Formula Student: FSUK 2016

The Southampton University Formula Student Team has worked all year to produce Stag 3, its 2016 Formula Student contender. With the lightest, fastest, and most advanced vehicle that the team has produced to date, we went into the summer with high hopes of a good finish at the events.

The Silverstone event was our best ever finish in the UK, and then strong performance in the dynamic events in the Czech Republic led to a 14^th place finish in a European event. Things did not go entirely smoothly along the way, but overall the results are just reward for the efforts of the team in 2016, and provide a very strong starting point for the 2017 car.

This article covers the manufacturing and logistics that have gone in to getting the car ready for two events, and some of the work behind the scenes which is already going on to prepare the team for the 2017 racing season.

Stag 3 at FSUK

The Build-Up

Manufacturing of the car started early in the year with the chassis, and continued in earnest at Easter with a big push on suspension, aerodynamics, and drivetrain components. The process was more carefully scheduled and controlled this year, learning from the mistakes of the previous year.

A list was kept of all of the components which needed to be manufactured, along with the processes required. This optimised our use of resources, so that as soon as a tool or machine became available it could be used.

We have a significant restriction in our build because we are only permitted to use power tools inside the university workshops, which are open 8-4:30 five days a week. This time forces us to be careful about planning machining operations and preparing materials and templates so that we can jump on and get the job done as soon as quickly as possible.

The build was paused during our exam period in May, and resumed at the start of June. A number of issues were found with the car when we came back after exams – fresh eyes and a break are always recommended because it is very easy to get tunnel vision on certain issues. We had a lot of work to do before the launch of the car at the University’s design show in the middle of June.

Due to conflicts with the university’s Eco-Marathon team, a number of parts which had been outsourced to the EDMC were over a month behind schedule arriving. Let that be another lesson – avoid scheduling conflicts and communicate with people who are sharing the same resources. It emerged that in order to present the car in a ‘mechanically complete’ form, we would have to improvise some uprights. The geometry of the uprights is such that this is not an easy task.

In the space of around three hours, MDF uprights were designed, laser-cut, glued together, and assembled to the car. We had no idea whether they would hold the weight of the car, but 6mm MDF seemed to be pretty strong.

Stag 3 after launch. The wooden uprights and cling film tyres are clearly visible.

The car was painted in the evening and then assembled, from the chassis outwards, overnight. This was the first time that the suspension had been bolted to the car in full, and it was testament to the massive improvements in manufacturing processes that it slotted into place first time. The car was packed up and taken to the design show in the morning, and covered in a delightfully coloured tarpaulin ready for launch.

The Launch

The car was launched at the opening to the university design show, which is a major attraction to business, industry, and academia. The opportunity to present the car to a distinguished crowd opens the team up for praise and criticism in equal measure – plenty of photo opportunities and people keen to get a look, but also lots of questioning from those keen to challenge some of our design decisions. This makes for good practice for the design presentation itself.

The team presenting Stag 3 at the University Design Show

As the first year that we have had wings on the car, there was plenty of interest in the aerodynamic features of the car, along with several comments about the carbon suspension and the cling film wrapped around the tyres to protect the rubber. Nobody mentioned the wooden uprights…

The launch event was very successful overall, beating previous years where we have struggled to get a complete car out on show. The interest in the car was very encouraging, and the work done to get the car mechanically ready well in advance of the race season proved to be very beneficial.

FSUK

Over the next few weeks, several more long shifts were pulled to get the powertrain and electronics ready for competition. The final few outsourced components trickled in and were assembled onto the car; the MDF uprights were replaced with their aluminium alternatives and the spare set of wishbone inserts arrived ready for manufacture of backup suspension.

The last remaining part to come back was the throttle body – a fairly critical part of the whole intake system. While waiting for the new intake system, we tested the car with our intake from 2015. The 2015 intake didn’t meet 2016 regulations, so could only be used for our testing and would have to be swapped out before the event. The testing was very successful – the car was quick, seemed to be reliable, and didn’t exhibit any major mechanical flaws after the shakedown.

Testing continued for a few days to stress the components repeatedly – brake tests and acceleration runs were practiced to put the suspension and powertrain systems at full load. Both responded fairly well, so we took the car to Silverstone with high hopes of a good result.

Stag 3 parked outside the R J Mitchell wind tunnel at Southampton University

The intake was finally finished on the Thursday of the event, so it was driven up separately and assembled on to the car at Silverstone. In the process of changing the intake, however, we discovered a number of metal components in the sump – never a good sign. It emerged that these were parts of the oil pump, which had failed at some point during testing.

We acquired a new oil pump from our spare engine (in Southampton) and fitted it on Friday, eventually getting through technical scrutineering late that afternoon. We moved on to the noise and brake test on Saturday, but had trouble getting the engine started. We continued to tweak the engine mapping, to try and get the engine to start, but it was never running for more than a couple of seconds at a time… and even then, it needed the throttle fully open to idle.

Despite spending all of Saturday and most of Sunday trying to get the engine running, it still wouldn’t cough in to life so we couldn’t pass the noise test. After getting the car back to Southampton, it emerged that the oil pump failure had caused the piston rings to melt, essentially writing off the engine. It was difficult to tell whether this failure had occurred in testing or at the event, but nonetheless it was clear that we were going to need the spare engine for our next event.

Although we didn’t pass scrutineering, the event was positive for a number of reasons. Firstly, we achieved our highest ever points total and highest ever finishing position at FSUK, courtesy of excellent scores in the design and business presentations. The team is getting quite accomplished at the static events. Secondly, one of our team members, Alvaro Sanchez Vela, was selected for the ‘Most Valuable Team Member’ award. It was absolutely deserved as his dedication to the team this year has been second-to-none.

FSUK was won in the end by Rennteam Stuttgart – a historic win for a combustion car in the era of electrical dominance. This followed the disqualification of a number of top electric teams for a variety of infringements, including aerodynamic exclusion zones (Delft) and exceeding power limits (Zurich). The lesson taken from the event is that speed is one thing, but that taking care to meet the regulations and design within the limits of the rules is part of the challenge. The Deflt team walked out of the awards ceremony as a protest against their disqualification, attracting much disdain from the remaining teams. The spirit of the competition is just as important as ever.

