Weight Estimation through Frequency Analysis

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Weight Estimation through Frequency Analysis

Hampus Johansson

Nicklas Höglund

Fluid and Mechanical Engineering Systems

Master thesis

Department of Management and Engineering (IEI) LIU-IEI-TEK-A—09/00638—SE

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Weight Estimation through Frequency Analysis

Thesis for the Degree of Master of Science Department of Management and Engineering (IEI) Division of Fluid and Mechanical Engineering Systems

Linköping University By

Hampus Johansson

Nicklas Höglund

Supervisor at Linköping University:

Karl-Erik Rydberg

Supervisor at Scania CV AB: Pär Degerman

Master thesis

Department of Management and Engineering (IEI) LIU-IEI-TEK-A—09/00638—SE

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Abstract

The weight of a heavy duty vehicle plays an important role when dealing with different control systems. Examples of control units in a truck that need this

parameter are the ones used to control the brakes, the engine and the gearbox. An accurate estimation of the weight leads not only to a more fuel efficient and safer transport, but also assures the driver that current law limits are not exceeded. The weight can be estimated with pretty good accuracy if the truck is equipped with air suspension. In trucks that lack this type of suspension other methods are used to estimate the weight. At present these methods are inaccurate. In this thesis a new method where the weight is to be estimated through frequency analysis of the truck’s driveline is developed and evaluated.

The results show that this method is not better than existing ways of determining the weight. The method could, however, be used for other purposes.

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Acknowledgements

It has been an interesting, developing and fun experience writing our master thesis at Scania. Throughout the project we have encountered many challenges and

difficulties which often led to discussions with different people at Scania. First, we would like to thank our supervisor Pär Degerman at Scania’s department for pre-development, REP. Pär gave us great responsibility and freedom to work in our own way and was always there for us to answer our questions and support and

encourage us when we encountered difficulties. We would also like to thank everyone else at REP for their guidance and feedback on our work. We really

appreciate the time they have spared to answer questions and explain how a Scania truck works.

Second, we send our thanks to Professor Karl-Erik Rydberg at Linköping Institute of Technology for helping us getting in contact with Pär and approving the thesis idea. Karl-Erik is professor in fluid power at the division for Fluid and Mechanical

Engineering Systems and is also the examinator for this thesis.

Finally, we would like to thank everyone else at Scania that has been involved in our project for their kindness and willingness to help us.

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1 Introduction

The weight of a heavy truck is of great importance. The weight varies with the load that the truck has to pull and accurate knowledge about this parameter is central to different control systems such as engine control, automated gearboxes, breaking aid systems and interactive driver training systems. In addition, it is vital for the driver to know the weight so the payload can be maximized without exceeding law limits. At present, the weight is estimated by the use of air suspension (if the truck is equipped with such), acceleration and longitudinal forces or by a combination of these.

1.1 Purpose and objective

The objective with this master thesis is to evaluate a new weight estimating method based on frequency analysis of the driveline. The method is evaluated and compared with today’s methods by the use of simulations and tests. The idea is to approximate the truck as a spring-mass system and determine the weight. The project is

associated with some requirements presented in the table below.

1.2 Method

First, to get an idea of how the problem is tackled today, meetings were held with people at Scania that have been working with mass estimation earlier. Second, a literature study was made to gather even more information and to see how people outside Scania have solved similar problems. During the literature study useful

information regarding mathematical modelling of a truck’s driveline was found. One of the discovered models later formed the basis for the driveline model used in this project. Data was collected from Scania’s test trucks for verification and evaluation of this driveline model. Throughout the whole working process, many meetings were arranged to broaden the knowledge about how a truck works and how its important control units communicate.

1_{Controller Area Network}

Requirement nr

Description Priority Comment

1. Only use existing sensors. Base 2. Determine if the proposed method is

feasible.

Base 3. Model the driveline as a spring-mass

system.

Base 4. The trucks CAN1-system has to be

used to measure all signals.

Extra 5. The weight estimate has to be better

than today’s methods that are used on trucks without air suspension.

Extra

6. The new method has to consider different driving scenarios and estimate the weight only when the results are reliable.

Extra Difficulties arise when driving up- or downhill.

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1.3 Delimitations

The task was to investigate this new weight estimation method and try to determine if it could work. There were no requirements of implementation or automation of the method. At this stage of the developing process it was good enough if the method would work on one single truck with a certain configuration. The time frame for this thesis work was set to six months.

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2 Pilot study

2.1 Methods used today

Currently, there are three methods used in Scania’s trucks to estimate the vehicle mass. Two of the methods are based on a change in acceleration and the third one is based on measuring the pressure in the air suspension’s bellows.

2.1.1 Estimation based on acceleration

The total weight can be estimated by measuring the wheel acceleration, the propulsive torque and other external forces that affects the truck and then apply Newton’s second law (∑F=m*a). The wheel acceleration can be determined by differentiating the wheel speed and the propulsive torque from the engine torque and the trucks gear ratio. One problem with this method is that the measurements of the wheel speed and engine torque have to be made during a short period of time to guarantee that the external forces can be approximated as constant [14]. The accuracy of this method is not high for a normal truck, but is even lower for heavier vehicles and/or weaker engines.

2.1.2 Estimation during gear change

Another method estimates the weight throughout a gear change. There is a big change in both acceleration and engine torque once the change is performed and by measuring these, the weight can be obtained from Newton’s second law (∑F=m*a). The benefit of using this method is that the big difference in acceleration and motor torque during the gear change makes the measurement errors less significant [14]. The disadvantage is the oscillations in the driveline which are induced by the big difference in acceleration and motor torque. The accuracy of this method is similar to that of the acceleration method.

2.1.3 Estimation based on air suspension pressure

The most accurate weight estimation method used at Scania is to measure the pressure in each of the air suspension bellows and then calculate the weight. The advantage with this method, more than its accuracy, is that it gives information about the weight distribution among the different wheel axles. The disadvantage is that it requires air suspension on all axles, which not every truck has.

2.2 The CAN protocol

Controller Area Network (CAN) is a protocol that enables different ECU’s2 to

communicate in a vehicle. The protocol uses serial communication and the different messages are prioritized to avoid collision between them. This means that the most critical message (e.g. brake request) get the highest priority and is sent before a less important message (e.g. climate control).

As seen in figure 1, the CAN protocol in a Scania truck has three different levels namely green, yellow and red. The red level is the most critical and deals with

messages related to the breaking system and the engine for example. The red level

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has the highest priority and if an error on the red level occurs, the truck cannot be driven. The yellow level is the second most critical. Therefore, it has priority number 2 and deals with messages related to the tachometer and the all wheel drive system for example. The green level is the least critical level, with priority number 3, and deals with systems such as climate control. The three buses are connected by the

coordinator system (COO).

Figure 1 - The structure of the Controller Area Network (CAN) in a Scania truck. There are three buses: green, yellow and red connected via the coordinator (COO).

