Pertti Virtala. RIDE-model. Definition of the RIDE-model. Liikenneviraston tutkimuksia ja selvityksiä nro/2017

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1 Pertti Virtala RIDE-model Definition of the RIDE-model Liikenneviraston tutkimuksia ja selvityksiä nro/2017 Liikennevirasto Helsinki 2017

2 Kannen kuvat: Kuvan ottajan nimi tai esim. Liikenneviraston kuva-arkisto ISSN-L ISSN ISBN xxx-x Verkkojulkaisu pdf ( ISSN-L ISSN ISBN xxx-x Painotalon nimi Paikkakunta 2017 Julkaisua (myy)/saatavana Painotalon nimi (jos myynnissä) tai vastuuyksikön nimi Faksi <Kirjoita tähän> Puhelin <Kirjoita tähän> Liikennevirasto PL HELSINKI Puhelin

3 3 Pertti Virtala: RIDE-mallin määrittely. Liikennevirasto, xxxosasto. Helsinki 201x. Liikenneviraston tutkimuksia ja selvityksiä nro/201x. xx sivua ja xx liitettä. ISSN-L , ISSN , ISBN xxx-x, ISSN (pdf), ISBN xxx-x (pdf) Avainsanat: xxx Tiivistelmä Päällysteiden kunnossapidossa on ollut Suomessa käytössä tien epätasaisuuteen liittyvä tunnusluku (IRI) jo 1980-luvulta lähtien. Se on ollut pääasiallinen tunnusluku niin uusien kuin vanhojen päällysteiden kunnonhallinnassa. Monissa tutkimuksissa on kuitenkin todettu, ettei se ole paras ajomukavuutta kuvaava tunnusluku. Sitä toteamusta tukevat myös käytännön kokemukset. Liikennevirasto onkin kehittänyt epätasaisuuteen liittyviä tunnuslukuja siihen suuntaan, että ne kuvaisivat paremmin koettua epämukavuutta. Uusi tunnusluku (tunnusluvut) lasketaan monipuolisemmalla mallilla, jonka laskentaperusteet on kuvattu tässä määrittelydokumentissa. Määrittely pohjautuu Liikenneviraston teettämään selvitykseen uudesta RIDE-mallista [2]. Määrittelyn soveltaminen edellyttää perustietojen [1] hallitsemista ajoneuvodynamiikasta ja differentiaalilaskennasta.

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5 5 Esipuhe Tässä dokumentissa on määritetty tien epätasaisuuteen liittyvien RIDE-tunnuslukujen laskentaperiaatteet. Dokumentti on tehty Liikenneviraston toimeksiannosta (Juho Meriläinen) ja sen on tuottanut Destia Oy (Pertti Virtala). Helsingissä toukokuussa 2017 Liikennevirasto Väylänpito/Kunnossapidon ohjaus ja kehittäminen

6 6 Table of Content 2.1 Standard terminology Coordinate system Vehicle Forces and moments Movements and angles Graphical model Motion equations Vehicle parameters Road Raw data Additional filtering Simulation speed Initial position of the vehicle Simulation Outcomes Outcomes sim_nop_ka pys_ki_std siv_ki_std nyö_ki_std yhd_ki_rms esal_std ltr_std Ityö_ka and Ityö_ha sim_nop_ha Reference Data Results APPENDIXES

