Department of Precision and Microsystems Engineering
Brake-by-steer concept
Steer-by-wire application with independently actuated wheels used for stopping a vehicle
Name: Ing. Bas Jansen
Report no: ME 10.009 Coaches: Ir. J.W. Spronck Ir. E.J.H. de Vries Dr. A. Reedman (SKF) Professor: Prof. Ir. R.H. Munnig Schmidt Specialisation: Advanced Mechatronics Type of report: Master Thesis Date: 04 March 2010
Acknowledgments
For this research project I have been working as an intern at the SKF European Research Centre in Nieuwegein, in the Mechatronics department. SKF provided me with the materials, test facilities and support to realize the steer-by-wire go-kart. I would like to thank Adam Reedman, who has been my mentor at SKF, for guiding me through the entire project. I also would like to thank Frank Sperling, former group leader at SKF, for creating this opportunity to work on a very interesting and fun project.
I would like to thank Dennis van Raaij and Krijn Wielinga for the substantive feedback on the content of my report and for the conversations we had which refreshed my mind and made me continue with the project.
Finally I would like to thank Annelies for the infinite patience when I, again, needed a little more time to complete my work. But now, it’s done!
iii iv Abstract Throughout the years cars are equipped with more and more convenience and safety increasing systems. Examples are power steering, Electronic Stability Program and Antilock Brake System. All these systems improve convenience and safety, but do not have the flexibility of mechanically decoupled drive-by-wire systems.
Before brake- and steer-by-wire can be accepted they need to be as failsafe as their hydraulic and mechanical predecessor. This can be achieved by using redundancy. Another method is proposed here as is brake-by-steer. The braking force, needed to stop the vehicle, is created by turning the front wheels such that the generated lateral tire force works in the longitudinal vehicle direction. With this concept the steering system can back-up a failing brake system without introducing redundant components in the braking system. Visa versa it is possible to steer the vehicle with uneven distributed brake force [10].
Main goal in this thesis is to investigate the possibility to stop a vehicle by turning the tire lateral force into the longitudinal vehicle direction. This is done by turning both wheels extremely in- or outwards. The performance is estimated by setting up a conceptual model that describes vehicle behaviour under large slip angles. Under these conditions the lateral tire force is completely saturated. This behaviour is described with simplified non-linear tire characteristic. The tire model is incorporated in a three wheeled vehicle model, which is an extension of the frequent used bicycle model.
Two brake-by-steer methods are developed. The first is symmetric toe, where both wheels are turned in- or outwards. The second is asymmetric toe, where one wheel is turned to the maximum and the second wheel used for lateral control of the vehicle. The model shows that the lateral behaviour changes drastically. The steering sensitivity is reduced to nearly zero and for some regions steering becomes inverted.
The theory is verified on a go-kart that is modified to a steer-by-wire vehicle with independent steerable front wheels. The mechanical steering system geometry has a large influence on the vehicle handling. The static and dynamic toe angles influence the lateral vehicle behaviour. These conventional settings already reveal part of the behaviour of the brake-by- steer concept. The kingpin angles influence the required steering torque. This input is necessary for the of actuation design of the steer-by-wire system.
The design consists of two wheel actuators and one at the steering wheel to provide a basic sense of passive force feedback. The required actuator performance is based theoretical expectations and measurement data from a separate equipped measurement kart. The major limitation in the mechanical design is the limited space in the small vehicle. A user interface makes it possible for the driver to switch between steering configurations where he can manipulate each wheel independent on top of a conventional steering setting. There is no vehicle state estimator incorporated in the controller. All strange behaviour needs to be compensated by the driver himself.
The results show that the braking performance of the brake-by-steer concept is approximately half of what conventional brakes achieve. This may be enough to stop the vehicle in an emergency situation. Although not successfully measured, the lateral behaviour of the kart did change to inverted steering. The results differ from the theory where the kart specific steering system geometry plays a role. These are not described by the model.
In order to make this system work in a car, the relation between steering angle and vehicle heading has to be restored by implementing a vehicle state estimator in the onboard control algorithm. The tire model needs improvement on describing the lateral tire forces for extreme large slip angles.
v
vi Table of content
Acknowledgments...... iii Abstract ...... v 1 Introduction...... 1 1.1 Steering system developments...... 1 1.1.1 Steering assists...... 1 1.1.2 Steer-by-wire...... 1 1.1.3 By-wire research and commerce...... 2 1.2 Problem introduction ...... 3 1.2.1 Research goal...... 3 1.3 Thesis Outline ...... 3 2 Modelling the Brake-by-Steering system ...... 5 2.1 Tire model...... 5 2.2 Vehicle model...... 6 2.3 Steering system geometry...... 7 2.3.1 Static Toe...... 7 2.3.2 Dynamic Toe...... 8 2.3.3 Kingpin inclination and Caster angle ...... 9 2.4 Brake-by-steering cases ...... 10 2.4.1 Symmetric toe braking ...... 10 2.4.2 Asymmetric toe ...... 12 2.4.3 Braking performance ...... 12 2.5 Inverted steering...... 13 2.5.1 Lateral and longitudinal vehicle force contributions...... 13 2.5.2 Behavior with linear tire model...... 13 2.5.3 Behavior with non-linear tire model ...... 15 3 Implementation on a Go-Kart ...... 17 3.1 Go-kart introduction ...... 17 3.1.1 Steering system ...... 18 3.2 Steering system performance and design requirements ...... 18 3.2.1 Steering wheel actuation design requirements...... 18 3.2.2 Wheel actuation design requirements ...... 18 3.2.3 Measured system performance ...... 18 3.3 Electro-Mechanical modifications ...... 19 3.3.1 Steering wheel ...... 19 3.3.2 Wheel actuation ...... 21 3.4 Control algorithm...... 24 3.4.1 Local control loop...... 24 3.4.2 Global control loop...... 25 3.5 Sensor systems and electrical layout ...... 25 3.5.1 Sensors...... 26 3.5.2 Electrical layout...... 26 3.6 Control hardware and software...... 28 3.6.1 CompactRIO hardware ...... 28 3.6.2 Controller software...... 28 3.6.3 FPGA software...... 30 3.6.4 Offline PC software...... 34 4 Results ...... 35 4.1 Test description ...... 35 4.1.1 Test track ...... 35 4.1.2 Test cases...... 35 4.2 Steering performance...... 35 4.2.1 System identification...... 36 4.2.2 Tracking error...... 36 4.3 Brake-by-steering performance ...... 37 4.3.1 Maximum measured braking performance ...... 37 4.3.2 Estimated performance...... 37 4.3.3 Lateral vehicle stability...... 38
vii 4.3.4 Asymmetric toe ...... 39 5 Conclusions and recommendations...... 41 5.1 Brake-by-steer concept...... 41 5.2 Recommendations & future work ...... 41 6 Bibliography...... 43 A. Go-Kart dimensions ...... 45 B. Measurement Kart ...... 46 a. Used equipment...... 46 i. Data acquisition...... 46 ii. Velocity sensor...... 46 iii. Absolute through shaft angle sensor ...... 46 iv. Accelerometer ...... 46 v. Force sensors...... 46 b. Measurement kart layout ...... 47 c. Measurement kart results ...... 47 i. Steering angle range...... 47 ii. Steering speed and frequency, hard cornering...... 48 iii. Steering speed and frequency, slalom...... 48 iv. Steering torques...... 48 v. Breaking performance...... 48 vi. Summary...... 49 C. Sensor list and layout ...... 50 D. Used materials ...... 45 a. National Instruments ...... 53 b. Maxon Motor ...... 53 E. Steer-by-wire go-kart...... 54
viii List of Figures
Figure 1 Brake-by-steer impression of symmetric toe in...... 3 Figure 2 Slip angle sign conventions...... 5 Figure 3 Tire characteristic, normalized representation ...... 6 Figure 4 Three-wheeled vehicle model ...... 7 Figure 5 Toe angle effect on vehicle handling...... 8 Figure 6 Dynamic toe angles...... 8 Figure 7 Kingpin inclination and Caster angle...... 9 Figure 8 Steering torque for vertical axle load...... 9 Figure 9 Torque for frame twisting...... 10 Figure 10 Brake-by-steer wheel configuration...... 11 Figure 11 Pacejka versus piecewise linear tire model for longitudinal force...... 11 Figure 12 Asymmetric toe...... 12 Figure 13 Braking force over full steering range ...... 12 Figure 14 Inverted Steering for toe in, lateral vehicle force...... 13 Figure 15 Momentum contribution from longitudinal and lateral vehicle forces, linear tire model...... 14 Figure 16 Resultant moment linear tire model ...... 14 Figure 17 Momentum contribution, longitudinal and lateral vehicle forces, non-linear tire model...... 15 Figure 18 Resultant moment non-linear tire model ...... 15 Figure 19 General impression of the go-kart...... 17 Figure 20 Steering system details ...... 18 Figure 21 Steering wheel actuation implementation ...... 20 Figure 22 Motor operating area, steering wheel motor ...... 20 Figure 23 Steering wheel interfaces...... 21 Figure 24 Wheel actuation exploded view (front view)...... 22 Figure 25 Wheel actuation implementation ...... 22 Figure 26 Front view wheel actuation...... 23 Figure 27 Fail safe steering design (top view)...... 23 Figure 28 Motor operating area, wheel motors ...... 24 Figure 29 Control system representation ...... 24 Figure 30 Steering wheel representation ...... 25 Figure 31 Block scheme of haptic control loop...... 25 Figure 32 Electrical layout ...... 27 Figure 33 CompactRIO...... 28 Figure 34 State machine of the software structure...... 29 Figure 35 control scheme and set point selection ...... 30 Figure 36 Test track...... 35 Figure 37 Frequency response of measured and identified system ...... 36 Figure 38 Steering angle behaviour on step input (toe in) ...... 36 Figure 39 Braking performance brake-by-steer,...... 37 Figure 40 Brake force data collection...... 38 Figure 41 Braking performance, wheel positions ...... 38 Figure 42 Inverted steering paths...... 39 Figure 43 Go-kart dimensions ...... 45 Figure 44 Measurement kart layout...... 47 Figure 45 Strain gage and steering angle detail...... 47 Figure 46 Braking performance reference kart...... 48 Figure 47 Sensor electronics...... 52 Figure 48 Steer-by-wire kart ...... 54 Figure 49 Steer-by-wire kart toeing-out...... 54
ix List of Tables
Table 1 Simplified Pacejka coefficients ...... 12 Table 2 Steering system performance original kart...... 19 Table 3 Sensor list...... 51 Table 4 Used material CompactRIO...... 53 Table 5 Used material MAXON Actuators...... 53
x 1 Introduction
1.1 Steering system developments
1.1.1 Steering assists Throughout the years cars are equipped with convenience increasing systems. Hydraulically power assisted steering was introduced in the mid twenties of the previous century. Here, the engine drives a hydraulic pump that provides the power to reduce the steering effort for the driver. Stronger environmental regulations and awareness and the increasing oil prices demand the manufacturers to design better energy efficient systems. A solution for this is electric power steering. This motor will only consume power when power assist is needed [28].
Power steering can be made variable in the amount it assists the driver by applying more or less torque, possibly varying at different speeds. A drawback is that the driver is less 'connected' with the road if high assistance is applied. Also the steering ratio does not change with increased assistance.
ZF Lenksysteme GmbH solved this problem by making the Active Front Steering system [22] [30]. A planetary gear is mounted in the steering shaft. The third exit of the gear set is connected to an electromotor. This system is capable of giving an offset to the steering wheel angle. It provides fast turning at low speed and a stable wheel movement at high speeds.
Next to the development of steering, the automobiles are equipped with a lot of intelligent safety systems. An example is the EPS or Electronic Stability Program from Bosch GmbH [25]. This system takes over part of the control when a vehicle tends to get unstable. With assist of ABS, the Antilock Brake System and Electronic Brake-force Distribution, EBD, it can brake individual wheels and prevent the vehicle from spinning out of control or roll over.
All these systems improve convenience and safety but do not have the flexibility of a steer-by- wire system where steering wheel and wheels are mechanically decoupled.
