Transportation Research Part D 92 (2021) 102717
交通研究D 部分 92 (2021) 102717
Effects of semi-trailer modifications on HGV fuel consumption
半挂车改装对 HGV 油耗的影响
Anil K. Madhusudhanan*, Daniel Ainalis, Xiaoxiang Na, Isabel Vallina Garcia, Michael Sutcliffe, David Cebon
Anil K. Madhusudhanan*、Daniel Ainalis、Xiaoxiang Na、Isabel Vallina Garcia、Michael Sutcliffe、David Cebon
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
剑桥大学工程系,Trumpington Street,剑桥 CB2 1PZ,英国
A R T I C L E I N F O A B S T R A C T
Keywords: Double-deck semi-trailers Heavy goods vehicle Fuel consumption Coast-down test | This article investigates the effects of aerodynamic and lightweight double-deck semi-trailers on fuel consumption of Heavy Goods Vehicles (HGVs). The HGVs were evaluated using in-service data, and computer-based simulations with coefficients of aerodynamic drag and rolling resistance estimated from coast-down tests conducted on a test track. The coast-down tests showed that the aerodynamic features reduced the coefficient of aerodynamic drag by approximately 7.2% and the wide single tyres on the lightweight trailers reduced the coefficient of rolling resistance by approximately 10%. The in-service data showed that the aerodynamic features on the aerodynamic vehicles have a statistical significance on fuel consumption. Computer-based simulations showed that the aerodynamic-lightweight trailer reduces the HGV’s fuel consumption by approximately 20.2% for a long-haul drive cycle. As these improvements don’t have significant barrier to implementation, which is the case with electrification of HGVs, fleet operators can employ these improvements to reduce their carbon emissions. |
Introduction
介绍
There are numerous technological opportunities in the short to medium term to improve the fuel efficiency of Heavy Goods Vehicles (HGVs) (Delgado et al., 2017). While tractors are often the focus of research and development into fuel efficiency technologies, trailers are generally considered as an afterthought due to their relatively low cost. Trailers play a vital role in road freight transport (McKinnon, 2006) and should be included in strategies to reduce the carbon emissions produced by the sector (Galos et al., 2015). Broadly speaking, three main technologies are available to reduce fuel consumption of trailers: low rolling resistance tyres, aerodynamic packages to reduce drag, and light-weighting using new and alternative materials to reduce mass and increase payload (Greening et al., 2015).
在中短期内,有许多技术机会可以提高重型货车 (HGV) 的燃油效率(Delgado 等人,2017 年)。虽然拖拉机通常是燃油效率技术研发的重点,但由于成本相对较低,拖车通常被认为是事后才想到的。拖车在公路货运中起着至关重要的作用(McKinnon,2006 年),应纳入减少该行业产生的碳排放的战略(Galos 等人,2015 年)。从广义上讲,有三种主要技术可用于降低拖车的燃料消耗:低滚动阻力轮胎、减少阻力的空气动力学包,以及使用新材料和替代材料实现轻量化以减轻质量并增加有效载荷(Greening 等人,2015 年)。
Aerodynamic drag is a significant component of energy consumption, particularly in long haul operations due to the high average speeds (Zhao et al., 2013; Lajunen, 2014). The aerodynamic drag is dependent on the design of the tractor and trailer, and the interaction between them. In (Wood and Bauer, 2003), the four primary sources of aerodynamic drag and their respective percentage contributions for a tractor-trailer are outlined: the tractor front (25%), the gap between the tractor-trailer (20%), the trailer’s underbody (30%), and the rear of the trailer (25%). Due to the considerable difference in tractor and trailer bodies in North-America and
空气阻力是能源消耗的重要组成部分,尤其是在长途运营中,由于平均速度高(Zhao 等人,2013 年;Lajunen,2014 年)。空气阻力取决于拖拉机和拖车的设计,以及它们之间的相互作用。在(Wood 和 Bauer,2003 年)中,概述了空气动力阻力的四个主要来源及其对牵引拖车的相应百分比贡献:牵引车前部 (25%)、牵引车拖车之间的间隙 (20%)、拖车底部 (30%) 和拖车后部 (25%)。由于北美的拖拉机和拖车车身存在相当大的差异,并且
This research was partly supported by the Innovate UK Grant RG87919: ‘Low Emission Freight and Logistics Trial - Lightweight Aerodynamic Double-Deck Trailer Trial’ and the Engineering and Physical Sciences Research Council Grant EP/R035199/1: ‘Centre for Sustainable Road Freight 2018-2023’.