7 7 1 Introduction The International Roughness Index (IRI) developed by the World Bank (1986) has been in use in the Finnish Transport Agency almost 30 years. It has been the main indicator describing the roughness (or unevenness) of a road pavement in the Asset Management Systems (RAMS) and in the Quality Assurance Standards (QS). Numeral studies have showed that IRI is not the best index concerning riding comfort. Kim et al. [3] performed correlation analysis to determine the relation between measured accelerations and subjective ratings of four expert drivers using a psychophysical power law. Nair et al. [5] have described the experience, accomplishments, and challenges of using pavement roughness to set specifications for ride comfort on Virginia s highways. The practical experiences in the Finnish Transport Agency support those statements. The pavement management system in Transport Agency works with the definition of the amount of pavements in poor condition. Tree main indexes (rut depth, IRI, and crack index) are classified into five distinctive classes (from poor to excellent) where two worst classes belong to the category of poor condition. The main weight is typically set to rutting of main roads and to the cracking of secondary roads. Roughness has not been as important as those two. It is a sort of secondary index affecting to the type of action or treatment when the main indexes exceed threshold values. There have clearly been problems in using the roughness information of pavements in pavement management during the past years. Typical statements have been that it does not represent the riding comfort of pavements well enough and it cannot show where the bad sections locate or what the type of roughness is. The conclusion is then that a better index describing the roughness of pavements is needed. It should locate the bad sections more precisely and it should give information of what kind of roughness exists. The relation of roughness index to the riding comfort should be better too. [2]. As a result of several studies funded by the FTA the conclusion has been to develop a better index to describe the roughness of road pavement. The main question was, what were the root causes for the problem, where IRI seems not to represent the riding comfort of a traveller in a car or in a truck well enough. A root cause analysis was conducted and the following potential root causes were found [2,3]: IRI is calculated using a quarter car model, where only one longitudinal profile is fed to the model and the outcome is therefore missing some important dimensions. One longitudinal profile cannot have any information of how the cross fall varies in transversal direction. Quarter car model is based on an American car where the suspension system differs from what is in a typical European or Japanese car or a truck. IRI represents the vertical movement of a car chassis which is not the best source for searching factors causing discomfort. (ISO 2631 uses vertical accelerations) [3]. The wavelength of longitudinal profile data used in calculating IRI is filtered to cover wavelengths between 0.5 and 50 m. Wavelengths shorter than 0.5 m can affect to the riding comfort as well. IRI is simulated using a constant speed 80 km/h. On high trafficked roads the speed of cars is usually much higher ( km/h). On low trafficked roads the speed of cars is usually much lower (50-60 km/h). The speed used in simulations of IRI differs from the real driving speed. The suspension system of the driver s seat is not included in the quarter car simulation model. The reporting interval of 100 m is too long to locate poor road sections accurately. It also averages the outcome too much and important transients in roughness cannot be recognized. Some of the parameters of the suspension system in a car are changing over time, which can affect to the riding comfort.

8 8 The decision has been to move from a 2-DOF IRI-model to a full-car 7-DOF RIDEmodel and introduce the indicators from RIDE-model to the Finnish RAMS. New indexes are based on vertical acceleration, roll acceleration, pitch acceleration and a combined vertical acceleration of vehicle sprung mass. This report describes the principles of the calculation of new indexes. A more detailed study of the new indicators is based on the results of the work done in [2].

9 9 2 RIDE-model 2.1 Standard terminology Coordinate system Axis system is a set of three mutually orthogonal X, Y, and Z axes. In a right-handed system, Z =X *Y [4]. Coordinate system is a numbering convention used to assign a unique ordered trio of numbers to each point in a reference frame. A typical rectangular coordinate system consists of an axis system plus an origin point [3]. Vehicle axis system (XV, YV, ZV) is a right-handed orthogonal axis system fixed in the vehicle reference frame, usually in the center of gravity (CG) of vehicle. The XV axis is primarily horizontal in the vehicle plane of symmetry and points forward. The ZV axis is vertical and the YV axis is lateral. The directions should coincide with the earth-fixed axis system when the vehicle is upright and aligned with the XV axis parallel to the XE axis [5]. Multibody vehicle dynamics models are typically generated using right-handed axis systems and coordinate systems. The axis orientation for ISO 8855 has X forward, Z up, and Y pointing to the left-hand side of the vehicle [5]. Figure 1. Vehicle body coordinate system as ISO standard [5]. Road axis system (XR, YR, ZR) right-handed orthogonal axis system whose ZR axis is normal to the road, at the center of tire contact, and whose XR axis is perpendicular to the wheel spin axis (YW). For an uneven road, a different road axis system exists for each tire Vehicle Size and weight Track width (W) is the distance between the centers of tire contact on one side of the vehicle. Wheelbase (L) is the distance between the front and rear axle. Distance of vehicle C.G. from front axle is marked with Lf and distance of vehicle C.G. from rear axle is marked with Lr.

10 10 Unsprung weight (mu) is portion of weight supported by a tire that is considered to move with the wheel. This usually includes a portion of the weight of the suspension elements. (SAE) [4]. Each wheel has an individual unsprung weight which is marked with letters describing the front ( f ) or rear ( r ) and left ( l ) or right ( r ), as mufl, mufr, murl and murr. Sprung weight (ms) is the weight of the vehicle chassis including driver, passengers, and loads. Total weight of the vehicle is the sum of sprung weight and unsprung weights Points C.G. (Center of gravity) is a point in the vehicle reference frame that coincides with the center of mass of the entire vehicle when the suspensions are in equilibrium and the vehicle is resting on a flat level surface. Vertical position is Z - ZE coordinate of the C.G. X position is X - XE coordinate of the C.G. Y position is Y - YE coordinate of the C.G. Pitch center is imaginary point in the XVZV plane through the lateral center of the vehicle reference frame at which a longitudinal force applied to the vehicle body is reacted without causing suspension jounce (front or rear). An alternate definition is that the pitch center is the intersection of the two lines shown in Figure 2. Note: this definition of pitch center does not take into account the wind up effects of drive train torque applied to the wheels from the vehicle body [4]. Figure 2. Pitch center [5].