FS Czech

After Silverstone, the team returned to Southampton to prepare for the event at Autodrom Most, in the Czech Republic. In addition to changing the engine and properly fitting and testing the as-yet untested intake system, more dynamic testing was done. This revealed some weaknesses in the lower wishbones – they were clashing with the tyres due to rear toe compliance, leading to the press-fit bearings coming out of the inserts.

Repairs were made to the wishbones using the spare inserts, and the toe compliance was given a temporary fix. After a little more testing, the car was ready to travel to the event. Transport was courtesy of one of the university’s UAV support vans. This was offered free for the whole week of the event, giving us a base which was the envy of the paddock.

Building on our results from Silverstone, and with two weeks of testing offering much better reliability, we started all of the dynamic events. A 14^th place finish was just reward for the team’s efforts this year. Unfortunately, a brake issue meant that we couldn’t finish the endurance, and we could have finished even higher up the field.

The wet conditions on Friday gave us an opportunity to test the car in more slippery conditions. Our drivers gave the crowd plenty to cheer about, with a number of pirouettes keeping the observers entertained. We also set some very competitive times, proving that all of the work done this year to improve the vehicle performance has paid off, and we have a very fast baseline to work from for 2017.

Wet conditions at Most gave us an opportunity to test the car in low-grip conditions.

2016 Handover

In the lead-up to the events, a huge handover process took place between the current committee and the next committee. The incoming team were elected around May, and since then I have worked on a handover document which explains the processes used to design and build the suspension system. It also covers a lot of the problems that have occurred in 2016, and offers suggestions to improve this for 2017.

Also included are walkthroughs of all of the tools and software we have used this year. Any scripts and code which has been written was documented and included, so that there is a reference for any future group leaders to refer to if they need to use the software or experience problems with it there is a guide which will allow them to fix it.

Recommendations are made within the document, and suggestions of areas to focus on for improvement are listed. However, there is a limit to the amount that can be transferred. Specific areas to change, blueprints and brand new designs, and direct instructions for the 2017 season are avoided. This both encourages the new group leaders to take ownership of their own design, and forces the information to be relevant for any year in the future of the team.

No such thing as ‘too much information’…

The document stretched to well over 50 pages, and was handed over with all of the documentation, software, and CAD files we have developed this year. The hope is that the new group leaders will be able to use this information as a starting point, and then take on their own ideas to develop and produce new concepts.

I would recommend writing something like this to every group and team leader in the Formula Student world. Knowledge transfer between years is vital to the success of the team over multiple years. Writing things down also reinforces the knowledge that has been acquired during the year; similarly, documenting code and cataloguing content produced during the year encourages it to be written well and produced carefully in the first place.

The handover process also included a number of meetings to pass information through face-to-face, and this form of knowledge transfer should be encouraged as much as possible. It allows ideas to be discussed, and gives more context to the suggestions that are made. Demonstrating how to use tools is more effective than writing a user guide, so as far as possible this is the approach that should be taken.

With the amount of information that has been passed on to the 2017 team, as well as the quality of the car to be used as a starting point, the 2017 season should be by far the best yet for the Southampton team.

Active Suspension: Kinematics and Control Part 2

The previous article in this series detailed the principles behind our suspension modelling and the way in which we will go about designing the system. The development of the system is intended to be a two-year project, with much of the preliminary work done this year before a system is designed from the outset for competition in 2017.

Over the last few months, in parallel with the design of a passive system for 2016 competition, we have built up the model. This has helped us to validate the design and validate the model simultaneously; this year’s geometry is a comprehensive set of coordinates that can be used for testing.

The development of the model has presented some interesting challenges, and one in particular is how to actually define the motion of the suspension. There are many linkages which all need to move synchronously and as a result the motion is nonlinear, with components of rotation, translation, and occasionally twist in the parts.

We also have a very cool way of integrating the system with our CAD work to streamline the design process.

We can see an output of how the system looks as it moves.

Dynamic Suspension Model

The custom dynamic model has been developed and refined to represent the movement of the suspension. Understanding the way that the suspension linkages move in tandem is key to controlling this movement. In particular, the motion of the push/pull rod in response to vertical suspension travel needs to be known.

The sensors for the suspension will be mounted on the pull rod or rocker. If we are to properly control the vertical position of the wheel, we need to know how the vertical position is related to the push/pull rod travel. We also need to know how to work the system in reverse, so that the actuator can be positioned or forced as required.

The dynamic model is the first step towards a full implementation of a kinematic model, which we can use to specify the forces required in the actuator. There are two main ways in which a system can be developed, and each has its own benefits. We are using a bespoke model programmed in C#, which will allow event based and functional programming as required.

Vector Model

The first option for implementing a model to investigate how the suspension travels is to define the position of a single point, and solve all of the contact constraints in the system as this point moves. Since we are interested in the motion as the suspension travels up and down, it makes sense to move the contact patch in the first instance.

All of the points in the car are defined using XYZ coordinates, which means it is trivial to generate and manipulate vectors in the suspension. If the vectors defining all of the points are used correctly, it is possible to calculate centres of rotation and motion paths.

The contact patch is rigidly fixed to the upright, so the motion conducted by the contact patch will match the motion of the upright. The most common way of implementing this motion constraint is to rotate all parts by a very small angle around the same axis. It can be shown that this maintains the shape and internal dimensions of the system.

The axis of rotation is determined as the axis normal to the forced direction of motion of two components. For a double wishbone setup, the axis of rotation is equivalent to the instant centre of rotation in the system.

Once the upright has been moved in this way, we need to find the new position of the steering, pull rod, rocker, and spring. These are all implemented in a similar way. The constraints are the fixed link lengths of the steering arm and pull rod, and their corresponding fixed ends. Once the position of the upright axis is defined, the steering arm upright end can only move on a circular path around the upright. It can also only move on a sphere, centred at the end of the steering rack.

Resolving these two constraints gives only two points in space that the upright pickup can be located. We find the location of the point which is closest to its previous location, representing a smooth motion, and then rotate the upright around its axis until the steering pickup point meets the required location.

Code used to find the location of the steering pickup on the upright. It finds the intersection of a sphere and a circle.

The pull rod is similar – the rocker pickup point can only move on a sphere centred at its pickup point on the lower wishbone, and a circle around the centre of the rocker mounting on the chassis. Between these two points, we can find the location that it must have moved to, and rotate the rocker until the points match. Once rocker rotation is known, the spring length can be calculated, and the position of any active actuator can be determined.