1.1.2 Steer-by-wire By-wire applications are well known in the aviation world. Slowly they now introduce themselves in automotive designs. The principle behind by-wire is that the mechanical connection is replaced by sensors and electrical driven actuators. In steer-by-wire a set of actuators controls the position of the tires and a motor at the steering wheel provides the driver with the needed force feedback. The program that controls the wheel positions has in many possibilities to assist the driver or completely overrule the driver intentions without the limitation of mechanical coupling of each wheel to the steering wheel. This method also brings cost reduction and design freedom to the car manufacturers. For the driver this means personalized driving characteristics, increased comfort and safety [18] [20] [21].
Steer-by-wire cars are not yet available for the consumer market as the mechanical coupling is nowadays mandatory by European law [29]. To become accepted the steer-by-wire needs to prove itself as failsafe as the mechanical coupled variant. To provide this level of fail safety, critical drive-by-wire components have a level of redundancy since one broken sensor may not be the cause of a defective steering system. A solution is to implement components multiple times, which means back up sensors, communication lines, actuators and a system that detects faults and switch to secondary systems [26][27].
Two new ideas are proposed here that, without additions, increase the level of safety of a drive-by-wire vehicle. The first is steer-by-brake, which is steering by uneven distributed brake force. The principle is similar to skid steer [10]. Here the braking systems can back up a failing steering system.
The second idea is brake-by-steer. The braking force is created by turning the front wheels such that the generated lateral tire force works in the longitudinal vehicle direction and stops
1 the vehicle. This can back up a failing braking system. Combining these two in one vehicle, reduces the level of redundant components in a complete drive-by-wire system.
1.1.3 By-wire research and commerce That by-wire is inevitable shows by the number of research projects and car manufacturers that build concept cars. Linköping University has a four wheel independently steered vehicle Sirius in cooperation with Volvo [4]. Stanford University is already working with their third generation P1 by-wire vehicle together with many car manufacturers [19]. Looking at the commercial businesses shows GM with the Hi-Wire proto type, Nissan with the Pivo and Renault with the Ellypse. Also the car manufacturer suppliers such as SKF, ZF and Delphi provide steer-by-wire solutions for future cars.
Looking at patents concerning independent steerable wheels and combinations with brake functionality shows four interesting patents
Michelin patented an "Active toe adjustment apparatus" [9]. Due to the suspension, braking and accelerating the toe angles of front and rear wheels vary. The active toe is used to assure perfect Ackermann steering under all conditions. With Michelin's invention the toe can be adjusted to the desired angle. This invention is, however, not meant to brake by with steering motion.
Another non-braking system is the patent by Mazda "Rear wheels steering apparatus for vehicles", where the steerable rear wheels have variable toe angles to increase vehicle handling and stability [8]. This is the same sort of system as Quadrasteer by Delphi [5]. Interesting of these systems is that they are applied on the rear wheels, which is allowed by regulations.
ZF Lenksysteme GmbH and Robert Bosch GmbH applied a patent in 2003 where they used a turned wheel as a parking brake [7]. This is a nice extra feature of the brake-by-steer principle, but not the intended goal here.
Delphi Technologies Inc. has a patent from 2004 called; "Control of independent steering actuators to improve vehicle handling and stopping" [6]. In this patent they describe a steering system that is capable of using a steering motion as a backup for stopping the vehicle. Results of the braking performance are very limited discussed.
2 1.2 Problem introduction Figure 1 gives an impression of the brake-by-steer concept. An increasing steering angle will increase the braking force as the lateral tire force is positioned more into the longitudinal vehicle direction. The lateral tire force is created by the slip angle that is forced up on the two tires. A side effect of this wheel configuration is that the lateral vehicle control and stability will change from what is traditionally expected.
Figure 1 Brake-by-steer impression of symmetric toe in
1.2.1 Research goal With the given conceptual ideas the research question is formulated as follows:
Is it possible to stop a vehicle with the brake-by-steer concept, while maintaining steering controllability?
As this idea of braking is relative new, the goal is to set up a conceptual model that can predict the vehicle behaviour. This model needs independent steerable wheels and deal with large slip angles. The concept will be verified on a test vehicle. The basis for this vehicle is a go-kart. This simple structured vehicle lends itself for easy modification and relative safe operation when the mechanical coupling between steering wheel and wheels is replaced by a system that allows independent steering of each wheel.
1.3 Thesis Outline This report continues with the model construction in chapter 2. It describes the tire and vehicle model and the steering system geometry. After these definitions the model is ready to deal with the brake-by-steer cases described in the last part of this chapter. Chapter 3 describes how the independent steerable wheels are designed and implemented in the go- kart on mechanical, electrical, software and system control levels. Chapter 4 describes the test cases with the results from test runs and theoretical model. This report ends with the conclusion and recommendations in Chapter 5.
3
4 2 Modelling the Brake-by-Steering system This chapter describes the construction of the conceptual vehicle model for the brake-by-steer method. It starts with section 2.1 about the relation between slip angle and lateral tire force. This relation is used in the equations of motion for a three wheeled vehicle described in section 2.2. Section 2.3 deals with the limitations imposed by the steering system geometry. With the model complete section 2.4 ends this chapter with describing the brake-by-steer concept. This section looks into the straight forward braking function and the inverted steering behaviour.
2.1 Tire model A wheel can be described as an object with no resistance in longitudinal motion, roll, but will resist movement in lateral direction. This lateral tire force origins from the angular difference of the tire heading and the actual travelling direction, “ V” and “ v” in Figure 2 respectively. This angle is defined as the slip angle α . The used sign convention is displayed in Figure 2.
, u V – Velocity vector α – Slip angle x,y – Tire coordinate system u,v – Local velocities F – Force M – Momentum
, v
Figure 2 Slip angle sign conventions The slip angle is derived from the vehicle heading and the orientation of the wheel. Since both the steering angles and the slip angle will be large, these can not be linearized. The slip angle is defined in Equation 1, where ‘ i ’ can be replaced by left or right wheel.
v α= δ +tan −1 − i Equation 1 i i u i
The relation between the slip angle and lateral force is described by the lateral tire characteristic, shown in Figure 3. There are many mathematical functions describing the tire characteristic. For this project it is important how a tire behaves and not why. Empirical tire models satisfy this need by describing the behavior without physical relation to the tire.
5
1
0.8
0.6 Pacejka Piecewise
0.4 Lateral tire force (N) Lateral C
0.2
0 0 5 10 15 Slip angle (deg) Figure 3 Tire characteristic, normalized representation For a small slip angle the tire stiffness can be seen as a linear function. At larger angles the grip saturates and stops increasing and even decreases. In the brake-by-steer application very large slip angles are applied, therefore it is not possible to use only a simple linear model. The conceptual model build here does not need to describe every detail of tire dynamics. A simplified model will loose accuracy, but gain in simulation ease [33]. For this project a simplified derivative of Pacejka’s Magic Formula [23] and the Piecewise linear model [32] are used. Equation 4 and Equation 3 describe the mentioned lateral force as function of the slip angle
Flat = C ⋅ α Linear Equation 2
C ⋅α, for α < α saturate FLat = Piecewise linear Equation 3 Fsaturate, for α≥ α saturate −1 Simplified Pacejka Fdlat =sin( c tan ( b ⋅ α )) Equation 4
Where for linear and piecewise C is the tire stiffness, α the slip angle, αsaturate the slip angle where the force saturates, Fsaturate the maximum force, and for simplified Pacejka; d the maximum force, c the shape factor and b stiffness factor.
2.2 Vehicle model Simple vehicle models are described by the so called bicycle or single track model. This model is valid for vehicles with a low centre of gravity and a limited roll [23]. The go kart satisfies these requirements. However, the lateral tire forces will, due to the large steering angles, end up in the longitudinal vehicle direction. Therefore the distance between the two front wheels has to be taken into account to describe the vehicle handling, as it contributes to a yaw moment on the vehicle. Adding a second front wheel to the bicycle model gives the possibility to incorporate this effect in the model. Figure 4 shows the model of the three wheeled vehicle.
6 VFL VFR δ FL δ FR
α Left α Right F xLeft F xRight y F L yFR
xi, u i X
yLeft yRight X1 y, v t1 Y i i
VR Vehicle Tire Coordinates Coordinates
α Re ar X2
F yR
Figure 4 Three-wheeled vehicle model
This model is described by the following equations. Here ui and vi represent the longitudinal and lateral velocity tire velocities respectively. The yaw speed is defined as r around the Z- axis. [17][23] mvVrF +=cosδ + F cos δ + F Equation 5 ( ) yFL( FL) y FR( FR) y R m( u −=− Vr) Fsin(δ) − F sin ( δ ) Equation 6 yFL FL y FR FR V ≥0 IrF =cosδ + F cos δ xF +− sin δ + F sin δ 1 t ( yFL()() FL y FR FR) 1 ( yFL()() FL y FR FR ) 2 1 Equation 7 + F x yR 2
This set of differential equations describes the vehicle behaviour on the variable steering angles δ Left and δ Right and vehicle speed V . All wheels in the model do not brake in a conventional manner and are not driven. The rear wheel is not steerable.
2.3 Steering system geometry This section describes the influence of the steering system geometry on vehicle handling. Normally the left and right wheel are fixed by the mechanical linkage. Since this will disappear it, is important to know if and how the steer-by-wire system needs to mimic this behaviour. Next to that, especially the toe angles will reveal the basics on lateral stability as the brake- by-steer manoeuvre is exaggerated adjustable toe.
2.3.1 Static Toe Static toe refers to the angle the wheels make when the steering wheel is centred. The angle of the left wheel is equal, but opposite in sign to the right wheel. When the vehicle drives in a straight line, the created lateral tire forces are in balance. So far there is no difference between toe in or out. Figure 5A shows these situations.
7 Ftire Ftire Ftire Ftire
A. Toe in Toe out
Fy vehicle Fy vehicle Ftire Ftire
Fx vehicle Fx vehicle
Track width Track width
+ + M vehicle M vehicle
B. Toe in Toe out
Figure 5 Toe angle effect on vehicle handling Differences occur when a steering angle is applied. Figure 5B shows the tire forces when the driver steers slightly to the left. Both situations have an equal lateral force Fy vehicle and longitudinal force or drag Fx vehicle . The difference is how the forces contribute to the yaw moment of the vehicle. In the toe-in situation lateral and longitudinal forces counter act each other, whereas in the toe-out vehicle they both contribute to a negative yaw moment. This principle makes vehicles with toe-in stable in straight line driving but sluggish in corners and toe out nervous in straight line driving and sensitive in cornering [35]
2.3.2 Dynamic Toe Next to the static toe, there is also dynamic toe. This is the difference in turning rate of left and right wheel when steering. The most common configuration is positive Ackermann steering. In a corner the inner wheel describes a smaller circular path than the outer wheel. To prevent tire scrub at low speeds the wheels are not steered parallel, but the inner wheel is rotated more such that the perpendiculars of all wheels point at the same point [16].
δ Left δ Right
Figure 6 Dynamic toe angles
8 Next to this quasi static effect, the difference in steering angle has also a dynamic component. In a turn part of the vertical load transfers from the inner to the outer vehicle side, due to centrifugal force. This increased vertical load on the outer tire creates the opportunity for the tire to bare larger lateral forces than the inner tire. This peak force can be increased if the slip angle increases. This is achieved by turning in the tire more. This principle is less common and applied in high slip angle situation, high cornering speeds or low grip roads (dirt and ice) [34][35][36].
2.3.3 Kingpin inclination and Caster angle The steering axis of each wheel has a caster angle and a kingpin inclination, see Figure 7. These angles create arms that together with the lateral tire force and the vertical axle load contribute to the torque in the steering axis.
ykart xkart Vehicle coordinates ztire ytire Tire coordinated ztire zkart zkart
Kingpin inclination Caster angle
Rotation path
Rear view Side view Left wheel Left wheel Rotation path Rear wheel
Lateral tire force Mechanic, point of application pneumatic trail Pneumatic trail Figure 7 Kingpin inclination and Caster angle The static vertical axle load is part of the vehicle mass. This vertical load is supported by the front wheel which rotates around a tilted axis. This causes a torque in the steering axis. Figure 8 shows the relation between the wheel angle and steering torque for the static vertical load.
