Tracking Ability of an MCV on a Rural Road

Transcription

1 25 th Coferece of Australia Istitute of Trasport Research Uiversity of South Australia, Adelaide 3-5 December 2003 Trackig Ability of a MCV o a Rural Road By Sadra Leie ad Dr Joatha Buker School of Civil Egieerig Queeslad Uiversity of Techology Cotact Author: Sadra Leie Ph: Fax: s.leie@qut.edu.au Keywords: Trackig Ability, Lae Width, Roughess, Multi-Combiatio Vehicles Multi-combiatio vehicles (MCVs) are road freight vehicles comprisig a prime mover towig two or more trailers. At each articulatio poit, movemets occur due to the driver, vehicle, road ad eviromet such as driver steerig, vehicle legth, road roughess ad side wid loadig, respectively. These lateral displacemets dictate the lae width required for vehicles usig the road ad, if igored or predicted iaccurately, ca affect the cost or safety of the road. Previous research (Prem et al., 1999) estimated the lae width requiremets for several MCVs o two routes with average roughess. I this curret study, a full scale testig programme was udertake o a rough road to measure the lateral displacemet of the rear trailer of a B-Double o a omially straight path. Video footage was recorded durig the tests from a camera o the top of the prime mover which was aimed at target boards at the rear of the vehicle. Lateral movemets of the trailers were extracted from the video data these were relative to a movig frame of referece, amely the prime mover which was subject to driver steerig iputs. Correctios were made for the relative agle betwee the prime mover ad the trailers, which was foud to vary with the applied steerig agle. These correctios were foud to result i a icreased estimate of the lateral displacemet ad hece the lae width required.

2 1 Itroductio Trackig ability describes the ability of the trailers of a multi-combiatio vehicle (MCV) to follow the path take by the drive uit. It is quatified by the total swept width, icludig the vehicle width ad the amout of lateral displacemet that trailers udergo whilst travellig at high speed over straight road sectios. It is used to determie the lae width requiremets of roads with the provisio that all wheels of heavy vehicles should remai o the sealed surface ad withi the allocated traffic lae. If the lae width is isufficiet, there is a icreased probability of trailers leavig the lae, causig shoulder damage or ecroachig ito traffic laes used by ocomig traffic (NRTC, 2001). Prem et al. coducted tests which were aimed at estimatig the lae width requiremets for certai heavy vehicle combiatios o straight path travel. It was foud that crossslope was the greatest cotributor to variatios i lateral displacemet, ad that this effect of cross-slope was quite predictable. Speed was aother factor that iflueced the amout of lateral displacemet. Lae width requiremets were determied for the differet vehicles by addig the width of the heavy vehicle (2.5m) to the maximum likely deviatios of the trailers i either directio (±3 stadard deviatios of the lateral displacemet). This would allow 99% of the displacemets to lie withi the specified lae width (Figure 2-1). The authors of the report recommeded that the lae width specificatio should be verified agaist a road that is kow to have poor trackig characteristics, before the widths are adopted ito ay guidelies (Prem et al., 1999; Leie et al., 2003). Figure 1-1: Limited lae width available for passig or overtakig (Mai Roads Wester Australia, 2001) The trackig ability performace depeds o vehicle factors such as the arragemet of trailers ad coectios, vehicle legth, suspesio ad tyre properties, operator steerig, speed ad misaligmet of the axles. Road ad evirometal factors iclude roughess, cross-slope ad side loadig such as wid-gusts (Prem et al., 1999). 2 Backgroud I the late 1970 s, the Alberta Departmet of Trasportatio specified that the rear uit travellig o smooth ad level surfaces should ot shift more tha 80mm to either side whe travellig i a straight lie (Prem et al., 1999). NAASRA (1978) adopted a figure of 100mm for use i Australia. Prem et al. (1999) explaied that further work was eeded to quatify parameters of speed, smoothess, ad grade for various types of heavy vehicles. 1. Figure 2-1: Lae Width Requiremets for Heavy Vehicles (Prem et al., 1999) 3 Testig Objectives A testig program was udertake by Queeslad Uiversity of Techology (QUT), Queeslad Departmet of Mai Roads (QDMR) ad Queeslad Trasport (QT), as reported i Haldae (2002). The overall project objectives from Haldae s (2002) prelimiary review of trackig ability testig are as follows: 1. To determie lateral displacemet history of a MCV o a straight route of high roughess. 2. To idetify the factors that most ifluece lateral displacemet so they may be