这项研究得到了 Innovate UK Grant RG87919:“低排放货运和物流试验 - 轻型空气动力学双层拖车试验”和工程与物理科学研究委员会 EP/R035199/1:“2018-2023 年可持续公路货运中心”的部分支持。
* Corresponding author.
* 通讯作者。
E-mail address: ak2102@cam.ac.uk (A.K. Madhusudhanan).
电子邮件地址:ak2102@cam.ac.uk (A.K. Madhusudhanan)。
https://doi.org/10.1016/j.trd.2021.102717
Available online 9 February 2021
2021 年 2 月 9 日在线提供
1361-9209/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
1361-9209/ © 2021 作者。 由 Elsevier Ltd. 出版 这是 一篇在 CC BY 许可下的开放获取文章
(http://creativecommons.org/licenses/by/4.0/).
the UK, e.g. long-nose tractor and variable tractor-trailer gap in North-American HGVs are not present in HGVs in the UK, the potential contributions can be different for HGVs in the UK. Nevertheless, a variety of technology packages are available to reduce the drag across all these sources. They include streamlining the shape of the tractor and trailer, adding side panels and fairings, and even complete redesigns which could theoretically reduce the drag coefficient by 42% in the long-term (Delgado et al., 2017). Note, however, that any reduction in payload due to changing the shape can have a negative effect on overal energy consumption. So such large drag reductions are not necessarily beneficial to reduce carbon emissions. This effect may happen in transport operations where the trailer is fully filled by volume before reaching its mass limit.
英国,例如北美 HGV 中的长头牵引车和可变牵引车-拖车间隙在英国的 HGV 中不存在,则英国 HGV 的潜在贡献可能不同。尽管如此,还有各种技术包可用于减少所有这些来源的阻力。它们包括简化拖拉机和拖车的形状,添加侧板和整流罩,甚至完成重新设计,从长远来看,理论上可以将阻力系数降低 42%(Delgado 等人,2017 年)。但请注意,由于形状改变而导致的有效载荷减少可能会对整体能耗产生负面影响。因此,如此大幅的减阻并不一定有利于减少碳排放。这种影响可能发生在运输操作中,即拖车在达到其质量限制之前被体积完全填满。
The average tractor weight increased over the last 20 years due to factors such as safety and comfort requirements, and the increasing stringency of pollutant emission standards (Hill et al., 2015). This trend highlights the need to reduce the mass of the tractor-trailer combination where possible in order to further increase the payload. Reducing the trailer’s unladen mass is one of the most straightforward vehicle design changes that can be made (Odhams et al., 2010). The most practical area for manufacturers to reduce trailer mass in the short-term is by using lightweight composites for trailer decking and side walls, and the design of the frame. In the long-term more radical changes are possible to significantly reduce trailer weight (Galos and Sutcliffe, 2019). For example, a composite chassis formed of carbon fibre reinforced polymer beams and a pultruded glass fibre reinforced polymer deck could drastically reduce overall trailer weight by up to 1326 kg (Galos and Sutcliffe, 2019). However, the materials are not yet affordable. In (Hill et al., 2015), the overall potential of light-weighting to reduce the emissions of heavy duty transport vehicles was examined. The results showed that it is possible to achieve mass reductions of 5% in the short-term and 17% by 2030.