15 Right wheel Left wheel 10 Sum
5
0
steering toqrue (Nm) toqrue steering -5
-10
-15 -25 -20 -15 -10 -5 0 5 10 15 20 25 wheel angle delta (deg)
Figure 8 Steering torque for vertical axle load When the front wheels are turned they twist the frame of the kart. The required momentum is also added as a vertical axle load. Figure 9 show the momentum when the steering wheel is
9 turned and both wheels rotate with the original steering linkage which is near perfect Ackermann.
600
400
200
0 Torque (Nm) Torque
-200
-400
-600 -80 -60 -40 -20 0 20 40 60 80 Steering angle (deg)
Figure 9 Torque for frame twisting A third origin of changing vertical load is the load transfer due to lateral and longitudinal accelerations of the centre of gravity. Since the height of this centre is very low, this effect is neglected.
The second force which contributes to the steering torque is the lateral tire force. The moment arm consists of the mechanical trail, which is constant and dependant on the steering system geometry, and the pneumatic trail which is variable and non-linear for large slip angles. There are too many uncertainties about the tire - road characteristics that it is not possible to say anything about the pneumatic trail and estimated lateral tire forces.
The last contributor is the torsional tire friction. This torque relaxes when the tire rolls a certain distance and plays a large roll at standstill. This torque is also dependent on the tire - road characteristics which are uncertain.
These torques are transmitted through the steering linkage to the steering wheel in the driver’s hands. This force sensing is important to be able to drive a vehicle [31][38]. An experienced driver can feel that the tire grip saturates by the decreasing steering torque in the hand wheel [24] . When the steering linkage is removed the left and right wheels do not balance each other and the force sensation does not reach the driver. These phenomena need to be implemented in the steering control system
2.4 Brake-by-steering cases Now that the behaviour is defined it is possible to zoom in on the brake-by-steer concept. Two methods are developed to generate brake force and be able to steer, being symmetric toe and asymmetric toe braking. Assuming the heading of the vehicle is straightforward it is possible to state that the steering angle and slip angle are equal.
2.4.1 Symmetric toe braking By turning in both wheels, the lateral tire force is partly directed into the longitudinal vehicle direction, creating a brake force. The forces in lateral vehicle direction are in balance. Figure 10 shows the wheel orientations described as symmetric toe in. Symmetric toe-out means that both wheels point outwards.
10 V V δ Right δ Left
α Right α Left F Lat Tire F Lat Tire
FLateral vehicle
Fbrake
Figure 10 Brake-by-steer wheel configuration The lateral tire force is generated by creating a slip angle. In order to get the lateral tire force work for a longitudinal vehicle deceleration, the steering angle must be large, since: F=sin δ ⋅ F brakevehicel ∑ ( i) Lattire i Equation 8 i= L, R But to maintain control of the vehicle in lateral direction the steering angle may not be to large, since: F=cos δ ⋅ F latvehicle ∑ ( i) Lattire i Equation 9 i= L, R
Most tires reach their maximum lateral tire force is below a slip angle of 15 degrees. A quick calculation shows that at this operating point only 25% of the lateral tire-force is translated into the longitudinal vehicle direction, see Figure 11. For maximum brake performance the tire lateral force needs to be completely saturated.
Figure 11 shows the difference between the Pacejka and the piecewise linear tire characteristic. Multiplying these with the sine of the steering angle, according Equation 8, the difference is marginal. For cases where the slip angle of the two front wheels is large, it is possible to use only the saturated part of the piecewise linear function, which is independent of the slip angle. For the rear wheel it is possible to use a linear relation assuming that the slip angle remains small.
1
0.8
0.6 Force (N) Force
0.4
Pacejka 0.2 sin δ ⋅ Piecewise Piecewise sin δ ⋅ Pacejka 0 0 10 20 30 40 50 60 70 80 90 Slip angle (deg)
Figure 11 Pacejka versus piecewise linear tire model for longitudinal force
11 2.4.2 Asymmetric toe Another strategy to be able to brake and steer at the same time is to turn one wheel to its maximum angle, for the braking force, and use the other for directional changes. The best orientations would be 90 degrees for the braking wheel and a small angle to correct for lateral vehicle forces on the other side.
V V
δ Left α + δ Right Left M α Right F Lat Tire F Lat Tire
x1 1 2 t1
Figure 12 Asymmetric toe Downside of this method is that only one wheel is braking, which means less performance. Advantage is that lateral control remains functional.
2.4.3 Braking performance Figure 13 shows the longitudinal vehicle force over the full range of left and right wheel. The largest forces are generated when both wheels are at the largest combined steering angles.
Figure 13 Braking force over full steering range This plot is made with the following values for the tire characteristic of Equation 4.
Coefficient Value b 8 [-] c 1.4 [-] d 755 [N] Table 1 Simplified Pacejka coefficients
12 2.5 Inverted steering The different brake-by-steer cases have their own braking performance, but the lateral forces are also influenced by these new wheel configurations.
2.5.1 Lateral and longitudinal vehicle force contributions Figure 14 explains what happens with the lateral vehicle force during a brake-by-steer action with a symmetric toe angle of 50 degrees while driving straight. If toe-in is applied point “ A” is the left wheel and point “ B” the right. At point “ 1” the lateral vehicle forces are in balance, there is no lateral movement. When a right-hand turn is initiated the left wheel will move to “A2 ” en the right to “ B2 ”. The sum of the lateral forces now points to the left! Steering has become inverted when looking at the lateral forces. This applies to both toe-in and toe-out.
1000
800 C1 A1 600 A2 400
200
0
-200 Lateral force (N) Lateral
-400 B1 -600 B2 -800
-1000 -80 -60 -40 -20 0 20 40 60 80 Slip angle (deg) Figure 14 Inverted Steering for toe in, lateral vehicle force Taking the longitudinal forces into account shows how toe-in is different from toe-out. The same effect as described in section 2.3.1 plays an important role. When applying toe-in the lateral tire force is partly directed into the longitudinal vehicle direction. The forces of left and right wheel contribute to an overall vehicle momentum. In toe-out the momentum behaves like the driver requests, for toe-in the effect is inverted.
2.5.2 Behavior with linear tire model For the following analysis it is assumed that the initial vehicle heading is straight ahead. The advantage is that the steering angle is equal to the slip angle and this also implies that the contribution of the rear tire can be neglected as there is no sideways motion. Another simplification is the usage of a linear tire model. This can not describe large slip angle behavior, but makes it easier to understand the responsible parts of the overall momentum.
Equation 9 is build up out of the longitudinal part, described by the sinus and the lateral part, described by the cosine part.
1 Σ=−MCvehicle( δ Lsin( δ L) + C δ R sin ( δ R)) ⋅+2 L Track Equation 10 ()CδLcos()() δ L+ C δ R cos δ R ⋅ x 1
Figure 15 shows the effect over the complete steering range for the longitudinal and lateral vehicle forces. The top left part describes toe-out, the bottom right toe-in. The colors only indicate to which direction the front of the vehicles tends to go. There are no actual numbers assigned, as they make no sense using the linear tire model.
13 The longitudinal force contributes the most if the wheel angle is large, dictated by the sine function and the linear increasing amplitude. The region where both angles are equal in size and equal, or opposite, in sign does not contribute to the overall vehicle momentum, indicated with the dashed line.
The cosine function in the lateral part of Equation 10 is large at low angles but the amplitude at a large angle. The overall lateral vehicle force is the biggest if the steering angles are equal in size and sign, as they both work in the same direction. This describes conventional steering. If the angles are their exact opposites the vehicle remains on a straight line. This is the neutral line from the top left to bottom right in Figure 15. Two other neutral regions can be defined where the lateral forces cancel each other out. This is explained by point “ C1 ” and “B1” in Figure 14. Beyond these lines Figure 15 shows that the lateral vehicle forces react inverted, for both toe-in and –out.
Longitudinal Lateral Figure 15 Momentum contribution from longitudinal and lateral vehicle forces, linear tire model
Adding the two effects results in Figure 16. it shows that the inverted region is now only seen in the toe-in region. In the far toe-out region the longitudinal parts of each wheel are equal, a change in steering angle has a direct effect on the lateral vehicle forces which results in inverted behavior.
Figure 16 Resultant moment linear tire model
14 2.5.3 Behavior with non-linear tire model A more realistic behavior is displayed in graph Figure 18. This graph is constructed with the non-linear tire model from Equation 4 and Equation 9. The lateral tire force will now saturate which makes the amplitudes of the sine functions in Equation 10 stop increasing and even decrease for large angles. This means that the longitudinal part has less effect on the overall momentum.
This shows directly in the longitudinal part of Figure 17 compared to Figure 15.
Longitudinal Lateral
Figure 17 Momentum contribution, longitudinal and lateral vehicle forces, non-linear tire model Adding these two effects results in Figure 18. The neutral regions are again indicated with dotted lines. Differences are the sharp edges along the lines of δL, δ L = 0 . The lateral tire force is now at its maximum at low slip angles even as the conversion to lateral vehicle force. Any changes in low slip angle region will cause high changes in lateral vehicle force. The inverted steering range for the toe-in configuration still remains.
Most important difference is the region for toe-out at the top left side. It starts with a small range where steering is still possible, but after the lateral tire force saturates, the gain, between steering angle and lateral vehicle force, drops drastically. At large angles the steering becomes inverted, but with a low sensitivity.
Figure 18 Resultant moment non-linear tire model
15
16 3 Implementation on a Go-Kart This chapter describes how the brake-by-steer system, with independent actuated wheels, is implemented in the go-kart. This vehicle will be the test setup to verify the brake-by-steer concept. It starts with describing the original configuration as the point of departure for the design. After this, section 3.2 describes the new functional requirements of the steering system and needed system performance. Section 3.3 will deal with the actuation concepts where motor choice and transmission design are defined. Section 3.4 looks closer into controlling the position of the wheels and steering wheel. Section 3.5 describes the sensor systems for measuring the vehicle state and describes the electrical layout. This controller hard- and software is described in section 3.6. Photos of the final result of the design are shown in Appendix E.
3.1 Go-kart introduction The go-kart that is used for this project is a standard “Sodi GT2” from Sodikart [11]. In general a kart is a miniaturized version of a car. Specific characteristics of a kart should however be kept in mind as they differ from passenger cars.
The wheels of the kart are not separately suspended. The flat tube frame of the kart acts as the suspension by bending and twisting on variable axle load. Other than in conventional vehicles not all four wheels are always kept on the ground as the deflection of the frame is very limited.
The fixed rear axle implies that the kart has bad cornering behaviour [13]. This is partly solved by the effect the kingpin angles introduce [14][15]. The kingpin makes angles in both the Z- and Y-plane, kingpin inclination and caster angle respectively, see also section 2.3.3 and Figure 20. Due to these angles the frame is lifted upwards where the wheel is turned inwards and visa versa. The overall roll of the front of the kart and the limited frame deflection decreases the vertical load on the inner rear wheel which decreases the effect of the fixed rear axle.
The driver can influence this effect by leaning sideways in a corner. His mass makes up approximately one third of the total mass. In the relative small kart this has a large contribution to the vehicle behaviour, but is very hard to incorporate in a model and remains an uncertainty.
Figure 19 shows an impression of the go-kart and the used vehicle coordinate system and views used in this report. Appendix A shows the detailed dimensions of the go-kart.
Top View Side View
Y Pitch
Roll
Rear View X Yaw
Z
Figure 19 General impression of the go-kart
17 3.1.1 Steering system Figure 20 shows the components of the original steering system. The rotational motion of the steering shaft is translated via the steering rods to the stub-axle on which the wheels are attached. This construction is limits the maximum steering angle by the dimensions of the steering shaft bracket. By decoupling the steering rods this maximum can be increased until the tires hit the tube frame. The steering shaft bracket provides the Ackermann effect by applying non-straight angles.
Ackermann angle
King pin inclination Caster angle
Steering shaft bracket
Figure 20 Steering system details
3.2 Steering system performance and design requirements This section sets the specifications for the steer-by-wire system with independently actuated wheels. The steer-by-wire system should provide similar steering as conventional and provide additional functionality to actuate the wheels independently on driver request.