Once all of these relations are defined, it is comparatively easy to run a sweep from the contact patch end and find the positions of the actuator, but just as easy to run the sweep in reverse, as we require.

If the system is event based, so that any change to a coordinate forces update of all of the other relevant systems, it becomes very easy to implement steering, bumps, and move towards a kinematic model which evaluates suspension travel in response to forces.

Equation Driven Model

The second method is to encode all of the above constraints, on fixed positions and link lengths, into a single function which defines the way that each point responds to motion of another. This equation is re-evaluated for each point every time the system is moved.

The motion of all of the points on the upright is governed by the intersection of their possible motion paths, as before. However, rather than solving all of the constraints as the parts move, and adjusting the positions accordingly, the equations handle the positioning, which makes each individual move more computationally efficient.

It is also trivial to adapt the equations to deal with forces if necessary, because the geometry and travel is already in place. This may simplify later stages of the calculations and programming.

More in-depth studies could be conducted, or more iterations run in each sweep, to reduce the accumulation of positional errors. However, it is not possible to reverse this method as easily as the vector method. It is a trade-off based on what we expect the system to do, and the resources that will be available to complete the tasks.

SUFST Suspension Model

I chose to implement a vector-type method in the SUFST suspension model. This means it can cover all forms of steering sweep, suspension travel, and active suspension modelling if necessary. The kinematic analysis will have to be handled separately and at a later time.

This is not to say that the equation driven model is inherently worse, because it is very effective for certain scenarios. The choice for our model is based on the most effective system for our particular situation and design brief.

The reference points used on the front corner of the suspension wireframe model.

CAD Integration

One of the neatest parts of this model is the integration of the suspension geometry with

our SolidWorks models. In a couple of clicks, we can export the coordinates of the suspension geometry from our CAD wireframe model and import them into the suspension model. We can sample a design iteration in around a minute, allowing us to run through multiple design changes very quickly if necessary. For optimising things like the Ackermann steering, rocker motion ratios, and dynamic camber change – all of which can be assessed through the suspension model – this is a very valuable tool.

It is done through the use of VBA macros in the SolidWorks program, and the location of reference points on the critical suspension nodes in the sketch. The macro scans for a specified reference points in the suspension setup, and measures their location relative to the origin to get the XYZ position. This is written to a csv file, along with an identifier for the point.

Or they can have additional information specified, with the XYZ coordinates tabulated.

The coordinates can be exported on separate lines

 

 

 

The C# program can read these csv files and load the coordinates directly into its model, overwriting any coordinates it had stored but maintaining other system parameters and settings. Since no calculations are performed in the system until we specifically move a part, there is no need to regenerate equations at this point – configurations can be freely swapped to investigate the effects of each.

The macro has been written in such a way that the output of the file can be modified very easily. We can set the coordinates to be output in just about any format, which means they can be imported directly into any program – Adams, other proprietary systems, our own system, Microsoft Excel, etc. – as and when we need them. The use of simple macros in this way has massively streamlined our design process and will prove useful for future years designs too.

Further Development

The next steps will focus on implementing an actuator into the system, and quantifying the relationship between actuator position and wheel travel. This is likely to be non-trivial due to a variable motion ratio as the rocker rotates.

Load transfer through the system will also be investigated to see how the actuators affect load transfer and peak load on components.

We are also in the build phase of the 2016 passive system – parts have been sent to manufacture ready for assembly at the same time as the chassis – and updates on that will follow soon.

Formula Student – Suspension Design

The suspension on the Formula Student Car

On Thursday 19^th November, I will be delivering part of a presentation by Southampton University Formula Student team. We are holding an event for IMechE members, university students, and staff, describing the processes undertaken to design, build, and race a Formula Student car. More details about the event can be found here.

My section of the talk will cover the design and modelling work required to produce a working suspension system. Putting together the talk has been a great opportunity to focus some of my thoughts from the last few weeks. This article covers the design process in a little more detail than I will have time to go through in the talk.

The Challenge

The first thing to consider when designing any part, component, system, procedure, or assembly, is the target outcome. This is the driver for all other design decisions. When we build a Formula Student car, the target outcome is something very simple: winning.

This target outcome is then broken down into smaller targets, until we reach a series of aims which form the design brief of the suspension system. That process normally happens automatically, through a series of highly developed engineering thought processes, but it is important to take note of nonetheless. For us, the first stage of breaking down the ‘winning’ criterion is to split out three separate design philosophies – safety, reliability, and time.

First of all, the car must be safe, to protect any driver and any marshal or spectator if things go wrong. The car must pass scrutineering in order to race, and in order to pass scrutineering it needs to be safe. Motorsport is dangerous, but all reasonable precautions are taken to minimise the risk to spectators and competitors.

The car also needs to finish the race. Not to be overlooked, this criterion requires that the car can last, unassisted by any mechanic or marshal, for about 30 minutes of flat-out driving. The magnitude of that challenge will become clear later, but suffice to say it puts significant constraints on the design process.

Any part that is put on the car is there for at least one of these three philosophies, often combining all three of them in order to come up with an optimum design. The third challenge, time, is by far the greatest avenue of development and consumer of design hours.

Time

To win any dynamic event means finishing it in the shortest possible time, and, as was realised long ago by a foolish hare, that means maintaining the highest possible average speed. We can investigate the course that we will race on to put this in context, and to determine what maintaining a high average speed requires from the car.

The track on which Formula Student UK 2015 was held (Credit: Formula Student)

The Formula Student endurance and sprint track is an autocross circuit, with slaloms, chicanes, and hairpins interspersed between short straights. The net result is that we will spend a lot of time going around corners, and a lot of time accelerating away from corners and braking into corners. To win, we need to maintain the maximum acceleration in the appropriate direction – something Peter Wright of Lotus F1 famously stated in the early days of F1.

We design a car which is very light, very short, very wide, and as powerful as the regulations and budgets allow, and the net result is a car which is optimised for going around an autocross track quickly. A low weight means that the available forces are put to maximum effect generating accelerations. A low centre of gravity, wide track, and short wheelbase allows the car to generate the maximum possible yaw rates and lateral accelerations, getting around corners quickly, and the power-weight ratio is better than anything which isn’t a supercar.

Performance

The time constraint on our vehicle has now become a performance target – our cornering and acceleration rates characterise the car’s performance, and the car’s performance needs to be increased as much as possible.

