UPTEC F17 045
Examensarbete 30 hp Augusti 2017
Dynamic torque clutch control for heavy duty vehicles using
a backlash size and position observer
Samuel Eliasson Godonou
Teknisk- naturvetenskaplig fakultet UTH-enheten
Besöksadress:
Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0
Postadress:
Box 536 751 21 Uppsala
Telefon:
018 – 471 30 03
Telefax:
018 – 471 30 00
Hemsida:
http://www.teknat.uu.se/student
Abstract
Dynamic torque clutch control for heavy duty vehicles using a backlash size and position observer
Samuel Eliasson Godonou
This master's thesis investigated the possibility to control the clutch torque in order to better traverse a Scania vehicles
powertrain backlash. When traversing a backlash the torque difference between the two gears will at the time of contact excite oscillations in the powertrain, and by controlling the torque these oscillations can be minimized. The master's thesis solves this issue in three major steps. First a Simulink model was created to mimic the actual vehicles powertrain as closely as possible. It was created using mostly Simdriveline components and then validated by comparing simulations to measurements from real drives. After that backlash position and backlash size observers were created in order to estimate them. Using the developed Simulink model these observers could then be evaluated, and the backlash position observer proved to be very precise while the backlash size observer was not as precise but still usable. Finally a control strategy was devised, by using
the estimates from the developed observers it was supposed to control the clutch torque in a better way than previously done. The
controller was a switching controller that simply used the full engine torque while the backlash was in contact, and a P controller to control the clutch torque while performing a backlash traverse.
The controller proved to perform well and was robust to errors in the backlash size. Future work to be done could be to develop a shaft torque observer for use in the already developed observers.
ISSN: 1401-5757, UPTEC F17 045 Examinator: Tomas Nyberg
Ämnesgranskare: Alexander Medvedev Handledare: Georg Åhrberg
Populärvetenskaplig sammanfattning
Examensarbetet "Dynamic torque clutch control for heavy duty vehicles using a backlash size and position observer" eller "Dynamisk kopplingsmomentsstyrning för tunga fordon med hjälp av en glapp storleks och positions observatör" utfördes i samarbete med Scania CV AB i Södertälje. Ett fordons drivlina innefattar allt det som överför moment från motor till drivhjul.
Det är en nödvändighet att det mellan två kugghjul existerar ett visst spelrum för att de ska kunna snurra. I Scanias fordons drivlina finns det kugghjuls par på flera ställen i växellådan, samt i slutväxeln. När man under en körning ska ta sig igenom dessa glapp så uppstår det efter att kugghjulen kommit i kontakt, svängningar i fordonets drivlina, som kan upplevas som obehagliga av fordonets förare. Dessa svängningar är oundvikliga, men blir olika stora beroende på hur stor skillnad i moment det är mellan de två kugghjulen vid kontakttidpunkten, och det är där man finner intresset till examensarbetet. Man vill på något sätt kunna styra det ingående momentet smartare, för att kunna ta sig igenom glappen ungefär lika snabbt som innan, men med lägre momentskillnad mellan de två kugghjulen vid kontakttidpunkten. Genom att göra detta kan man minska på de svängningar som uppkommer vid kontakt, och därmed öka komforten för föraren av fordonet. För att lösa detta så valde delades projektet upp i tre delar.
Den första delen som skulle lösas var att i Matlab programmet Simulink modellera Sca- nias fordons drivlina för att likna verkligheten så mycket som möjligt. Komponenterna som främst användes kom från toolboxen Simdriveline, dessa komponenter var specifikt framtagna för att modellera drivlinor. De delar som modellerades var fordonets motor, koppling, väx- ellåda, kardanaxel, slutväxel, drivaxlar och hjul. När modellen var färdigbyggd så jämfördes simuleringar på modellen med mätningar från verkliga körningar med fordon. Med hjälp av mätdatat så trimmades parametrar på komponenternas styvhet, dämpning och tröghet in för att simuleringarna skulle följa mätningarna så bra som möjligt och när detta ansågs bra nog så kunde andra delen av projektet påbörjas.