11 11 Figure 3. Roll center [5]. Roll center is an imaginary point in the YVZV plane containing the two wheel centers of an axle, at which a lateral force applied to the vehicle body is reacted without causing suspension roll angle (ISO, SAE). An alternate definition is that the roll center is the intersection of the two lines shown in Figure 3. (Note: the figure shows a nonequilibrium position of the vehicle.) [5] Suspension Spring is a part which combines the wheel to the chassis for each corner. Spring stiffness (k fl, k fr, k rl, k rr) define the amount of load the spring is needed to be pressed to reach a certain compression. z sfl m sfl k sfl c sfl z ufl m ufl z Rfl k tf c tf Figure 4. Suspension of a vehicles front left corner. Damping coefficient is the ability of a shock absorber to resist movement. It is marked with a letter locating the corner in the vehicle (cfl, cfr, crl, crr). A tire can have a spring parameter (kt) and a suspension parameter (ct) Forces and moments Damping force Fd is a compressive force applied to the vehicle body by a damper (Fdfl, Fdfr, Fdrl, Fdrr).

12 12 Spring force Fs is a compressive force applied to the vehicle body by a suspension spring (Fsfl, Fsfr, Fsrl, Fsrr). Vertical tire force Fz is the ZR component of ground resultant force. (SAE16, ISO15) (Fzfl, Fzfr, Fzrl, Fzrr). Suspension roll moment Mroll is a total static roll moment applied to sprung roll angle. A positive moment causes positive vehicle roll. Suspension pitch moment Mpitch is a total static pitch moment applied to sprung pitch angle. A positive moment causes positive vehicle pitch Movements and angles Vertical displacement z s is the Z component of displacement vector of the C.G. Vertical velocity z s is the Z component of velocity vector of the C.G. Vertical acceleration z s is the Z component of acceleration vector of the C.G. Pitch θs is an angle from X axis to XV axis, about Y axis. (SAE, ISO) [5]. Pitch velocity θ s is the Y component of angular velocity vector of vehicle reference frame. Pitch acceleration θ s is the Y component of angular acceleration vector of vehicle reference frame. Roll φs is the angle from XEYE plane to YV axis, about X axis (SAE, ISO) [5]. Roll velocity φ s is the X component of angular velocity vector of vehicle reference frame. Roll acceleration φ s is the X component of angular acceleration vector of vehicle reference frame. Figure 5. Roll, pitch and yaw of a vehicle.

13 Graphical model The full-vehicle suspension system is represented as a linear seven degree-offreedom (DOF) system. It consists of a single sprung mass (car body) connected to four unsprung masses (front-left, front-right, rear-left and rear-right wheels) at each corner. The sprung mass is free to bounce, pitch and roll while the unsprung masses are free only to bounce vertically with respect to the sprung mass. All other motions are neglected for this model. Hence this system has seven degrees of freedom and allows simulation of tyre load forces in all four tyres, body acceleration and vertical body displacement as well as roll and pitch motion of the car body. The suspensions between the sprung mass and unsprung masses are modelled as linear viscous dampers and linear spring elements, while the tyres are modelled as simple linear springs without damping. For simplicity, all pitch and roll angles are assumed to be small [6]. The model of a full-car suspension system is shown in Figure 6. The full-vehicle suspension model is represented as a linear seven degree of freedom system. The lateral dynamics of the vehicle are ignored. It consists of a single sprung mass m (car body) connected to four unsprung masses m1 m4 (front-left, front-right, rear-left and rearright wheels) at each corner. The suspensions between the sprung mass and unsprung masses are modelled as linear viscous dampers and spring elements. The dampers between the body and the wheels represent sources of conventional damping such as friction between the mechanical elements. For the vehicle modelling fullcar will be used as a good approximation of the entire car [6]. L (m) L f (m) L r (m) front right W (m) rear right front left rear left Figure 6. Graphical vehicle model. There are some assumptions made in this model. The vehicle aerodynamic effect is neglected and the road is assumed to be level except for road disturbance. That means that the geometry of the road is neglected. The vehicle is also assumed to be rigid where the load transfer from one point to another is one hundred percent effective. Parameters of the vehicle are also assumed to be constant throughout the simulation process such as tire stiffness, spring stiffness, and damper coefficient.