The current world record for an electric car’s 0-100kph time is 1.779s, and it is held by

The Saturn V rocket launch (Credit: NASA)

Stuttgart’s Formula Student team. The acceleration during that run is an average of over 1.5 times the force of gravity, which means the car will out-accelerate anything on two wheels or four wheels that isn’t designed for a drag strip. If lined up side-by-side, it will beat a Saturn V away from the lights, although if you’re planning on going to space or racing your Formula Student car again, this experiment is generally ill-advised.

Eurofighter Typhoon at Goodwood 2014 (Credit: GRRC)

The cornering numbers are even more impressive. Formula Student cars, thanks to the short wheelbase and low weight, achieve yaw rates of over 70 degrees per second. This is faster than anything on four wheels, including go-karts, anything on two wheels, and even faster than the roll rate of a Eurofighter Typhoon.

Design

When it comes to the specification and design of the suspension system, all of the comparisons and superlatives go away. We instead turn to the tyres, and a graph known as a traction circle, or a g-g diagram. This graph shows the maximum possible force available from the tyres in any direction, normalised by the vertical load. Our aim for the suspension is two-fold – to stay on the very edge of this circle for as much of the race as possible, and to maximise the size of the circle by keeping tyre parameters in their optimum conditions.

The traction circle, or g-g diagram, for our car

The first of these points is the reason we have suspension on the vehicle at all. To help the drivers stay on the limits of friction at all times requires a consistent and predictable car, and requires the car to not be unsettled by bumps, jolts, and accelerations from the vehicle itself. The suspension will compress and rebound in order to keep the chassis as level as possible, absorbing bumps and jolts and dissipating the energy in dampers so that the tyre loads are smooth and continuous, maintaining traction with the road surface for the maximum possible time.

The second of these points is massively complicated by the fact we have suspension; the fact that the wheels move relative to the chassis means that the tyre parameters – camber, toe, contact patch area, slip angle, slip ratio, and vertical load – are all continuously changing and highly variable.

Most Formula Student cars use a double-wishbone suspension setup and coil-over-dampers. This setup is a proven, effective way of transferring loads and providing adjustability in the suspension, while maintaining independent wheel travel on all four corners to absorb bumps. The layout push/pull rod system and spring/damper arrangement is then chosen to make the handling consistent and predictable, so that the driver can drive to the maximum of the circle at all times.

To try and optimise the second point requires delving deeper into the tyre parameters. Tyres will provide different amounts of longitudinal and lateral force depending on their alignment with the road (slip angle), angle to the vertical (camber), pressure, and vertical force. To a greater or lesser extent, these are the parameters which it is our task as suspension designers to keep in their optimal performance window.

To do this, a tyre model is developed. For us, this means taking raw data from rig testing and analysing it to create a model of how the tyre behaves under different conditions. In our case, we used tyre data provided and developed MATLAB scripts to extract various parameters and trends. This involves selecting appropriate data points and plotting the relationship between one parameter and another, by making educated guesses about what could and could not affect each parameter.

The trends we are interested in are the ones which show how normalised lateral and longitudinal force vary with the above parameters, since these normalised forces are what make up the traction circle. To maximise the circle size, we need to maximise these parameters. Once the trends have been characterised, we can find the parameter values at which the maximum points occur.

Thus, the challenge has been further reduced into maintaining as close to optimum parameter values as possible. To do this, we use a combination of further models. We model the vehicle in Adams, to see how the vehicle accelerations are likely to change during particular manoeuvers on track, and we use a bespoke model, developed in-house and detailed in other posts, to see what these accelerations translate to in terms of suspension forces and displacements.

There is some crossover between these models, so one can be used to validate the other. This validation is very important because the whole process is built on assumptions which may or may not be valid. Understanding how the model could be wrong is just as important as understanding the results it provides.

Finally, with our ideal parameter values and the variations in them identified, we build a wireframe model of all of the suspension nodes. All of the suspension positions can be defined using solely the parameters we have optimised for the car, and as such once the parameters are defined, the suspension design comes together quite quickly.

A SolidWorks wireframe model of the suspension system on the car, fully parametrically defined in terms of optimum suspension setup.

To actually keep these parameters as consistent as possible requires modifying swing arm lengths and instant centre locations, and setting geometric roll centre heights and anti-pitch features. These are all numbers which relate loads on the wheels to the behaviour of the chassis. We also set ideal ‘static’ values of the suspension setup, so that when the car is finally built, everything is in place and adjustments can be used for fine-tuning.

Using our model of the suspension, we can build components to specified sizes, design the shape of rockers and uprights in line with the dimensions required for the optimisation process, and specify the stiffness of springs, dampers, and anti-roll bars to deal with the expected loading conditions adequately.

Validation

There is an extensive validation process to go through once this has been completed. In particular, the suspension design will be passed back through our bespoke model to evaluate the loads that will be carried by each component, and these components will be tested using a combination of physical testing and finite element analysis to ensure that they are strong enough.

Finite Element analysis on a rocker of the car

The model will also go back into Adams to predict vehicle behaviours and ensure that nothing has changed since the design was specified, and it will be tested in lap time simulators so that the parameters which remain adjustable – camber, toe, spring rate and tyre pressure – can be chosen appropriately for each of the different events that we will compete in.

Modelling

The word ‘model’ has been mentioned a lot here, and for good reason. Nothing that we have done to design the suspension has gone anywhere near the physical car – since it has not been built yet. We cannot build the car before it has been designed, but more than this, the design has been a process entirely driven by analysis of data and equations.

The design process has been, in this respect, entirely mathematical, based on principles which are universal. The work we have done could be applied to any Formula Student car, or further, any component in any location in the universe.

Models are the present and the future in engineering, and they are developed out of mathematics which is universal and fundamental. I find the idea that our perception of a Formula Student car can be reduced to pure mathematics very exciting, and it is what drives my curiosity to understand more about the world.

More Information

To find out more about Formula Student, the Southampton Formula Student Team, and the work that is going on behind the scenes in the team on a regular basis, see the links below:

• Formula Student: http://events.imeche.org/formula-student/
• Southampton University Formula Student Team website: http://www.sufst.com/
• Updates on Formula Student from this blog: https://amccormick21.wordpress.com/category/formula-student/

Active Suspension: Kinematics and Control Part 1

Having previously modelled a potential active suspension in a very simplistic, static way, and proved that it will work, the next challenge is to accurately model the system dynamically. This will lead to fine-tuning of the control algorithms and more detailed predictions of its responses to different stimuli.