Den andra delen av projektet var att ta fram en observatör med vars hjälp man kunde skatta storleken av glappen mellan kugghjulen, samt en observatör med vars hjälp man kunde skatta den position man har i glappet i varje tidpunkt. Den slutliga produkten skattade endast slutväxelns glapp. För att först ta fram positionsobservatören togs först fysikaliska ekvationer fram, för att representera drivlinan och glappet. Med hjälp av dessa ekvationer kunde sedan en tillståndsmodell ställas upp. Då ett glapp är en olinjäritet så behövde detta tas om hand i tillståndsmodellen, detta gjordes genom att göra ett växlande system med två olika lägen med en tillståndsmodell vardera. De två lägena var ett kontaktläge, som användes när kugghjulen var i kontakt, samt ett glappläge, som användes när man tog sig igenom glappen. Växlingen skedde med vissa villkor för att försäkra sig om att man använda kontaktläget när man var i kontakt och glappläget när man var i glappet. Sedan togs en observatör fram med hjälp av en EKF eller Extended Kalman Filter, med vars hjälp man sedan kunde skatta positionen i glappet. Resultaten av denna observatör blev goda och med hjälp av simuleringar med den tidigare framtagna modellen kunde det visas att den skattade position mycket väl. För att skatta storleken på glappet gjorde man detta på ett liknande sätt som för positions observatören. Först togs ekvationer fram för att beskriva drivlinan, i detta fall utan att inkludera glappet. Istället valde man att införa ett offset som beskrevs av skillnaden mellan positionen på växellådans utgående axel och hjulen. Detta offset uppdaterades som två separata offset, ett positivt som
uppdaterades vid positiv kontakt samt ett negativt som uppdaterades vid negativ kontakt. När man var i glappet uppdaterades ingen av offseten, utan man var i ett vänteläge. Observatören fungerade alltså som en växlande observatör precis som för glapp positions observatören, men i detta fall med tre olika lägen, och även här togs observatören fram med en EKF. För att veta vilket läge man var i detekterade observatören teckenändringar i det ingående momentet, och bytte först från antingen positivt eller negativt kontaktläge till vänteläge, och sedan efter en viss vänte tid till det andra motsvarande kontaktläget. Resultaten av glappstorleksobservatören var hyfsat goda men hade ett litet fel jämfört med den sanna glapp storleken.
Med de två observatörerna framtagna kunde till sist en reglerstrategi utvecklas. Som nämnt var målet att styra kopplingsmomentet så att glappgenomgången sker så snabbt som möjligt men med en låg moment skillnad mellan de två kugghjulen vid kontakttidpunkten. Precis som med observatörerna tillämpades här en växlande reglerstrategi, där man använde sig av positionsobservatörens skattning av glapp positionen för att bestämma vilket läge man var i.
Om man var i kontaktläge så valdes att ha kopplingen i full kontakt och alltså släppa igenom hela det efterfrågade motormomentet. Om man däremot var i glappläget, så tillämpades en P regulator, vars uppgift var att styra glappgenomgången så snabbt som möjligt med en låg momentskillnad vid kontakttidpunkten. Denna P regulatorn fungerade genom att använda glappets storlek som referens, och glapp positionsobservatörens skattning av glapp positionen som styrsignal. Skillnaden mellan dessa två multiplicerat med en valbar parameter avgjorde sedan vilket kopplingsmoment som P regulatorn ville sätta ut. Resultatet av reglerstrategin var gott och svängningarna gick att sänka avsevärt samtidigt som den efterfrågade accelerationen uppnåddes nästan lika snabbt som innan. Det visade sig även att regulatorn klarade av att använda sig av storleksobservatörens skattning av glapp storleken och fortfarande uppnå goda resultat, trots att den skattningen inte var perfekt. Slutsatsen kunde sen dras att de tre delarna av projektet hade klarats av och att det formulerade problemet gick att lösa med den föreslagna metoden.
Förord
Jag vill tacka alla på Scania som hjälpt mig
Contents
1 Introduction 1
1.1 Background . . . . 1
1.1.1 Powertrain . . . . 1
1.1.2 Backlash. . . . 3
1.2 Problem formulation . . . . 4
1.3 Purpose . . . . 5
1.4 Boundaries . . . . 5
1.5 Method . . . . 5
1.6 Structure of the report . . . . 6
2 Frame of reference 7 2.1 Literary study. . . . 7
2.1.1 Powertrain . . . . 7
2.1.2 Backlash. . . . 8
2.1.3 Observer . . . . 8
2.1.4 Control . . . . 8
2.1.5 Vehicle parameters . . . . 8
2.2 Patent search . . . . 9
3 Modeling 10 3.1 Analysis of the powertrain . . . 11
3.2 Comparison of existing models at Scania . . . 12
3.2.1 Comparison of powertrain models. . . 12
3.2.2 Comparison of backlash models . . . 15
3.2.3 Comparison of state space representations . . . 15
3.3 Modeling of the powertrain . . . 18
4 Simulations 26 4.1 Analyses of existing Simulink models . . . 26
4.2 Final model . . . 26
4.3 Validation of new model . . . 33
5 Observer 39 5.1 Observer for estimation of backlash position . . . 39
5.2 Observer for estimation of backlash size . . . 40
6 Control 42 6.1 Development of controller . . . 42
7 Results 44 7.1 Simulation with developed observers included in model. . . 44
7.1.1 Backlash position observer. . . 44
7.1.2 Backlash size observer . . . 49
7.2 Simulation with developed controller included in model . . . 52
7.2.1 Using the true backlash size . . . 52
7.2.2 Using backlash sizes with error . . . 56
7.2.3 Testing of the code in a vehicle . . . 58
8 Discussions and conclusions 61 8.1 Evaluation of the Simulink model . . . 61
8.2 Evaluation of the backlash position observer . . . 61
8.3 Evaluation of the backlash size observer . . . 61
8.4 Evaluation of the control strategy. . . 61
8.5 Suggestions for future work . . . 62
9 Appendix 63 9.1 Summary of patents . . . 63
9.1.1 System and method of inhibiting the effects of driveline backlash in a hybrid propulsion system - Patent US7971667 B2 . . . 63
9.1.2 Method to reduce backlash in a drive train - Patent US20070082787 A1 . 63 9.1.3 Backlash elimination in the drivetrain of an electric vehicle - Patent US5821720 A . . . 63
9.1.4 A method of controlling driveline backlash - Patent GB2448671 (A) . . . 63 9.1.5 Transmission with pinion for reduced backlash - Patent US2016305529 (A1) 64
10 References 65
1 Introduction
This introductory chapter will present the background of the master’s thesis, the problems that where needed to be solved, why it was of interest to solve these issues, some limitations of what the master’s thesis would process, the methods used to solve the presented problems, and finally the structure of the report.
