裝配圖大學(xué)生方程式賽車設(shè)計（制動與行走系統(tǒng)設(shè)計）（有exb圖+中英文翻譯+開題報告）,裝配,大學(xué)生,方程式賽車,設(shè)計,制動,行走,系統(tǒng),exb,中英文,翻譯,開題,報告,講演,呈文 2010智能計算技術(shù)與自動化國際會議 研究匹配策略和模擬連續(xù)可變傳輸系統(tǒng)的拖拉機 徐里有 周之禮 曹青梅 張明珠 河南科技大學(xué)，洛陽，河南省，中國 加我qq：1985639755要英文原文 摘要——本文根據(jù)發(fā)動機測試結(jié)果,建立了發(fā)動機輸出轉(zhuǎn)矩模型和油耗模型。發(fā)動機轉(zhuǎn)速特性是在當(dāng)發(fā)動機工作在最優(yōu)經(jīng)濟模式和滿負(fù)荷的工況下，表示發(fā)動機轉(zhuǎn)速和節(jié)流之間的關(guān)系?；谝陨瞎ぷ?提出了連續(xù)變量傳輸(HMCVT)系統(tǒng)的匹配策略。根據(jù)在不同的野外環(huán)境工況,以仿真方法研究了HMCVT系統(tǒng)匹配的策略。這個研究為測定HMCVT系統(tǒng)提供了理論設(shè)計基礎(chǔ)和控制方法。 關(guān)鍵詞——拖拉機;振動連續(xù)變量傳輸;匹配策略;仿真 1. 介紹 無級變速傳輸系統(tǒng)(HMCVT)是一種新型的一個機械傳動(MT)聯(lián)合一個具有一對液壓單元液壓傳動(HST)組成的傳動裝置。HMCVT通過組合MT和HST有一個連續(xù)的變量轉(zhuǎn)移率并在在M[1,2]狀態(tài)下達(dá)到高的效率。只有當(dāng)合理匹配HMCVT系統(tǒng)和發(fā)動機,HMCVT系統(tǒng)可以發(fā)揮其優(yōu)勢。匹配的關(guān)鍵是根據(jù)實際的工作條件和發(fā)動機特性,發(fā)動機通過HMCVT系統(tǒng)調(diào)節(jié)速度比工作在最佳狀態(tài),。拖拉機HMCVT系統(tǒng)速度比的調(diào)節(jié)可以通過控制位移比的變量液壓泵(PV)和固定液壓馬達(dá)(MF)來實現(xiàn)。 目前,國內(nèi)外的連續(xù)變量傳輸系統(tǒng)的研究匹配主要集中在汽車[3、4、5),并且這個關(guān)于拖拉機研究還沒有被報道。拖拉機不僅與汽車在結(jié)構(gòu)有區(qū)別,其惡劣的工作條件和頻繁的外載荷波動也是與汽車的區(qū)別。這些所有的要求速度比改變都是為了以及時適應(yīng)拖拉機變化的負(fù)載和運動阻力,確保動態(tài)性能和經(jīng)濟性。本文的目的是為拖拉機解決匹配策略和HMCVT系統(tǒng)的模擬問題,為了拖拉機的控制方法提供理論依據(jù)。 2. 發(fā)動機輸出特性 A. 發(fā)動機輸出轉(zhuǎn)矩 發(fā)動機是一個更復(fù)雜的系統(tǒng),其輸出轉(zhuǎn)矩是通過節(jié)流閥開放和發(fā)動機的轉(zhuǎn)速來改變?；诎l(fā)動機試驗的結(jié)果,發(fā)動機穩(wěn)態(tài)輸出轉(zhuǎn)矩和節(jié)氣門打開和旋轉(zhuǎn)速度的關(guān)系可以使用多項式擬合來建立。發(fā)動機輸出扭矩和油門開啟和旋轉(zhuǎn)速度之間表面關(guān)系用多項式擬合能得到圖.1。 圖1發(fā)動機輸出轉(zhuǎn)矩與節(jié)氣門打開和旋轉(zhuǎn)速度的關(guān)系 b .發(fā)動機的通用特性 發(fā)動機功率和燃料消耗之間的關(guān)系,可以根據(jù)發(fā)動機負(fù)載的每個轉(zhuǎn)速特性曲線被實現(xiàn)。然后發(fā)動機有效燃料消耗和旋轉(zhuǎn)速度和轉(zhuǎn)矩之間的曲面關(guān)系可以通過利用曲線插值擬合獲得。普遍發(fā)動機特性曲線(圖2)可以使用發(fā)動機的數(shù)值模型得到。 在圖2中,曲線ABC是外部特征曲線;曲線BFS和CGT是速度調(diào)節(jié)特性曲線,A、B和C三點分別是最大輸出功率點。在不同的油門位置，盡管引擎可以工作最大輸出功率點,在一些最大輸出功率點如點B和C發(fā)動機有純淬裝載能力,這很容易導(dǎo)致發(fā)動機的熄火。因此,在不同的油門位置,發(fā)動機的最大輸出功率點應(yīng)設(shè)置為圖2的點A,F和G。因此,通常,曲線AFG被稱為最佳動力性工作曲線,即D曲線。 如果有相同功率的燃油消耗最小點(圖2)是相連的,發(fā)動機的最優(yōu)燃料經(jīng)濟性能工作曲線隨著圖2中的曲線AST的實現(xiàn),即E曲線。 圖2引擎通用特性曲線 c .調(diào)節(jié)功能的發(fā)動機轉(zhuǎn)速 發(fā)動機轉(zhuǎn)速的發(fā)動機調(diào)節(jié)功能是當(dāng)負(fù)載的輸出軸改變,車輛傳動裝置速度比率是為了維護發(fā)動機功率的相對價值進(jìn)行獨立煩的控制。如果發(fā)動機工作在每個相對功率之間最低燃料消耗的轉(zhuǎn)速，油門開啟和轉(zhuǎn)速的關(guān)系是轉(zhuǎn)速的最優(yōu)燃料經(jīng)濟性能。如果發(fā)動機的每個相對節(jié)流開放工作在最大轉(zhuǎn)矩的旋轉(zhuǎn)速度，,油門的打開和轉(zhuǎn)速的關(guān)系是轉(zhuǎn)速的最佳動力性能。發(fā)動機轉(zhuǎn)速的調(diào)節(jié)功能可以擬定為圖3。在圖3,曲線D和E分別是發(fā)動機調(diào)節(jié)特性曲線的優(yōu)化功率和最佳燃油經(jīng)濟性能。 圖3發(fā)動機的轉(zhuǎn)速調(diào)節(jié)特性 III.匹配策略的HMCVT系統(tǒng) HMCVT系統(tǒng)的匹配策略如圖.4。發(fā)動機可以通過HMCVT系統(tǒng)控制發(fā)動機油門打開和調(diào)節(jié)速度比使其工作在最優(yōu)功率性能工作曲線D或最好的燃料經(jīng)濟性能工作曲線E。在實際的工作，工作重點應(yīng)該是落在發(fā)動機的速度特性曲由最低穩(wěn)定旋轉(zhuǎn)速度曲線l,外特性曲線w和監(jiān)管線t的區(qū)域。