由于安全性和舒适性要求以及污染物排放标准日益严格等因素,拖拉机的平均重量在过去 20 年中有所增加(Hill 等人,2015 年)。这一趋势凸显了在尽可能减少牵引车-拖车组合质量以进一步增加有效载荷的必要性。减少拖车的空载质量是可以进行的最直接的车辆设计更改之一(Odhams 等人,2010 年)。对于制造商来说,在短期内减少拖车质量的最实用领域是将轻质复合材料用于拖车甲板和侧壁,以及框架的设计。从长远来看,更激进的改变有可能显着减轻拖车的重量(Galos 和 Sutcliffe,2019 年)。例如,由碳纤维增强聚合物梁和拉挤玻璃纤维增强聚合物甲板组成的复合材料底盘可以大大减轻拖车的整体重量,最高可达 1326 公斤(Galos 和 Sutcliffe,2019 年)。然而,这些材料还不能负担得起。在 (Hill et al., 2015) 中,研究了轻量化减少重型运输车辆排放的整体潜力。结果表明,短期内有可能实现 5% 的减重,到 2030 年实现 17% 的减重。
In (Galos et al., 2015), a study was carried out in the UK to assess the potential for improving trailer design through light-weighting. It found a particularly attractive opportunity for double-deck trailer operations. Their analysis of loaded double-deck trailers for a UK grocery fleet operator found the average number of cages transported per trailer was only 83% of the maximum allowable 75 cages, due to reaching the axle load limit. Their analysis highlights the opportunity to improve the payload capacity by light-weighting the trailer. This paper focuses on evaluating a trial of new Lightweight and Aerodynamic Double Deck (LADD) trailers developed through the Low Emissions Freight Trial (TRL).
在 (Galos et al., 2015) 中,在英国进行了一项研究,以评估通过轻量化改进拖车设计的潜力。它为双层拖车运营发现了一个特别有吸引力的机会。他们对英国杂货车队运营商的装载双层拖车的分析发现,由于达到轴重限制,每辆拖车运输的平均笼子数量仅为最大允许的 75 个笼子的 83%。他们的分析强调了通过减轻拖车重量来提高有效载荷能力的机会。本文重点介绍了通过低排放货运试验 (TRL) 开发的新型轻型和空气动力学双层 (LADD) 拖车的试验。
During the project, 2 aerodynamic trailers, 2 lightweight trailers and 2 aerodynamic-lightweight trailers were manufactured. All of them were double-deck semi-trailers, meant for long haul transport operations. These trailers were then operated by a supermarket chain for transport operations between their distribution centres and outlets. The main project objective was to evaluate the fuel consumption of the prototype vehicles against baseline HGVs. Both the prototype and baseline HGVs were tractor semi-trailer combinations. This article shares the analysis from this project, including coast-down tests to estimate the reduction in coefficient of aerodynamic drag from the aerodynamic features and the reduction in coefficient of rolling resistance from the use of wide single tyres, instead of dual pairs, on the lightweight trailers.
在项目期间,制造了 2 辆空气动力学拖车、2 辆轻型拖车和 2 辆空气动力学轻型拖车。它们都是双层半挂车,用于长途运输作业。然后,这些拖车由一家连锁超市运营,用于其配送中心和网点之间的运输业务。项目的主要目标是根据基线 HGV 评估原型车的油耗。原型和基线 HGV 都是拖拉机半挂车组合。本文分享了该项目的分析,包括滑行测试,以估计空气动力学特性对空气动力阻力系数的降低,以及在轻型拖车上使用宽单轮胎而不是双对轮胎对滚动阻力系数的降低。
The main contributions of this article are as follows:
本文的主要贡献如下:
Estimation of coefficients of aerodynamic drag and rolling resistance of the double-deck HGVs.
双层 HGV 的空气动力阻力和滚动阻力系数的估计。
Evaluation of the double-deck HGVs for in-service drive cycles using telematics data.