1.1 Background
The master’s thesis was made in collaboration with Scania CV AB, whom for a while have been looking to increase the comfort for the drivers of their vehicles. The name of the master’s thesis, Dynamic torque clutch control for heavy duty vehicles using a backlash size and position observer gives a good first description of what was supposed to be achieved. The goal was to be able to use the clutch torque to control a backlash traverse in heavy duty vehicles powertrain in a fast but smooth manner in order to reduce the oscillations in the driveline. If then the control of the backlash is successful the result would be less driveline oscillations which would make it more comfortable for the driver of the vehicle.
1.1.1 Powertrain
The powertrain is the part of the vehicle which gives it momentum and propels it forward and all the parts from the engine to the wheels are included in the powertrain. When instead talking about the driveline it is the same as the powertrain except without the engine. In Scania’s vehicles the most important parts of the powertrain can be summed up to the engine, the clutch, the gearbox, the propeller shaft, the final gear or final drive, the drive shafts, and the wheels. The design of the powertrain is well described by Petterson in [1], in which he investigated two different vehicles from Scania.
The engine is the component that produces and delivers torque to the following parts of the powertrain. In Scania’s vehicles they come in many different types of fuel, electric and hybrid engines.
The clutch makes sure that no torque can be transferred from engine to gearbox during a gear change. It is comprised of a clutch disc which will connect to the clutch cover when in stick mode. During a gear change the clutch will perform a stick-slip change. Stick mode is when the clutch disc is engaged to the clutch cover and while in this mode the entire torque is transmitted from engine to gearbox. Slip mode is when the clutch disc is disengaging from the clutch cover, but is still in contact with it. This means that during this phase power will still be transmitted from engine to gearbox, but not the entire amount produced by the engine.
The amount transmitted depends on how much slipping that is going on between clutch disc and clutch cover and the power not transmitted is lost due to friction. The clutch will be in slip mode from the moment it leaves stick mode until it has passed the contact point. The contact point is the distance between clutch disc and engine flywheel where slip starts and thus torque is first transmitted between the engine and the gearbox. When the clutch disc and clutch cover distance is larger than the contact point distance, torque is no longer transmitted from engine to gearbox and thus it is safe to perform a gear change.
Most of Scania’s gearboxes are comprised of three different parts with their own conversion ratio, together these three parts make up the total conversion ratio of the gearbox. Breaking
down the gearbox GRS905 which was used in the vehicle that was tested on during this master’s thesis, there is first a split gear, then a main gear, and finally a range gear. An example of how a similar gearbox may look can be seen in Figure1 where the black vertical lines corresponds to different gears. A longer line stands for a gear with more teeth than a shorter one. The first conversion takes place in the split gear in the blue area of the figure. It has two different gears, split low and split high. The second conversion takes place in the main gear in the red area of the figure. For the GRS905 it has three different gears, 1, 2 and 3 as well as a crawl gear and a reverse gear. The last conversion is done in the range gear in the green area in the figure.
It has two different gears, range low and range high. The split gear and main gear are made of ordinary gears with different radius and number of teeth in order to get different conversion ratios. The range gear is instead of ordinary gears made of a planetary gear, which consists of one big cog wheel in the middle, with several smaller cog wheels rotating around it. All of them are rotating inside a big ring, the big cog wheel can either be fixed to the big ring, giving no conversion. It can also rotate along with the smaller cog wheels inside the ring giving it some other conversion ratio. With these three different parts of the gearbox it is possible to achieve several different final conversion ratios of the gear box, in the GRS905 gearbox we get 14 different conversion ratios as well as some reverse drive conversion ratios. After performing the conversion the gearbox will transmit the transferred torque through the propeller shaft, which is a flexible shaft. The torque that is transferred to the propeller shaft will be proportional to the conversion ratio of the gearbox and the torque generated by the engine.
The last conversion in most of Scania’s vehicles is made in the final gear, which will receive a torque from the propeller shaft. It will then through a constant conversion transfer a torque to the drive shafts, proportional to the torque transferred by the propeller shaft and the conversion ratio of the final gear. The drive shafts are just like the propeller shaft, flexible shafts and they will finally transmit a torque to the wheels. This can either be done directly through the drive shaft without a conversion, or in some vehicles via the gear hub to the wheels. Just like the final gear this conversion is constant and is done for example in order to get another torque on the drive shafts.
Figure 1: The figure shows an example of how the gearbox layout can look with in order the split gear low and high in the blue area, the main crawl gear, gear 1, 2 and three in the red area and the range gear low and high in the green area.