Modelling the control of the system, and the way that it interacts with the rest of the car, is no simple task because there are a series of mechanisms between the chassis and the ground which all require their own model. The first step modelling the system dynamically is to build these models and see how the suspension will work in principle.

Modelling the geometry of the system in SolidWorks

Conventional Suspension Modelling

Any active suspension system implemented on the Formula Student car will be in addition to a conventional system, so modelling the conventional system needs to be done first before the effect of the active suspension is added. This involves modelling every component that links the chassis to the ground.

These models will contain information about the geometry of the system, and the forces and loads carried by the linkages. Some parts will be purely geometric, while there are other models which will require parameters to be specified, such as the spring rate or the gearing of a system. In essence, for the whole car to be accurately modelled, each component within it must be modelled along with the relations between these parts.

There are three different classes of model. Firstly, there are the geometric models which are used for positioning and calculating motion paths. Secondly, there are models which are related to the way that forces are transferred through the system and between linkages. Calculating the forces in each bar has many advantages including optimisation of the structure and prediction of failure modes, but it will also be used for calculating the accelerations (and therefore positions) of all of the components dynamically. The third type of model is a dynamic model, where the parameters are a function of time. It will describe how the system behaves dynamically, and requires the static positions and predicted loads to calculate how the suspension will respond.

Geometric Models

The first model to be built is the wheel model, which specifies things like the wheelbase, track width, wheel diameter, and unsprung mass. This defines the position of all four corners of the car, and the size and shape of the footprint. The unsprung mass will also be important when it comes to modelling the way that the suspension behaves dynamically.

The wheel is connected to the chassis via six linkages. Four of these are part of the A-arms, or wishbones, and then there is a pull/push rod and a steering arm or toe link. The wishbones define the motion path that the wheel takes as it travels vertically, defining things like the roll centre and the instant centre. The pull/push rod controls the vertical position through a rocker linked to a spring, and the steering arm is connected to the upright to control the wheel’s position around the steering axis. The wishbones, and steering arm are purely geometric models, but the pull rod is more complex and is a hybrid of the geometric and kinematic models.

Kinematic Models

A Matlab plot showing how tyre spring rate varies with tyre pressure. Axis values are removed to protect intellectual property.

Kinematic models deal with the way that forces are transferred through the suspension system. Any deformable components, and the links between them, are models fitting in this category. This includes the tyre, which will be modelled as a spring. While the equations governing the spring are trivial, calculating parameters such as the spring rate is not so easy; extensive manipulation of tyre data provided by the manufactures has revealed how the spring rate varies according to a range of different parameters, such as pressure, and the tyre model will also require these parameters to be specified in order to determine the spring rate.

The pull rod and spring are part of the same model, because their displacements and the forces are closely interlinked. In particular, the position and force in one is fully defined by the position and force in the other, so it makes sense to combine the models. The two are linked by a rocker, which controls the motion ratio and relative spring rates.

The motion ratio is the distance moved by the spring for each unit distance moved by the rocker. This is a function of both the radius at which both parts attach to the rocker, and the direction the rod points in; it is based on a triple vector product of the rocker rotation axis, the direction of the rod, and the vector radius of the pickup point. Because it depends on the direction of the rod, it will vary as the suspension travels, which complicates the dynamic modelling substantially. The spring force is multiplied by the motion ratio twice; first the displacement is reduced and then the force itself is scaled, so the force ratio is the motion ratio squared.

The code for calculating the loads in the suspension members.

There is also a kinematic model for calculating the wishbone and steering arm loads. This is based on the solution to a matrix equation which states the force and moment equilibrium cases for wheel. It assumes that the wheel displacement must be held steady, but allows for vertical and lateral forces to be applied at the wheels to see how this affects the member loads. Using this also allows us to see the steady state force in the pull rod, and hence choose an appropriately stiff spring for the static case where the car is resting on the ground.

Dynamic Models

The dynamic models are models where the inputs and outputs are functions of time. The dynamic wheel model calculates the forces on the wheel at any given time as a function of body accelerations and spring positions. These forces will typically be imbalanced, hence accelerations, velocities and positions can be derived from an integral process.

As the position of the wheel updates, the spring position will change and hence the forces on the wheel will be different. In the next round of calculations, this will also affect the accelerations, velocities, and position of the wheel, so that over time the wheel behaviour can be analysed.

The active suspension component adds another level to this. If it is to be controlled as suggested before, based on the wheel position, it too will be a dynamic model. The active suspension control model will be fed the position of the wheel, mimicking the sensor inputs available in the car, and will respond with a command to the actuator.

The actuator force is therefore a function of time, and when it is added to the model, the actuator force will work alongside the spring force to control the position of the wheel. The actuator force will be fed back in to the dynamic wheel model to update the forces accordingly.

A range of different control algorithms can be tested to find the most effective one, defined as the one which produces the least overall unintentional wheel travel. By modelling the system computationally, the controller parameters can be optimised without doing any physical testing. It is also possible that this control model could lead to an unstable feedback loop, but if it does it will be discovered in the code before the physical parts are assembled, allowing time for design changes.

PID Controllers

The actuator force will be driven by a control algorithm which uses the vehicle ride height, or wheel position, as its input. However, purely driving the algorithm based on position is not necessarily effective. More effective controllers can be built which can reduce the overall error in the position by also taking into account the speed at which the position is changing, and the accumulation of errors over time.

This type of controller is known as a PID controller, with the terms standing for ‘Proportional-Integral-Derivative’. Three components make up the output of the controller, based on the sum of a value proportional to the error, a value proportional to the integral of the error over time, and a value proportional to the rate of change of the error. It is also possible to extend this to the second derivative of the error, which in this case represents the acceleration of the wheel, linked to the deficit or excess force provided by the passive system.

The PID controller needs to be tuned, by applying different multiples to each of the terms. Each term has a slightly different effect, and changing the weighting changes the response of the controller. This can be used to iron out high frequency inputs, or to try and pre-empt any significant roll or pitch, and correct before it starts.

