim Used in the Creation of Breakthrough Vehicle Driving Simulator Technology

Maple mathematics software is helping broadcast network operator Arqiva to model antennas and analyze systems, ensuring that broadcast signals are received over the specified range.

Responsible for much of the UK’s broadcast and mobile communications infrastructure, Arqiva delivers wireless, satellite, and terrestrial broadcast services to a growing number of countries around the world. All land-based transmissions for UK television stations, including the new digital networks as well as wireless provision for cellular, wireless broadband, voice, and data services for both commercial and government markets, are handled by the company. Ensuring that its stations conform and deliver the power and coverage needed is paramount.

Arqiva engineers are constantly upgrading the capabilities of their products and the software tools they use. “In order to fully understand how our products work and the nature of the maths behind it, we need something to quickly and simply check what is happening,” says Arqiva Senior Technologist Karina Beeke. “Maple offers just that, with 3-D graphics and an easy interface.”

Maple allows analysis in engineering and science projects to be streamlined and the quality enhanced. With fly-through animations and 3-D plot annotations, the package includes advanced mathematical functions and point-and-click tools for control systems design. With features such as context-sensitive menus and powerful problem-solving tools, the software is intuitive and can be used with little training.

Having a wealth of features useful to Arqiva, Maple includes space curve, aptitude, curve fitting, and the ability to rotate and zoom in to elements. A major benefit, according to Karina, is its flexibility and range, “With Maple we can start simply and then develop as we go without having to completely understand the full capability.” Arqiva also uses the Maple Global Optimization Toolbox to help with matching antenna features for best fit.

Karina is also positive about the ‘very good support’ and the extensive online resources available from Maplesoft. A user forum complements an online library of algorithms and a troubleshooting guide.

As automotive manufacturers compete on features of efficiency and safety, they are also battling to provide the best driving experience for their customers. As a result, vehicle engineering is becoming more complex, involving multiple disciplines. There is a growing desire to provide test drivers and evaluators with simulated driving experiences, so that their feedback can be incorporated early in the design process. Based on this, automakers are introducing a new element in the complex assessment process between virtual prototyping and vehicle on-road testing.

With support from Maplesoft, VI-grade, an engineering simulation software provider, has produced the award-winning, breakthrough driving simulator technology, VI-DriveSim Dynamic. This high-end driving simulator allows automotive OEMs and racing teams to test full vehicle configurations, from the engine through the transmission to the suspension and tires, using a human driver and a virtual vehicle.

Very often, test drivers and track engineers cannot sufficiently influence the vehicle design, because their feedback comes far too late in the prototyping process. VI-DriveSim Dynamic enables the implementation of a new validation stage in the design cycle by letting real drivers drive the virtual car. Driver feedback can then be taken into account and improvements made before any expensive physical prototypes are built. The simulator needs to be so accurate that the most sensitive professional driver can feel the smallest change in vehicle performance.

The VI-DriveSim Dynamic simulator works by running a virtual mathematical model of the vehicle and track, and linking it to a 6 degree of freedom motion platform designed expressly for automotive requirements by Ansible Motion. The inputs to the virtual model are supplied by actions of the human driver in the simulator as he shifts, steers, brakes, and accelerates. In turn, the platform controller provides real-time input to the platform actuators, according to what happens to the vehicle model as it responds to the inputs. The physical simulator platform thus provides inertial feedback to the driver, allowing him/her to interact in a natural way with the virtual vehicle model.

An inverse kinematics/dynamics model of the motion platform is required so the software knows what changes to the platform will produce the correct forces on the driver to simulate the vehicle in motion. The challenge here is to acquire these inverse

relationships, which will provide the most accurate response of the system. To accomplish this, Ansible Motion used Maplesoft’s system-level modeling and simulation tool, MapleSim, to build the platform model, and to analytically solve for the inverse kinematic equations. Having access to these equations is crucial, and could not have been achieved without a symbolic/analytical computational engine such as Maple, the mathematical engine behind MapleSim. In effect, MapleSim gives the controller an exact analytical solution for the inverse kinematics, giving the best possible simulation.

“Driving simulator technology is emerging as an integral part of the vehicle development process for motorsports teams and production vehicle manufacturers,” said Kia Cammaerts, Technical Director, Ansible Motion. “MapleSim was a big part of our ability to develop this technology. Our team would not have been able to efficiently develop our systems for VI-grade or our other clients without a tool such as MapleSim, which we used to develop the inverse kinematic solutions for the actuators, saving us months of painstaking, error-prone effort.”

VI-grade’s flagship solution, VI-CarRealTime, powers the system with a real-time validated vehicle model. The partnership between Maplesoft and VI-grade makes real-time modeling applications more cost and time-effective by integrating MapleSim models with the VI-CarRealTime framework.

“The combination of MapleSim and VI-CarRealTime allows for the fast, accurate modeling of automotive subsystems, such as powertrains, suspensions, and steering mechanisms,” said Paul Goossens, Vice President of Applications Engineering at Maplesoft. “Automotive engineers can easily do innovative work, exploring their designs in new and deeper ways, detecting problems earlier in the design cycle, and developing high-quality, practical solutions to their design challenges.”

VI-DriveSim Dynamic, has been awarded “Development Tool of the Year 2012” by Vehicle Dynamics International Magazine.

27www.maplesoft.com

Arqiva Ansible Motion • VI-grade

MapleSim was a big part of our ability to develop this technology.

- Kia Cammaerts, Ansible Motion

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A C y b e r n e t G r o u p C o m p a n y

About MaplesoftMaplesoft, a subsidiary of Cybernet Systems Co. Ltd. in Japan, is a global provider of high-performance software tools for engineering, science, and mathematics. Its product suite reflects the philosophy that given great tools, people can do great things.

Maplesoft’s products help to reduce errors, shorten design times, lower costs, and improve results. Maplesoft’s core technologies include the world’s most advanced symbolic computation engine and revolutionary physical modeling techniques. Combined together, these technologies enable the creation of cutting-edge tools for design, modeling, and high-performance simulation.

Engineers, scientists, and mathematicians use Maplesoft products to enable them to work better, faster, and smarter. Maplesoft’s customers include Ford, BMW, Bosch, Boeing, NASA, Canadian Space Agency, MDA, Microsoft Research, Ulysse Nardin, Liebherr, Mitsubishi Securities, Cleveland Golf, Stanford University, the University of Waterloo, TU Wien, Cornell University, the State University of New York, and the University of Notre Dame, covering sectors such as automotive, aerospace, robotics, electronics, defense, energy, financial services, entertainment, and academia. With Toyota, Maplesoft founded the Plant Modeling Consortium to promote the development of new design techniques for automotive and related industries.

About Cybernet Systems Co., Ltd.CYBERNET SYSTEMS in Japan provides world-class solutions and services in the CAE and IT areas. For more information, visit www.cybernet.co.jp/english/.

www.maplesoft.com

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