1.1.2 Backlash
It is impossible to avoid backlash between gears while still being able to turn. This means that there will be some play between the teeth of the cog wheels which will lead to no transfer of torque between the two cog wheels if their teeth are not in contact. The cog wheels need to be able to turn in either direction and the backlash has to be traversed every time it switches between the forward and backward directions. This will in turn lead to a lot of backlash traverses taking place. After a backlash traverse the teeth of the two cog wheels will collide with some torque. This torque will create oscillations in the powertrain which will be felt by the driver and can be seen in later chapters, for example in Figure44. The size of the backlash will have a major impact on the amplitude of these powertrain oscillations and therefore it is desired to keep the backlash as small as possible. The size of the backlash is mainly decided by the production and a smaller size will be more expensive due to a need of smaller error tolerance. The size will other than by the production, also be affected by wear and temperature, which leads to more factors that are hard to control. This leads to the conclusion that it would be better to tackle the problem at hand, without actually reducing the size of the backlash and that is what was studied during this master’s thesis. In [3] it is clearly and thoroughly described what the effects of a backlash are and how the backlash can be modeled. Lagerberg also describes in what ways it is possible to estimate the size of the backlash, as well as the current position in it. Finally Lagerberg mentions possible control strategies that can be applied to solve the problem caused by the backlash traverse.
1.2 Problem formulation
As previously mentioned it is impossible to eliminate backlash completely and also, that the existence of this backlash will result in oscillations in the powertrain after it has been traversed.
The amplitude of these oscillations will vary depending on the difference in torque between the two gears when they collide, hence it is desirable to keep this torque difference as small as possible at the time of contact. This can often be achieved in the production of the gears by minimizing the backlash size. This will lead to a higher cost every time these parts are produced and thus it is desired to solve the problem in some other way. A good solution would be to develop software with some control strategy that could handle the backlash traverse in satisfying manner to achieve less oscillations in the powertrain.
In current Scania vehicles this has been solved in a pretty simple manner, two different torque ramps has been used during the backlash traverse, first a slow torque ramp followed by a fast torque ramp. The initial slow torque ramp is used to keep the torque difference between the gears as small as possible at the time of contact and it is intended to be long enough for the backlash to have been traversed for all cases of gears and driving situations. Then when the gears are in contact it is desired to reach the requested acceleration as quickly as possible, thus the slow torque ramp is followed by a fast torque ramp to achieve this goal. The idea behind this is good but unfortunately the time that these two ramps are in effect is not very good in most cases. This is due to the fact that when choosing the time for these ramps they tested different lengths of them and tried to feel and measure how long the slow torque ramp needed to be without exciting oscillations in the powertrain. This lead to a choice of ramp time that is constant in all cases and since the size of the backlash differs due to a lot of different parameters such as different vehicles, gears, engine torque, wear, and temperature, the time of the torque ramps are often not good enough. Often the slow torque ramp is too long which means that it is still in effect after the time of contact between the gears. This means the time to reach the requested acceleration will be longer than it would be if the fast torque ramp would have been switched on immediately after the time of contact. In some cases the slow torque ramp is instead too short, thus the fast torque ramp will be in effect at the time of contact between the gears. This will lead to oscillations in the powertrain that will be uncomfortable for the driver.
It might also lead to a longer time reaching the desired acceleration since the gears might jump in and out of contact.
In Scania’s vehicles, the backlash is mainly between the gears in the gearbox and the final gear. There also exists something similar to backlash in the shafts due to the wind up that takes place since the shafts are not entirely stiff, however it is negligible compared to the backlash between the gears. As previously mentioned, the gearbox consists of a split gear, a main gear and a range gear, where all three of them have a separate backlash. The backlash of the split gear however may not create any problems since it will often be traversed before the main gear and no torque can be transferred from the gearbox to the propeller shaft before the backlash of the main gear has been traversed. The range gear also has a backlash, it is often smaller than the one of the main gear. To simplify the gearbox was first viewed as one backlash so only the total backlash traverse in the gearbox as well as the backlash traverse in the final gear needed to be observed and controlled. This did not work as well as expected and thus two other methods were tried. First to observe and control the backlash of each part of the gearbox as well as the final gear separately. Second to only observe and control the final gear backlash.
As mentioned in [3], it is of great importance to have precise knowledge of the size of the backlash as well as the current position in it in order to be able to control the backlash traverse satisfactorily. The size of the backlash can be measured either during production or by performing tests on the vehicle, unfortunately it will vary between vehicles and due to the temperature as well as wear in the gears. This means that it is desirable to be able to estimate the size of the backlash continuously in order to get an accurate estimate. The real time position in the backlash during a traverse also needs to be estimated. These two parameters are very important to know precisely in order to be able to control the traverse in a good way. In [3]
Lagerberg mentions good methods of deriving observers for the purpose of estimating these parameters.
1.3 Purpose
The reason why there is an interest in investigating possibilities of controlling backlash traverses is because of the oscillations that may occur in the powertrain as an effect of these traverses.