Building the Models

There are a range of tools that can be used for this form of modelling. Microsoft Excel is a very powerful tool and is used for validation of the models, along with Matlab. Matlab is well suited to building models such as these, and integrates well with the requirements of the modelling: to perform vector and matrix multiplications and to draw graphs of the output. Matlab also includes a PID tuning library so is a very attractive prospect.

Validating the wishbone load model using Microsoft Excel.

MSC Adams is the industry standard system for modelling suspension systems. This can be used to show how the suspension deflects in response to loads, calculate the loads in members, and specify springs and rockers. It can also optimise these components. However, the support for a user-configured active suspension system is limited.

As a result, a bespoke system may be the answer, written and developed for the SUFST team in C#. This is the type of challenge I enjoy taking on. It will allow the model to be built with only the required functions, which is beneficial when it comes to ease of use and development. In addition, building a bespoke system lends a much better understanding of the way the dynamics work, and can be integrated easily with Solidworks.

The bespoke suspension model can show the geometry of the car projected on to the three main planes. Here, the front and rear suspension layout can be seen based on the 2014 SUFST car

The models are in development at the moment and future posts will show exactly how the dynamic models are used to evaluate and adapt the design.

Active Suspension Modelling

My previous post discussed the potential for implementing an active suspension system in a Formula Student car. Modelling and development has now taken place to prove that the system can work properly, and does provide an improvement over a passive system.

Which Type?

Of the five types of active system discussed previously, only two provided adequate redundancy in the case of failure. These two consist of an actuator in parallel with the spring, and an actuator in series with the spring. Both perform essentially the same task, the only difference being that the parallel system has full authority over position and therefore secondary authority over spring rate, and the series system has full authority over spring rate and thus secondary authority over the position.

The two possible layouts for the active suspension system

The two systems can be customised to provide exactly the same range of functionality when it comes to actually managing the suspension. The differences come in layout, packaging, and failure modes.

The series system requires a rocker at both ends of the spring, with the pull rod at one rocker and the actuator at the other end. The actuator is permanently carrying the full load of the wheel, which could be up to 1000N, as it is acted on directly by the spring. If it fails to a locked position, the suspension continues to work as if it was passive, but if it fails open, the sprung mass will collapse and could drag along the ground.

The parallel system is the opposite – if it fails open, the system will continue to work as if it was passive. A passive system also has the spring and actuator connected to the same rocker at the end of the pull rod, which allows improved packaging. The actuator and spring can both be located outside of the chassis so as not to encroach on driver and steering space at the front, and exhaust, battery, and engine mounting points at the rear.

As a result of the benefits in packaging and reduced impact in the result of a failure, which is more likely to be a failure to an open position.

Implementation

The main ways of powering actuators are pneumatics and hydraulics. However, electromechanical options have recently become more efficient and could provide an alternative. Choosing the actuation medium required a careful study of the weight and cost of systems involving electronics and pneumatics. A hydraulic system was ruled out due to the power loss caused by driving a hydraulic pump from the engine.

It was established that a pneumatic system is marginally lighter, at 3.5kg rather than 4kg, because despite requiring eight solenoid valves, the electromechanical actuators are much heavier. They are also locked unless powered, requiring them to be installed in a series configuration. This leaves the pneumatic system as the only viable way of powering the actuators.

The additional complexity of a pneumatic system is something that will provide challenges during the design, manufacturing, and installation stages, so it is helpful to have clear layout diagrams to show how the system will be installed.

The additional weight is somewhat of a concern – 3.5kg is more than 1% of the car’s total weight, and will have an impact on the handling, acceleration, and braking. The system will have to work effectively and reliably in order to be justified.

Modelling

Now that the system type and layout has been prescribed, modelling can take place. The first step was to create the components in SolidWorks, and build an assembly which accurately models how the components interact. This means ensuring that bearings are correctly mated, and the actuator and spring are installed with the correct spring stiffness and available force. The rocker motion ratio is also chosen based on the required wheel rate and spring rate.

The active suspension design, modelled in SolidWorks

SolidWorks provides Motion Studies – these allow forces to be applied to the components to observe how they respond under load. This is of particular use to the active suspension system: a load can be applied to the pull rod and the actuator, and a spring modelled where the spring/damper is installed. The study can then be run to investigate how the suspension moves over time, and work out what effect the actuator has.

To test a variety of different frequency inputs, the pull rod is set to provide a constant static load, in addition to loads at 7Hz, 0.8Hz, and a ramp. This provides a load pattern as shown. The actuator is configured to respond to these loads in a range of different ways in different tests – more on that in a later post.

The function describing variation of pull rod loading with time, including a graph of how it varies

When all of the force inputs have been defined, the spring parameters have been specified, and the initial position of the system is configured, the study can be run. Here, the study has been configured to track the forces in the pull rod (bottom graph) and the actuator (middle graph). It also shows the displacement of the spring (top graph).

The actuator is switched off half way through, to allow a direct comparison between the behaviour with and without the active component. This is the control in the experiment. Calculations are completed once every 0.025s, or at 40Hz, to try to accurately represent the behaviour of the system.

 

 

 

 
 
 
 As a result of the models, it is clear to see the benefit that active suspension provides – if it is correctly controlled. The top two graphs show a reduced level of overall suspension travel, although there are some spikes on the left-hand one. The lower two, however, barely reduce the travel at all. There are some methods of controlling the actuator here which are not suitable for the car, as they in some cases increase the amplitude of the oscillations. The third and fourth control methods are the most effective at keeping the mean position of the spring constant, thus allowing the spring to deal with bumps while maintaining the level car due to driver inputs.

For now, it is sufficient to prove that the active system works in theory. It responds properly to the inputs and does not tend to cause any spikes that could cause a loss of control. It maintains a stable platform, but leaves the coil spring to deal with high frequency inputs. Having proved that the concept works in theory, the next step is to take it to something which could work in practice. That means designing the system, laying it out, sourcing components, and building the control software. It’s an exciting summer ahead!

Block layout diagram of a pneumatic system (click for high resolution).

Active Suspension – Formula Student

In racing terms, Silverstone is long in the past and the Formula Student team has already moved on to designing for next year. It was always my intention, if I was elected as group leader, to develop an active suspension system for the car.

Why?

Active suspension has previously been used most extensively on aerodynamically dependent cars, such as Formula 1 cars, where providing a stable platform – and crucially a consistent ride height – is key to getting the aerodynamics to work effectively.