3.2.1 Steering wheel actuation design requirements The desired functionality of the steering wheel part is to measure the steering angle of the steering wheel as a set point for both wheels. Next to this conventional setting, it should be possible to create additional angle data for each individual wheel to steer them independently.
The second function is to provide a force feedback to the driver to improve drivability [31][38]. The actuator must also indicate the end-stop by an increased feedback force when the steering wheel reaches its maximum angle. From a safety standpoint of view it is important that the steering wheel can still rotate, even if there is no power provided to it. And when, in an error state, the steering wheel actuator counteracts the driver’s intentions.
3.2.2 Wheel actuation design requirements The main function of the wheel actuation systems is to let the wheels follow the desired set point created by the steering wheel system. Each wheel has to be actuated independently.
The position data of each wheel is needed to control the system and can be used to provide a force feedback sense to the driver.
The brake-by-steer concept requires large steering angles. The construction of the kart limits the maximum wheel angle. This means that the new design needs to provide a construction to increase the steering angle range.
3.2.3 Measured system performance The specific performance of the two subsystems is measured in a test setup, described in detail in appendix B. Table 2 shows the results of how the original kart performs.
18
Item Measured at Value Limited by Maximum range Steering wheel +/-85º Steering linkage Left wheel +25, -32º Left wheel +35, -55º Tire to frame contact Turning rate Steering wheel typical 160 º/s Steering wheel extreme 600 º/s Driver Wheel typical 80 º/s Wheel extreme 300 º/s Steering frequency Steering wheel 1 Hz Driver Steering torque Nominal 8 Nm
Peak 50 Nm Steering wheel torque Max 5 Nm Driver Braking force Front wheels 1200 N Tire grip Table 2 Steering system performance original kart The goal of the new design is to perform similar to the typical behavior of the original kart. The required torques have to be extrapolated as the mass of the vehicle will increase by the added steer-by-wire components.
3.3 Electro-Mechanical modifications This section describes the electro-mechanical design for the new steering system. It consists of an actuator-sensor combination and the mechanical transmission from the actuator to the stub-axle or steering wheel. The guidelines presented in [1] and [2] are used for the motor selection.
The best design concept is chosen from different drive concepts and actuator types and worked out in detail. Factors that decide the best design are speed, torque and measuring requirements, consumed space, suitable transmission and robustness, avoiding irreversible changes to the kart, time to design, time to implement, costs and fault tolerance. The following subsections look into the steering wheel design followed by the design for the wheel actuation.
3.3.1 Steering wheel
3.3.1.1 Sensing and actuation The angle of the steering shaft is measured with a magnetic absolute encoder ring. This is mounted directly on the steering shaft which excludes play in the system. Figure 21 shows the encoder ring when extracted from its encoder house where the actual sensor is mounted in. The encoder measures the absolute position which avoids calibrating the neutral position of the steering wheel at each system start.
The feedback force is provided by a brushed DC-motor with gear mounted to it, which is connected to the steering shaft with a belt transmission. The available motor-gear combination, at the manufacturer, exceeds the maximal desired torque at the steering wheel. See Appendix A for the used materials. By limiting the current output of the motor controller, in the hardware, this torque is limited within safe limits. Figure 22 shows that the operating point is well within the motor safe operating area.
Both subsystems are mounted on the same support block and replace the original steering shaft guiding. This makes the design very compact and does not make and irreversible changes to the original steering system.
19
Steering Bearing wheel houses Toe handles
Gear
DC motor Transmission belt
Encoder Support block
Encoder housing Gas tank Steering shaft Encoder ring
Figure 21 Steering wheel actuation implementation Figure 22 shows that the maximum steering rate from Table 2, with a gear ratio of 1:113 this is approximately 11.000 rpm, does not lie within the safe operating area. The limited allowed speed is a trade-off in the design.
Continues operation
Short term operation
Driver safety operation area
Figure 22 Motor operating area, steering wheel motor The belt transmission was quick to design and implement, but has a design flaw. The limited allowed axial load on the gear exit-shaft, limits the tension in the belt and therefore the possible transmitted torque is also limited. The additional bearing in the support bracket did not relief this load enough. A better design would be to support the pulley on the gear shaft on both sides.
3.3.1.2 Toe lever and user interface The independent actuation of each wheel is provided by two “toe-wings”. These are two levers attached to the steering wheel and can be activated while the driver holds the steering wheel, see Figure 23. The angle of the levers is measured with a potentiometer. With
20 switches on the steering wheel the actuation setting can change from symmetric toe-in and toe-out, to asymmetric toe of each wheel independently. Other switches and indicators provide functionality to control the system states, see section 3.6.2 for further details.
Toe wings
EMO button
Switches
Indication LED’s
Figure 23 Steering wheel interfaces An emergency off button is mounted in the middle of the steering wheel. This will shut down the complete system when pushed. This is the only safety related part of the steering design. It is a deliberate choice not to implement any redundant hardware in the system. This makes the system complex and time to design and implement long. The created risks are accepted.
3.3.2 Wheel actuation Each wheel has its own individual actuator which is mounted directly to the steering axis, as shown in Figure 24 and Figure 25. The required speed and torque have a one-to-one relationship to the motor and gear specifications and makes controlling the motor position straight-forward. The design has very little moving parts which makes the design robust. And the motors and transmission are located in a free volume in the kart and to not claim already taken space. See Appendix A for the used materials.
Additional steering range is created by inserting extension brackets in the brackets that hold the stub-axle in the original kart, see Figure 24 and Figure 25. This provides design freedom for the motor–stub-axle interface as it can be designed from scratch and does not interfere with the original structure of the kart. The extension bracket assembly consists of a number of plates with filler rings that is bolted to the kart frame. In this way the original orientation of the steering angle, caster angle and kingpin inclination, is maintained. The front of the kart is lowered slightly, but has no negative side effect.
21 Encoder
Wheel
DC Motor Motor-stub interface
Gear Extension brackets Support frame Bearing
Stub axle
Bearing
Kart frame Extension brackets
Outwards displacement 40 mm Angle sensor Figure 24 Wheel actuation exploded view (front view)
Encoder
DC Motor
Wheel axle Gear
Motor-stub interface
Support frame
Figure 25 Wheel actuation implementation Figure 26 shows the front view of the actuation system. Each actuator is in line with the king pin and therefore inclined inside and backwards. An additional absolute angle sensor is mounted to the bottom of the king pin.
22 Batteries
Actuator
Angle sensor
Figure 26 Front view wheel actuation There is no safety or fault tolerance build into the wheel system to avoid complexity. It has been considered to apply a third motor in between the two stub axles where the steering rods were originally located, as shown in Figure 27. This system, based on the Active toe adjustment apparatus [9] design, is able to rotate each wheel independent and one of the motors may fail, without losing functionality.
Figure 27 Fail safe steering design (top view) Next to available space and applicable linear actuator, a control system, fault detection and intervention program are required to implement this configuration. This is beyond the initial goal and will exceed the available time to design.
The safe operating area for the applied motor-gear combination is shown in Figure 28. The operation point lies within the continues operation area. The short term operating area is limited by the allowed temperature of the windings. The overloud duration for the chosen motor is up to one minute in an ambient temperature of 25º C [12]. The steering-by-brake system will operate in open air, T < 25º C, and under driving wind conditions, therefore the temperature limit can be stretched.
23 Continues operation
Short term operation
Figure 28 Motor operating area, wheel motors This combination will not be able to deal with the extreme high peak loads from Table 2. with a gear ratio of 1:100 this is approximately 6500 rpm. This is a design trade-off. Limiting factor in the motor selection is the maximum 24 Volt that is supplied from two on board batteries. More power full, motors require a higher voltage.
3.4 Control algorithm The control strategy is split up into two parts. The local control algorithm lets the steering wheel and wheels follow their given set point. The global control algorithm ties the two local loops together, where the position output of the first is the set point for the second.
3.4.1 Local control loop
3.4.1.1 Wheel actuation The feedback loop for the wheel positioning is shown in Figure 29. The controller acts on the position error signal to generate a torque on the wheel. This is added to the sum of all other external forces, described in section 2.3.3 . The vehicle state is however, not implemented in the real time controller. Advantage would be that the lateral tire forces and changing vertical axis loads can be estimated and anticipated for, but this would require a sophisticated vehicle model, which is not created to that extend for the modified go-kart. The applied controller is modelled as a straight forward closed loop PD control system acting on a second order plant. The dashed part enclosed by the blue rectangle in Figure 29 Control system representation is not implemented.
Speed Vehicle
Steering angle Steering set point + angle + Controller + Wheel −
Figure 29 Control system representation The controller parameters are partly based on the theoretical estimated forces coming from subsection 2.3.3. The actual system is identified with a chirp signal on the actuator. With the
24 wheels on the ground the system shows to be higher than second order. The high frequency part of the system is not successfully identified.
The input of this system comes from the measured steering signal of the steering wheel. The measurement kart showed that typical steering behaviour has a steering frequency around 1 Hz. This means that any signal much higher than 1 Hz does not come from the driver and does not need to be inserted in to the controller.
3.4.1.2 Hand wheel actuation The hand wheel actuation is implemented as a passive spring-mass-damper system as shown in Figure 30 Steering wheel representation. A larger displacement from the initial centre position results in a higher feedback feel. The stiffness of this system, k, is speed dependent to mimic the effect of increasing lateral tire force at higher speeds. The stiffness and damping factor for this system are experimentally tuned to a “good” steering feel.
γ Tactuator steer angle
k()V
Jtot
d T driver Figure 30 Steering wheel representation The steering angle of the steering wheel is limited by a simulated end stop. The stiffness of the feedback force increases stepwise at the limit angle. This is an indication for the driver that the end of the steering range has been reached.
3.4.2 Global control loop It was initially indented to create a haptic feedback loop. In this loop, schematic shown in Figure 31, the displacement made by the driver on the steering wheel is fed to the wheel actuator. The wheel interacts with the environment, road, and these forces are send back to the driver. With this feedback feel the driver has additional and essential vehicle information.
Driver Steering Communication Wheels Environ wheel channels ment
Figure 31 Block scheme of haptic control loop In conventional vehicles the feedback force reflects the lateral tire forces of the front wheels and indirect together with vehicle speed the heading of the vehicle. The lateral tire forces in the brake-by-steer configuration do not have this same relation for steering wheel angle and vehicle heading. A vehicle state estimator could calculate the vehicle heading on the fly and reproduce the expected feedback force, but this is not implemented in the system.
The driver needs to act on the unconventional vehicle behaviour, for example the inverted steering effect.
3.5 Sensor systems and electrical layout This section describes the complete electrical and software design for the steer-by-wire system. It consists of a real-time controller that processes and stores the data of the sensors in the kart and executes the control algorithms. The sensors need to measure position data
25 for the control loops and vehicle parameters to check vehicle behaviour under brake-by-steer circumstances. Factors that decide the best design are data processing capacity, number of I/O channels, sensor accuracy, time to design, time to implement, costs and fault tolerance.
3.5.1 Sensors The most important sensors are listed here. Table 3 in appendix C displays all applied sensors.
Steering angle The steering wheel angle is measured with an absolute magnetic encoder. It is mounted directly on the steering axis. This sensor is part of a combined sensing bearing unit.
Toe angles The additional data for the brake-by-steer actuation is implemented in the toe wings. These levers are mounted on the steering wheel and are connected to a potentiometer. The toe method can change, by switches on the steering wheel, from toe-in and toe-out, toe left or right wheel in or toe left or right wheel out.
Wheel angle relative The position of each wheel is measured with the encoder that is mounted on the back of the actuator. A design concession made here is that the play the gearbox can not be compensated.
Wheel angle absolute At system start the relative position data from the encoder is calibrated with the predefined absolute position. A potentiometer is mounted to the bottom of the kingpin and measures directly the steering angle of each wheel.
Velocity sensor The velocity of the kart is measured with an optical sensor. It scans the road passing underneath and calculates the absolute velocity in longitudinal vehicle velocity. The lateral velocity of the vehicle is not measured.