These oscillations will be felt by the driver as a shunt and shuffle in the vehicle and can be thought of as uncomfortable. Besides the comfortability aspect the oscillations might as mentioned also result in a a longer time needed to reach a desired acceleration of the vehicle, which implies reduced performance. Thus it is due to these two effects of the oscillations in the powertrain that it is of interest to be able to control a backlash traverse in a good manner. For this to be possible it is as previously mentioned, important to have precise knowledge of the size and current position of the backlash. This is in order to eventually be able to minimize the oscillations in the powertrain after a backlash traverse, and hence achieve a more comfortable driving experience.
1.4 Boundaries
The master’s thesis will not deal with delays and errors in the driver requested torque but will assume that the final controller can put out the exact torque it requests instantly. The resulting observer and controller will only deal with straight drives and will thus believe that it is driving straight when even when turning. The observer and controller will not differentiate between vehicles, and won’t change it’s method depending on if it’s a fuel driven vehicle, a hybrid or an electric vehicle.
1.5 Method
First of all the powertrain needed to be modeled analytically in order to get a good under- standing of the physics and its effect on the different parts of the powertrain. This was done similarly to how it was done in [1] and [3] and by comparing the different adjustments that were done in the previous master’s theses [4], [5] and [6] which were all on the same subject.
With the help of these books and studies a conclusion was drawn about how to model the powertrain in the best way in order to achieve good results in the master’s thesis. After this existing Simulink models previously derived at Scania was studied and by using these as help some updated versions were created for the use during this master’s thesis. Using this model it was possible to simulate the behavior of the powertrain using different inputs and driving situations in order to validate the model to the true parameters of the vehicle as well as to mea-
surements from drives. After the Simulink model was considered satisfactory an observer can was derived, the purpose of this observer was to estimate the backlash size and current position in the backlash. This was also validated with the help of simulations that was compared to the expected values. After the estimates of size and position was considered good enough the next step was to add the sensor and actuator dynamics to the Simulink model to better mimic the real vehicle. After that a controller capable of traversing the backlash as fast as possible with the limitation of not inducing any oscillations in the powertrain was derived which then was simulated in order to evaluate how well the controller performs. When the controller and observer were deemed good enough through simulations they were tested in a vehicle in order to see how much improvements that were achieved in reality.
1.6 Structure of the report
The report will after this introductory chapter begin with a frame of reference which will go through how the literary study was performed as well as how the patent search was performed and if any conclusions could be drawn about future patents or if there were any limitations on possible patents. The chapter after that is about the modeling of the powertrain, it includes comparisons and analyses of models previously derived at Scania and finally how a new model was created for this master’s thesis. The following chapter describes the building process of the Simulink models that were used to validate parameters and simulate the powertrain and its behavior. After that there is a chapter about how the observer that estimates the size and current position in the backlash was derived, as well as its theoretical performance. The following chapter addresses the choice of control strategy, how it was implemented and its theoretical performance. After that the results of the master’s thesis is handled and discussions and conclusions of the results will be drawn and explained. The chapter after is an appendix with patent descriptions and other relevant information. In the following and also last chapter there are references to the studies and books that has been the foundation of the master’s thesis.
2 Frame of reference
The frame of reference is a description of the literary study and patent search that was performed as a part of the master’s thesis. The literary study was the foundation of the knowledge which was needed and used during the master’s thesis. The patent search was performed in order to get a clearer picture of existing patents in case there would be an interest to file for a new patent at the end of the master’s thesis, without violating the existing ones.
2.1 Literary study
The Literary study included investigations on the existing literature of the central parts that make up the master’s thesis. The study started with what a powertrain is made up of and how it could be modeled, especially the powertrain in Scania’s vehicles. Secondly how a backlash in the powertrain affects the powertrain and the resulting oscillations after a backlash traverse.
Then how the backlash size and current position could be estimated using an observer. Then how the backlash traverse could be traversed in a suitable manner using some control strategy.
Finally an investigation about the parameters of the test vehicle to used was performed. To find literature that could be relevant for the work of the master’s thesis parts of Scania’s data base was searched, some was initially provided by the supervisor and some provided after requested, and finally searches were made using Google, DiVA, Google patent search, Espacenet and Patent och registreringsverket.
2.1.1 Powertrain
The functions of the powertrain as well as the components it consists of was first of very well described in [1] where Petterson describes this for two different Scania vehicles. This book is the main foundation of the knowledge that was gathered to be able to get a good understanding of the powertrain and how it could be modeled. The other references that analyzes the powertrain [3], [4], [5], [6] and [9] are all based upon the principles that Petterson describes in [1]. The combination of all these books and studies gave a very good and clear picture of how the powertrain works and how it is possible to model it. In Figure 2, the analytical model of the powertrain that is used and described by Lagerberg in [3] can be seen. It is a simple model that consists of an inertia on the engine side of the powertrain which is driven by a torque which is transmitted by the engine itself. This torque is in turn transmitted into the gearbox, propeller shaft, final gear and drive shafts which have been modeled as a conversion, and a flexible shaft with a backlash. After the backlash has been traversed the gearbox will transmit a torque over an inertia on the wheel side of the powertrain. The two inertias of engine side and the wheel side are lumped together with all of the real inertias of the powertrain. In the same way the stiffness in the shaft is a sum of all the stiffnesses in the powertrain and the backlash is a sum of all the backlashes in the powertrain.