對于HMCVT系統(tǒng)的拖拉機,每點發(fā)動機的有效工作范圍有一個和拖拉機的駕駛速度相對應(yīng)的驅(qū)動力,其具體表達(dá)式給出了公式如下 圖4匹配的HMCVT系統(tǒng)示意圖 這里，F(xiàn)q是拖拉機的動力,kN;Me是發(fā)動機嗎轉(zhuǎn)矩,N·m;ne是轉(zhuǎn)速的發(fā)動機,r / min;rd是駕駛的動態(tài)半徑wheel,m;i是HMCVT系統(tǒng)的傳動比,是HMCVT的系統(tǒng)效率;v是拖拉機速度,km/h;是練習(xí)場的跟蹤效率，輪式拖拉機=1. 通過引用文中的計算方法[6],每個發(fā)動機的點的有效工作范圍都對應(yīng)拖拉機驅(qū)動特性圖的(圖。4)。圖4中,曲線l’,‘w’和t”是分別相對應(yīng)的發(fā)動機理想的工作邊界曲線l,w和t,h線是拖拉機受地面膠粘劑力的影響可以提供最大驅(qū)動力。 可以從圖4看出,在穩(wěn)定和優(yōu)化電力和燃料經(jīng)濟性能條件下,當(dāng)拖拉機工作在一定的速度,有一個獨特的理想的發(fā)動機工作曲線對應(yīng)的拖拉機的工作狀態(tài)。在發(fā)動機的通用特性曲線，每個點工作條件都是明確的。發(fā)動機節(jié)氣門打開,理想的轉(zhuǎn)速和轉(zhuǎn)矩有一一對應(yīng)的HMCVT系統(tǒng)的速度比。 發(fā)動機可以通過控制油門打開發(fā)動機和調(diào)節(jié)HMCVT系統(tǒng)的速度比工作在最優(yōu)功率性能工作曲線D或最好的燃油經(jīng)濟性性能工作曲線E。根據(jù)事先確定發(fā)動機的節(jié)流開放和輸出功率的對應(yīng)關(guān)系,發(fā)動機可以通過控制發(fā)動機節(jié)氣門打開和HMCVT系統(tǒng)的調(diào)節(jié)速度比工作在特定的工作點。 可以從圖2和圖3看出,不管最佳動力性和最佳燃油經(jīng)濟性性能,發(fā)動機節(jié)氣門打開、旋轉(zhuǎn)速度和輸出功率有一一對應(yīng)的關(guān)系。在每個發(fā)動機節(jié)氣門打開時,確保拖拉機可以工作用不同的速度，HMCVT系統(tǒng)必須有相對速度比,以保證發(fā)動機工作最優(yōu)工作點。當(dāng)發(fā)動機工作在最優(yōu)動力性能的傳輸目標(biāo)速度比率如圖5。當(dāng)發(fā)動機工作在最佳的燃料經(jīng)濟性能時的傳輸目標(biāo)速度比率如圖6。目標(biāo)速度比率可以存儲在內(nèi)存單元的控制器內(nèi)。根據(jù)拖拉機實際的工作條件,發(fā)動機工作點可以通過控制HMCVT系統(tǒng)的速度比率調(diào)節(jié)。這樣拖拉機可以在這樣工作的條件下提供最佳動力性和最佳燃油經(jīng)濟性性能。 圖5。目標(biāo)速度比率的發(fā)動機最優(yōu)功率 圖6。目標(biāo)速度比率的發(fā)動機最佳燃油經(jīng)濟性 四。仿真分析 在拖拉機實際操作中,通常存在兩個典型工作條件:一是工作在恒定的拖拉機牽引阻力和發(fā)動機可變節(jié)流打開條件,另一個是工作動機油門打開發(fā)和的拖拉機變量牽引電阻條件。在此基礎(chǔ)上,以采取最好的燃料經(jīng)濟性能的發(fā)動機為例,仿真系統(tǒng)進(jìn)行了對HMCVT兩個條件的分析:一是拖拉機的牽引阻力是常數(shù)和發(fā)動機節(jié)流閥打開變量,另一個是發(fā)動機節(jié)流閥打開是常數(shù)和拖拉機牽的引阻力是可變的。在這種情況下,發(fā)動機的轉(zhuǎn)速可以工作目標(biāo)工作點,調(diào)節(jié)HMCVT系統(tǒng)速度的比率。 a .常數(shù)牽引阻力和可變節(jié)流 仿真工作條件,拖拉機牽引阻力Ft=40 kn并保持不變,發(fā)動機起始節(jié)流閥打開?a=50%;經(jīng)過十年,發(fā)動機節(jié)流閥打開增加到100%;當(dāng)拖拉機跑到30年，發(fā)動機節(jié)氣門打開減少到70%。仿真結(jié)果表現(xiàn)為圖7。 圖7仿真結(jié)果曲線恒牽引阻力和 可變節(jié)流工況 可以從圖7看出,在t = 10年,發(fā)動機節(jié)流閥打開突然從50%增加100%,拖拉機是在加速開車期間,發(fā)動機可以工作在HMCVT系統(tǒng)新目標(biāo)旋轉(zhuǎn)速度調(diào)節(jié)速度比。然后，發(fā)動機油門打開保持在100%,拖拉機是在穩(wěn)定的駕駛周期。在t = 30年,發(fā)動機油門打開突然從100%降低到70%,拖拉機是在減速駕駛期間,和發(fā)動機也可以工作調(diào)節(jié)MHCVT系統(tǒng)速度比新目標(biāo)的旋轉(zhuǎn)速度。在加速度和減速駕駛期間,HMCVT系統(tǒng)有一些時間延遲效應(yīng)、發(fā)動機實際輸出扭矩波動的發(fā)生?？梢詮姆抡娼Y(jié)果曲線看出,當(dāng)拖拉機牽引阻力的常數(shù)和發(fā)動機節(jié)流閥打開是可變的時,發(fā)動機的輸出轉(zhuǎn)速和扭矩基本上可以通過調(diào)節(jié)HMCVT系統(tǒng)的速度比穩(wěn)定在最佳的燃料經(jīng)濟性能的工作曲線。 b常數(shù)節(jié)流和變量牽引阻力 仿真的工作條件是發(fā)動機油門打開a=70%,保持不變,拖拉機牽引阻力Ft等于60 kn;開始之后十年,拖拉機牽引阻力減少到30 kn;當(dāng)拖拉機跑到30年,拖拉機的牽引阻力增加到60 kn。仿真結(jié)果表現(xiàn)為圖8。 圖8。仿真結(jié)果曲線恒節(jié)流和變量牽引 可以從圖8看出,在t = 10年前,發(fā)動機的實際輸出轉(zhuǎn)矩之間和拖拉機的牽引抵抗扭矩的平衡可以保持,拖拉機是在穩(wěn)定的駕駛狀態(tài)。在t = 10年,拖拉機的牽引抵抗扭矩突然從60kn的減少到30 kn,發(fā)動機的轉(zhuǎn)速有增加的趨勢。為了保持發(fā)動機轉(zhuǎn)速在目標(biāo)速度旋轉(zhuǎn),需要增加HMCVT系統(tǒng)的速度比。拖拉機是在加速期,直到開車新的力量平衡點出現(xiàn)。這樣,拖拉機在穩(wěn)定的駕駛周期。在t = 30年代拖拉機牽引阻力突然從30 kn增加到60 kn,拖拉機是在減速駕駛期。在穩(wěn)定的駕駛期間,隨著HMCVT系統(tǒng)速度的比率變化速率是不夠的,有一個發(fā)動機和目標(biāo)工作點之間的某些錯誤的工作點。 