14 Motion equations At time t, the vertical profile of the road (road roughness) corresponding to the front right wheel is denoted by zrfr(t), the road roughness corresponding to the front left wheel is denoted by zrfl(t), the road roughness corresponding to the rear left wheel is denoted by zrrl(t), finally the road roughness corresponding to the rear right wheel is denoted by zrrr(t). In fact, since a straight road is considered here, the road roughnesses zrfl(t) and zrfr(t) are encountered by the front wheels (right and, respectively, left wheels) at time t, while the right and left rear wheels encounter the same road roughnesses after Δt L/v (so at t +Δt), where L is the wheelbase and v the constant car speed. Thus: zrfl(t) = zrrl(t +Δt) and zrfr(t) = zrrr(t +Δt). The vertical dynamics equations of the 7 DOF model are obtained using the Newton- Euler formulation, as provided widely in the literature. There are 3 scalar dynamic equations of the sprung mass: one in terms of vertical forces (z direction), one in terms of moments with respect to the longitudinal x axis and the third one in terms of moments with respect to the transversal y axis. The dynamic of the sprung mass is defined by: m s z s = k sf (z Rfl z sfl ) + k sf (z Rfr z sfr ) + k sr (z Rrl z srl ) + k sr (z Rrr z srr ) + c sf (z ufl z sfl ) + c sf (z ufr z sfr ) + c sr (z url z srl ) + c sr (z urr z srr ) F zfl F zfr F zrl F zrr + m s g Where, m s = the mass of the vehicle chassis (kg) without wheels and axels z s = the body vertical acceleration (m/s 2 ) z R = road profile for each wheel (m) (front left, front right, rear left and rear right) z s = vertical displacement (m) of the sprung mass for each corner z s = vertical displacement velocity of the sprung mass for each corner (m/s) (front left, front right, rear left and rear right) k s = spring coefficient (N/m) for the spring in each corner (front left, front right, rear left and rear right) c s = damping coefficient (Ns/m) for the damper in each corner (front left, front right, rear left and rear right) z u = vertical displacement velocity (m/s) for the unsprung mass in each wheel (front left, front right, rear left and rear right) The roll effect of the vehicle is given by: J x φ = +{[k sf (z ufl z sfl ) + c sf (z ufl z sfl ) + k sr (z url z srl ) + c sr (z url z srl )] [k sf (z ufr z sfr ) + c sf (z ufr z sfr ) + k sr (z urr z srr ) + c sr (z urr z srr )] (F zfl + F zrl ) + (F zfr + F zrr )} W 2 Where, JX = the moment of inertia about x-axis (kgm 2 ) φ = the roll acceleration (rad/s 2 ) W/2 = the length of the vehicle from the center of gravity to the right end or to the left end of the vehicle (m). The pitch effect of the vehicle is given by: J y θ = [k sf (z ufl z sfl ) + c sf (z ufl z sfl ) + k sf (z ufr z sfr ) + c sf (z ufr z sfr )]L f + [k sr (z url z srl ) + c sr (z url z srl ) + k sr (z urr z srr ) + c sr (z urr z srr )]L r + (F zfl + F zfr )L f (F zrl + F zrr )L r

15 15 Where, JY = the moment of inertia about y-axis (kgm 2 ) θ = the pitch acceleration (rad/s 2 ) Lf = the length of vehicle from the center of gravity to the front axel (m) Lr = the length of vehicle from the center of gravity to the rear axel (m) Acceleration at unsprung mass for each wheel is given by: m ufl z ufl = k tf (z Rfl z ufl ) + c tf (z Rfl z ufl ) + k sf (z sfl z ufl ) + c sf (z sfl z ufl ) + F zfl + m ufl g m ufr z ufr = k tf (z Rfr z ufr ) + c tf (z Rfr z ufr ) + k sf (z sfr z ufr ) + c sf (z sfr z ufr ) + F zfr + m ufr g m url z url = k tr (z Rrl z url ) + c tr (z Rrl z url ) + k sr (z srl z url ) + c sr (z sfr z url ) + F zrl + m url g m urr z urr = k tr (z Rrr z urr ) + c tr (z Rrr z urr ) + k sr (z srr z urr ) + c sr (z srr z urr ) + F zrr + m urr g 2.4 Vehicle parameters Table 1. Vehicle parameters for car and truck. RIDE-sim parametrit Nro Muuttuja Yksikkö HA KA 1 Kokonaismassa kg Akseliväli L (m) m Taka-akselin et. Painopisteestä L f m Etuakselin et. Painopisteestä L r m Etupyörien raideväli W f m Takapyörien raideväli W r m Etupyörän massa m uf kg Takapyörän massa m ur kg Korin massa m s kg Renkaan jousivakio k t N/m Renkaan vaimennuskerroin c t Ns/m Etujousen jousivakio k sf N/m Takajousen jousivakio k sr N/m Etuiskarin vaimennuskerroin c sf Ns/m Takaiskarin vaimennuskerroin c sr Ns/m Inertia J X kgm Inertia J Y kgm Painopisteen korkeus h CG m Heilahduskeskiön korkeus h ROLL m