Accelerometers Two accelerometers measure the lateral and longitudinal accelerations. The sensors need to be mechanically isolated from the frame to prevent the sensors to saturate on the heavy frame vibration form the engine. The final solution for this was to attach them to the framework supporting the two batteries
A yaw rate sensor or digital compass that provides the heading information of the vehicle would be of great value to make an estimate of the complete vehicle state. Yih added a GPS system to his test vehicle [18]. These sensors, however, are very expensive and not within budget for this project.
3.5.2 Electrical layout All sensors receive their power supply from a DC/DC converter. This reduces the 24 Volt from the double battery pack back to 12 Volt. The motor controllers and the CompactRIO are direct connected to the 24 Volts. Figure 32 shows the layout of the electrical system of the kart. Figure 47 in Appendix C shows the detailed connection of each sensor.
26 Externel Externel Power 12V F11:0.75A F3:0.7A C C V1 V2 Secundary Secundary Power Switch NI cRIO-9004 Controller NI cRIO-9411 NI cRIO-9423 NI cRIO-9474 Analogue ModuleAnalogue Output NI 9263 Analogue Input Module Analogue Input NI 9205 2 2 DI1a 4 +5 Supply Vout Vsup 0 Digital input TTL Module Digital Module Input Digital Module Output 3DI2a 5 +5 Supply Vout 6DI3a 7DI4a 8 DI5a 9DI0b 2 2 DI2 4 DI4 2 AO1 4 AO2 2 DO2 4 DO4 AI0 AI1 AI2 AI3 AI4 AI5 AI6 AI7 AI8 AI9 AI10 AI11 AI12 AI13 AI14 AI15 AI16 AI17 AI18 AI19 AI20 AI21 AI22AI23 & AI24-AI29, AI31 AI30 AIS 1 DI0a 10DI1b 11DI2b 12CommonCOM 13DI3d 14DI4b 15DI5b 1 COM 0DI0 3DI3 5 DI5 6DI6 7DI7 8 NC. 9COM 0AO0 3 COM 5 COM 6 AO3 7COM 0DO0 3 DO3 5 DO5 6 DO6 7DO7 8 Vsup 9COM COM 1 1 DI1 1 COM 1 DO1 Dsub 1 Dsub
nc Vref g_lat tau11 CM CM alpha tau12 g_lon MC11 MC12 MC20 MC11 MC12 LED 1 LED 2 LED MC20 DCDC delta11 delta12 MC12 MC11 MC11 MC12 MC12 MC20 MC20 MC11 MC20 Sym toe S9 S7 S7 P2 P1 S1 S8 Vcheck12 Logging MC20 S15 Omega11 Omega12 F7:0.35A Omega2B
S10 Omega2A Asym toe S2 Asym out S3
SP3 SP3 SP3 SP8 SP8 Log fileLognr. SP8 Invert steer Start button Off switch SP2 SP2 SP1 SP2 SP1 SP1 SP2 SP1 SP1 SP9 SP9 F8:6.3A A,B,I A,B,I 11 A,B,I 12 SP9 Feedback Power Check Power Datron abs V Datron S17 SP7 S18 S5 S19 S4 S21 S6 S20 Gate IN Gate Switch Switch S12 S13 S14 Switch Switch S11 Switch Free AI Free file Lognr. Switch Switch Switch StateIndicator LED { Dsub3 F4: F4: 20A NI9263 NI9263 NI9263 NI9263 NI9263 NI9263 NI9205 NI9205 NI9205 NI9205 NI9205 NI9474 NI9474 NI9474 Motor12 Motor20 Motor11 NI9205 NI9205 NI9205 AO0 COM AO1 COM AO2 COM F5: F5: 20A F6:10A Relay Relay 1 AI19 DO0 AI3 AI11 DO1 AI4 AI12 DO2 AI18 AI5 AI13 EmergencySwitch MC Switch On/Off Diode
Gnd 4 Gnd Gnd 4 Gnd 4 Gnd Gnd 12 Gnd 12 Gnd 12 Gnd Enable 3 Enable Enable 3 Enable 3 Enable Ready 9 Ready 9 Ready 9 Ready - Motor 2 Motor - 2 Motor - 2 Motor - Monitor n 7 Monitor n Monitor I I 8 Monitor I 8 Monitor I 8 Monitor 1 + Motor 1 + Motor 1 + Motor (14) - Set value2 Set - value2 Set - + Value Set1 + Value Set1 + Value Set1 - Set Value Set - 2 Value (S12) (S13) (S4) (S5) (S6) +Vcc 24 +Vcc VDC 4 24 +Vcc VDC 4 24 +Vcc VDC 4 5 Power Ground 5 Power Ground 5 Power Ground Motor Motor Controller 12 Power Motor Motor Controller 11 Power Motor Controller 20 Power Ground Safety Earth 3 Ground Safety Earth 3 Ground Safety Earth 3 Signal Signal Signal NI9205 AI10 NI9205 NI9205 S11 NI9205 NI9205 Gnd NI9423 NI9423 AI2 AI7 AI5 AI9 DI2 DI3 Vcc Gnd NI9205 NI9423 S3 S8 NI9205 NI9205 4 NI9205 Vcc Vcc Gnd Gnd DCDCindicator F9:8A S21 S20 Vcc Gnd DI1 S10 Vcc Vcc 3 Gnd Gnd 1 tau12 delta12 AI1 AI6 AI14 AI8 Vref 2 Vref Shield Shield 5 Omega2 g_lon (S16) NI9423 DatronSwitch S19 Vcc 4 S2 S7 Gnd NI9205 DI0 Vcc Vcc Gnd Gnd S17 S9 S9 Vcc Vcc 3 AI0 tau11 Gnd 1 delta11 Omega12 Vref2 Shield Shield 5 g_lat (S15) Vcheck12 S18 Vcc Gnd Power Supply Power S1 12 V 12 Vcc Gnd NI9411 Omega11 alpha NI9263 NI9263 Pin Pin 12 Pin 3 Pin 1 Pin 4 Pin 2 Pin 12 Pin 8 Pin 6 Pin 5 Pin 7 Dsub 1 - - OUT + + OUT - Sense - Sense + + Sense AO3 COM Gnd 1 Gnd Gnd 1 Gnd 4 Vcc Vcc 4 Vcc Ch I 2 Ch I 2 Ch B Ch B 5 Ch B Ch B 5 Ch A 3 Ch Ch A 3 Ch A,B,I A,B,I 11 Encoder A,B,I A,B,I 12 Encoder dc - dc Converter dc 24V - 12 + + INput 24V Gate IN - INput F3: F3: 6.3A NI 9474 L1 L3 L2 DO3 Power Power Supply 24 V HeadSwitch F1: F1: 40A
Figure 32 Electrical layout
27 3.6 Control hardware and software This section describes the functionality of each piece of software running on the different components of the hardware controller. The section is split up in a short description of the CompactRIO, followed by the software description running on the controller, the FPGA and the offline PC. The in and output signals are in the software domain.
3.6.1 CompactRIO hardware The CompactRIO from National Instruments [37] is used as the real-time stand-alone controller. It is programmed with NI Labview. It is build up with a real-time processor and a reconfigurable FPGA. It is possible to use different types of I/O cards, which can be inserted in the I/O bay of the FPGA chassis. For the project a 30 channel analog input card, a six channel digital TTL input card, a four channel analog output card, a nine channel digital in and a nine channel digital output card are used. The configuration used is displayed in Figure 33. Appendix A shows the detailed information of the used materials.
Mains Analog in Digital in Digital out
Encoder in Analog out
Ethernet link
Controller Chassis with FPGA
Figure 33 CompactRIO The I/O modules are directly connected to the FPGA without a shared bus. The FPGA is also connected to the controller with a local PCI bus. The variables defined on the FPGA are available for the controller for manipulation. The program running on the controller and the one running on the FPGA are downloaded from a PC with the ethernet link.
3.6.2 Controller software The controller is configured as host of the CompactRIO. On start-up it will open the connection towards the FPGA for data transfer. Each variable defined in the FPGA code can be imported to the controller domain and vice versa. The other tasks of the controller are executing the “state-machine”, execute the data logging program and performing motion control calculations.
3.6.2.1 State machine The top level of the software is controlled with a state-machine. During start-up, various functions are enabled and configured. This is graphically displayed in Figure 34. The main sequence is described as follows, starting from the green balloon on the top left; - At power on the steer-by-wire system will be in an “idle” state. Only the CompactRIO controller is powered and starts running this state-machine program. Herein in activates the connection towards the FPGA, which makes it possible to use actual I/O.
28 - On a push of the start button the electrical system will “Start-up”. The motor controller are enabled and the DC/DC converter for sensor power supply is enabled. - In the “Check all” state the previous step is checked. All power supplies are checked and all power amplifiers need to report “status OK”. - In the “Init / Reset” state the system is functional, but not calibrated. The wheel angles are (re-) calibrated to their zero position. A separate set of controller parameters, with large integrator gains, moves the wheels to the stored wheel position with the absolute sensor and sets the zero for the encoder measurements. If needed the positions can manually be adjusted with the toe levers. It is also possible to reset the zero position of the steering wheel in this step. - In the “Ready” state all systems are active and calibrated. The software switches to the operational controller parameter set. Only the encoder data is now used for the position measurement of the wheels. - During the complete walkthrough of all states and in the final “Ready” state, all critical functions are monitored. If for example power supplies or motor controllers behave out of normal, the system will go to an “Error” state. The driver will be notified by the indication LED’s on the steering wheel. The driver can choose to overrule the error, or go back to the idle state. - The driver has the opportunity to stop and recalibrate the wheels in the “Ready” state, via the “Stop” state. In this state the electrical application are shut down, but calibrated wheel positions are still saved. From this stop state it is also possible to go to the idle state and shut down the complete system.
Figure 34 State machine of the software structure
3.6.2.2 Data logging The data packages coming from the FPGA is locally written in the controller on operator request. The data is saved under a test number which is set in the user interface.
29 3.6.2.3 Motion control Figure 35 show the control scheme from the steering wheel inputs, to the wheel position output. The setpoints for each wheel are calculated from the steering wheel angle and the individual toe lever angles depending on the selected toe mode. In the FPGA these analogue signals go through a low-pass filter. The steering angle is reformatted to wheel angles and is corrected with an Ackermann angle. The angle is limited to prevent set-points out of the wheel angle range. It is also possible to tie an analogue input or software defined variable to the set- point input of the controller via a switch, which is convenient for analyses purposes.
The controller is a straightforward PD controller with limiting output range to prevent over current on the motor and amplifier. The wheel positions are calculated in the FPGA and the value is passed through to the controller where the controller.
Mechanical / electrical hardware I/O boards FPGA Controller
Toe lever Left Sensor I/O Gain
Toe lever Right Sensor I/O Gain +
Steering Sensor I/O Position Ackermann wheel calculation correction Switch Switch
I/O Gain
SW input
I/O boards
+ Controller I/O Amplifier Motor Wheel angle -
Position I/O Sensor calculation
Controller FPGA I/O boards Mechanical / electrical hardware
Figure 35 control scheme and set point selection
3.6.3 FPGA software The FPGA is used for basic signal import and export. Initially the control loops were built in the FPGA. But during development of the code this was unpractical as each new feature requires a full time consuming rebuild of the FPGA code. The following functions with in and output are executed in the FPGA.
3.6.3.1 Clock Generate basic clock, used throughout the program to synchronize different functionality.
Inputs Funtion Outputs - Clock 4 kHz Timing Stamp
30 3.6.3.2 Read in analog input card Read in all data coming from the analog input card. Each signal is stored as a 16-bit integer. Due to the lack of digital inputs, some logic digital signals, not timing critical, are fed to the analog card. A trip hand made trip-level provides the digital behaviour.
Inputs Funtion Outputs Timing Stamp Read analog input Steering angle Wheel angle left Wheel angle right Motor current left Motor current right Motor current steering wheel Toe handle angle left Toe handle angle right Motor speed steering wheel Free analog input 1 Free analog input 2 Lateral acceleration Longitudinal acceleration Absolute velocity Status motor controller left wheel Status motor controller right wheel Status motor controller steering wheel Sensor reference voltage CompactRIO temperature Status on/off Status force feedback Status EMO Status data logging Status start button Status 12 Volt supply Logfile number
3.6.3.3 Read and process encoder signal The ‘A’ and ‘B’ signal from the encoders are read in by a dedicated digital TTL encoder card. The pulses from the encoder are counted and processed to position data. The motor position data needs a 32-bits integer to for storage.