3 moderated i future vehicle ad road desig. 3. To provide relevat iformatio, which will assist the developmet of the stadard titled Route Assessmet Guidelies for Multi-Combiatio Vehicles i Queeslad (QDMR, 2003). 4 Testig Procedure Haldae s (2002) trackig ability tests were udertake betwee 6 ad 21 August Six MCV s, ragig i size from a B-double to a Triple Road trai, were drive alog a straight route whilst the lateral displacemets of the trailers were recorded o video tape from a camera located o top of the prime mover cabi. Agular trasducers measured the steer agle betwee the tyre directio ad the prime mover body. I this curret study, this data will be used to correct for the camera beig mouted o a movig frame of referece, due to yawig of the prime mover. 6. A secod camera was positioed o the vehicle to capture images of the frot right had wheel ad part of the road. This picture eables verificatio of the prime mover s positio withi the lae. This image was displayed i the bottom of the video scree (Figure 4-1). 7. The test vehicle was straighteed ad the cross hairs o the video scree were calibrated to the middle of the trackig boards by visual determiatio (Haldae, 2002; Leie et al., 2003). The test commeced with the vehicle acceleratig uder ormal coditios from a stadig positio to the testig speed. The recordig of chaiage, date, time ad video images commeced immediately. Test preparatios were coducted as follows: 1. QDMR Pavemets Materials ad Geotechical Divisio collected roughess data at 20m itervals for both the ier ad outer wheel paths. NAASRA Roughess (NRM) ad Iteratioal Roughess Idex (IRI) were determied. 2. A start lie ad fiish lie were paited alog the road for calibratio purposes. 3. A video camera was attached to the haulig uit ad directed to the rear of the vehicle. This would allow for the recordig of the rear trailer s movemets. 4. Trackig ability boards were attached to the top of the trailers, so that the lateral displacemets could be measured. 5. A otebook computer was set up to record distace ad time measuremets ad to place cross hairs o the video scree. The cross hair is a dotted lie o the video scree which idicates the positio of the prime mover cetre-lie, relative to which the lateral displacemet of the trailers (trackig ability boards) could be measured. This image was displayed i the top half of the video scree. (Figure 4-1). Figure 4-1: Output from video recordigs (Haldae, 2002) 5 Test Vehicle The test vehicle aalysed i this curret study was a B-Double with a legth of 25.36m ad a mass of toe (Figure 5-1). (Haldae, 2002; Leie et al., 2003) Figure 5-1: B-Double test vehicle (Haldae, 2002) 2.

4 6 Test Site The vehicle was tested o a 4.21 km sectio of the Toowoomba-Cecil Plais Road i Souther Queeslad. The aligmet was geerally straight, except for oe sweepig curve towards the ed of the sectio, data for which was excluded from processig. The speed limit alog this sectio of road was 100km/h. The road had a average cross fall of 3% from the crow of the road (accordig to costructio plas) ad cosisted of a flexible graular pavemet. Roughess of the road was geerally betwee 50 ad 100 NAASRA couts/km, with occasioal spikes up to 150 couts/km. Seal width varied betwee 6.2 ad 7.0 m. The average aual daily traffic for the sectio of road was 162 vehicles (Haldae, 2002). The road is curretly desigated as a Double Road Trai Route ad is a importat freight lik for the Easter Dows of Queeslad (EDROC & Queeslad Trasport, 1999). 7 Video Footage Data Processig The data was processed i two stages: The first stage, discussed i this sectio, ivolved processig the lateral displacemet of the rearmost trailer s trackig ability board relative to the prime mover cetre-lie, as represeted by the cross-hairs o the video footage. This data processig was aalysed ad reported i Leie et al. (2003) with the iitial itetio of capturig the lateral displacemets of the trailers ad determiig a lae width requiremet for each vehicle. However, a bias was observed, which required further aalysis to determie the absolute lae width requiremets. The origial procedure eabled the lateral displacemets of the trailers to be measured relative to the directio of the prime mover. This is correct whe the prime mover is travellig parallel to the road (Figure 7-1 left). However, as i ormal drivig, the driver frequetly altered the steerig of the prime mover, therefore chagig the bearig of the prime mover relative to the road (Figure 7-1 right). Ucorrected, this created a bias i the determiatio of the trailer lateral displacemet relative to the axis of the road (Leie et al., 2003). To correct for this bias, the steer agle history of the prime mover was aalysed to determie the prime mover positio ad bearig with respect to the road. Figure 7-2 illustrates the data processig procedure Figure 7-1: Chage i prime mover directio produces a bias i lateral displacemet results 3.