使用远程信息处理数据评估用于在役驾驶循环的双层 HGV。
Model-based evaluation of the double-deck HGVs for standard drive cycles and different vehicle weights.
对标准驾驶循环和不同车辆重量的双层 HGV 进行基于模型的评估。
The in-service evaluation used telematics data, whereas the evaluation for standard drive cycles used model-based simulations with experimentally estimated coefficients of aerodynamic drag and rolling resistance. The coast-down experiments to estimate these coefficients were conducted on a test track.
在役评估使用远程信息处理数据,而标准驾驶循环的评估使用基于模型的模拟,通过实验估计空气动力阻力和滚动阻力系数。估计这些系数的滑行实验是在测试轨道上进行的。
Fig. 1. The semi-trailer aerodynamic features: boat tail, deflector and fin.
图 1. 半挂车的空气动力学特点是:船尾、导流板和鳍。
Aerodynamic and lightweight semi-trailers
空气动力学和轻型半挂车
The aerodynamic features on the aerodynamic HGVs and aerodynamic-lightweight HGVs reduced their aerodynamic drag. These features are shown in Fig. 1. The semi-trailers are 13.58 m long and 2.55 m wide. At the rear end of the trailer, there is a tapered 1.48 m long ‘boat tail’ at an angle of 4.5 deg. The boat-tailing was only applied to the sides of the trailer, as can be inferred from Fig. 1. It was not applied to the trailer top to avoid undesired loading issues, which may result in undesired transportation efficiency. Wind tunnel tests on a 110th scale model (Garcia et al., 2018) showed approximately 3.4% reduction in the coefficient of aerodynamic drag due to this modification. Although a larger taper (up to 9 deg) would have been more beneficial, the angle was constrained by the necessary width of the rear doors. The front end of the trailer has a deflector and fin to prevent cross flow due to side winds. These showed approximately 2.5% and 2.4% reductions in drag, respectively, in the wind tunnel tests. Note that the type of tractor used in this work, which is shown in Fig. 3, and the scale model used in the wind tunnel tests have the same aerodynamic features, including the roof deflector, side extenders and tractor-trailer gap. Together, all three aerodynamic features reduced the aerodynamic drag by approximately 8%. The project and baseline trailers were fitted with full-length side skirts, optimised to reduce underbody flow and hence drag. The 8% drag reduction is in addition to the performance improvement from the side skirts.
空气动力学 HGV 和空气动力学轻型 HGV 的空气动力学特性降低了它们的空气动力学阻力。这些特征如图 1 所示。半挂车长 1358 m,宽 255 m。在拖车的后端,有一个 148 m 长的锥形 “船尾”,角度为 45 度。船尾部仅适用于拖车的侧面,从图 1 中可以推断出。它没有应用于拖车顶部,以避免意外的装载问题,这可能会导致意外的运输效率。1 10比例模型(Garcia 等人,2018 年)的风洞测试表明,由于这种修改,空气动力阻力系数降低了约 34%。虽然更大的锥度(最高 9 度)会更有利,但角度受到后门必要宽度的限制。拖车的前端有一个导流板和鳍,以防止由于侧风引起的交叉流动。这些结果表明,在风洞测试中,阻力分别减少了大约 2 5% 和 24%。请注意,本工作中使用的拖拉机类型(如图 3 所示)和风洞测试中使用的比例模型具有相同的空气动力学特征,包括车顶导流板、侧延长器和拖拉机-拖车间隙。所有三种空气动力学特性共同将空气动力学阻力降低了约 8%。项目拖车和基线拖车配备了全长侧裙,经过优化以减少车身底部流动,从而减少阻力。8% 的阻力减少是侧裙性能改进的补充。
The trailer mass was reduced by using lighter materials for the chassis, lower and upper decks, doors, running gear, and for the side- walls of the semi-trailer. The light-weighting features included high strength steel rolling chassis, and composite materials for the upper and lower decks. The lightweight trailers were fitted with wide single tyres, which lowered the coefficient of rolling resistance compared to the dual pairs. The prototype light-weight trailer had a mass of 8.8 t compared to the baseline mass of 11.3 t, i.e. a reduction of 2.5 t. However, shortly after commencing transport operations, the trailer decks and side-walls developed defects. Therefore, these parts need reinforcement and this activity is ongoing. This work used the proven mass reduction of 1350 kg from the chassis. From previous research (Galos and Sutcliffe, 2019), a proposed mass reduction of 500 kg from the side-walls, 120 kg from the decks and 40 kg from the doors were also used.