In order to check diagnostics and change ECU algorithms it is possible to connect a laptop to CAN on test vehicles held at Scania. By creating this connection it is also possible to log different CAN messages that are sent over the network. By the use of a device called M-LOG (showed in Figure 2) CAN messages can be stored during a test drive and used for analysis and diagnostic purposes. The messages on CAN are not sent with a fixed frequency which complicates the procedure of logging data. However, the M-LOG is quite competent in that sense because it can handle these signals (as well as offsets and different units) and convert them to physical units.

COO Coordinator system SMS/SMA Suspension management system AWD

All wheel drive system ICL Instrumental cluster system TCO Tachometer system GMS Gear management system EMS Engine management system BMS Brake management system CSS Crash safety system ACC Automatic climate control CTS

Clock and timer system

Green

Red

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Figure 2 – M-LOG, a device that is used for storing CAN data.

The CAN data can be converted to mat-files, which are compatible with the computer software MATLAB, containing the different messages. This makes it possible to analyse and process the data in a more convenient and easy way using an M-LOG compared to other programs such as CANalyser.

2.3 FFT – Fast Fourier transform

The Fast Fourier transform (FFT) is an algorithm that computes the Discrete Fourier transform (DFT) in a more efficient way than according to the definition of DFT. The DFT transforms a digital (discrete) signal to the frequency domain and thus making it possible to see the frequencies and amplitudes that build up the signal. For example, the signal Y =2⋅cos(2π⋅t)+cos(2π⋅5t)has one frequency at 1 Hz with amplitude 2 and one frequency at 5 Hz with amplitude 1. The Fourier transform of this signal is shown in Figure 3.

Figure 3 - The signal to the left contain the two frequencies 1 and 5 Hz with amplitude 2 and 1 respectively, which is displayed in the FFT spectrum to the right.

It is now easy to see the frequencies as peaks in the frequency domain, with the height of the peak corresponding to the amplitude of the oscillation with that frequency.

The Fourier transform works on signals of infinite duration. The Fourier transform assumes that any signal can be created by adding a series of sine or cosine waves of infinite duration. Because sine waves are periodic, the Fourier transform works as if the data were periodic for all time. This induces problems when an integral number of cycles do not exactly fit into the measurement time. In that case the end point of one signal segment in the infinite FFT signal does not connect

FFT 0 1 2 3 4 5 6 0 1 2 f [Hz] A m pl itu de 0 0.5 1 1.5 2 2.5 3 -5 0 5 t [s] Y

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smoothly with the beginning of the next, resulting in broadened frequency peaks. This phenomenon is called frequency leakage and is illustrated in Figure 4.

Figure 4 - Frequency leakage occurs when the oscillation period does not exactly fit the measurement time.

If not, false frequency peaks will show in the spectrum If the signal period is an integer multiple of the measurement time, the spectrum will be true.

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2.4 Window function

A way of solving the problem of frequency leakage is to use a technique called windowing. This is done by multiplying the measured signal with a window function. The purpose of doing so is to match the beginning and the end of the signal and thus minimizing the frequency leakage. It is important to study the frequencies present in the signal before it is windowed in order to verify that no vital frequencies are lost. The theory of windowing is illustrated in Figure 5.

Figure 5 - Window functions can match the beginning and the end of the signal and thus minimize the frequency leakage.

2.4.1 Blackman window

The equation for the Blackman window signal, which is used in this report, is

N n N n N n n w  ≤ ≤      +       − =0.42 0.5cos 2 0.08cos 4 , 0 ) ( π π

where N is the window length

n_{is the data index}

Because the window signal is zero at the beginning and the end, the windowed signal segments will connect perfectly in the infinite FFT signal.

If the signal period is NOT an integer multiple of the measurement time, spectral leakage will occur.

×

However, if the signal is windowed, the leakage is reduced.

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2.5 Test vehicles and sensors

Two test vehicles have been used throughout the project and these can be seen in Figure 6. It is tradition at Scania to name the different test vehicles in order to

separate them from each other. The first vehicle is called Mulle and is an R500 rigid truck with a 16-litre V8 engine and 500 horsepower. Mulle has air suspension on all axles so the weight of the truck can be calculated by measuring the pressure in the air bellows. The second vehicle is called Ebola and is an R440 tractor with a 13-litre inline 6 cylinder engine with 440 horsepower. Ebola has leaf springs on the front axle and air suspension on the rear axle.

Figure 6 – The two test vehicles used throughout the project: Mulle (left) is a R500 rigid with a V8 engine and air suspension on all axles. Ebola (right) is a R440 tractor with an inline 6 cylinder engine and leaf springs on the front axle and air suspension on the rear axle.

The weight was changed during the tests with Ebola by connecting specially made weight frames to the tractor. There is a certain coupling underneath the frame that connects to the turntable of the tractor and the legs that support the frame can be raised and secured. In addition, a trailer can be connected to the tractor to increase the weight.

Figure 7 – One of the weight frames that were used to change the weight of the tractor Ebola. This particular frame has a weight of approximately 5 tonnes.

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The sensors that have been used to measure the vehicle’s speed are a fair few and only two will be covered here. The first one is called a tachometer and is attached to the propeller shaft just after the gearbox. The tachometer is a sensor that measures rotational speed and by passing this information on via CAN it can be transformed into translational vehicle speed in an ECU. The second sensor is called an RPM sensor and measures the revolution per minute of the engine’s crank shaft. Again, the signal from this sensor can also be transformed from rotational speed into vehicle speed in an ECU.

The signals are sampled at a rate of 50 Hz through the CAN system which may seem like a low rate. However, the frequencies of interest in this project are up to roughly 15-20 Hz and thus still fulfilling the Nyquist criteria at 25

2 50

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3 Driveline modelling

Two driveline models have been used to analyze the frequencies in the driveline. The first model includes all parts of the driveline that are considered important for the driveline dynamics. The second model includes the same components but is simplified to a one degree of freedom system, where the equivalent stiffness is calculated at the drive shafts.

Figure 8 - Schematic picture of the driveline.

Because the truck’s driveline is a very complex system it has to be simplified so as to describe its dynamic properties in a manner that does not demand unnecessary complicated calculations. The first simplification done in this thesis was to neglect the damping that existed in the system and only consider the stiffnesses and moments of inertia. Only the weakest parts of the driveline have been included in the model, namely the clutch, the gearbox, the propeller shaft and the drive shafts.

3.1 Driveline model

To determine which components in the driveline that are the weakest, the references [8], [16], [5] were studied and calculations according to Appendix 3 and 4 were carried out. The weakest parts of the driveline were the clutch, the gearbox, the propeller shaft and the drive shafts resulting in the model described by Figure 9.