五結(jié)論 基于發(fā)動機試驗結(jié)果,發(fā)動機輸出轉(zhuǎn)矩模型和燃料消耗模型被建立,發(fā)動機轉(zhuǎn)速調(diào)節(jié)的特點被確定。在上述工作的基礎(chǔ)上,研究了匹配HMCVT系統(tǒng)的策略。對這個拖拉機兩個典型的工作條件進(jìn)行了分析法。結(jié)果表明,匹配策略確定本文是正確的和可行的,合理的匹配引擎和HMCVT系統(tǒng)可以實現(xiàn)。 致謝 本文的一部分是通過格蘭特2010 b460009支持醫(yī)生科學(xué)研究河南省教育部門基金科學(xué)和河南大學(xué)基金的自然科學(xué)與技術(shù)的內(nèi)容。 引用 [1]徐里有，周治理,張明珠,等等.設(shè)計的流體力學(xué)的無級變速傳動的拖拉機.交易的中國農(nóng)機協(xié)會.37卷.2006年7月.5 - 8頁(在中國) [2]),Hiroyuki Mitsuya, Keiji Otanl, Tsutomu Ishino,等等.推土機發(fā)展振動傳輸.SAE 94177紙.159 - 168頁 [3]張寶生,傅鐵軍,周云山,等等.匹配的三角皮帶式無級變速傳動系統(tǒng)與發(fā)動機及其控制戰(zhàn)略.《吉林大學(xué)(工程和技術(shù)版).2004年1月.65 - 70頁 (在中國) [4]胡建軍,秦大同,蜀香港.速度比匹配策略金屬v形帶式無級變速系統(tǒng).《重慶大學(xué)(自然科學(xué)版)》24卷.6.2001.12.12 - 17頁 (在中國) [5]t . Udaegawa.模擬方法的影響比改變速度的一個金屬v形帶CVT車輛響應(yīng).車輛系統(tǒng)設(shè).、1995.6.35 38頁 [6]徐里有.振動特性研究的不斷變量傳輸?shù)耐侠瓩C.博士論文.西安:西安科技大學(xué).2007(在中國) 7 Available at v h ch, ch, significantly cheaper than liquid fuels since it is left behind as 2 and additionally can be produced from waste [1]. Hydrogen as overpressure. Thus, it is of great interest to developers, the All these situations can be simulated on chassis dynam- ARTICLE IN PRESS INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 33 (2008) 863–869 C3 Corresponding author: Tel.: +41448234679; fax: +41448234044. fuel for fuel cells as well as for I.C. engines is likely to play an important role in future vehicle propulsion technology. The development of hydrogen-powered vehicles is also driven by ometers embedded in climatic chambers. However, it is only possible with enormous effort to keep such climatic cham- bers so airtight that the evaporative emissions can be 0360-3199/$-see front matter in C0 X m C3 G;out , qm G qt ? m C3 G;vent_in tm C3 G;car C0 X m C3 G;out . e1T qm G qt denotes the change in mass of gas G within the cell, P m C3 G;in the sum of all mass flows of gas G into the chamber and P m C3 G;out the sum of all mass flows of gas G out of the chamber, m C3 G;vent_in the mass flow into the chamber from ventilation and m C3 G;car the source flow of interest. All variables are functions of time. A mass flow of gas G into the chamber occurs if this matter is found in the ambient air. Thus, the mass flow of ventilation air and the concentration of gas G in the intake air need to be ARTICLE IN PRESS INTERNATIONALJOURNALOFHYDROGENENERGY33 (2008) 863–869864 Drivers aidAirstream ventilator Max. flow: 100’000 m 3 /h Internal ventilation, air conditionning heat exchanger V intake * * V leakage Fig. 1 – Sketch of climatic chamb Chassis dynamometer V air,vent_in * * * V exhaust V air,vent_out er with ventilation flows. In cha location. Natur be determine m air ? r air V air . (2) ARTICLE IN PRESS OGEN The contained mass flow of gas G then is m C3 G ? c G r G V C3 air , (3) where c G is the concentration of gas G and r G its