通过在底盘、上下甲板、车门、行走装置和半挂车的侧壁上使用更轻的材料来减轻拖车的质量。轻量化特点包括高强度钢滚动底盘和上下甲板的复合材料。轻型拖车配备了宽大的单轮胎,与双对轮胎相比,这降低了滚动阻力系数。原型轻型拖车的质量为 88 吨,而基线质量为 113 吨,即减少了 25 吨。然而,在开始运输操作后不久,拖车甲板和侧壁出现了缺陷。因此,这些部分需要加固,并且这项活动正在进行中。这项工作使用了底盘减轻 1350 kg 的经过验证的质量。根据以前的研究(Galos 和 Sutcliffe,2019 年),还建议使用侧壁减重 500 公斤、甲板减重 120 公斤和门减重 40 公斤。
Methodology
方法论
This section describes the data collection and evaluation methods, and the types of vehicles used in each evaluation method. Telematics data from two aerodynamic HGVs and a baseline HGV were collected for a period of 5 months, while these vehicles performed their normal transport operations. This data was used to perform an in-service analysis of these vehicles to understand the benefits of the aerodynamic HGVs for their normal transport operations.
本节介绍数据收集和评估方法,以及每种评估方法中使用的车辆类型。收集了来自两辆空气动力学 HGV 和一辆基线 HGV 的远程信息处理数据,为期 5 个月,同时这些车辆执行正常的运输操作。这些数据用于对这些车辆进行在役分析,以了解空气动力学 HGV 对其正常运输操作的好处。
The analysis of telematics data has limitations arising from numerous factors, including different wind velocities, road slope profiles and route profiles. In addition, telematics data was not available for the lightweight vehicles. Therefore, model-based evaluations were also performed to analyse performance of the HGVs. This analysis was performed for the baseline HGV, aerodynamic HGV, lightweight HGV, aerodynamic-lightweight HGV, HGV with lower rolling-resistance and HGV with lower Unladen Vehicle Weight (UVW). Note that the lightweight HGVs have lower rolling-resistance and UVW. Table 1 shows the parameters of each vehicle type. The model-based evaluations were performed for six drive cycles, and they used coefficients of aerodynamic drag and rolling resistance, which were estimated using coast-down experiments conducted on a test track.
远程信息处理数据的分析受到许多因素的限制,包括不同的风速、道路坡度剖面和路线剖面。此外,轻型车辆的远程信息处理数据不可用。因此,还进行了基于模型的评估以分析 HGV 的性能。该分析针对基线 HGV、空气动力学 HGV、轻型 HGV、空气动力学轻型 HGV、滚动阻力较低的 HGV 和空载车辆重量 (UVW) 较低的 HGV。请注意,轻型 HGV 具有较低的滚动阻力和 UVW。表 1 显示了每种车辆类型的参数。基于模型的评估对 6 次驾驶循环进行了评估,他们使用了空气动力阻力和滚动阻力系数,这些系数是通过在测试跑道上进行的滑行实验来估计的。
Data collection
数据采集
This section describes data collection from the telematics system and coast-down tests. The telematics data were collected in- service, whereas the coast-down tests were performed on a test track.