J1 J=J_1 clutch c=k_c J2 J=J_2 gear_box c=k_t gear__box=i_t J3 J=J_3 prop_shaft c=k_p J4 J=J_4 final_gear=i_f drive_shaft c=k_d J5 J=J_5

Figure 9 - The driveline model visualized with the simulation and modelling tool Dymola. The clutch, the gearbox, the propeller shaft and the drive shafts are considered to be the weakest parts of the driveline and they are therefore included in the model.

Final drive Propeller shaft Drive shaft Engine Gearbox C lu tc h Wheel

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The inertias in the model are distributed as follows:           + + = + + = = = + + = v w d f d f p p t c fw e J J J J i J J J J J J J J J J J J 5 2 4 3 2 1 2 2 (3.1.1)

where the indices represents: e – engine fw – flywheel c – clutch

t – gearbox transmission p – propeller shaft

f – final gear d – one drive shaft w – wheels

v – vehicle

v

J represents the inertia from the gross weight (m) of the vehicle. Because the

propulsion force of the truck is actuated in the contact point between the road and the wheel, the truck can be represented as a point mass with the wheel radius (r_w) as its distance to the centre of rotation [3], [12] and [14].

Figure 10 - The total weight of the truck is represented as a point mass with the wheel radius as its distance to the centre of rotation.

This results in the following equation 2

w

v mr

J =

By applying Newton’s second law of rotation (

∑

τ

=J

θ

&&) on each inertia, the system

can be identified.

First inertia (J1): J &1θ&1=Me−kc

(

θ1−θ2

)

(3.1.2)

Second inertia (J2): J2θ&&2 =kc

(

θ1−θ2

)

−kt

(

θ2−θ3it

)

(3.1.3)

Third inertia (J3): J &3

θ

&3 =kt

(

θ

2−

θ

3it

)

⋅it−kp

(

θ

3−

θ

4

)

(3.1.4)

w r

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Fourth inertia (J4): J4

θ

&&4 =kp

(

θ

3 −

θ

4

)

−kd

(

θ

4 if −

θ

5

)

if (3.1.5)

Fifth inertia (J5): J5

θ

&&5 =kd

(

θ

4 if −

θ

5

)

−Fwrw (3.1.6)

w

F represents the external forces acting on the vehicle.

α F F F Fw = a + r + (3.1.7) where 2 2 2 1 w w a a w a c A r

F = ρ θ& is the air drag force (3.1.8)

(

r r w w

)

r m c c r

F = 1 + 2

θ

& is the rolling resistance force (3.1.9)

where c_r₁and c_r₂ are the rolling resistance coefficients

( )

α

α mgsin

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3.1.1 State space equations

To model this system as a state space system, the states were chosen to get as simple equations as possible. The easiest way was to select the torsion of each spring and the velocity of each inertia as states. The states are represented by the variables x1 to x9.                 = = = = = − = − = − = − = 5 9 4 8 3 7 2 6 1 5 5 4 4 4 3 3 3 2 2 2 1 1

θ

& & & & & x x x x x i x x i x x f t (3.1.11)

By using equation (3.1.2) to (3.1.11) the state space equations can be written as follows.

(

)

(

)

(

)

( )

(

)

                                + − − − =         − = − = − = − = − = − = − = − =

α

ρ

sin 2 1 1 1 1 1 1 1 2 9 3 11 2 2 4 5 9 4 3 4 8 3 2 3 7 2 1 2 6 1 1 5 9 8 4 8 7 3 7 6 2 6 5 1 g c m r x r A c x r mc x k J x i x k x k J x x k x i k J x x k x k J x x k M J x x i x x x x x i x x x x x x r w w a a w w r d f d p p t t t c c e f t & & & & & & & & & (3.1.12)

The easiest way to calculate the natural frequencies of this system is to describe it on matrix form and calculate the eigenvalues of the system matrix.

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                                  + − +                                   − +                             − − − − − − − − − = )) sin( ( 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 / 0 0 0 0 0 0 0 0 ) /( / 0 0 0 0 0 0 0 0 / / 0 0 0 0 0 0 0 0 / / 0 0 0 0 0 0 0 0 / 1 / 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 2 3 2 2 5 4 4 3 3 2 2 1 α ρ r m c g x r A c x r mc J k i J k J k J k J i k J k J k J k i i x r w w a a w A w r d f d p p f t t c c f t 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 7 6 & (3.1.13)

where A is the system matrix.

3.1.2 Natural frequencies

The air drag makes the states nonlinear, which is not preferred when analyzing the system. Because the air drag is a relatively static force at small time intervals where the speed is constant, it has been neglected when analyzing the frequencies in the driveline.

According to [17], the rolling resistance of truck tires is normally lower than that of passenger cars due to the higher inflation pressure in truck tires (typically 620-827 kPa for trucks and 193-248 kPa for passenger cars). In addition, [17] also states that the influence of speed on the rolling resistance may be ignored in initial calculations. The second coefficient of rolling resistance (c_r₂) has therefore been neglected in the

calculations of the natural frequency.

The natural frequencies of the mechanical system described by equation (3.1.13) is given by the eigenvalues (λ) of the system matrix ( A ).

π

λ

π

ω

2 ) ( 2 abs f n n = = (3.1.14)

The eigenvalues, in turn, are given by the equation

(

)

0

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where λ represent the eigenvalues and I is the identity matrix.

3.2 Simplified driveline model

The simplified driveline model is based on the references [3] and [12]. To make the model accurate the inertias are calculated in different ways for different gears and all stiffnesses in the driveline model are used to calculate an equivalent stiffness. This stiffness is always calculated at the drive shafts because these are often the weakest part of the driveline.

J1 J=J_1 J2 J=J_2 equivalent_stiffness c=k_eq gear_box=i_t final_gear=i_f

Figure 11 - The simplified driveline model visualized with Dymola. The equivalent stiffness includes all stiffnesses in the extended model but is calculated at the drive shafts. The moments of inertia, J1 and J2, varies dependent on which stiffness that is the weakest.

( )

          <         + + + + + + < + + + < + + = c t f t d t f d f p t c fw e f t d c t t c fw e f t d t c c fw e k k i i k i i J J J J J J J i i k k k J J J J i i k k k J J J J , if , if , if 2 2 2 2 2 1 (3.2.1)

( )

           < + + < + + +         + + < + + +         + + + = c t f t d w w d f t d c t w w d f f d f p f t d t c w w d f f d f p f t t k k i i k mr J J i i k k k mr J J i i J J J i i k k k mr J J i i J J J i i J J , if , if , if 2 2 2 2 2 2 2 2 2 2 2 2 (3.2.2)

Newton’s second law for rotation (

∑

τ

=J

θ

&&) ⇒

First inertia (J1):

( )

t f f t eq e ii i i k M J _       − − = 2 1 1 1

θ

&& (3.2.3) Second inertia (J2): w w f t eq F r i i k J _−       − = 1 ₂ 2 2

θ

&& (3.2.4)

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3.2.1 State space equations

To analyze this system in a good way it is preferred to describe it on state space form. The drive shaft torsion, the engine speed (

θ

& ) and the wheel speed (₁

θ

& ) are ₂

used as state variables (x1, x2 and x3).