density. Since C3 the da duct of air density r air and volume flow V air . C3 pro the cell. It is thus sufficient to measure the air inflow. addition, since the concentration inside the climatic mber is homogenous, it needs to be measured at just one ally, a flow of gas G as the inflow m C3 G;vent_in cannot measured directly. By assuming ideal gases, it may be d as follows. Any mass flow of air m C3 air is the C3 into measured. The second mass flow into the chamber is the evaporation from the vehicle, which is of interest. There are different possibilities for flows of gas G out of the chamber: C15 Intended ventilation. C15 Leakage. The doors of the chamber as well as channels for cables and pipes are not airtight, so some air leaks. Most climatic chambers operate with a slight overpressure to ensure that air flows out at all openings, since inflowing humid air, when operating at low temperatures, would cause dangerous ice formation and additionally disturb the humidity control of the chamber (Fig. 1). C15 If the vehicle is running and is propelled by a system that consumes air (engine or fuel cell system), either the corresponding air supply can be from outside the chamber or air from the room is used. Since the exhaust gases are typically led outside the chamber and measured there, the latter case is also an outflow for the mass balance of gas G. It is obviously not possible to measure the mass flow and concentrations of gas G at all the outflow locations, but this problem can be bypassed by the following approach. The chassis dynamometers for exhaust emission measure- ments are equipped with fans for the cooling of the vehicle. Together with the ventilation of the air conditioning of the cell, this can cause such high turbulence that the concentra- tion of gas G in the room can be considered to be homogeneously distributed. In other words the mixing time constant in the room must be significantly lower than the air exchange rate. It must be ensured that no dead zones where ventilation is poor exist inside the climatic chamber. In other words, in most cases where chassis dynamometers are installed in climatic cells, the rolls of the dynamometer as well as the breaking electric motor are in an under-floor compartment that is contained in the cell. It must therefore be possible for this compartment to be ventilated intention- ally by opening covers and adding additional ventilators. If the concentration of gas G inside the chamber is indeed homogenous and measured, this concentration also holds for all the outflows of the cell. As long as the pressure remains stable within the cell, which is controlled by the ventilation, the total mass flow of air out of the cell is equal to the flow INTERNATIONAL JOURNAL OF HYDR tests take place in a climatic chamber and do not last