本节介绍从远程信息处理系统和滑行测试中收集的数据。远程信息处理数据是在服务中收集的,而滑行测试是在测试跑道上进行的。
Telematics data
远程信息处理数据
Telematics data from two tractors, each pulling an aerodynamic double-deck semi-trailer, and from a tractor, pulling a baseline double-deck semi-trailer, were collected in-service for a period of 5 months in 2019. All three tractors were of the same model and make, ‘MB Actros 2545’ from Daimler Truck AG, and were fitted with telematics systems from Daimler Fleetboard GmbH. The
2019 年,在役 5 个月期间收集了来自两台拖拉机(每辆牵引车牵引一辆空气动力学双层半挂车)和牵引车(牵引基线双层半挂车)的远程信息处理数据。所有三台拖拉机都是相同的型号和品牌,即戴姆勒卡车公司的“MB Actros 2545”,并配备了戴姆勒 Fleetboard GmbH 的远程信息处理系统。这
Fig. 2. Satellite image of the twin-straights test track at Horiba-MIRA Ltd, UK, where the coast-down tests were performed.
图 2. 英国 Horiba-MIRA Ltd 的双直道测试跑道的卫星图像,在那里进行了滑行测试。
Fig. 3. A photograph of the instrumented baseline heavy goods vehicle.
图 3. 配备仪表的基线重型货车的照片。
Table 1
表 1
Coefficients of aerodynamic drag times frontal area (CdA), coefficients of rolling resistance (Cr) and UVWs of different vehicle types.
不同车辆类型的空气动力阻力系数乘以正面面积 (CdA)、滚动阻力系数 (C) 和 UVW。
HGV type | CdA [m | Cr [-] | UVW [t] |
Baseline | 8.45 | 0.0050 | 19.566 |
Aerodynamic | 7.84 | 0.0050 | 19.566 |
Lightweight | 8.45 | 0.0045 | 17.556 |
Aerodynamic-lightweight | 7.84 | 0.0045 | 17.556 |
Lower Rolling Resistance | 8.45 | 0.0045 | 19.566 |
Lower UVW | 8.45 | 0.0050 | 17.556 |
telematics data set included date (yyy:mm:dd), average speed (km/h), diesel used (l), transport work (t.km), distance (km), driving style, operational time (hh:mm:ss), vehicle start time (hh:mm:ss) and vehicle stop time (hh:mm:ss), at a frequency of once per day. Here, driving style is a driver performance variable out of 1000, and it depends on the acceleration and deceleration values.
远程信息处理数据集包括日期 (YYY:MM:DD)、平均速度 (km/h)、使用的柴油 (l)、运输工作 (t.km)、距离 (km)、驾驶方式、运营时间 (HH:MM:SS)、车辆启动时间 (HH:MM:SS) 和车辆停止时间 (HH:MM:SS),频率为每天一次。在这里,驾驶风格是 1000 分的驾驶员性能变量,它取决于加速和减速值。
Coast-down tests
滑行测试
Coast-down tests were conducted to estimate the coefficients of aerodynamic drag and rolling resistance of an HGV with an aerodynamic-lightweight double-deck semi-trailer and of an HGV with a baseline double-deck semi-trailer. These tests were carried out on the twin-straights test track at Horiba-MIRA Ltd, UK, shown in Fig. 2. In each direction, the horizontal track is 1.6 km long and the two straights are joined by banked loops at each end.
进行了滑行测试,以估计带有空气动力学轻量级双层半挂车的 HGV 和带有基线双层半挂车的 HGV 的空气动力阻力和滚动阻力系数。这些测试在英国 Horiba-MIRA Ltd 的双直道测试跑道上进行,如图 2 所示。在每个方向上,水平轨道长 1.6公里,两条直线在两端由倾斜的环连接起来。
Fig. 4. A typical example of the measured speed profile from one of the coast-down tests.
图 4. 滑行测试中测得的速度曲线的典型示例。
These tests had two objectives: 1) estimate the reduction in coefficient of aerodynamic drag due to the aerodynamic features of the aerodynamic trailers, and 2) estimate the reduction in coefficient of rolling resistance due to the wide single tyres on the lightweight trailers. The reduction in coefficient of aerodynamic drag is applicable for the aerodynamic HGVs and the aerodynamic-lightweight HGVs. The reduction in coefficient of rolling resistance is applicable for the lightweight HGVs and aerodynamic-lightweight HGVs.