         = = − = 2 3 1 2 2 1 1 θ θ θ θ & & x x i i x f t (3.2.5)

(

)

         − =         − = − = w w f t e f t r F kx J x x i i k M J x x i i x x 1 2 3 1 1 2 3 2 1 1 1 & & & (3.2.6)

On matrix form the state space equations for the simplified driveline model yields

( )

(

)

( )

(

)

          + − +             − +           − − − = α ρ sin 0 0 2 1 0 0 0 0 0 1 1 0 1 2 3 2 2 2 1 g c m r x r A c x A r mc J k i i J k i i x r w w a a w w r eq f t eq f t 4 4 4 4 4 4 8 4 4 4 4 4 4 7 6 & (3.2.7)

where A is the system matrix.

3.2.2 Natural frequencies

The air drag (F_a) and the second coefficient of rolling resistance (cr2) have been neglected when analyzing the frequencies as mentioned in section 3.1.2. The natural frequencies are calculated as in equations (3.1.14) and (3.1.15). For this simplified system, the determinant can be calculated analytically and equation (3.1.15) yields

        + ± = = ⇒ =         + − ⇒ =           − − − − 2 2 1 3 , 2 1 2 2 1 3 2 1 1 ) ( 1 and 0 0 ) ( 0 0 0 / 0 ) /( 1 ) /( 1 det J i i J k J k i i J k J k i i J k i i f t eq eq f t eq eq f t eq f t

λ

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Equation (3.1.14) then gives the following expression for the natural frequency for the simplified driveline model, using the second or third eigenvalue.

( )

       + = 2 2 1 1 1 2 1 J i i J k f f t eq n

π

(3.2.8)

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4 First weight estimation strategy

This strategy is based on frequency analysis of speed data via CAN. If the vehicle’s driveline dynamics are approximated as a spring-mass system with the drive shafts as the weakest link, the equation for the natural frequency would be (analogous with equation (3.2.9)):       + = ₂ 1 2 1 1 2 1 i J J k f_n _eq

π

(4.1.1)

where i is the total gear ratio, keq is the equivalent stiffness of the driveline and J1 and J2 are the two inertias, respectively. For high gears the ratio ( i) is small making

1

J₁i2 >>

1

J₂ and thus simplifying the expression to

2 1 , 2 1 high eq high n i J k f

π

= (4.1.2)

where the index “high” indicates that the expression is valid at high gears. An example that validates this simplification is that, for Ebola

2 2 1 1 343 1 J i J = ⋅ at the highest gear and a vehicle weight of 40 000 kg.

Every vehicle has its own specific constants like for example the wheel radius,

number of cylinders in the engine and stiffness of the drive shafts. These parameters are stored in the different ECU’s control systems in the truck and are used to

optimize the vehicle’s performance. Using some of these parameters to calculate the moment of inertia (J₁), where the number of included elements depends on the

model’s complexity, it is possible to determine the equivalent stiffness of the driveline from equation (4.1.2):

(

)

2 1 2 , 2 _n_high _high eq f J i k =

π

. (4.1.3)

If frequency analysis is applied, the natural frequency (

ω

_n,_low) of the driveline can be determined. In accordance with the reasoning in section 3.1 the truck’s overall mass can be approximated as a rotating point mass with the wheel radius (r_w) as its

distance to the centre of rotation. The second moment of inertia (J₂) may then be

described by 2 2 Jw mrw

J = + . (4.1.4)

Combining the equations (4.1.1 – 4.1.4) leads to the following expression for the vehicle weight:

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(

)

       − − = _w eq low low n low eq w J k i f J i J k r m ₂ , 1 2 1 2 2 1

π

.

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5 Simulation results

Simulations are important because they illustrate mathematical relationships that are sometimes hard to see in equations and they are often useful to verify analytic

calculations. In this chapter the results from various simulations are presented. First, the results from the two driveline models described in chapter 3 are displayed where the natural frequency of the driveline is shown in relation to different gears and vehicle weights. Second, the models are compared with each other and the analytic results are verified by Dymola simulations. Finally, the results from the simulations are concluded.

The constants that define the driveline’s rotational dynamics have to be accurately known to make a good estimation of the frequency. Appendix 1 and 2 show the constants for Ebola and Mulle, respectively.

5.1 Driveline model

Solving equation (3.1.15) for the state space system described by equation (3.1.13) and using equation (3.1.14) for the second eigenvalue, representing the first

oscillation mode of the driveline, gives the results plotted in Figure 12 for Ebola and Figure 13 for Mulle.

CRL 1 3 5 7 9 11 _0.5 1 1.5 2 2.5 3 3.5 4 _{x 10}4 0 1 2 3 4 5 6 7 8 X: -1 Y: 5000 Z: 1.766 Vehicle weight [kg] Natural frequency of the driveline for the driveline model

X: -1 Y: 4e+004 Z: 0.8852 X: 12 Y: 5000 Z: 7.612 Gear X: 12 Y: 4e+004 Z: 7.525 N at ur al f re qu en cy f or t he d riv el in e [H z]

Figure 12 - The natural frequency for the driveline model for Ebola. The extreme values of the weight and gear are pinpointed which makes it easy to see that the frequency depend more on the weight for lower gears than for higher.

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CRL 1 3 5 7 9 11 _0.5 1 1.5 2 2.5 3 3.5 4 _{x 10}4 0 1 2 3 4 5 6 7 8 9 X: -1 Y: 5000 Z: 1.65 Vehicle weight [kg] Natural frequency for the driveline for the driveline model

Figure 13 - The natural frequency for the driveline model for Mulle.

The labeled corners of the surface point out that the natural frequency depend more on the weight for low gears than for high. This makes it easier to estimate the weight for low gears.

Another conclusion that can be made from studying Figure 12 and Figure 13 is that for higher vehicle weight, the frequency is not as dependent on the weight. Graphically, this means that the slope of the curve along the weight axis gets steeper with decreasing weight and thus making it easier to estimate the weight at low vehicle weight.

5.2 Simplified driveline model

Figure 14 (for Ebola) and Figure 15 (for Mulle) shows the natural frequency for the simplified driveline model, described by equation (3.2.8), for different weights and gears. The constants that have been used for this model are attached in Appendix 1 and 2. The equivalent stiffness has to be calculated for each gear because it

depends on the gear ratio and the gearbox stiffness.

( )

1 2 2 2 1 1 1 1 −         + + + = d f p f t t f t c eq k i k i i k i i k k (5.2.1)

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CRL 1 3 5 7 9 11 _0.5 1 1.5 2 2.5 3 3.5 4 x 104 0 1 2 3 4 5 6 7 8 X: -1 Y: 5000 Z: 1.765 Vehicle weight [kg] Natural frequency for the driveline for the simplified driveline model

Figure 14 - Natural frequency for the simplified driveline model for Ebola. Once again it is noticeable that the frequency depend more on the weight for low gears than for high gears.