16 Road Raw data The raw data is a data consisting of the longitudinal profile data of a 3.2 m wide lane with 100 mm intervals. Currently the raw data is measured with the GE manufactured (Greenwood Engineering Ltd) point laser-based high speed monitoring vehicle. The measurement beam is locating in front of the vehicle and it has at a minimum of 17 point-lasers which measure the vertical distance of the road surface from the beam. The beam construction has usually more sensors in both wheel paths than in between. If the wheel path is measured with five sensors then the longitudinal profile is calculated as a mean of information collected with those five sensors. Longitudinal profile for left wheel path is obtained from sensors measuring the left wheel path and for the right wheel path respectively from sensors measuring that. The reference point of raw data is the data of the left wheel path at the location of 0 meters. All other vertical data is measured proportional to that. The raw data is filtered as is usually filtered when calculating the IRI. Road is given to the dynamic simulation as a profile for the left wheel path and for the right wheel path in 10 cm intervals. It is given as: z Rfl (t) = mean(p 3 (t), p 4 (t), p 5 (t), p 6 (t), p 7 (t)) z Rfr (t) = mean(p 11 (t), p 12 (t), p 13 (t), p 14 (t), p 15 (t)) z Rrl (t) = mean(p 3 (t t), p 4 (t t), p 5 (t t), p 6 (t t), p 7 (t t)) z Rrr (t) = mean(p 11 (t t), p 12 (t t), p 13 (t t), p 14 (t t), p 15 (t t)) Where, pi(t) = individual parallel profiles in one wheel path covering a 50 cm width (m) where i is the sensor number in a point laser profilograph with 17 sensors in transversal direction starting from the left side t = time (s) starting from 0 and ending to the tmax representing the time travelled to the end of a road section using speed v (m/s) Δt = time interval (s) defined by the axel base L and speed v (m/s) zr(t) = road profile (m) for each wheel (front left, front right, rear left and rear right) at the moment of t (s) This principle is designed to work with the current measurement technologies. However it is possible to produce the longitudinal profiles for each wheel using other technologies and calculation methods. Generally the rear wheels get the same profile than front wheels but the profile information flow is delayed with time interval Δt Additional filtering Many low-volume roads are hilly or curvy meaning that the gradient in vertical direction or the curvature in lateral direction is varying quite a lot. Some parts of those roads cannot be driven with a car using constant speed representing the speed limit. That means that the simulation cannot either be driven with that speed. To avoid expanding simulations covering unlimited amount of different speed limits the longitudinal profile is necessary to be re-filtered. Re-filtering should be made according to the following principles: 1. Finding filtering parameters a and b