for ys, it may be assumed that both temperature and pressure remain stable, and thus that densities are constant. It is thus sufficient to measure the volume flow of air and the concentration of gas G to determine its mass flow. For the chamber it correspondingly holds that m G ? c G r G V ch . (4) The index ch stands for chamber. Assuming that the volume flow of air out of the chamber is equal to the inflow and that the distribution of gas G in the chamber is homogenous, Eqs. (1)–(4) give qc G;ch qt r G V ch ? c G;vent_in r G V C3 air;vent_in t m C3 G;car C0c G;ch r G V C3 air;vent_in . e5T And this can be solved for the mass flow of the source, thus the car m C3 G;car ? qc G;ch qt r G V ch C0 c G;vent_in r G V C3 air;vent_in t c G;ch r G V C3 air;vent_in . e6T So, the system emissions as mass per time unit can be calculated by knowing the chamber volume, the density of gas G (thus temperature and pressure) and measuring the volume flow of air into the chamber as well as the gas concentration of G inside the chamber and in the air intake. As pressure and temperature in inflow and outflow are alike, densities for both flows can be considered to be equal. 2.2. Measurement equipment A commercial gas chromatograph (Reduction Gas Analyzer (RGA3), Trace Analytical Inc., California, USA) was used to measure H 2 inside the climatic chamber. The RGA3 is an ultra-trace level gas detection system capable of monitoring low ppb concentrations of reducing gases such as H 2 . The instrument consists of a microprocessor-controlled gas chromatograph which utilises method of reduction gas detection. Synthetic air preconditioned by molecular sieve 5A ? and SOFNOCAT to remove H 2 O and reaction impurities (CO and H 2 ) is used as carrier gas. Aliquots of air samples are flushed with a rate of 20ml/min over a 1ml sample loop. After equilibration, the sample volume is injected onto the columns. Sample components of interest are separated chromatographically in an isothermal mandrel-heating col- umn oven. The chromatographic precolumn (Unibeads 1S, 60/80 mesh; 1=8 00 C230 00 ) is mainly used to remove CO 2 ,H 2 O and hydrocarbons. Subsequently H 2 and CO are separated by the analytical column (molecular sieve 5A ? , 60/80 mesh; 1=8 00 C230 00 ) and pass into the detector which contains a heated bed of mercuric oxide. Within the bed a reaction between mercuric oxide (solid) and H 2 occurs and the resultant mercury vapour in the reaction is quantitatively determined by means of an ultraviolet photometer located immediately downstream of the reaction bed. The columns are kept at 751C; the detector is heated to 2701C. The amount of H 2 in the air sample is proportional to the amount of mercury that is determined. ENERGY 33 (2008) 863–869 865 During the quasi-continuous observations of the H 