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CRL 1 3 5 7 9 11 _0.5 1 1.5 2 2.5 3 3.5 4 _{x 10}4 0 1 2 3 4 5 6 7 8 X: -1 Y: 5000 Z: 1.65 Vehicle weight [kg] Natural frequency for the driveline for the simplified driveline model

Figure 15 - Natural frequency for the simplified driveline model for Mulle.

The corners of the surfaces are labeled to point out that the natural frequency depend more on the weight for low gears than for high gears, which was expected because Figure 12 showed the same property. This property can also be seen in equation (3.2.9) where the gear ratio (i_t) is high for low gears making the second inertia (J₂) contribute more to the natural frequency (remembering that J₂ includes

the vehicle weight).

5.3 Comparison between the models

To compare the two driveline models, the natural frequency for the driveline model was subtracted from the natural frequency for the simplified driveline model. The results from this subtraction are displayed in Figure 16 (for Ebola) and Figure 18 (for Mulle).

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CRL 1 3 5 7 9 11 0.5 1 1.5 2 2.5 3 3.5 4 x 104 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 X: 7 Y: 5000 Z: -0.01894 Gear

Difference in natural frequency of the driveline between the driveline model and the simplified driveline model

Vehicle weight [kg] N at ur al f re qu en cy d iff er en ce [ H z]

Figure 16 - Comparison between the models for Ebola. The simplified driveline model is a good approximation for gears lower than the seventh.

The difference between the two driveline models is close to zero for gears lower than the seventh for Ebola. For higher gears than the seventh, it is clear that the difference between the models becomes more significant. It is important to remember from section 5.1 that the weight is easier to estimate at lower gears, making the simplified model a reasonable approximation.

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CRL CRH0 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 10 12 14 16 18x 10 4 Gear S tif fn es s [N m /r ad ]

The stiffnesses which are compared in the simplified driveline model drive shafts (k_d/(i_t2i_f2))

gearbox (k_t) clutch (k_c)

Figure 17 - The three stiffnesses, compared in section 3.2 to distribute the inertias, for Ebola. Note that the drive shafts hold the lowest stiffness for all gears except the twelfth, where the clutch is the

weakest.

Figure 17 reveals that the drive shafts hold the lowest and hence the dominant stiffness for all gears but the twelfth. At the twelfth gear, the clutch has the lowest stiffness. The inertias are therefore moved, according to section 3.2, so that the value of the first inertia (J₁) gets lower and the frequency higher. This explains the

appearance of Figure 16 for the highest gear. The reason that the difference between the two models is small for low gears (as seen in Figure 16) is that the drive shaft stiffness is by far the lowest there, making the simplification accurate. For higher gears, the drive shaft stiffness approaches the clutch stiffness, which makes the simplification less accurate. When the drive shaft stiffness is moved, to be able to compare it with the gearbox and the clutch stiffness, it is in inverse proportion to the quadratic of the gear ratio

( )

       2 f t d i i k

. The difference displayed in Figure 16 seems to mirror this behaviour, which strengthens the theory described above.

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CRL 1 3 5 7 9 11 1 2 3 4 x 104 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 Vehicle weight [kg] Difference in natural frequency of the driveline between

the driveline model and the simplified driveline model

X: 8 Y: 5000 Z: -0.02919 Gear N at ur al f re qu en cy d iff er en ce [ H z]

Figure 18 - Comparison between the models for Mulle. The simplified driveline model is a good approximation for gears lower than the eighth.

The difference between the two driveline models is close to zero for gears lower than the eighth for Mulle, making the simplified driveline model a good approximation for those gears.

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CRL CRH0 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 10 12 14 16 18x 10 4 Gear S tif fn es s [N m /r ad ]

The stiffnesses which are compared in the simplified driveline model drive shafts (k_d/(i_t2i_f2))

gearbox (k_t) clutch (k_c)

Figure 19 - The three stiffnesses, compared in section 3.2 to distribute the inertias, for Mulle. The drive shaft stiffness is the lowest for all gears.

In Figure 19 it is obvious that the drive shafts has the lowest stiffness for all gears, which explains why Figure 18 does not show the same behaviour as Figure 16 does for the highest gear.

5.4 Dymola simulations

Dymola is a multi-engineering modelling and simulation tool used in the automotive industry to simulate complex and integrated systems. By the use of Dymola, two models representing the driveline were created and can be viewed in Figure 20 and Figure 21. The idea was to verify that the analytic models were correct and hence secure that the results from these could be trusted. As mentioned earlier in this chapter, the models consist of blocks that represent the driveline’s different parts in terms of stiffness and moment of inertia.

J1 J=J_1 clutch c=k_c J2 J=J_2 gear_box c=k_t gear__box=i_t J3 J=J_3 prop_shaft c=k_p J4 J=J_4 final_gear=i_f drive_shaft c=k_d J5 J=J_5

Figure 20 – Illustration of the Dymola model that represents the rotational dynamics of a truck’s driveline.

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J1 J=J_1 J2 J=J_2 equivalent_stiffness c=k_ekv gear_box=i_t final_gear=i_f

Figure 21 – The simplified Dymola model for a truck’s driveline.

Both models were linearized in Dymola and by the use of a MATLAB script written by Eric Gomez at Scania, the natural frequencies were determined through the

eigenvalues of the systems. These calculations showed the exact same frequencies as the ones displayed in Figure 12 to Figure 15. Thus, the analytic calculations are correct.

5.5 Simulation conclusions

As stated in section 5.2, the equivalent stiffness varies between different gears because the gear ratio as well as the gearbox stiffness is not constant for different gears. Furthermore, the simplified driveline model does not match the driveline model for high gears. This unfortunately leads to the conclusion that the strategy that has played a central role during the project is not going to work as intended remembering from chapter 4 that the equivalent stiffness ( keq) has to be the same for both high and

low gears. A new successful strategy would be to analyze the natural frequency of the driveline at low enough engine speed for the engine to excite this frequency (described further in section 6.2.1). In addition, the stiffness of the driveline is determined by the use of constants instead of being calculated from the natural frequency. The resulting frequency could then be used to determine the vehicle weight.

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6 Frequency analysis

It is important to have knowledge about what frequencies to expect when analyzing dynamic systems. This chapter explains how the data that form the basis for the frequency analysis have been selected. In addition, it also gives details on how the natural frequency of the driveline can be determined and how the engine and the propeller shaft contribute to driveline oscillations.