Figure 2: The figure shows an example of how the powertrain can be modeled in a simple way with just the engine, two inertias, one conversion, one stiff shaft and one backlash.
2.1.2 Backlash
The backlash dynamics and its effect on the powertrain is investigated in [3]. There Lagerberg first goes through both how a model of a backlash traditionally looks like in the form of a dead zone, and then he also describes the shortcomings of the model which is the basis for the derivation of a more physically correct model. He also describes this physically correct model and goes through in what situations which model is preferred. Both [5] and [6] uses Lagerberg’s work as the foundation for their master’s thesis’ and they try to use and develop upon his work in order to better suit their specific projects. Since this master’s thesis is partly based on theirs they are also valuable to the project.
2.1.3 Observer
Both the actual position in the backlash as well as the size of the backlash are often unknown or uncertain, this leads to the need to be able to estimate them using for example an observer.
This is also something that was studied and described by Lagerberg in [3]. Lagerberg shows how it is possible with an observer to estimate the current position of the backlash and also with a little bit more complex observer also estimate the size of the backlash. In [2] the estimation of nonlinear systems is described using different methods. Their work as well as the work in [5]
are the foundation of the derivation of an observer in this master’s thesis.
2.1.4 Control
Just as for the backlash and the observer Lagerberg described several linear and non linear methods in [3], that could be used as control strategies in order to traverse the backlash in a satisfactorily manner. Furthermore this is improved upon in [8] and [9] with Lagerberg’s work as a foundation. In Tunhag’s master’s thesis [6] he further describes some additional methods on how this can be done. By means of all of these studies a control strategy is derived for this master’s thesis.
2.1.5 Vehicle parameters
The vehicle parameters that were available from measurements and have been of use during the master’s thesis are described here. In [10] there are measurements on the stiffness and damping
of the propeller shaft as well as the counter shaft of several different production models. In [11]
there are measurements of the stiffness and the conversion ratio of the gearbox GRS905 for the 12 gears, the two crawl gears and the two reverse gears. In [12] there are measurements of the size of the inertia on the input shaft as well as for separate components in the gearbox GRS905.
In [13] there are measurements of the size of the backlash in different parts of the drive shafts and final gear. In [14] there are measurements of the backlash in the gearbox GRS905 for all the 12 different gears as well as the two crawl gears and the two reverse gears.
2.2 Patent search
The patent search was performed in order to get a better picture about the existing patents that process the specific areas of the master’s thesis. This is important to gain the knowledge necessary to be able to decide if there already are any patents on the area of dynamic torque clutch control in heavy duty vehicles by controlling the backlash traverse. The patent data bases that were searched was Google patent search, Espacenet and Patent och registreringsverket.
With Google patent search three relevant patents were found and with Espacenet two relevant patents were found.
The patents have been summarized in the appendix. Patent US2016305529 (A1) that was found using Espacenet and it describes a method of minimizing the backlash by the control of the gear change. Since this master’s thesis is not going to control the gear change the conclusion that this patent is not going to be violated can be drawn. Patent US5821720 A which was found by using Google patent search will not be violated by the master’s thesis either since it describes a method of eliminating the backlash only if the the brakes are engaged by using an electric motor to engage the teeth of the gears before applying the driving torque. Since this master’s thesis is not going to be limited by the existence of an electric motor and also since the control is going to be present even if the brakes are not engaged this patent will not be violated by the methods of the master’s thesis. Patent US7971667 B2 which was also found using Google patent search and Patent GB2448671 (A) which was found using Espacenet are both methods of controlling the backlash by the use of hybrid engines and for the same reason as for the electric motor patent this master’s thesis will not violate these patents since it is not going to be limited by the use of hybrid engines in the vehicles as well as the control being performed by using the electronic clutch actuator. The patent that is most similar to the master’s thesis is Patent US20070082787 A1 which was found using Google patent search. The method described by the patent uses the angular velocity measurements that are obtained from several sensors in the vehicle. By using these measurements some control unit puts out an appropriate torque using the clutch to traverse the backlash. This is pretty similar to what will be performed in this master’s thesis, although for the patent it will be done for four-wheel drive vehicles. It also uses some predefined backlash size while in the master’s thesis an observer will be used in order to first estimate the backlash size and position in it to better be able to control the backlash traverse. The conclusion that was drawn from this patent search is that the method that was developed during the master’s thesis is not violating any existing patents, although it would be good to further investigate this if a patent application is desired.
3 Modeling
This chapter describes an analysis of the powertrain physics and the development of different analytical models that describe the system well enough for the purpose of backlash estimation and control. Below is a table with the notation descriptions used in the master’s thesis.