In Formula Student, we are not aerodynamically dependent. However, we do see a variation in vertical load in excess of 10% of the weight of the car over the course of a race. The endurance race requires a driver change and will burn approximately 10kg of fuel, contributing to up to a 20kg change in vehicle mass.

We also run on a range of tracks which can be very bumpy – we race on a small autocross track set out on part of Copse corner, crossing onto and off of the track and the pit lane, for example. For our small, light car, the seams in tarmac and the inevitable build-up of debris causes bumps and ridges which must also be negotiated.

To design the car to cope with bumps, which are high frequency oscillations, requires soft suspension. This allows each corner to act individually to absorb the bump smoothly. To control the weight change, which is a low (zero) frequency change, very stiff suspension is needed, so that the car setup does not change significantly between drivers and as the fuel burns off.

Getting a balance between the soft, compliant suspension and stiff suspension normally requires a compromise closer to the stiff end, resulting in poor performance over bumps. Using active suspension, we can let soft springs do all of the work over bumps, and use active control of actuators to maintain the ride height, and setup regardless of the static weight.

We also compete in a variety of different events: the autocross (sprint) requires excellent cornering performance, but the acceleration test is simply a 75m drag race, and requires good traction. Different suspension characteristics are optimal for each, and the ability to do things like raise the car’s ride height while doing the straight line test to reduce drag will help improve our times. Likewise, the skidpan is a figure-eight circuit which we complete against the clock, and controlling body roll to reduce ‘snap’ as the car changes direction is key here.

How?

There are a number of different implementations of active suspension, which I have broadly characterised into five different groups.

1. ‘Fully Active’ actuated suspension: an actuator is installed in parallel to the primary spring-damper mechanism. This is directly linked to the wheel and hence has direct ride-height control through the variation of position. This system is a simple application which is nearly as effective as (3).
2. ‘Semi-Active’ actuated suspension: an actuator is installed in series to the primary spring-damper mechanism. This must act through the spring and thus has direct control over spring rate, but only indirect control over ride-height. It was used by Leyton House in Formula 1 to control their sensitive aerodynamic platform.
3. Active springs: the spring rate is directly controlled using mechanical or fluidic means to achieve similar results to arrangement (2) in a more compact mechanism. This was used by Williams in their exceptionally successful FW14 from 1991 and 1992, and the FW15 in 1993.
4. Active dampers: the damping in bump and rebound is modified by variation of orifice diameter, fluid viscosity, or other means. This cannot control wheel position but can control the rate at which the spring extends or retracts. This is a common system which can be implemented simply, and it is seen on many performance road cars.
5. Full authority active: there are no springs or dampers and the system has full control over wheel position. Lotus exploited this system on their Formula 1 cars in the 1980s with some success.

The intention will be to use either system (1) or (2), due to the comparative simplicity of the mechanical side of system. They have the coil-over dampers installed as a failsafe system so that the car will remain controllable even in the event of a failure. With reliability so critical to the endurance, this is a key requirement.

Further posts at a later date will confirm which system we use, demonstrate proof-of-concept using modelling, and start to produce some designs. Until then, here’s a taster:

Modelling of a possible type 1 active suspension system, including layout and kinematics.

Formula Student UK 2015

Welcome to Silverstone Banner

At the University of Southampton this year, I have been part of the ‘SUFST‘ Formula Student team. We compete annually at Silverstone and this year the event was held from the 9th-12th July. The team is in its third year and continues to grow and improve, bringing in more team members, more knowledge, and more expertiese each year. This year it has also seen the departure of some members to destinations including Formula One teams – testament to the value placed on this kind of engineering challenge by employers.

The Challenge

Formula Student, an IMechE sanctioned event, requires teams from universities to design and build cars from scratch each year. The ‘formula’ is defined by standardised SAE regulations from the USA, modified for European competition in order to suit local racing authority requirements. It is a very open formula with a wide variety of cars competing, with different chassis types, electric and petrol vehicles, and a wide range of aerodynamic assists permitted and racing together in the same class.

The variety and international nature of the compeitition is what draws so many people together to compete. Universities from India and Turkey were present at the Silverstone race, as well as several from Western Europe. The competitiveness drives huge improvements in technology from year-to-year, including a nearly 10% improvement in lap time from the fastest cars this year.

To compete, cars must be designed from scratch each year, and every part must be accompanied by a design report and a cost report. At the event, the design reports and cost reports are presented to judges who assess how effective the reports are at detailing exactly how the component could be made industrially, and use them to make a judgement on the quality of vehicle design. There is also a business presentation, where the teams attempts to gain sponsorship and interact through social media are assessed.

Scrutineering

Scrutineering sticker

Once the judging is complete, cars take part in six stages of stringent scrutineering. Firstly, they must pass chassis inspection, which ensures that the chassis will withstand the loads required in the event of an accident. Technical inspection is the hardest to pass as it checks that all parts of the car conform to the substantial technical regulations document, and are safe and well designed. Once this is complete, a final safety inspection checks that drivers will be safe in the car and that it conforms to local (MSA) regulations in the seat, harness, and driver egress areas.

Three dynamic scrutineering events follow. Firstly, the car is filled with fuel and tilted to 60 degrees to simulate a high-g turn. Fluids must not spill out below 45 degrees, and then the car must stay on all four wheels up to the full 60. The drivers have a lot of fun at this point. Next is the noise test – the car must be below 100dB at idle, and 110dB at 75% of the redline. Often exhaust muffling is required to get the car to pass this point, because the motorbike engines are fitted with long exhausts and large diameter exits to improve power. Finally, the car must accelerate up to speed and lock all four wheels simultaneously through application of the brakes. This is required to demonstrate that the brakes have enough power to stop the car as quickly as possible, and is often the hardest test to pass. The brakes need to be well balanced and the driver needs to be fully committed. It is also the first time the car runs under power at the event, which makes it a stumbling block for a lot of cars.

SUFST 2015

It has been a remarkable year, taking the car from designs and ideas, sketches and concepts, through to a manufactured, working racing car. From paper to track has taken just 10 months, involved nearly 100 team members and many more working to supply the team with components, sponsorship, logistics, and software. It is a triumph of engineering that the team is simply at the event with a car, even before the remarkable achievements and innovations on this year’s car are considered.