6.1 Data selection

Two methods were used in order to find the frequencies present in the driveline dynamics. The first method includes measuring the vehicle speed with the

tachometer described in section 2.5. A typical graph of the vehicle speed during a test drive from Södertälje Technical Centre (STC) to Oxelösund 090129 is displayed in Figure 22. 0 500 1000 1500 2000 2500 3000 3500 4000 0 10 20 30 40 50 60 70 80 90 Time [s] V eh ic le s pe ed [ km /h ]

Vehicle speed from tachometer sensor

Figure 22 – The vehicle speed during a test drive with Mulle between Södertälje Technical Centre and Oxelösund 090129.

Now, if this signal would be used to form the basis for a frequency analysis, the mean value would first have to be removed so that only the frequencies that originate from the vehicle dynamics would appear. This work can become quite extensive and challenging because the speed varies a lot over time and hence making it hard to decide the length of the segment where the mean value should be subtracted.

The second method is based on the ratio between the engine speed (measured with the RPM sensor) and the tachometer speed. The gear ratio, which thereby is formed, oscillates about a gear specific value. The advantage with this method is that the oscillations are preserved at the same time as possible trends are removed. This ratio is plotted in Figure 23 for the test drive STC – Oxelösund 090129. It is clear that

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this data set is much easier to analyze because the oscillations occur about a specific value (the gear ratio).

0 500 1000 1500 2000 2500 3000 3500 4000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time [s] G ea r ra tio

Gear ratio for the gearbox

Figure 23 – The ratio between the input and output shaft speed of the gearbox during the same test drive as displayed in Figure 22.

6.2 Frequency selection

As seen in the figures in chapter 5, the natural frequency of the driveline should approximately lie in the range 1 Hz to 8 Hz, for the test truck Ebola, depending on the gear and the vehicle weight. To measure the natural frequency, there has to be resonance in the driveline. The most likely excitation source is the engine, which oscillates because of the ignition and the forces and moments created when the cylinders move up and down. Another excitation source could be the unbalance in the propeller shaft. To decide with confidence, where the frequencies come from, an oscillation order analysis has been done. This is described in sections 6.2.1 and 6.2.2.

6.2.1 Engine frequency

The cylinders in the engine introduce several frequencies. The highest frequency originates from the motion of each cylinder, i.e. every time a cylinder in the engine changes direction. The lowest frequency comes from the ignition of one single cylinder. The oscillation mode with order one is something that happens once every revolution of the crank shaft. This oscillation mode does not depend on the type of engine, because all truck engines are of four stroke type, but only on the crank shaft speed. The same applies for the oscillation mode of order ½, representing the ignition frequency from one cylinder (a four stroke cylinder ignites every other revolution of the crank shaft), which is the frequency that is most likely to excite the natural frequency of the driveline (see equation (5.1.1)).

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60 2⋅ = n f e e

ω

(5.1.1) where cycle per Strokes [RPM] speed Engine [Hz] 1/2) (order cylinder one from frequency Ignition = = = = n f e e

ω

For a certain engine speed at each gear the engines first oscillation mode may excite the driveline’s natural frequency.

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2 4 6 8 10 12 14 16 18 20 Ig ni tio n fr eq ue nc y fr om o ne c yl in de r [H z] Engine speed [RPM] Ignition frequency from one cylinder

Figure 24 - The ignition frequency from one cylinder in a truck engine. The frequency varies between approximately 3.5 Hz and 20 Hz in a normal engine speed range for a truck.

Figure 24 shows that the ignition frequency from the engine is 8 Hz at an engine speed of approximately 1000 RPM. This means that the engine frequency may excite the natural frequency in the driveline at engine speeds of 1000 RPM and lower. The lowest engine frequency possible is approximately 3.5 Hz because of the truck’s idle control system. At gears lower than the sixth, where the natural frequency of the driveline lies beneath 3 Hz, the engine frequency should therefore not excite the natural frequency in the driveline.

An example of the gear ratio Fourier transform is illustrated in Figure 25. In this case it is easy to distinguish between the engine frequency at 10.4 Hz (see Figure 24) and the natural frequency in the driveline at 7.7 Hz.

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0 5 10 15 20 25 30 35 40 45 50 0 1 2 x 10-4 X: 10.44 Y: 0.0002037 Frequency [Hz] A m pl itu de

FFT for the gear ratio at the specified time interval

X: 7.701 Y: 0.0001722 X: 1.532 Y: 6.301e-005 X: 20.89 Y: 7.052e-005 X: 29.07 Y: 4.124e-005 X: 39.51 Y: 6.41e-005 X: 42.26 Y: 2.794e-005

Figure 25 - Fourier transform for the gear ratio for Ebola at the highest gear and ~1200 RPM. The peaks at 10.4 Hz and 7.7 Hz probably correspond to the ignition frequency and the natural frequency for the driveline, respectively.

Because the engine frequencies depend on the engine speed, there should be an engine speed where the ignition frequency oscillates in resonance with driveline, resulting in a high amplitude gain for that specific frequency. To investigate the presence of resonance, the engine speed has been varied for each gear and plotted in 3D-plots. Figure 26 shows that resonance occurs at 3.9 Hz and 487 RPM for the eighth gear for the truck Ebola.

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0 10 20 30 40 50 0 500 1000 1500 2000 2500 0 0.01 0.02 0.03 0.04 0.05 0.06 X: 3.906 Y: 487.1 Z: 0.05445 Frequency [Hz] FFT for the gear ratio at gear no. 8 after windowing

Engine speed [RPM] A m pl itu de

Figure 26 - The Fourier transform for the gear ratio at varying engine speed for Ebola. Resonance occurs at 487 RPM and 3.9 Hz.

If the first order engine frequency is used to normalize the frequencies from the Fourier analysis, it is easy to decide whether an oscillation comes from the engine or not. The first engine oscillation mode frequency represents something that happens once every crank shaft revolution, i.e. it is the same as engine speed in revolutions per second and can be expressed as

60 1 , e e f =

ω

(5.1.2)

where

ω

_e =Enginespeed[RPM]

The oscillation order with respect to the engine is then calculated as

1 , e f f order=

where f =Measuredfrequency by FFT[Hz]

In Figure 27 an example is shown were the natural frequency is excited by the engine frequency of order 0.5 (the ignition frequency from one cylinder) and a very clear peak at 0.5 is visible. The smaller peaks at 0.4, which are visible for each engine speed, cannot come from the engine because 1/0.4 is no integer. It does not,

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however, vary with the engine speed so it has to be connected to the speed of the crank shaft in some way. For other gears these smaller peaks occur at other frequencies saying that they must originate from something after the gearbox, for instance the propeller shaft.

0 0.5 1 1.5 2 0 1000 2000 3000 0 0.01 0.02 0.03 0.04 X: 0.4123 Y: 2359 Z: 0.0008808 X: 0.5013 Y: 479.3 Z: 0.0403

FFT for the gear ratio at gear no. 8 after windowing

Oscillation order with respect to the engine

X: 1.083 Y: 486.9 Z: 0.01103 Engine speed [RPM] A m pl itu de

Figure 27 - It is obvious that it is the engine frequency of order 0.5 that excites the driveline.