17 17 % =========== FILTERING PARAMETERS ========================== % First calculate average 10 m values and standard deviations for curvature and gradient for sections longer than 300 m if (size(raakadata0, 1) > 3000); Interval=10; % [m] = 10 * 10 [cm] mn100 = (Interval * 10); nn2 = round(size(raakadata0, 1) / mn100, 0) + 1 GradientAvg=zeros(1, nn2); % each meter of the data onted is 10 * 10cm CurvatureAvg=zeros(1, nn2); % same space for curvature ii1=0; ii2=0; index_c=0; %use this to avoid name conflict for index_c=1:nn2; if ((index_c * mn100) <= size(raakadata0, 1)); ii1 = ((index_c - 1) * mn100) + 1; ii2 = (index_c * mn100) - 1; CurvatureAvg(1, index_c)=mean(raakadata0(ii1:ii2, 19)); GradientAvg(1, index_c)=mean(graakadata0(1, ii1:ii2)); end end end We now have the curvature parameters calculated from raw-data level curvature and gradient at 10 m level. Then a cutoff distance is calculated using the geometry parameters calculated above. Cutoffdistance must be limited to a range of v = 1; %Timo Eskola calculate filter cut off distance % do not try to calculate if site is less than 300m long if (size(raakadata0, 1) > 3000) cstd = std(curvatureavg(20:nn2)); %std dev of curvature gstd = std(gradientavg(20:nn2)); %std dev of gradient cutoffdistance = round(((21-0.5*cstd) + (21-76*gstd)) / 2, 0); %if values got by formula exceed limits cut them to be border if (cutoffdistance>30); cutoffdistance=30; elseif (cutoffdistance<4); cutoffdistance=4; end else cutoffdistance = 17; %default for really short sites end %sample distance is fixed to 10cm sampledistance = 0.1; Fs = v/sampledistance; %sample frequency lets keep v = 1 m/s => Fs = 1 / sample distance N = 3; %order of butterworth filter Fc = v/cutoffdistance; %cut off frequency => Fc = 1 / cut of distance (cut of distance has to be at least 2 times sample distance) h = fdesign.highpass('n,fc', N, Fc, Fs); Hd = butter(h); [b, a] = tf(hd); % This function gives parameters a and b %End of filtering design 2. Filtering profiles using parameters a and b p_v(:,2)=filtfilt(b,a,p_v(:,2)); p_o(:,2)=filtfilt(b,a,p_o(:,2)); where p_v() represents the left road profile and the p_o() represents the right road profile

18 18 Profiles are now filtered. a=filtering parameter b=filtering parameter Simulation speed RIDE-simulations are made using the actual speed limits on each road section. Simulation with car model should be made using actual summer time speed limits. Simulations with truck model should be made with actual summer speed limits but the individual speed limit of a truck (80 km/h) should be taken into account as well. When a road section has several speed limits, simulation should be made with all speeds. The area between the urban traffic signs is also a speed limit (50 km/h). The final outcome should be collected for each part defined by speed limit from corresponding simulation. Simulation speed is constant inside every 10 m section length. A further discussion on how to deal with so called local point speed limits should be done. It might be that speed limits shorter than certain threshold length would not be simulated. The main simulation speeds would then continue over local spot like limits. 2.6 Initial position of the vehicle Motion equations are describing the dynamic behavior of the vehicle during the simulation. The initial position of the vehicle should be calculated as initial values in z- direction. Main principle in that calculation is that the suspension (springs) takes an initial position due to the weight of the vehicle. En example of a Matlab code for that part is presented below: % Initial position massa=(m_k(i)+m_to(i)+m_tv(i)+m_eo(i)+m_ev(i)); % Wheel loads according to the C.o.G F_rr_stat(i)=m_k(i)*g*L_f(i)/L(i)/2; F_rl_stat(i)=m_k(i)*g*L_f(i)/L(i)/2; F_fr_stat(i)=m_k(i)*g*L_r(i)/L(i)/2; F_fl_stat(i)=m_k(i)*g*L_r(i)/L(i)/2; % Initial displacement due to gravity as_afl(i)=-(m_fl(i)*g+f_fl_stat(i))/k_rfl(i);%+p_l(1,2); as_afr(i)=-(m_fr(i)*g+f_fr_stat(i))/k_rfr(i);%+p_r(1,2); as_arl(i)=-(m_rl(i)*g+f_rl_stat(i))/k_rrl(i);%+p_l(1,2); as_arr(i)=-(m_rr(i)*g+f_rr_stat(i))/k_rrr(i);%+p_r(1,2); % initial displacement of front right due to gravity as_fr(i)=-f_fr_stat(i)/k_fr(i)+as_afr(i); % initial displacement of front left due to gravity as_fl(i)=-f_fl_stat(i)/k_fl(i)+as_afl(i); % initial displacement of rear right due to gravity as_rr(i)=-f_rr_stat(i)/k_rr(i)+as_arr(i); % initial displacement of rear left due to gravity as_rl(i)=-f_rl_stat(i)/k_rl(i)+as_arl(i); % Initial state of the rear center z_kr(i)=sin(asin((as_rr(i)-as_rl(i))/l_r(i)))*l_r(i)/2+as_rr(i); % Initial state of the front center z_kf(i)=sin(asin((as_fr(i)-as_fl(i))/l_f(i)))*l_f(i)/2+as_fl(i); % Initial Pitch angle as_pitch(i)=asin((-z_kr(i)+z_kf(i))/l(i)); % Initial displacement of C.o.G as_k(i)=z_kr(i)+sin(as_pitch(i))*l_r(i); z_l(i)=sin(asin((as_fl(i)-as_rl(i))/l(i)))*l_r(i)+as_rl(i); z_r(i)=sin(asin((as_fr(i)-as_rr(i))/l(i)))*l_r(i)+as_rr(i); s(i)=l_t(i)*sin(atan((l_f(i)-l_r(i))/(2*l(i)))); as_roll(i)=asin((z_r(i)-z_l(i))/(l_r(i)));%+2*s(i))); %Alkuheilahduskulman pitäisi olla nolla