Inputs Funtion Outputs Time Stamp Read Encoder signal Rear wheel speed Front left wheel speed Front right wheel speed Left wheel motor position Right wheel motor position
3.6.3.4 Read digital inputs The digital input signals exist of the status of the toe selection switches on the steering wheel.
Inputs Funtion Outputs Time Stamp Read Digital input Status asymetric toe switch Status symetric toe switch Status inverted steering switch Status toe-in / toe-out switch
31 3.6.3.5 Write digital outputs The digital outputs are used to enable electrical components in the system. the second function is to control the LED’s on the steering wheel to provide the driver with the needed feedback on the system state.
Inputs Funtion Outputs Time Stamp Write digital - Enable motor controller left output wheel Enable motor controller right wheel Enable motor controller steering wheel Enable dc/dc converter Enable LED 1 Enable LED 2 Enable LED 3 Free digital out
3.6.3.6 Write analog outputs The calculated setpoints for the motor controller are fed directly to the analog output card. The fourth output is connected to a analog Volt meter. This display gives a speed indication to the driver while driving.
Inputs Funtion Outputs Timestamp Write Analog out - Setpoint left wheel controller Setpoint right wheel controller Setpoint steering wheel controller Velocity out
3.6.3.7 Wheel position calibration This calibration loop provides the functionality to reset the home position of the steering wheel. This angle is measured with an absolute sensor, which means this is only required after dis- and reassembling the steering unit. The second calibration is required each time the system is has been shut down. The control of the wheel position is done with the relative encoder signals. These are zeroed with the stored absolute angle measurement of the potentiometers. It is possible for the driver to adjust the angle with the two toe handles to vary the offset or correct the initial angle.
Inputs Funtion Outputs Steering wheel angle Position calibration Steering wheel angle ofsett Left wheel angle Left wheel home angle Right wheel angle Right wheel home angle Start reset signal Left wheel home angle analog Right wheel home angle analog
32 3.6.3.8 Toe mode selection and execution The two levers on the steering wheel are used to steer the wheel independent from each other. The different modes; toe in, toe out, symmetric or asymmetric, are selected with switches on the steering wheel. This function calculates the toe angle that is superimposed on the steering angle set-point from the steering wheel. After each shutdown, or manual reset, the home position of the handles is stored.
Inputs Funtion Outputs Toe handle angle left Position calibration Steering wheel angle ofsett Toe handle angle right Left wheel home angle Status toe-in / toe-out switch Right wheel home angle Reset toe handle angles Toe angle setpoint left Toe angle setpoint right Toe mode status Toe handle offset angle left Toe handle offset angle right
3.6.3.9 System monitoring During operation the status of the motion controller and the level of the main 24 Volt supply are monitored. The maximum duration of an over current of the motor / amplifier is also monitored.
Inputs Funtion Outputs Time stamp System monitoring Max motor current exceeded signal Enable motor controller left Status motor controller left wheel wheel Status motor controller right wheel Enable motor controller right Status motor controller steering wheel wheel Enable motor controller steering wheel Setpoint left wheel controller Setpoint right wheel controller Setpoint steering wheel controller Status motor controller left wheel Status motor controller right wheel Status motor controller steering wheel Max overcurrent dureation Status 24 Volt supply
33 3.6.3.10 Data logging Some signals are combined into one big array. This data is transferred by Direct Memory Access to onboard memory of the controller. There are 18 variables of 16 bit arrays and 3 arrays of each 32 bits, being the time stamp and two wheel positions.
Inputs Funtion Outputs Timing Stamp Data logging - Steering angle Wheel angle left Wheel angle right Motor current left Motor current right Motor current steering wheel Toe handle angle left Toe handle angle right Lateral acceleration Longitudinal acceleration Absolute velocity Sensor reference voltage Logfile number DMA Cycle time ADC Cycle time Rear wheel speed Front left wheel speed Front right wheel speed Left wheel motor position Right wheel motor position
3.6.4 Offline PC software
The offline PC is only used to retrieve the logging data which is stored on the controller. It opens an FTP connection to the CompactRIO and gets the data file, unwrap it and stores it as a comma separated file on a local directory.
34 4 Results
4.1 Test description
4.1.1 Test track The tests are performed on the test track described by Figure 36. It consists of two rings connected by a straight lane of 90 meters.
Figure 36 Test track All braking tests are performed on the straight road of the test track.
4.1.2 Test cases The following test cases generate the experimental data, to verify the design, measure real braking performance and to get a better understanding of how the lateral stability is influenced by the unconventional wheel setting.
Test set-up, design verification 1. Verify the steering system performance
Braking performance 2. What is the maximum measured braking performance Run a series of test and get the highest value. 3. How does this relate to the original kart compare this number with the maximum measured braking performance of the conventional braking system. The changed mass and vertical axle load have to be taken into account. 4. What is the performance over the full range? What are unexpected results Does it match the theory
Lateral behaviour 5. What happens to the lateral movement when toeing? Is there a difference between toe in and toe out? What happens when toeing asymmetric Do expected phenomena occur (inverse steering)
4.2 Steering performance This section describes how well the design performs in the go-kart.
35 4.2.1 System identification The transfer function is derived from the gain part of the bode plot and displays the relation between steering angle input and wheel position output of the closed loop system. Figure 37 only shows data from the left wheel.
50 Measured system Identified system 0
-50 Gain (dB) Gain
-100 0 1 2 10 10 10 Frequency (Hz)
1
0.5 Coherence
0 0 1 2 10 10 10 Frequency (Hz)
Figure 37 Frequency response of measured and identified system
4.2.2 Tracking error Figure 38 shows how well the wheels follow the set points. The setpoint, in this case, is build up out of the toe handle output with superimposed to that the steering angle position. This is needed to keep the kart on track as the lateral behaviour becomes unpredictable. 60 Setpoint Measured 50 Error Steering angle 40
30
20 Angle (deg) Angle
10
0
-10 0 1 2 3 4 5 6 7 8 9 Time (sec) Figure 38 Steering angle behaviour on step input (toe in) The set point rises in 0.15 seconds to its maximum value. After this event it takes 0.7 second for the wheel to settle below an error smaller than one degree from the steady state error. The steady state error is ~ 3 degrees, which comes down to an error of ~ 6%.
The steady state error can be eliminated by an improved integrator action or with better system estimation in the feed forward part of the controller. An error this size is, however, easy to compensate by the driver.
36 4.3 Brake-by-steering performance
4.3.1 Maximum measured braking performance Figure 39 shows the deceleration profile when the kart performs a brake-by-steer action. In this case the wheel positions are 50 and -60 degrees. The two red lines, solid and dashed, represent the acceleration in m/s 2. The solid line is the derivative of the velocity signal and the dashed the measured signal from the accelerometer. The delay in the accelerometer signal is caused by the electronic filter applied in the measurement system. The very gentle deceleration after the peak velocity is the rolling resistance and air drag of the kart. 10 Velocity (m/s) 8 Acceleration (m/s 2) Brake Force (kN) 6
4
2 Various) ( 0
-2
-4
-6 0 1 2 3 4 5 6 7 Time (sec) Figure 39 Braking performance brake-by-steer, The maximum deceleration is approximately 5 m/s 2. Taking the total moving mass in account the braking force generated by the toed wheels is 1.3 kN. This is the maximum value in the measurement series. Compared to the reference data measured with the conventional kart, the deceleration is almost equal, see appendix B.
The difference between the two set ups is the increased vertical axle load. The steer-by-wire kart is significant heavier on the front than its conventional counterpart. Taking this into account shows the difference in maximum braking performance.
Fbrake 1300 N Brake-by-steer performance: = = 0.90 Equation 11 Fz1450 N z
Fbrake 1200 N Reference performance : = = 1.35 Equation 12 Fz889 N z From this standpoint the brake-by-steer performance is 67% of the conventional maximum braking performance when braking with two wheels.
Trying to compare this to a real car gives the following rough estimate. In passenger cars the brake force distribution is about ⅔ to ⅓ for front and back respectively. This brings the braking performance for the brake-by-steer concept, if it was applied on a car, to 50% of the conventional braking system.
4.3.2 Estimated performance Figure 40 displays a collection of brake performances. The effective toe angle is the summation of both left and right absolute toe angle. Through the data point runs a red dashed fitted and a solid blue estimated result.
37 0 Toe in -0.2 Toe out One wheel Theoreticle data -0.4 Fitted data
-0.6
-0.8
Brake Brake force (kN) -1
-1.2
-1.4
-1.6 0 20 40 60 80 100 120 140 160 180 Effective toe angle (deg) Figure 40 Brake force data collection The data points follow the expected theoretical trend. The main cause for differences is the speed dependent factor which is not separated for the different points. Figure 39 shows that a decreasing speed causes an increase in the deceleration. Another effect that explains the variation is the tire and road condition which varies for the different measurements.
4.3.3 Lateral vehicle stability Figure 41 shows the wheel angles belonging to the deceleration profile of Figure 39. This figure shows that the path of the kart in not straight. A sudden lateral motion occurs, for which the driver compensates with correctional steering. 60 Left Wheel (deg) Right Wheel (deg) 40 Steering angle (deg) Lateral accel*10(m/s 2) 20
0 Various)
( -20
-40
-60
-80 0 1 2 3 4 5 6 7 Time (sec) Figure 41 Braking performance, wheel positions The theory predicted large ranges where steering would be inverted. The inverted steering did occur during the tests but this phenomenon has not been successfully recorded. It appeared that the region is much smaller than the theory tells. During the few seconds it takes to decelerate to zero speed this specific wheel position has to be found and hold, and the vehicle has to be controlled, while the steering switches between regular and inverted steering. The engine of the kart does not have enough power to push through the brake force of the front wheel to prolong the test period.
38 Figure 42A shows the theoretical behavior for toe-in. The graph shows the driven path of the vehicle in X- and Y-direction. The blue, red and green lines correspond to a symmetric toe angle of 30, 40 and 50 degrees respectively. Each setting is plotted five times with a steering angle increase of two degrees in positive, right, direction. Figure 42B shows the same for symmetric toe-out and with 40, 50 and 60 degrees for the blue, red and green line.
-0.06 -0.04
-0.04 -0.02
-0.02 0
0 0.02 Y [m] Y [m]
0.02 0.04
0.04 0.06
0.06 0.08 0 0.2 0.4 0.6 0.8 1 1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 X [m] X [m]
A: Toe-in B: Toe-out Figure 42 Inverted steering paths The smallest toe setting behaves normal, steering to the right results in a movement to the right. The middle setting is the turning point to inverted steering. The vehicle responds very little to a steering input. The largest toe angles result in inverted steering. The brake force increases with increasing toe angles which results in decreased path length.
4.3.4 Asymmetric toe The asymmetric toe variant has shown not be very successful during the experiments with the go-kart.
If one wheel is turned outwards the vertical load on the tire increases and it gains more grip than the wheel that points straightforward. The lateral force is too large to compensate for the straight wheel. It is impossible to drive in a straight line with the steer-by-wire kart; it will always make a turn. The kart reacts very aggressive on this steering maneuver. The rear wheels loose grip making the kart uncontrollable.
The change of the vertical axle load is not implemented in the model. Therefore this effect was not predicted.
The opposite of this effect happens when toeing in. Now the toed wheel has less grip than the straight wheel which decreases the braking performance of the already reduced brake force.
39
40 5 Conclusions and recommendations
5.1 Brake-by-steer concept The brake-by-steer concept has shown that it can be a back-up system for failing brakes. Although the maximum performance is much lower compared to conventional braking, it may be enough to stop the vehicle in an emergency situation.
The focus in this report is on braking while driving on a straight line. The best braking performance is achieved with symmetric toe method. There is no difference between toe-in and toe-out on the braking performance.
The difference between the two symmetric settings is on the lateral behavior when trying to make a turn or make small steering corrections.