Noticeable are the smaller hills at order 0.4, which cannot come from the engine because 1/0.4 is no integer.

6.2.2 Propeller shaft frequency

The propeller shaft frequency of order one can be expressed as

t e p p i f 60 60 1 ,

ω

= =

where

ω

_p =Propellershaftspeed[RPM] [RPM] speed Engine = e

ω

ratio gear Gearbox = t i

The oscillation order with respect to the propeller shaft is then calculated as

1 , p f f order =

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Figure 28 shows a propeller shaft order plot for the same data as in Figure 27. The small peaks were, as predicted, from the propeller shaft because they all lie at order one. 0 0.5 1 1.5 2 2.5 3 0 1000 2000 3000 0 0.01 0.02 0.03 0.04 0.05 X: 1 Y: 1216 Z: 0.001658

Oscillation order with respect to the propeller shaft

X: 1.219 Y: 481.5 Z: 0.04936 X: 2.651 Y: 486.1 Z: 0.01329 Engine speed [RPM] A m pl itu de

Figure 28 - The small peaks at oscillation order one represents something that happens once per revolution of the propeller shaft.

It is important to account for where the resonance comes from to know if it really is a resonance and to exclude other frequencies.

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7 Development of weight estimation method

As discussed in section 5.5, the equivalent stiffness of the driveline is not constant for different gears and thus making it difficult to determine the weight using the first strategy. However, if the relation between the stiffness, gear and weight could be approximated by simulations then this information could be used to determine the weight. This concept is investigated further in this chapter.

7.1 Second weight estimation strategy

This method is based on the theory that if a simulation manages to reassemble a real system in an acceptable manner it can be used to calculate certain parameters. By analyzing measured data from the real system and using that information as input to the driveline model simulation, the weight can be estimated. The flow chart of the strategy is showed in Figure 29.

Figure 29 – The flow chart for the second weight estimation method.

0 500 1000 1500 2000 2500 3000 3500 4000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time [s] G ea r ra ti o

0 10 20 30 40 50 0 500 1000 1500 2000 2500 0 0.01 0.02 0.03 0.04 0.05 0.06 X: 3.906 Y: 487.1 Z: 0.05445 Frequency [Hz] FFT for the gear ratio at gear no. 8 after windowing

Engine speed [RPM] A m pl itu de CRL 1 3 5 7 9 11 1.5 1 0.5 2 2.5 3 3.5 4 x 104 0 1 2 3 4 5 6 7 8 X: -1 Y: 5000 Z: 1.766 Vehicle weight [kg] Natural frequency of the driveline for the driveline model

X: -1 Y: 4e+004 Z: 0.8852 X: 12 Y: 5000 Z: 7.612 Gear X: 12 Y: 4e+004 Z: 7.525 N a tu ra l fr eq u en c y fo r th e d riv el in e [H z] Speed Gear ratio Frequency & Gear Weight

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8 Results

This chapter presents the results of this thesis. First the results from the frequency analysis are presented, and then the mathematical driveline models are verified followed by the actual weight estimation results.

8.1 Frequency analysis

In this section the results from the frequency analysis are presented together with the results from the driveline model simulation. The test drives have been chosen to highlight the differences between different vehicle weights.

Test drive: Ebola with a weight frame, 090506 on Scania’s test track Weight: 12 240 kg

This test drive was carried out with the intention to get resonance in the driveline. The main resonance source is the ignition frequency which varies with engine speed. Therefore, the engine speed was varied through its whole range by accelerating the vehicle making it possible to analyze and compare the frequency for different engine speeds. When resonance occur in the driveline the amplitude of the oscillation will become amplified and when it reaches its maximum that is where the natural

frequency is (this can be seen in Figure 26 - The Fourier transform for the gear ratio at varying engine speed for Ebola. Resonance occurs at 487 RPM and 3.9 Hz.Figure 26). The result from this method, for gears where the resonance was possible to detect, is displayed in Figure 30.

6 7 8 9 10 11 12 3 3.5 4 4.5 5 5.5 6 6.5 7 X: 9 Y: 4.883 N at ur al f re qu en cy f or t he d riv el in e [H z] Gear

The measured natural frequency of the driveline

Figure 30 - The natural frequency of the driveline (for Ebola) has been decided by analyzing resonance frequency peaks as in Figure 26. The ninth gear is pinpointed as an example of the frequency analysis method because there is a clear resonance at this gear.

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6 7 8 9 10 11 12 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 X: 9 Y: 4.919 Gear N at ur al f re qu en cy o f th e dr iv el in e [H z]

The natural frequency of the driveline at the vehicle weight 12240 kg for the driveline model

Figure 31 - The natural frequency of the driveline described in section 3.1 for Ebola. By comparing this plot with Figure 30 it is clear that they do not match exactly. They match relatively well at the lower gears where the weight affects the frequency the most.

At the ninth gear there is a clear resonance in the gear ratio signal. Therefore, this gear is pinpointed in Figure 30 and Figure 31. This resonance is shown in Figure 32 and Figure 33 and occurs at low engine speeds where the engine frequency excites the natural frequency of the driveline.

0 5 10 15 20 25 500 1000 1500 2000 2500 0 0.005 0.01 0.015 0.02 Frequency [Hz] (X) FFT for the gear ratio at gear no. 9 after windowing

X: 4.883 Y: 478.3 Z: 0.01321

Engine speed [RPM] (Y)

A m pl itu de [ -] Z

Figure 32 - Fourier transform of the gear ratio during a test drive with Ebola. At 4.883 Hz, the engine frequency excites the natural frequency at 478.3 rpm.

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1600 1650 1700 1750 1800 1.8 1.85 1.9 1.95 2 2.05 2.1 Time [s] G ea r ra tio [ -]

Figure 33 – The calculated gear ratio at the ninth gear where the resonance in the driveline is obvious. This is why the frequency shown in Figure 32 is so easy to spot.

Test drive: Ebola with a trailer, 090506 on Scania’s test track Weight: 36 320 kg

The test method was the same as the one described above. When driving in uphill slopes at low gears and low engine speed, the engine torque was so high that the wheels slipped. At plane ground, the engine’s idle control made it impossible to achieve resonance (described in section 6.2.1) for lower gears than the seventh. Comparing Figure 34 and Figure 35 it is obvious that the model does not fit the measured data well, other than for gear seven. These results are still important because the weight estimation method is better for lower gears (as explained in section 5.1).

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7 8 9 10 11 12 3 3.5 4 4.5 5 5.5 6 6.5 N at ur al f re qu en cy f or t he d riv el in e [H z] Gear

Figure 34 - The measured frequency should be a little lower for this test drive than for the one described above because of the higher vehicle weight, which it is.