19 Simulation RIDE-simulation reads first the source data and formulates some needed starting positions. In practice, this is done by setting the simulation parameters like vehicle type and simulation speed. Then reading the source data file, which is profile, geometry and speed limit data of a certain road section in 10 cm interval. 1. Reading simulation parameters means that the program reads what are the vehicle parameters which have to be used in simulation (a car or a truck) (Table 1). 2. Reading road data means that the program reads the source data which defines which road section is to be simulated and the road profile data at least from left and right wheel paths and the speed limit (to be used as a simulation speed). In mass calculations a batch procedure is useful to do so that the batch program takes a bunch of road sections and orders them one by one to be simulated and stores the results section by section. 3. Filtering road data means that roads with low-level geometry, simulation responses some times go high and a filtering (smoothing) is nessessary. Filtering parameters a and b are calculated using hilliness and curvature of a road section. Parameters are then used to filter the road profiles. 4. Left profile is calculated using average values of five laser sensors and the right profile is calculated using five laser sensors on the right side respectively. 5. The initial vertical position of a vehicle is calculated before starting the actual simulations. 6. The distance vector of the data is transformed into time domain that is time values using speed and distance intervals. 7. Simulation happens by calling the simulation procedure. Simulation is made using Simulink model (or what ever model the user has) starting from time 0 to the end of the road section. Simulink model is made using the motion equations. Main outcomes are the vertical, rolling and pitch accelerations of the vehicle chassi (CoG) and the point where the driver sits. Road load (ESAL), Load transfer ratio (LTR) and the work of shock absorbers are calculated in simulation as well using wheel loads and suspension outcomes. Simulink model has not been defined here. 8. After simulation the data of simulation is taken and the time domain is transformed back to distance domain. 9. Raw data level results are transferred to 10 m level taking averages, standard deviations etc. from each 10 m section. 10. Data is finally saved in a file with road addresses and main simulation parameters. Before starting the simulation of a road section, a pre-simulation is good to do. That means that the first values of the road are copied 1000 times and a pre-simulation is done using that smooth road so that the vehicle sets down first. Then the simulation continues from the first data point on to the end of the section. Only the real part of the road section is stored as results.

20 20 Start Read sim parameters Calculate ESAL Read Road data Calculate LTR Filter Road data Calculate left and right profiles Calculate work in shocks Calculate vehicle initial position Transfer data from time domain to spatial domain Transfer data from spatian domein to time domain Calculate 10 m data Simulate model fromt=0 to end Save data End Figure 7. Flow chart of the RIDE-simulation model. Main outcomes from the simulation part are the following: - vertical acceleration of the vehicle z - rolling acceleration of the vehicle chassi φ - pitch acceleration of the vehicle chassi at each time interval t. Outcomes of these three are calculated as a standard deviation for each 10 m interval. Combined acceleration is calculated using the formula below (2.8.6). 2.8 Outcomes Outcomes Table 2. List of outcomes from RIDE-simulations. sim_nop_ka Num 3 0 Kuorma-autosimuloinnissa käytetty nopeus (km/h) pys_ki_std Num 4 2 Kuorma-auton korin pystykiihtyvyyden hajonta (m/s2) siv_ki_std Num 3 0 Kuorma-auton korin sivuheilahduskiihtyvyyden hajonta (astetta/s2) nyö_ki_std Num 3 0 Kuorma-auton korin nyökkimiskiihtyvyyden hajonta (astetta/s2) yhd_ki_rms Num 4 2 Kuorma-auton kokonaiskiihtyvyyden RMS (m/s2) esal_std Num 4 2 Kuorma-auton tierasituksen hajonta (ESAL) ltr_std Num 4 2 Kuorma-auton pyöräpainosiirtymän hajonta