At toe in, steering becomes inverted for part of the steering range. This makes the steering ratio change from its original setting to negative values as function of the toe-angle. The control used algorithm does not compensate for this behavior which makes it challenging for the driver to maintain control over the vehicle. The theory shows this effect and during the tests this effect occurred, but it is not successfully captured in measurement data.
When toe-out is applied the vehicle reacts very aggressively to a steering input. This is contrary to what the theory predicts. This is can be explained by the go-kart specific suspension system of the front wheels. The kingpin angles together with the limited frame deflection vary the vertical axle load of the steerable wheels. The inner wheel will have a significantly higher load than the outer. This changes the saturation of the lateral tire force in the tire characteristic such that the inner wheel generates higher lateral forces. While making a turn the inner wheel is turned out the most and dictates the vehicle behavior.
Asymmetric toe is presented, by theory, as a way to brake with less performance but maintain lateral control over the vehicle with one wheel. The same effect as described for the symmetric toe modes changes the expected behavior. The wheel that is turned inwards looses vertical load. This reduces the lateral tire force and longitudinal vehicle force. Toeing- out with one wheel results in an unintended steering motion, instead of just a braking. Therefore this configuration was left out of the further tests.
5.2 Recommendations & future work With this project the basic concept of brake-by-steer has been proven. In order to make this system work in a car, the relation between steering angle and vehicle heading has to be restored. This means that the vehicle model has to be embedded into the steer-by-wire system and calculate real-time how to position the wheels to generate the needed brake force and follow the steering input from the driver as he expects. There will always be a trade of between the braking performance and the lateral control of the vehicle. Further research on how to position the wheels to reach the optimum between these two is needed.
The tire models used here are strong simplifications of actual tire behavior. What needs to implemented in the future model is more precisely how tires behave under extreme large slip angles at high speeds. The simplified Pacejka and piecewise linear model are not capable of doing this very accurately.
The steer-by-wire go-kart has been a good test vehicle to proof the brake-by-steer concept. The small vehicle was easy to adapt. However the available space was very limited. This resulted in the positioning of the electronics box and heavy batteries right on top of the front axle. This changed the vehicle behavior and demanded significantly more effort for the steering motors. Although there was not an easy alternative, this has been a design choice that will not be made again.
There were features in the mechanical construction of the kart that influence the vehicle dynamics such that it is hard to extrapolate the results to a passenger car. A follow up test
41 bed should be a conventional car. Interesting to point out is that the ‘P1’ prototype vehicle of Stanford University [19] has independent steerable wheels, but there was no references found of brake-by-steering there.
42 6 Bibliography [1] Prof. Dr. Ir. Compter, J.C., “ Mechatronics - Introduction to electromechanics” . Philips Centre for Industrial Technology, October 2000. [2] “Spec a Motor”, http://www.specamotor.com/ . Accessed September 2009. [3] Beckman, B., “Kart Steering, Physical Forces and Setup - Theory and Practice”. http://www.karting.co.uk/KandK/Tech/KartSetup.html , 2002. Accessed September 2006. [4] Degerman, P., Wiker, N., “Analysis and Design of a Redundant X-by-Wire Control System Implemented on the Volvo Sirius2001 Concept Car”, Master Thesis, Linköping University, 2003. [5] “Delphi QUADRASTEER System Application Expands Onto Additional GM Truck and SUV Models”. Delphi press release, February 2002. [6] Demerly J.D., "Control of independent steering actuators to improve vehicle stability and stopping". Unites States Patent, US6.719.087B2. Delphi Technologies Inc., April 2004 [7] Budaker et al., "Fremdkraft-oder Servolenkung". Offenlegungsschrift Int.Cl. B62D6/00, ZF LenksystemeGmbH and Robert Bosch GmbH, July 2003. [8] Kondo, T. and Yamamoto, T., "Rear wheels steering apparatus for vehicles". Unites States Patent, 4.786.006. Mazda Motor Corporation, November 1988 [9] Miller G.R. and Couratier J.P., "Active toe adjustment apparatus". Unites States Patent, 5.143.400. Michelin Recherche et Technique, September 1992. [10] Den Boer, M. and Van der Lijn, D., “Study on brake-by-wire and implemtation on a Go-kart”. Bachelor thesis at Hogeschool van Utrecht and SKF Nieuwegein, May 2006 [11] Sodikart, http://www.sodikart.com [12] Maxon motor, http://www.maxonmotor.com [13] Amato, T., et al, “Handling behaviour of racing karts”. SAE paper nr. 2002-01-2179, July 2002 [14] Vitale, E. et al, "A lumped parameters model for the analysis of kart dynamics”, 7 th International Conference ATA, Florence, 2001 [15] Ponzo, C. and Renzi, F., “Parametric multi-body analysis of kart dynamics“. Technical paper for students and young engineers, Fisita world automotive congress, Barcalona, February 2004. [16] “Ackermann Steering Geometry“, Wikipedia The free encyclopaedia http://en.wikipedia.org/wiki/Ackermann_steering_geometry . Accessed May 2009. [17] Rill, G., “Vehicle dynamics”, Lecture Notes, Regensburg University of Applied Sciences, March 2009 [18] Yih, P., “Steer by-wire: Implications for vehicle handling and safety”. Ph.D. dissertation, University of Stanford, 2005. [19] Dynamic Design Lab, Stanford University http://ddl.stanford.edu/ . Accessed September 2009 [20] Bretz, E.A., “By-wire cars turn the corner”. Automotive Electronics, IEEE Spectrum, April 2001 [21] “Vehicle of the future here now“. Evolution - the business and technology magazine from SKF, www.SKF.com , Nr. 4 November 2002
43 [22] W. Klier, G. Reimann and W. Reinelt, “Concept and Functionality of the Active Front Steering System“, SAE paper 2004-21-0073, 2004 [23] De Vries, E., “Vehicle dynamics A’, lecture notes course wb3404 - Vehicle dynamics- A“, March 2002 [24] Smith, N.D., “Understanding parameters influencing tire modelling“. Colorado State University, Formula SAE Platform, 2004 [25] Liebemann, E. K., Meder, K., Schuh, J., Nenninger, G. “Safety and Performance Enhancement: The Bosch Electronic Stability Control (ESP) “. Proceedings - 19th International Technical Conference on the Enhanced Safety of Vehicles, Washington, D.C., June, 2005 [26] Christopher, D. G., Shad M. L., J. Christian. “Eliminating the Need for Sensor Redundancy in Diagnostic Systems for Steer-by-Wire Vehicles“. SAE Paper Number: 20062976, August 2006. [27] Juan R. Pimentel, “An Architecture for a Safety-Critical Steer-by-Wire System“, SAE paper 2004-01-0714, January 2004 [28] Noguchi, M., “Trends and Future Prospects Regarding Steering System Technology“. Koyo Engineering Journal English Edition No. 159E, 2001. [29] De Raad van de Europese Gemeenschappen, 'Richtlijn 92/62/EEG van de Commisie van 2 juli 1992 betreffende aanpassing aan de vooruitgang van de techniek van Richtlijn 70/311/EEG van de Raad betreffende de stuurinrichting van motorvoertuigen en aanhangwagens daarvan' 2 July 1999 [30] ZF Aktivlenkung für Pkw der Mittel und Oberklasse. Product information ZF- Lenksysteme [31] Toffin, D. et al., "Influence of steering wheel torque feedback in a dynamic driving simulator". Renault – Technical Centre for Simulation, Renault Technocentre and Laboratoire de Physiologie de la Perception et de l'Action, CNRS – Collège de France [32] Narby, E., “Modeling and Estimation of Dynamic Tire Properties“. Thesis report, Department of Electrical Engineering, Linköping University, February 2006. [33] Beckman B., “The Physics of racing“. http://phors.locost7.info/files/Beckman_- _The_Physics_of_Racing.pdf , reformatted April 2008. Accessed September 2009 [34] “Ackermann Explained (Part 1)“. Racecar engineering, IPC Media, Vol. 11 nr.6, June 2001 [35] “Ackermann Explained (Part 2)“. Racecar engineering, IPC Media, Vol. nr. 7, July 2001 [36] “Ackermann Explained (Part 3)“. Racecar engineering, IPC Media, Vol. nr. 8, August 2001 [37] National Instruments, CompactRIO http://www.ni.com/compactrio/ . Accessed September 2009 [38] Cole, D., “Steering Feedback”. ATZ Autotechnology 002008 Volume 8
44 A. Go-Kart dimensions
501 N 708 N
measurement point centre of garvity kart weight = 1322 N
539 N 638 N centre of garvity 706 N 745 N kart plus driver weight = 1975 N centre of garvity by-wire kart weight = 1962 N centre of garvity by-wire kart plus driver weight = 2687 N
centre of garvity heigth = 247 mm by-wire kart, no driver
Original front axle
Extended front axle
363 N 422 N 677 N 559 N
224 N 591 N597 N 676 N
Figure 43 Go-kart dimensions
45 B. Measurement Kart
a. Used equipment The measurement kart is used to identify the performance of the steering system and vehicle behavior as a point of departure for the design and as a reference for the brake-by-steer system. This appendix shows the used materials, the layout and results.
i. Data acquisition USB Data acquisition
Description Type Product name DT9804-EC-I-BNC-16SE Analogue inputs 16 SE Input resolution 16 bit Throughput 100 kHz http://www.datatranslation.com/products/dataacquisition/usb/dt9800-ec-i.asp
ii. Velocity sensor Measures Type Range Sensitivity Supplier Velocity Optical analogue 0 – 400 km/h 25 mV/km/h Datron Dartron is an optical absolute velocity sensor used in the automotive branch. It measures the speed of the road passing underneath. http://www.corrsys-datron.com/optical_sensors.htm
iii. Absolute through shaft angle sensor Measures Type Range Sensitivity Supplier Angle Through shaft magnetic ring 0-360 ° 11 mV/ ° SKF This sensor provides the absolute steering angle of the steering wheel. The angle of the wheels is derived from this. The sensor is part of a combined bearing sensor system. http://www.skf.com/portal/skf_rev/home/products?contentId=079776#Label4
iv. Accelerometer Measures Type Range Sensitivity Supplier Acceleration Accelerometer +/- 5 g 400 mV/g SKF In house (SKF) build custom sensing system.
v. Force sensors Measures Type Range Sensitivity Supplier Force Strain gage -35.5 N/V SKF Force Strain gage -21.9 N/V SKF In house (SKF) build custom sensing system. The steering torque is not measured directly at the steering wheel and wheels. Instead the forces are measured with strain gages in the steering rods.
46 b. Measurement kart layout
Data acquisition
Angle sensor
Accelerometer Datron
Strain gages
Figure 44 Measurement kart layout
Angle sensor
Strain gages
Figure 45 Strain gage and steering angle detail
c. Measurement kart results
i. Steering angle range The maximum wheel angles are 32 degrees for the inner wheel and 25 for the outer wheel. The difference is caused by mechanical linkage that mimics the Ackermann effect.
47 ii. Steering speed and frequency, hard cornering The maximum rotation speed of the steering wheel is 300 degrees per second. The angle made is 50 degrees (from -25 to +25), resulting in a maximum steering frequency of 1 Hz. During this aggressive driving test the rear wheels of the kart broke away. This is the point where the tires physically limit the performance of the kart.
iii. Steering speed and frequency, slalom The slalom test gives also information about the bandwidth of the steering rate that can be made with the go kart. The biggest amplitude is at the frequency the slalom is executed. The peak-peak value of the slalom is 45 degrees, at a frequency of 0.95 Hz.
iv. Steering torques Static load The static load is around 5 Nm when the wheels are pointing forwards. Turned, the torque goes up to 16 Nm. The difference between the two can be seen as an indication for the torque at the steering wheel. Precondition is that there are no additional lateral forces on the tires
Quasi static load During a ride the forces are around the 8 Nm at the wheels and 5 Nm at the steering wheel during steady state circular path driving.