7 8 9 10 11 12 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Gear N at ur al f re qu en cy f or t he d riv el in e [H z]

Figure 35 - The natural frequency from the driveline model described in section 3.1 for Ebola. Comparing this figure with Figure 34 it is clear that only the seventh gear match the measured data well.

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Test drive: Mulle, 090525 on Scania’s test track Weight: 12 590 kg

This test was performed in the same manner as the tests described previously in this section. 4 5 6 7 8 9 10 11 12 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 N at ur al f re qu en cy f or t he d riv el in e [H z] Gear

Figure 36 - The measured frequency for Mulle. The reason why the frequency is the same for the eighth and the ninth gear is explained later in this section.

4 5 6 7 8 9 10 11 12 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 Gear N at ur al f re qu en cy f or t he d riv el in e [H z]

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It is obvious that the model fits the measured data better at low gears than at high, just as for Ebola. The best matches are found at the fourth, seventh and eighth gear. The resonance should occur at lower engine speeds for lower gears. However, for this test drive the resonance for the eighth gear occurs at a higher engine speed than for the ninth, which can be seen in Figure 38 and Figure 39. This means that the true natural frequency of the driveline at the eighth gear is probably lower than the

measured and could not be seen because the engine speed was not low enough. The resonance at the eighth gear must then be due to the engine frequency being close to the natural frequency and not exactly the same.

0 5 10 15 20 25 500 1000 1500 2000 0 0.005 0.01 0.015 0.02 0.025 X: 4.004 Y: 508.9 Z: 0.02067

Frequency [Hz] (X) Engine speed [RPM] (Y)

A m pl itu de [ -] ( Z )

Figure 38 - The Fourier transform for Mulle at the ninth gear and varying engine speed. Noticeable is that there are a number of resonance peaks around the natural frequency of the driveline.

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0 5 10 15 20 25 500 1000 1500 2000 0 0.005 0.01 0.015 0.02 X: 4.004 Y: 515.7 Z: 0.01836

Frequency [Hz] (X) Engine speed [RPM] (Y)

Figure 39 - The Fourier transform for Mulle at the eighth gear and varying engine speed. The resonance peak at 4.004 Hz could be a frequency close to the natural frequency of the driveline, which has been amplified as in Figure 38.

An example of the phenomenon that the resonance peak is spread over several different engine speeds is shown in Figure 40. This is why it is so difficult to determine if a peak is the actual natural frequency.

0 5 10 15 20 25 400 600 800 1000 1200 1400 0 0.005 0.01 0.015 0.02 Frequency [Hz] (X) FFT for the gear ratio at gear no. 11 after windowing

X: 5.762 Y: 709.3 Z: 0.0165

Figure 40 - The Fourier transform for Mulle at the eleventh gear and varying engine speed. It is clear that there is resonance at several different engine speeds, but the peak is higher for the pinpointed speed indicating that this must be the natural frequency of the driveline.

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Test drive: Mulle, 090121 Södertälje to Nyköping Weight: 12 590 kg

At this test drive it is difficult to see resonance peaks at any gear. Most data is

collected for the twelfth gear because the test was carried out mostly on a motorway. Although there is a lot of data for this gear, as seen in Figure 41, there is no

resonance because of the high engine speed when driving on the motorway.

0 5 10 15 20 25 900 1000 1100 1200 0 0.5 1 1.5 x 10-3 X: 7.324 Y: 1151 Z: 0.0007747 Frequency [Hz] (X) X: 5.957 Y: 949.4 Z: 0.0007775

Figure 41 - Fourier transform of the gear ratio for the test drive from Södertälje to Nyköping with Mulle. There is no sign of any resonance in the driveline. The only visible frequencies are the ones that originate from the ignition, which are pinpointed at two different engine speeds.

8.2 Model verification

Comparing the measured frequencies (for example Figure 30) and the modelled frequencies (for example Figure 31) it is easy to see that the driveline model described in section 3.1 gives a good estimate of the natural frequency of the driveline for low gears, but not for high. The simplified model (Figure 42 and Figure 43) does not give as good results as the driveline model for low gears, where the most accurate weight estimation is possible, and has therefore not been used for weight estimation.

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6 7 8 9 10 11 12 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Gear N at ur al f re qu en cy f or t he d riv el in e [H z]

The natural frequency of the driveline at the vehicle weight 12240 kg for the simplified driveline model

Figure 42 - The simulation results from the simplified driveline model for Ebola with a weight of 12 240 kg. This model does not match the Fourier transform results in Figure 30 for low gears and has therefore not been used when estimating the weight.

4 5 6 7 8 9 10 11 12 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Gear N at ur al f re qu en cy f or t he d riv el in e [H z]

The natural frequency of the driveline at the vehicle weight 12590 kg for the simplified driveline model

Figure 43 - The simulation results from the simplified driveline model for Mulle with a weight of 12 590 kg. This model does not match the Fourier transform results in Figure 36 for low gears and has therefore not been used when estimating the weight.

It is difficult to see any resonance peaks for low gears and for high gears, the frequencies from the driveline model and the measured data does not match well.

(51)

This means that the weight should be estimated at the lowest gear where the resonance frequency is detectable.

8.3 Weight estimation

As described in chapter 6 the weight is estimated by using the driveline model described in section 3.1. Doing so, the weight can be estimated without solving the complex driveline equations analytically. This section presents the results of this weight estimation method.

Test drive: Ebola, 090506 on Scania’s test track Weight: 12 240 kg

As an example of this weight estimation method, the frequency as a function of the vehicle weight at the ninth gear is given in Figure 44. The measured frequency (see Figure 30) is pinpointed in Figure 44 and corresponds to the estimated weight 20 580 kg. 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 x 104 4.86 4.87 4.88 4.89 4.9 4.91 4.92 4.93 4.94 X: 2.058e+004 Y: 4.883 Vehicle weight [kg] N at ur al f re qu en cy f or t he d riv el in e [H z]

The natural frequency of the driveline at the 9:th gear for the driveline model

Figure 44 - The natural frequency of the driveline as function of the vehicle weight at the ninth gear for Ebola.

The same principle has been applied to all gears where it is possible to see any resonance peaks (gears 6 to 12) and the result is presented in Figure 45.

Weight Estimation through Frequency Analysis

Weight Estimation through Frequency Analysis

Hampus Johansson

Nicklas Höglund

Weight Estimation through Frequency Analysis

Hampus Johansson

Nicklas Höglund

Supervisor at Linköping University:

Karl-Erik Rydberg

Supervisor at Scania CV AB: Pär Degerman

Abstract

Acknowledgements

Contents

1 Introduction

1.1 Purpose and objective

1.2 Method

1.3 Delimitations

2 Pilot study

2.1 Methods used today

2.2 The CAN protocol

2.3 FFT – Fast Fourier transform

2.4 Window function

×

2.5 Test vehicles and sensors

3 Driveline modelling

3.1 Driveline model

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