5 . Stage 1: Video Aalysis Video Footage Data Processig Agle betwee Prime Mover & Rear Trailer Stage 2: Lateral Displacemet Aalysis Prime Mover Steer Agle Prime Mover Travel Path Model Prime Mover Movemet withi Icremet Updated Trailer Bearig Updated Orietatio relative to Kigpi Bias Correctios also made This step is processed oce for the etire vehicle movemet. Other steps are processed & accumulated icremetally. Figure 7-2: Process for derivig lateral displacemet evelope To do this the prime mover bearig ad the agle betwee the prime mover axis ad the trailer axis was eeded. By kowig the lateral displacemet ad the distace betwee the trackig ability boards ad the camera, agle ψ (Figure 8-1) ca be determied as follows: Equatio X TPM ψ ta LT where : ψ = Agle betwee prime mover axis ad rear trailer axis, X TPM = Lateral displacemet as recorded from video footage (Figure 4-1), ad L T = Aliged distace from camera to boards 8 Lateral Displacemet Aalysis The secod stage ivolved processig the steer agle data to correct the bias observed i the previous stage. The raw steer agle data i its origial form was ot suitable for the correctios, ad as a result, a umber of geometric adjustmets were eeded. Figure 8-1: Agle betwee prime mover ad trailer The derivatios of the prime mover motio relate to the prime mover solely. The trailers are cosidered afterwards. Data-samplig itervals for the two data collectig processes differed quite sigificatly (3.4m vs. 9m). Therefore, whe the calculatios were combied, the loger samplig rate was adopted. The data was aliged accordig to chaiage usig a spreadsheet lookup fuctio. 8.1 Prime Mover Steer Agle Steer history plots provided data o the agle, θ, betwee the steerig tyres ad the prime mover body as well as the correspodig distace ad time measuremets. This iformatio reflected that, eve though the test route was straight, the driver made small adjustmets to the steerig i respose to road ad vehicle iputs, which resulted i the vehicle followig a path that oscillated about a straight lie of travel o the road. 4.

6 Figure 8-2: Radius calculated from steer agle Assumig that the steer agle (θ) is the same for both ier ad outer steer wheel paths, which is cosidered acceptable for small agles, ad that the cetre of the wheel path of the rear bogie tracks as show i Figure 8-2, the radius of the curve tracked by the cetre wheel path of the bogie may be approximated as follows: usig this icremetal circular path assumptio. A vehicle starts at the bottom of the figure ad travels o a straight path (R 1 = ) through the first icremet. Durig the secod icremet, the vehicle yaws right at a costat radius of curvature (R 2 ). Similarly, i icremet three, the vehicle yaws left with a costat radius (R 3 ). As a result, the actual travel path of the prime mover (darkeed lie) oscillates about a straight travel path axis, which is the driver s iteded path. L R siθ where: R = Radius of curve, L = Prime mover wheelbase, ad θ = Steer agle. Equatio 8-1 This assumes there is o tyre slip at either the steer or drive tyres, so that the prime mover ca be assumed to be rotatig about a poit give by the itersectio of lies perpedicular to the tyres. 8.2 Prime Mover Travel Path Model The data logger recorded measuremets every 3.4m o average; however, a further assumptio was eeded to model the prime mover travel path over the etire route icludig itermediate poits withi these 3.4m icremets. Each icremet is defied as a sectio of the test route startig at a steer agle measuremet ad edig at the followig measuremet. Itermediate steer agle poits were modelled usig a average of the steer agles at the start ad ed of the icremet. Durig a particular icremet, the prime mover is assumed to move alog a arc of costat radius (R). Figure 8-3 shows how the prime mover trajectory may be modelled 5. Figure 8-3: Travel path model for the prime mover 8.3 Prime Mover Movemet withi Icremet Chage i Prime Mover bearig over a icremet It is assumed that the prime mover s drive axle group moves alog a arc with a iteral agle ( φ ) as show i Figure 8-3.