21 21 (%) Ityö_ka Num 5 0 Kuorma-auton iskunvaimentimien tekemä työ (J/10m) sim_nop_ha Num 3 0 Henkilöautosimuloinnissa käytetty nopeus (km/h) Ityö_ha Num 5 0 Henkilöauton iskunvaimentimien tekemä työ (J/10m) sim_nop_ka Simulation speed for truck (km/h) pys_ki_std The final indicator (pys_ki_std) is calculated as a standard deviation of vertical acceleration (m/s 2 ) of a chassi (VERT_a) over the reporting interval (10 m) siv_ki_std The final indicator (siv_ki_std) is calculated as a standard deviation of roll acceleration (degrees/s 2 ) of a chassi (ROLL_a) over the reporting interval (10 m) nyö_ki_std The final indicator (nyö_ki_std) is calculated as a standard deviation of pitch acceleration (degrees/s 2 ) of a chassi (PITCH_a) over the reporting interval (10 m) yhd_ki_rms Combined acceleration yhd_ki_rms is calculated as a rms-value (root mean square) of combined acceleration of a driver seat over the reporting interval (10 m). Combined acceleration has three components taken from vertical acceleration, roll acceleration and pitch acceleration calculated with the following formula: a ratax = r ROLL_a a ratay = r PITCH_a a yhd = VERT a 2 + (1.4 a ratax ) 2 + (1.4 a ratay ) 2 where r is the distance from the seat of driver to the C.o.G. For ROLL movement r = 0.8*W/2 and for PITCH movement r=0.8*lf esal_std Road load is calculated for truck with the following formula: ESAL = ( P f 80 ) 4 + ( P r 100 ) 4 where Pf is the axle load (kn) of front axle and Pr is the axle load of rear axle (kn).

22 22 The final indicator (ESAL_std) is calculated as a standard deviation over the reporting interval (10 m) ltr_std LTR is a Load Transfer ratio (%) and it is calculated for a truck with the following formula using wheel loads: LTR = 100 ( P fr + P rr P fl P rl P fr + P rr + P fl + P rl ) The final indicator (ltr_std) is calculated as a standard deviation over the reporting interval (10 m) Ityö_ka and Ityö_ha Ityö_ka is the sum of energy used in shock absorbers in truck over the reporting interval (10 m). It is calculated in each shock by multiplying the velocity of the vertical movement of a corner of chassi (m/s) by the suspension coefficient cij (Ns/m) and the displacement of the spring sij (m). Ityö_ha is the same but with car parameters. The unit is Joule/reporting interval sim_nop_ha sim_nop_ha is the simulation speed (km/h) used for car model. 2.9 Reference Data The reference road profile for left and right wheel paths are presented in the following figure. Y-axis is in mm and x-axis is in meters. The bump is 100 mm high and 5 m long. Left bump comes first and after that the right one Profile Left wheel path Right wheel path Figure 8. Reference road profile.

23 Results The vertical displacement of car body due to the bump is presented in the following figure. X-axis is in seconds and Y-axis in mm. The simulation speed is 40 km/h. 63 mm Figure 9. Vertical distance of the car body (heavy vehicle). The pitch displacement of car body due to the bump is presented in the following figure. X-axis is in seconds and Y-axis in degrees. The simulation speed is 40 km/h. ±1.9 degrees Figure 10. Pitch angle (in degrees) of the car (heavy vehicle) body Reference 2 A reference input road file has been used produce reference results. The source data and main results has been presented in an attached excel-file.

24 24 3 Litterature 1. Thomas D. Gillespie. Fundamentals of Vehicle Dynamics. Published by SAE International (1992). ISBN 10: ISBN 13: Virtala Pertti, Alanaatu Pauli, Eskola Timo (2016): Tien epätasaisuustunnusluvun kehittäminen. RIDE-ajoneuvomalli. Liikenneviraston tutkimuksia ja selvityksiä 46/ Pertti Virtala & Juho Meriläinen (2017): New Indicators of Riding Comfort From Vehicle Dynamics. World Conference on Pavement and Asset Management, WCPAM2017 Milan, Italy - June 12/16, Michael Sayers (1996): Standard Terminology for Vehicle Dynamics Simulations The University of Michigan Transportation Research Institute (UMTRI). 5. ISO 8855, Road vehicles Vehicle dynamics and road-holding ability Vocabulary (1991). 6. Abramov, S., Mannan, S., & Durieux, O. (2009): Semi-Active Suspension of Engineering Systems Modelling and Simulation, 1(2/3),

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