2 con- centration in the test chamber, measurements were taken every 2min. At the beginning and end of each test cycle the ambient air concentration (concentration of the ventila- tion inflow) was measured for 30min. Typically the concen- trations were very constant over the short time of one test cycle and in the range of the mean of 576C694ppb at Duebendorf [9]. Two high concentration reference gases (50 and 100.2ppm H 2 ; Messer Schweiz, Switzerland) were dynamically diluted with zero air to the range of interest by means of a dilution unit (MKAL diluter, Breitfuss Messtechnik GmbH, Harpstedt, Germany). The dilution unit was indirectly referenced against the primary gas flow standard of the Swiss Federal Office of change substantially; thus average concentration during one sampling step is approximated by the mean of the values So the mass emitted during the sampling interval k is m G;car;k ? r G ec G;ch;k C0 c G;ch;kC01 TV ch t V C3 air;vent_in;k T C18 C2 c G;ch;k t c G;ch;kC01 2 C0 c G;vent_in;k C18C19C19 . e9T Mathematicallymore complexbut also more accurate is the discretisation by solving the differential equation (5) analyti- cally for one time step, what needs certain assumptions. Here there is freedom to assume all input signals (i.e. V C3 air;vent_in etT, c G;vent_in etT, m C3 G;car etT) as arbitrary functions of time. ARTICLE IN PRESS INTERNATIONALJOURNALOFHYDROGENENERGY33 (2008) 863–869866 measured at either end of it. The mass balance results in m C3 G;car;k ? c G;ch;k C0 c G;ch;kC01 T r G V ch C0c G;vent_in;k r G V C3 air;vent_in;k t c G;ch;k t c G;ch;kC01 2 r G V C3 air;vent_in;k . e8T * m G,car ( t ) t Case: early peak Case: constant * m G,car ( t ) Metrology. The different mixtures of the two high concentra- tion standards showed excellent agreement with each other and the NOAA/GDM scale [10]. Detection limit for H 2 was C610ppb and the standard uncertainty of the measure- ment 5%. 2.3. Analysis methodology As described in the previous section the low concentrations of the gases of interest cannot be measured with high time resolution, i.e. within seconds. The equipment described above allows a sampling rate of 2min. Thus Eq. (6) needs to be solved discretely. The most direct and simple approach of discretisation is replacing the derivative of the chamber concentration by the difference of the last two measured values. For time step k this results in qc G;ch qt et ? kTTC25 c G;ch;k C0 c G;ch;kC01 T , (7) where T is the sampling interval [11]. Since both ambient concentration of gas G and ventilation air flow typically change very little over one time interval, it does not matter if the values at the beginning or the end of the sampling interval are used. The chamber concentration, however, may (k-1)T kT (k-1)T Fig. 2 – Most extreme possibilities of