这些测试有两个目标:1) 估计由于空气动力学拖车的空气动力学特性而导致的空气阻力系数的降低,以及 2) 估计由于轻型拖车上较宽的单轮胎而导致的滚动阻力系数降低。空气动力阻力系数的降低适用于空气动力学 HGV 和空气动力学轻型 HGV。滚动阻力系数的降低适用于轻型 HGV 和空气动力学轻型 HGV。
The HGVs were instrumented with an inertial and navigation system, ‘RT3022’, from Oxford Technical Solutions Ltd. The processing unit with a built-in inertial measurement system was installed inside the tractor cabin. The primary GPS antenna was installed on the tractor roof. Before each test, the ‘RT3022’ was initialised using the manufacturer instructions.
这些 HGV 配备了 Oxford Technical Solutions Ltd. 的惯性和导航系统“RT3022”。带有内置惯性测量系统的处理单元安装在拖拉机驾驶室内。主 GPS 天线安装在拖拉机车顶上。在每次测试之前,'RT3022' 都使用制造商的说明进行初始化。
The coast-down tests were performed with an unloaded trailer and with an almost fully loaded trailer. When loaded, the trailer was loaded with concrete blocks to a Gross Vehicle Weight (GVW) between 43 and 44 t. The GVW was measured using the weighing bridge at the test facility.
滑行测试是用空载的拖车和几乎满载的拖车进行的。装载时,拖车装载有混凝土块,车辆总重 (GVW) 在 43 至 44 吨之间。GVW 是使用测试设施的称重桥测量的。
During each test, the HGV was accelerated to a maximum speed close to 84 km/h and was allowed to coast-down. As the twin- straights test track is only 1.6 km long in each direction, it is not long enough for the HGV to coast-down from 84 km/h to standstill in one go. Therefore, when the vehicle approached the end of a straight segment, the final vehicle speed was noted. The vehicle was brought back to the start of the same straight segment with a slightly higher speed than the noted final speed from the last coast- down lap. This process was continued until the vehicle stopped. This whole process was done for both directions of travel along the twin-straights test track, i.e. North East and South West in Fig. 2. The track is very close to level with no measurable change of elevation between the two ends. Fig. 4 shows the longitudinal vehicle speed profile during one of the coast-down tests. In addition to the vehicle’s longitudinal speed, longitudinal acceleration was measured.
在每次测试期间,HGV 被加速到接近 84 公里/小时的最高速度,并被允许滑行。由于双直道测试跑道每个方向只有 1.6公里长,因此 HGV 无法一次性从 84 公里/小时滑行到静止。因此,当车辆接近直线段的终点时,会记录最终的车速。车辆被带回同一直线段的起点,速度略高于最后一个滑行圈的记录最终速度。这个过程一直持续到车辆停下来。整个过程是针对沿双直线测试轨道的两个行驶方向完成的,即图 2 中的东北和西南。轨道非常接近水平,两端之间没有可测量的高程变化。图 4 显示了其中一次滑行测试期间的纵向车速曲线。除了车辆的纵向速度外,还测量了纵向加速度。
The longitudinal equations of motion of a vehicle (Madhusudhanan et al., 2020; Hunt et al., 2011) is as follows:
车辆的纵向运动方程(Madhusudhanan et al., 2020;Hunt et al., 2011)的裁决如下:
Pw(t) = ma(t)v(t)+Pa(t)+Pr(t)+Pg(t) (1)
Pw(t) = 马(t)v(t)+Pa(t)+Pr(t)+Pg(t) (1)
1 2
Pa(t) = ρairCdA(v(t) − vw) v(t) (2)
Pa(t) = ρ空气CdA(v(t) − vw) v(t) (2)
2
Pr(t) = Crmgv(t) (3)
Pr(t) = Crmgv(t) (3)
Pg(t) = mgsinθ(t)v(t) (4)
Pg(t) = mgsinθ(t)v(t) (4)
Here Pw is the engine power transmitted to the wheels, m is the gross vehicle mass, a is the longitudinal acceleration, v is the longitudinal speed, Pa is the power dissipated by aerodynamic drag, Pr is the power dissipated by rolling resistance, Pg is the power required to ascend the road gradient, ρair = 1.225 kg/m3 is the density of air, Cd is the coefficient of aerodynamic drag, A is the vehicle’s frontal area, vw is the component of the wind speed along the South West direction in Fig. 2, Cr is the coefficient of rolling resistance, g = 9.81 m/s2 is the acceleration due to gravity and θ is the road gradient. The effective mass of rotating components, driveline mechanical losses and speed dependence of rolling resistance coefficient McAuliffe and Chuang (2016), were ignored while estimating the coefficients. Although these are drawbacks of the estimation method, their effects were assumed negligible to compare two vehicles with the coefficients obtained using the estimation method used in this work.