Stag 2 parked in the garage

Despite using the same engine and gearbox as in the 2014 car, the total weight was reduced from 282kg down to 223kg – representing over a 25% reduction in chassis weight. This is a huge gain, only possible thanks to the exceptional engineering skills of the team and the dedication to the task.

The Week

The finishing touches to the car were applied at the start of the week in Southampton: final suspension components and driver controls were added. The car was loaded into a van an taken to Silverstone on Wednesday night, while the team set up camp at the Copse Grandstand campsite. A barbecue is the clear choice of dinner for a hungry group of sleep-deprived engineers.

On Thursday morning the garage was assembled and the car unloaded. Work began to prepare the car for scrutineering – completing checklists, checking regulations, and testing components before we were sure the car was ready. Thursday and Friday also host the design, cost, and business presentations. Throughout the car build, each part must be designed and costed accurately and then the resulting reports presented to judges at the event. Marks for these reports form nearly half of the available points at the event, so doing well is critical.

After a fast food tea in Towcester and a night back at the campsite, work continued to prepare the car on Friday. By this stage the exciting bits were going in to place: the throttle, clutch, and the fancy electronics in the steering wheel. The car made it to scrutineering on Friday evening and passed chassis inspection before scrutineering closed for the night. A range of recommendations were acted upon in the evening so that the car was prepared for safety and technical inspections on the Saturday morning.

On the way out of the circuit on Friday night: a good omen. The spectacular setting of Silverstone in rural Buckinghamshire can only be improved by an even more spectacular sky, as the sun sets over Woodcote corner at the North East of the circuit. Red sky at night and the weekend was falling in to place.

Sunset from Battery Bridge at the entry to Silverstone

Another early start on Saturday morning brought the car into the line for the final scrutineering inspections. The team watched eagerly as scrutineers checked everything from bolt lengths to suspension geometry. Then, to complete the safety inspection, all four drivers must perform an egress test: they must exit the car in under five seconds so that in the case of a fire there is no risk of harm. Here, we set a record for the weekend – driver Titas managed to get out of the car in 2.41 seconds, the fastest egress seen in 2015. He had time to get back in before the clock stopped!

Tilt testing: the car is tilted to 60 degrees to ensure it remains stable. The right-hand wheels must not leave the table.

Once the inspection stickers had been added, we were ready to take on the dynamic aspects of scrutineering. Firstly, the car was filled with fuel and all other necessary liquids so that it was ‘ready to race’. Then, it was tilt tested, which was spectacular but was passed without incident.Titas jumped out with a grin as wide as the helmet when we had finished.

Next up is the noise test. Modern road cars have no trouble with this because the exhausts are insulated, silenced, and carefully designed for noise reduction. In Formula Student, power rules all so the exhausts are very noisy and often muffling devices are required. In order to do the noise t  est, however, the engine has to be running (for obvious reasons). This proved to be somewhat of a challenge; due to the air intake design the car was very sensitive to fuel mixture, and required a lot of throttle to idle. It took a couple of batteries to run flat in testing before we managed to fire up, at which point it became clear that we had a lot of noise cancelling to do! A quick trip to some other teams to ask for advice and then some careful exhaust packing did the trick, and we passed the noise test with seconds to spare before the mandatory engine shutdown at 6pm.

With only the brake test remaining, all that separated us from racing on the Sunday afternoon was a bit of suspension setup and a heavy dose of burnt rubber – locking all four wheels simultaneously within a defined area is no simple task. The suspension was designed with adjustability in mind – as such it was very easy to set camber, toe, and ride height to optimum levels for the brake test.

On Saturday night, in stark contrast to Friday, a heavy rainstorm forced us to abandon the garages early and retreat back to the campsite. In the end, the rain passed relatively lightly, but everyone was glad of an early finish.

Sunday morning – race day. We arrived at the track early to get the brake test finished and get prepared for the race. Wheeling the car over there was a real sense of optimism in the team that things would go to plan and we would be in the race in the afternoon. Unfortunately that wasn’t to be – the car had other ideas and broke its diff carriers during the acceleration run.

With limited testing available before the race weekend, such component failures are simply a part of racing and we learn to accept them. While disappointing, the team can take a tremendous sense of satisfaction from the improvements made to the car over the last year. There is much more to do and the focus is already on next year.

An afternoon off gave us the opportunity to take some team photos and watch the endurance event. In a drama-filled afternoon, Bath University combined exceptional driving with perfect timing, completing their 22-lap run just as the rain came down. That left the top universities, Delft, Zurich, Stuttgart and Graz, battling it out over lower placings as they could not match the pace of the Bath car in the dry. Delft still set a fastest lap of the weekend, but the electric car could not maintain the pace and also fell behind Zurich.

When all looked to be settled with just two laps to go however, Zurich ground to a halt on the far side of the track with a faulty isolator switch, handing the endurance event win to Bath, the dynamics win to Delft, and the overall event win to the defending champions from the Netherlands.

While Zurich were crushed by coming so close, many teams were thrilled with their final results. The sense of achievement from everyone in the paddock afterwards was uplifting and genuinely inspiring.

It’s not all about the race

The racing isn’t everything – Silverstone is a chance to go away and spend time with your friends – people who share a common interest in racing. The teams have a community atmosphere and everyone is excited to be at the home of British motorsport.

The best moments of the weekend come from times when we are not preparing the car. On Saturday evening, a pub dinner was called for everyone, at the White Horse in Silverstone Village. Taking a break from the pressure of the event to let our hair down, talk about unrelated subjects, and generally enjoy ourselves led to several entertaining and some very special moments:

Pub dinner!

At this point it is obligatory to shout out to everyone else in the team who has worked so hard to bring this year together. Although it wasn’t the result we expected, it was brilliant fun and these guys are a fantastic group of friends and colleagues.

We have experienced and learned a lot from the challenges this year and next year we will have our strongest team ever. Engineering is all about progress and each year builds on the last to go faster, quicker, lighter, and finish higher.

Next Year

Planning for next year has already started, the team leaders have been selected, and I am delighted to be working alongside Al as suspension group leader. We will be working hard on some new innovations to improve reliability and reduce weight, as well as getting test data off the old car and running some new simulations.

Looking forward, it should be a year where there is plenty of knowledge and experience to build on, and one where we improve the car extensively to take part in some dynamic events and go racing, which, after all, is what we are here to do.

Watch this space for updates throughout the year.