7 This agle represets a fractio of a circle of 2π radias, which i tur is proportioal to the fractio of the legth of the arc divided by the total circumferece. This is reduced to: d Equatio 8-2 φ = R where: φ = chage i bearig over icremet d = distace moved durig icremet (arc legth) Updated Prime Mover Bearig The curret prime mover bearig may be determied by summig the chages i bearig from every previous icremet as show below. It is assumed that the bearig at the begiig of the test is zero, correspodig to the straight travel path axis. φ = φ 1 + φ Equatio 8-3 φ = φ1 + φ2 + φ φ 1 + φ 8.4 Updated Trailer Bearig The bearig of the prime mover ad the agle betwee the prime mover ad trailers were able to be determied by completig the derivatios i previous sectios of this paper. To this poit, oly the prime mover positio was cosidered, igorig the positios of the trailers. It is ow ecessary to cosider the etire combiatio. Figure 8-4, for simplicity, shows a outlie of the prime mover followed by a rectagular shape represetig all of the trailers of the MCV combiatio. Agles ψ ad φ (derived from Equatio 7-1 ad Equatio 8-3 respectively) are show o the diagram. The bearig of the trailers (β) relative to the solid lie (vehicle cetrelie) is the give by β = ψ φ Equatio 8-4 Figure 8-4: Notatio where: β = Trailer bearig, φ = Prime mover bearig, ψ = Agle betwee trailers ad prime mover, L T = Trailer legth betwee kigpi ad back of the rearmost trailer, L PM = Prime mover legth forward of the kigpi, X PM =Lateral distace betwee the frot cetre of the prime mover ad kigpi positio, ad X T = Lateral distace betwee the rear cetre of rearmost trailer ad kigpi positio 8.5 Updated MCV Orietatio relative to Kigpi Lateral positios of the cetre frot of the prime mover ad cetre rear of the last trailer from the vehicle cetrelie are approximated as follows: X = siφ Equatio 8-5 PM L PM X = si β Equatio 8-6 T L T 6.

8 8.6 Bias: Accumulatio ad Removal Further data aalysis was udertake to remove two additioal sources of bias from the model described above Raw Steer Agle Data Offsets Table 8-1 is a excerpt of the data file for the B-Double over a distace of 5.1 m ad time of secods from the startig positio. Table 8-1: Extract of Steer Agle Data from the begiig of the test (B-Double) Time (msecs) Dist (m) Steer (deg) This table shows that the average recorded steer agle (θ) for the B-Double over this iterval was approximately 0.54 degrees. This is also show as the dark lie i Figure 8-5. O first glace, this idicates that the prime mover would have bee yawig to the left quite rapidly eve though the test sectio was straight. However, this was ot the case. This may have bee caused by iaccurate equipmet calibratio or error accumulatio. The darker plot i Figure 8-5 shows the raw steer agle data for the B-Double. The steer agle appears to oscillate aroud a value other tha zero. Iitially the value appears to oscillate aroud 1.0 degrees; however, this icreases to 1.3 degrees towards the ed of the test. Three methods for filterig the raw steer agle data were cosidered, as follows: Subtractig sample average Subtractig tredlie equatios Subtractig progressive averages Figure 8-5: Correctig steer agle offset by subtractig the progressive average The last method aimed to correct for iitial offset ad the creep i offset. This method was foud to produce the best results ad retured a steer agle history that oscillated about zero. Figure 8-6: Bearig bias for prime mover corrected to oscillate aroud zero (B-Double) 7.

9 8.6.2 Bias due to Varyig Samplig Itervals This sectio refers to data processig methods described i the Prime Mover Travel Path Model (Sectio 8.2). The method of separatig the test route ito small icremets of circular travel paths itroduced modellig iaccuracies whe distace ad time measuremets were ot recorded at set itervals. For example, durig the B-Double testig, the data logger failed to record measuremets for 4.2 s or 91m startig at a chaiage km, whereas o average the logger made records every 3.7m over the legth of the road. At this poit, the steer agle recordig was 1.4 degrees. Accordig to the above icremet assumptio, the vehicle would be modelled as travellig at the set agle of 1.4 degrees for 91m producig a large curve (the light plot i Figure 8-6) i the vehicle path, which did ot exist i reality. Correctios were made by subtractig the average of the surroudig 40 bearig values from the raw bearig i a similar approach to Sectio The corrected prime mover bearig is show as the dark plot i Figure 8-6. This correctio also ameds smaller errors due to the logger recordig at varyig itervals throughout the remaider of the test. 9 Prelimiary Results Figure 9-2 is a graph of the lateral distace perpedicular to the road betwee the kigpi ad 1. Frot cetre of the Prime Mover ad 2. Rear cetre of the Rearmost Trailer The graph shows that the sig of the displacemets for the prime mover are opposite to the trailer for 85% of the test duratio, idicatig that the combiatio most ofte travelled o a slight agle to the directio of the road as show i Figure 9-1. Figure 9-1: Commo vehicle orietatios Figure 9-2: Prime mover ad trailer lateral width due to trackig ability (B-Double) 8.