其中 Pw 是传递到车轮的发动机功率,m 是车辆总质量,a 是纵向加速度,v 是纵向速度,Pa 是空气动力阻力耗散的功率,PR 是滚动阻力耗散的功率,Pg 是上升道路坡度所需的功率,ρ空气 = 1225 kg/m3 是空气密度,Cd 是空气阻力系数,A 是车辆的正面面积,vw 是图 2 中沿西南方向的风速分量,Cr是滚动阻力系数,g = 981 m/s2 是重力加速度,θ 是道路坡度。在估计系数时,忽略了旋转部件的有效质量、传动系统机械损耗和滚动阻力系数的速度依赖性 McAuliffe 和 Chuang (2016)。尽管这些是估计方法的缺点,但假设它们的影响可以忽略不计,将两辆车与使用本研究中使用的估计方法获得的系数进行比较。
When a vehicle coasts-down on a horizontal road, Pw = 0 as the vehicle is in neutral gear and Pg = 0 as the road gradient is zero. Therefore, Eq. (1) can be simplified as follows:
当车辆在水平道路上滑行时,Pw = 0 表示车辆处于空档, P g = 0 表示道路坡度为零。因此,方程。 (1) 可以简化如下:
1 2
ma(t) = − 2ρairCdA(v(t) − vw) − Crmg (5)
马(t) = − 2ρ空气CdA(v(t) − vw) − Crmg(5)
Estimation of the coefficient of aerodynamic drag, Cd, and the coefficient of rolling resistance, Cr, involved two steps: 1) estimation of the wind speed, vw, and 2) estimation of the coefficients.
空气动力阻力系数 Cd 和滚动阻力系数 Cr 的估计包括两个步骤:1) 估计风速 vw 和 2) 估计系数。
For the first step, Eq. (5) was rewritten as follows:
对于第一步,Eq. (5) 被重写如下:
1 2
a
一个(t) = −ρairCdA
一个(v(t) − vw) − Crg (6)
2m
2米
[ 1 ][ w 2 ] (7)
[ 1 ][w 2 ] (7)
= −ρair
空气CdA
一个 − Crg (v(t) − v )
2m 1
2米1
= CT[(v(t) − vw)2 ] (8)
= C[(v(t) − vw)2 ] (8)
1
Here C = −ρairCdA − Crg is the coefficient vector. Using the model form in Eq. 8, the coefficient vector, C, can be estimated so that a linear model relating (v(t) − vw)2 and a(t) can be found. This linear model fitting was used in the following optimisation problem
其中 C = −ρairCdA − Crg 是系数向量。使用 Eq 中的模型形式。 8 中,可以估计系数向量 C,以便找到与 (v(t) − vw)2 和 a(t) 相关的线性模型。此线性模型拟合用于以下优化问题