Notation Description
θ Angular position [rad]
θ˙ Angular velocity [rad/s]
θ¨ Angular acceleration [rad/s2]
T Torque [Nm]
J Inertia [kgm2] n Conversion ratio k Shaft stiffness [Nm/rad]
c Shaft damping [Nms/rad]
b Viscous friction [Nms/rad]
α Backlash size [rad]
F Resisting force
Index Description
in Input to a backlash out Output to a backlash
s Shaft windup
b Backlash position
d Shaft windup plus backlash position
eng Engine
os Output shaft
ms Main shaft
ds Drive shaft
w Wheels
gbx Gearbox
f d Final drive
co Backlash in contact
co+ Backlash in positive contact co− Backlash in negative contact bl Backlash not in contact
coco Gearbox and final drive backlashes in contact cobl Only gearbox backlash in contact
blco Only final drive backlash in contact
blbl Neither gearbox nor final drive backlashes in contact o+ Positive offset parameter
o− Negative offset parameter
3.1 Analysis of the powertrain
An analysis of the powertrain and its components is performed in order to be able to gain knowledge on how to possibly model the powertrain analytically. It is important to capture all the physics well enough to be able to develop good observers for the size and state estimation of the backlash and to be able to control the backlash traverse in a satisfying manner.
In [1] Petterson describes the powertrain as "combinations of rotating inertias connected by damped shaft flexibilities". According to Petterson the most flexibility of the powertrain will be found after the gearbox, mainly in the propeller shaft and the drive shafts. Because of that the powertrain can be modeled as stiff up to the gearbox and be thought of as a flexible shaft after the gearbox. In conclusion he models the powertrain from engine to wheels as first an inertia corresponding to the engines total inertias which is driven by the engine output torque. This inertia then transfers the torque through the clutch which is modeled as closed and thus a single inertia consisting of the clutch cover and clutch disc. Followed by the clutch is the gearbox which is modeled as a single inertia and a conversion ratio dependent on the current gear. It then transfers the torque to the propeller shaft modeled as an inertia and a flexible shaft. The propeller shaft transfers the torque to the final gear which is modeled as an inertia and a constant conversion ratio. Then torque is transferred to the drive shafts which are modeled as a single inertia and flexible shaft. The wheels are also modeled together but only as an inertia. This lumping works when driving straight forward since then the wheels have the same angular velocity but when the wheels are turning both the two drive shafts and the two wheels have to be modeled separately for more accuracy.
In [3] Lagerberg further develops this way of modeling by also including backlashes into that description of the powertrain. Lagerberg simplifies the model in order to make it easier and instead of modeling all the parts he just uses two inertias and one flexible shaft followed by a backlash. The first inertia is the engine and the clutch, it is driven by the engine output torque into a total conversion ratio for the whole powertrain. This is followed by a flexible shaft that corresponds to the total powertrain stiffness, that shaft is connected to a backlash consisting of the total backlash size in the powertrain. After the backlash is the second inertia which consists of the gearbox, the propeller shaft, the final gear, the drive shafts, and the wheels. The reason for making the model simpler is because he includes the backlash which complicates a lot of computations. The model he uses is the one described in section2.1.1in Figure2. Lagerberg describes a few different ways to analytically describe a backlash. First of he describes the traditional model, which is when the backlash is thought of as a dead zone. There the shaft torque T is described as in equation1 where α is half the backlash size, k is the shaft stiffness, c the shaft damping. Finally θd = θ1− θ3 is the total shaft displacement between θ1 which is the angle at the beginning of the shaft and θ3which is the angle after the backlash. This model will not be physically correct since when a fast rotation of the shaft occurs the torque will have a non-physical change of sign while the shaft is still in contact on one side of the backlash gap.
T =
k(θd− α) + c ˙θd if θd> α 0 if |θd| < α k(θd+ α) + c ˙θd if θd< −α
(1)
Lagerberg also describes a more physically correct model called the Physical model. It introduces another variable θb= θ2− θ3, which is the position in the backlash and where θ2 is
the angle of the shaft right before the backlash. The shaft torque T will now be described by equation2where ˙θd is the angular velocity of the backlash and shaft windup. ˙θb is the angular velocity of the backlash position which is described by equation3. By using the physical model there are no longer any non-physical changes of sign for the torque and this is the model that Lagerberg chose to continue working with.
T = k(θd− θb) + c( ˙θd− ˙θb) (2)
θ˙b=
max(0, ˙θd+kc(θd− θb)) if θb= −α θ˙d+kc(θd− θb) if |θb| < α min(0, ˙θd+kc(θd− θb)) if θb= α
(3)
3.2 Comparison of existing models at Scania
3.2.1 Comparison of powertrain models
Three analytic powertrain models developed for previous master’s theses at Scania have been compared to better be able to decide on how to best model the powertrain for this master’s thesis. This was done to take the best parts from all the models and eliminate parts that aren’t needed. The first model that was compared is from [4]. Olsson used one model for when the clutch was engaged and one for when it was slipping. The engaged clutch model can be seen in Figure 3. It consists of two lumped inertias that include all inertias from engine to one of the drive shafts and one inertia lumped together by the second drive shaft’s inertia as well as the inertia of the wheels.
Figure 3: The figure shows the analytic model of the powertrain defined by Olsson in [4] for when the clutch is engaged.
The other model that he used was for a slipping clutch and it can be seen in Figure4. Here the model starts from the clutch disc and is modeled as an inertia for the clutch disc, one for the gearbox, one for the propeller shaft, one for the final gear, and then the drive shafts modeled as two inertias connected by a flexible and damped shaft which is finally connected to an inertia consisting of the wheels.