10 Figure 9-3: Corrected ad ucorrected lateral displacemet results Further, Figure 9-2 shows a oscillatig patter idicatig that the total lateral displacemet either side of the vehicle cetrelie should be summed whe determiig the fial lae width requiremets. Sice the rage of prime mover lateral displacemets ever exceeded the rage of lateral displacemets from the trailers, the prime mover displacemets are ot critical. 9.1 Compariso to Ucorrected Results The dark lie i Figure 9-3 shows the origial, ucorrected, lateral displacemet relative to the prime mover s bearig. The lateral displacemet relative to the road axis, show as the lighter lie, appears to be amplified; however geerally is of the same sig. Referrig back to Figure 7-1, this diagram shows how the perceived lateral displacemet icreased whe it is take relative to the road axis rather tha the prime mover directio. Some icosistecies are oticeable betwee the chaiages km ad km, which may be due to irregular steer agle samplig itervals. Future aalysis will cosider the road segmets outside these chaiages separately to avoid the effect of bias. 10 Discussio Oscillatios of the frot of the prime mover ad rear of the rearmost trailer were commo throughout the tests as show i Figure 9-2. The prime mover was foud to oscillate at a slower rate (9 oscillatios/km) ad with a lesser amplitude. The rear trailer oscillated at 14 times per km o average. The lower amplitude is possibly caused by the shorter wheelbase legth o the prime mover tha the trailers ad the lower frequecy may occur because the driver had more cotrol of the positio of the prime mover tha the positio of the trailers. As a result, it is recommeded that further full scale testig be completed o the effects of icreasig the trailer positio cotrol o trackig ability performace, for example through the use of steerable axles o trailers. Figure 10-1 shows the calculated extra lateral width ad the correspodig road roughess at the same chaiage. A visual compariso shows mior correlatios that are offset i chaiage. It is expected that the offset occurs because roughess will have a delayed effect o the displacemets of the trailers. Whe five outliers are removed ad roughess ad displacemet are offset (by chaiage), the 9.

11 strogest correlatio is 0.36 idicatig that some depedece may occur. vehicle width, lateral drift ad the effect of trackig ability. The effect of steerable axles o trackig ability. 13 Refereces Figure 10-1: Compariso of extra lateral width ad road roughess 11 Coclusio The study idetifies a method for combiig prime mover steer agle measuremets with lateral displacemet data collected from a rearward-facig video camera o top of the prime mover. The two measuremets were merged by cosiderig the prime mover bearig, trailer bearig ad the agle betwee the prime mover ad the trailer. The results show that the prime mover displacemets ever exceeded the trailer displacemets i ay oscillatio, so the prime mover s positio is ot critical. Further, correctio for the prime mover headig agle has bee see to lead to a icreased estimate of lateral displacemet. 12 Future Aalysis This project has idetified several areas requirig further aalysis: Improved methods for correlatig roughess that better icorporate the delay betwee the road roughess ad whe the oscillatios are experieced by the rear trailer. The lateral drift of the prime mover i the lae due to steerig. This will ifluece the fial lae width requiremets for the vehicle. The trasiet lateral evelope of the vehicle durig oe oscillatio icludig 10. EDROC, & Queeslad Trasport. (1999, March). Regioal Trasport Framework for the Easter Dows. Retrieved 22d October, 2003, from sf/b61987be056b4fd94a2566fd f/ b61ec97e4eabeb944a25674d00126ec3/$fi LE/ATT3ZA8S/Regtras.pdf Haldae, M. (2002). Assessig the Impacts of Multi-Combiatio Vehicles o Traffic Operatio ad Safety. Master of Egieerig Research Degree Thesis, Queeslad Uiversity of Techology, Brisbae. Leie, S., Haldae, M., & Buker, J. (2003, May). Evaluatio of Trackig Ability of Multi-Combiatio Vehicles. Paper preseted at the 21st ARRB ad 11th REAAA Coferece: Trasport our highway to a sustaiable future, Cairs, Queeslad, Australia. Mai Roads Wester Australia. (2001, 9 Jue). Regioal Road Trai Summits Kalgoorlie ad Geraldto. Paper preseted at the Norther Regio Road Trai Cosesus Coferece, Geraldto, WA. NRTC. (2001). Defiitio of Potetial Performace Measures ad Iitial Stadards (No ). Melboure, Victoria, Australia: Natioal Road Trasport Commissio by ARRB Trasport Research Ltd. Prem, H., Ramsay, E., Fletcher, C., George, R., & Gleeso, B. (1999). Estimatio of Lae Width Requiremets for Heavy Vehicles o Straight Path: Austroads. QDMR. (2003). Draft Route Assessmet Guidelies for Multi-Combiatio Vehicles i Queeslad. Brisbae: Queeslad Departmet of Mai Roads.