Dynamic load During a test run with continues fast changing steering angles the torque is between the 25 and 30 Nm. In the sharp turns in the test track the torques spike to values of 50 Nm.
v. Breaking performance The maximum braking performance is 1.2 kN for the two front wheels. The graph is shown below. Measurement data 10 Velocity (m/s) 8 Acceleration (m/s 2) Brake Force (kN) 6
4
2 various) ( 0
-2
-4
-6 0 1 2 3 4 5 6 7 Time [s] Figure 46 Braking performance reference kart
48 vi. Summary Parameter Value Unit Nominal torque 10 Nm Peak torque 50 Nm Nominal speed 64 / 10.7 ˚/s / rpm Max. rotating speed 175.9 / 29.3 ˚/s / rpm Steering frequency 1 Hz Braking performance 1.2 kN Vertical load change front wheels 300 N /rad
49 C. Sensor list and layout The table below shows all used sensors in the steer-by-wire kart, their function, configuration and supplier.
Module I/O DIN Function name Description and Supplier I/O Signal Sensitivity Supply nr. config min / zero / max Voltage Current AI0 1 Handwheel angle Absolute through shaft analog manetic senor, [SKF] ± 5 V 0.5 / 2.5 / 4.5V 11.1 mV / degree 12 V 35 mA AI1 2 Front left steering angle Conductive plastic potentiometer, model 357, [VISHAY] ± 10 V 2.88 / 4.95 / 7.01 V 35.2 mV / degree 12 V 10 mA AI2 3 Front right steering angle Conductive plastic potentiometer, model 357, [VISHAY] ± 10 V 6.72 / 4.70 / 2.67 V 32.1 mV / degree 12 V 10 mA AI3 4 Monitor I Amplifier [11] Amplifier ADS 50/10, [MAXON] ± 10 V -10 / 0 / 10V -0.4 V / A 24 V AI4 5 Monitor I Amplifier [12] Amplifier ADS 50/10, [MAXON] ± 10 V -10 / 0 / 10V -0.4 V / A 24 V Analogue AI5 6 Monitor I Amplifier [20] Amplifier ADS 50/5, [MAXON] ± 10 V -10 / 0 / 10V -0.8 V / A 24 V IN AI6 7 Toe Wing 1 21 mm Cermet Potentiometer, CP21, [PIHER] ± 5 V 1.00 / 0 V 4.14 V/deg 12 V 0.12 mA NI 9205 AI7 8 Toe Wing 2 21 mm Cermet Potentiometer, CP21, [PIHER] ± 1 V 0.87 / 0 V 4.14 V/deg 12 V 0.12 mA AI8 9 Lateral acceleration Acceleromter Model 3145 - 005, [ICSensors] ± 5 V 0.5 / 2.5 / 4.5 V 400 mV / degree 12 V 5 mA AI9 10 Longitudinal acceleration Acceleromter Model 3145 - 005, [ICSensors] ± 5 V 0.5 / 2.5 / 4.5 V 400 mV / degree 12 V 5 mA AI14 15 Zero G reference Acceleromter Model 3145 - 005, [ICSensors] ± 5 V 2.5 V AI10 11 Absolute longitudinal speed Optical speed sensor DLS-1, [CORRSYS - DATRON] ± 10 V 0…10 V 25 mV / km/h 12 V 2.5 A AI11 12 Ready Status MC11 Amplifier ADS 50/10, [MAXON] ± 10 V on = 0 V, off = 10 V AI12 13 Ready Status MC12 Amplifier ADS 50/10, [MAXON] ± 10 V on = 0 V, off = 10 V AI13 14 Ready Status MC20 Amplifier ADS 50/5, [MAXON] ± 10 V on = 0 V, off = 10 V AI15 16 Log file number Thumbwheel switch 180011G [Eeco] ± 10 V high / low , 0 / 10V AI16 17 Check V12 DC-DC converter 100W, VI-221 EW, [VICOR] ± 10 V ok = 10 V, error = 0 V 12 V 8.2 mA AI17 18 Switch Feedback ± 10 V on = 0 V, off = 10 V 24 V AI18 19 Monitor n Amplifier [20] Amplifier ADS 50/5, [MAXON] ± 10 V -10 / 0 / 10V AI19 20 MC Power checking Battery G40s, 12 V, 38Ah/20h, [Exide] ± 10 V 0 / 8.16 V 1.47 V / V 24 V 1 mA AI20 Switch Logging Switch SPDT, 'no', [C&K] ± 10 V on = 0 V, off = 10 V 12 V AI21 Switch Start Button Switch SPDT, 'no', [C&K] ± 10 V on = 0 V, off = 10 V 12 V AI22 AI22 ± 10 V AI23 AI23 ± 10 V AI24 Log file number Thumbwheel switch 180011G [Eeco] ± 10 V high / low , 0 / 10V AI25 Log file number Thumbwheel switch 180011G [Eeco] ± 10 V high / low , 0 / 10V AI26 Log file number Thumbwheel switch 180011G [Eeco] ± 10 V high / low , 0 / 10V
50 AI27 Log file number Thumbwheel switch 180011G [Eeco] ± 10 V high / low , 0 / 10V AI28 Log file number Thumbwheel switch 180011G [Eeco] ± 10 V high / low , 0 / 10V AI29 Log file number Thumbwheel switch 180011G [Eeco] ± 10 V high / low , 0 / 10V AI30 Off switch Switch SPST, [C&K] ± 10 V high / low , 0 / 10V AI31 Log file number Thumbwheel switch 180011G [Eeco] ± 10 V high / low , 0 / 10V DI0 21 Front left wheel speed Digital ferrite ring, RV-BMB-6209/080SA [SKF] 12 V 10 mA 160 CPT, 80 poles, single DI1 22 Front right wheel speed Unipolar Hall-effect sensor, SS411A, [Honeywell] 12 V 10 mA Digital DI2 23 12 V 20 mA Rear axle speed Sensor bearing BMB-6206/064S2/EA002A, [SKF] 256 CPT, 64 poles, quad IN DI3 24 12 V 20 mA NI 9423 DI4 25 Switch - Toe selection modes Switch DPCO, [C&K] on = 12 V, off = 0 V 12 V DI5 26 Switch - Toe selection modes Switch DPCO, [C&K] on = 12 V, off = 0 V 12 V DI6 27 Switch - speed dependent FB Switch DPDT, [C&K] on = 12 V, off = 0 V 12 V DI7 28 Switch - Toe selection, asym Switch DPCO, [C&K] on = 12 V, off = 0 V 12 V Digital DI0a Front left motor rotation HEDL-5540 with RS-422 (EIA-422) line driver 500 CPT, qudrature 5 V 4 mA IN t/m subD Front right motor rotation HEDL-5540 with RS-422 (EIA-422) line driver 500 CPT, qudrature 5 V 4 mA NI 9411 DI5b Analogue AO0 32 Motor Control signal 11 -10 / 0 / 10 V OUT AO1 34 Motor Control signal 12 -10 / 0 / 10 V NI 9263 AO2 36 Motor Control signal 2 -10 / 0 / 10 V AO3 38 Variable analogue output 0 / 10 V DO0 41 Enable MC11 1' = [Usup]V, '0' = [0 - 2.5]V 24 V 1.6 mA DO1 42 Enable MC12 1' = [Usup]V, '0' = [0 - 2.5]V 24 V 1.6 mA Digital DO2 43 Enable MC20 1' = [Usup]V, '0' = [0 - 2.5]V 25 V 1.6 mA OUT DO3 44 Enable DC/DC 0' = on, '1' = off 24 V 75 µA NI 9474 DO4 45 LED 1 0' = on, '1' = off 24 V 12 mA DO5 46 LED 2 0' = on, '1' = off 24 V 12 mA DO6 47 State indicator LED 0' = on, '1' = off 24 V 12 mA DO7 48 nc.
Table 3 Sensor list
51 The following figure shows the detailed electronics of each individual sensor.
Vcc = 12 V 1 Vcc 24 V NI-9205 MC and EM Switch S_gamma 3 AI0 External power supply Vcc = 12 V 24V R = 22k 0 2 AI SENSE U = 2.9 V Motor Encoder [11] AI19 NI9205 R2 = 100k Dsub +5V NI-9205 2 Vcc Vout S_delta11 Reg AI1 R = 3k 6 0.5 ... 4.5 V ch A DI0a 11.1 mV / degree 8 cRIO -9411 C2 = 0.1e-6F ch B DI1a 35 mA C1 = 30e-6F 9 0 ch I DI2a AI SENSE Vcc = 12 V 0 / 2.88 V GND COM 0...10 V 9.6 mA .... mV / degree 12 mA I = 10 mA R1 = 200 Ohm
TTL 2-channel 500 CPT 10 V 20 mA per channel max
Vcc 12 V R2 = 1 kOhm NI-9205 External power supply S_delta11 AI1 24V
MC11 C2 = 0.1e-6F Motor Encoder [12] C1 = 30e-6F MC12 Dsub +5V 0 Vcc = 12 V MC20 9 2 Vcc Vout Reg AI SENSE R = 10k 0...10 V ch A 6 DI3a cRIO -9411 29.4 mV / degree 8 AI11 NI9205 for MC11 ch B DI4a 10 mA R2 = 100k 0 NI-9205 AI12 NI9205 for MC12 9 1 AI13 NI9205 for MC20 ch I DI5a S_delta11 AI1 Vcc = 12 V GND COM I = 1.2 mA R = 50k C1 = 30e-6F C2 = 0.1e-6F I = 0.2 mA 0 R1 = 200 ohm AI SENSE '0' = 10 V GND 0...10 V '1' = 0V .... mV / degree 12 mA
R2 = 1 kohm NI-9205 TTL 2-channel Lateral acceleration 500 CPT S_delta12 AI2 1500 pf 4700 pf 20 mA per channel max dc - dc Converter C1 = 30e-6F C2 = 0.1e-6F 24 - 12 V 0 - INput 24V - OUT Vcc = 12 V AI SENSE 4700uf - Sense + INput + Sense Vcc NI-9205 + OUT Vref AI14 Gate IN R1 = 5k6 Ω BC107B NI-9423 AI11 4700pf 0...10 V 1500pf 29.4 mV / degree Vcc = 12 V Sensor VSignal > 11 V 10 mA DI0 AI SENSE 10k 1.2 mA COM 0.5...4.5 V 400 mV / g GND 5 mA 330k NI-9474 DO3 BC107 Dsub2 Vcc = 12 V 0...24 V = 100 k Ω 7.3e-2 mA '0' = on, '1' = off = Switch 1 Switch 2 160 CPT longitudinal accelereation 2.1 mA
DI5 NI9423 DI6 NI9423 Vcc NI-9205 DI4 NI9423 AI7 NI9423 Vcc = 12 V Vref AI15 NI-9205 Switch 3 AI12 Vcheck R1 = 470 Vcc = 12 V DI7 NI9423
AI16 AI SENSE Check V12 = 8.16V R1 = 5k6 Ω BC107B NI-9423 0.5...4.5 V 400 mV / g R2 = 1k 5 mA Sensor VSignal > 11 V DI1
COM
GND
0 / 8.16 V 8.2 mA
NI-9205 160 CPT 2.1 mA Vcc = 12 V GND
AI11
AI SENSE Vcc = 12 V
R1 - 850 Ω R1 - 850 Ω NI-9423 Signal B 0...10 V Sensor Signal A 400 mV / km/h DI2 6000 mA Sensor DI3 GND COM 256 CPT 14 mA per channel
Figure 47 Sensor electronics
52 D. Used materials
a. National Instruments Description Type CompactRIO Controller NI cRIO-9004 CompactRIO Chassis NI cRIO-9102 Analogue input module NI-9205 Digital input module cRIO-9423 Digital input module cRIO-9411 Analogue output module NI-9263 Table 4 Used material CompactRIO
b. Maxon Motor Description Type Wheel motor F2260.885-51.216-200 Gear GP62 110505 Digital encoder HEDS 5540 4-Q-DC Servo amplifier ADS 50/10
Steering wheel motor + gear RE36 24V, GP42C Digital encoder HEDL 55 4-Q-DC Servo amplifier ADS 50/5 Table 5 Used material MAXON Actuators
53 E. Steer-by-wire go-kart
Steering wheel actuator
Speed indicator
Speed sensor Electronics box
Batteries Wheel actuator
Figure 48 Steer-by-wire kart
Figure 49 Steer-by-wire kart toeing-out
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