Figure 4: The figure shows the analytic model of the powertrain defined by Olsson in [4] for when the clutch is slipping.
The second powertrain model that was compared is from [5] and can be seen in Figure5. It is comprised of three parts, the first being the engine which drives a torque through an inertia consisting of the engine, engine flywheel, clutch, and gearbox input shaft. It is followed by the split gear conversion ratio, then the inertia of the lay shaft and finally by the main gear modeled as a conversion ratio on a flexible shaft connected to a stiff backlash. The second part consists of the main shaft’s inertia followed by the range gear conversion ratio, then a lumped inertia of the output shaft, propeller shaft, and final gear. It is followed by the final gear conversion ratio and finally the inertia of one drive shaft. The third part of the model consists of the drive shafts modeled as a flexible shaft followed by a lumped inertia of the second drive shaft, the wheels and the vehicle mass.
Figure 5: The figure shows the analytic model of the powertrain defined by Eriksson and Farahani in [5].
The third and final powertrain model that was compared is from [6] and can be seen in Figure6. It is a lot smaller than the two previous models and is modeled as a torque delivered by the engine driving a lumped inertia consisting of all the inertias from engine to the gearbox.
It is followed by the gearbox and final gear modeled as a total conversion ratio on a flexible shaft connected to a stiff backlash. Finally this is followed by an inertia consisting off all inertias from the propeller shaft to the wheels.
Figure 6: The figure shows the analytic model of the powertrain defined by Tunhag in [6].
3.2.2 Comparison of backlash models
The backlash models used in the previous master’s theses were also different between them.
In [4] Olsson decided to model the powertrain without any backlash at all while both in [5]
Eriksson and Farahani, and in [6] Tunhag modeled their backlashes as in Figure7. They got this model from Lagerberg in [3], along with the equations of the backlash. Although they used the same model, they didn’t use the same physical equations to describe the backlash.
Eriksson and Farahani decided to use the more physically correct model called the physical model described in equation 2. Tunhag decided to go with the simpler model called the dead zone model described in equation1.
Figure 7: The figure shows the backlash model defined by Lagerberg in [3].
3.2.3 Comparison of state space representations
The last part of the powertrain modeling that was compared was the different state space representations. Just as for the analytic models Olsson decided to go for two different cases, with an engaged clutch and with a slipping clutch. In the case of the engaged clutch he uses the states defined in equation 4where the first state is the total windup of the powertrain, the second state the engine angular velocity, and the third state the wheel angular velocity. For when the clutch is slipping he uses the states defined in equation5where the first state is now the windup of the drive shafts, the second state the drive shafts angular acceleration, and the third state the wheel angular acceleration.
x =
θeng
n − θw θ˙eng
θ˙w
(4)
x =
θds
n − θw
θ¨ds
θ¨w
(5)
In [5] Eriksson and Farahani chooses to use the state defined as in equation6. Here the first state represents the engines angular velocity, the second state the total windup of the backlash including flexibilities, the third state the position in the backlash, the fourth state the angular
velocity of the main shaft, the fifth state the position of the main shaft, the sixth state the position of the wheels, and the seventh and final state the angular velocity of the wheels. The state space representation is of a switching nature with different modes when the gears are in the backlash and when the gears are in contact. In equation 7 we see the state space matrix A when in contact mode and in equation 8 we see the state space matrix A when in backlash mode. In equation 9 we can see the state space matrices for the control signal B and for the external force on the wheels F .
x =
θ˙eng θd=nθeng
snm − θms
θb
θ˙ms θms
θw θ˙w
˙ x =
(Acox + BTeng+ F Tw, co
Ablx + BTeng+ F Tw, bl (6)
Aco =
−c1
J1(nsnm)2
−k1
J1nsnm
−k1
J1nsnm
c1
J1nsnm 0 0 0
1
nsnm 0 0 −1 0 0 0
0 0 0 0 0 0 0
c1
J2nsnm
k1
J2
−k1
J2
1 J2
c1+c2
(nrnf d)2
−k2
J2(nrnf d)2
k2
J2(nrnf d) c2
J2(nrnf d
0 0 0 1 0 0 0
0 0 0 0 0 0 1
0 0 0 J c2
3(nrnf d)
k2 J3(nrnf d)
−k2
J3
−c2
J3
(7)
Abl=
0 0 0 0 0 0 0
1
nsnm 0 0 −1 0 0 0
0 0 0 0 0 0 0
0 0 0 J −c2
2(nrnf d)2
−k2
J2(nrnf d)2
k2 J2(nrnf d)
c2 J2(nrnf d
0 0 0 1 0 0 0
0 0 0 0 0 0 1
0 0 0 J c2
3(nrnf d)
k2 J3(nrnf d)
−k2 J3
−c2 J3
(8)
B =
1 J1
0 0 0 0 0 0
F =
0 0 0 0 0 0
1 J3
(9)
In [6] Tunhag chooses to use the states defined as in equation10. Here the first state is the total windup of the powertrain, the second state is the engine angular velocity, and the third state the wheel angular velocity. This state space representation is also of a switching nature but with three different modes, one when the gears are in the backlash and one when in positive contact and one when in negative contact. In equation11the state space matrix A is defined, it