time functi Hence, if necessary it might be possible to measure the ventilation air flow at high time resolution and use that time function for the calculus, but usually this flow is reasonably constant. The ambient concentration of the gas G typically is constant too if not working downwind of a huge non-uniform gas source. Of course the time function m C3 G;car etT of how the vehicle emits the gas G is unknown. If the total mass emitted during one time step m G;car;k is given, the most extreme case for the calculus is if all of it is released immediately after the time interval starts or immediately before the time interval ends (peak functions, Fig. 2). The ‘‘a(chǎn)verage’’ case happens if the vehicle is constantly emitting gas G. For benchmarking the quality of this methodology in Section 3.2, Eq. (5) is solved subsequently for all three assumptions. In the case of the early peak, the solution of Eq. (5) for the time t ? kT is c G;ch;k ? c G;vent_in t c G;ch;kC01 t m G;car rV C0 c G;vent_in C18C19 e C0eV C3 =VTT , (10) and thus, the mass of gas G emitted in one time period is m G;car;k ? rV c G;ch;k C0 c G;vent_in e C0eV C3 =VTT t c G;vent_in C0c G;ch;kC01 ! . (11) For the late peak case we obtain c G;ch;k ? c G;vent_in tec G;ch;kC01 C0 c G;vent_in Te C0eV C3 =VTT t m G;car rV , (12) m G;car;k ? rVec G;ch;k C0 c G;vent_in tec G;vent_in C0c G;ch;kC01 Te C0eV C3 =VTT T. (13) t t Case: late peak * m G,car ( t ) kT (k-1)T kT ons of gas release for benchmarking. And for the average case of a constant emitting source m C3 G;car etT?m G;car;k =T: c G;ch;k ? c G;vent_in t m G;car rTV C3 t c G;ch;kC01 C0 c G;vent_in C0 m G;car rTV C3 0 @ 1 A e C0eV C3 =VTT , (14) m G;car;k ? rTV C3 V c G;ch;k C0 c G;ch;kC01 e C0eV C3 =VTT 1C0e C0eV C3 =VTT C0 c G;vent_in 0 @ 1 A . (15) Even though Eqs. (11), (13) and (15) look rather different, their outputs remain similar as long as the sampling interval Tis small compared to the ventilations time constant V=V C3 .So the quality of this method rises if both the sampling interval values belong to this test equipment. heat exchange units, etc., are difficult to describe. Thus a test where a well-defined volume of helium was released im- 3.2. Identification of volume flow and validation If the volume flow of the ventilation is not possible to be measured directly, but is constant over time, it is possible to determine it by the following test. As above, a certain volume of a measurable gas such as helium is injected into the cell (with ventilation running). After the mixing phase in the cell the helium concentration will follow Eq. (5) or one of its solutions (10), (12) or (14) with a zero source activity of the car m C3 G;car etT?0. Measurements are shown in Fig. 3. Subtracting the background concentration and building the logarithm of the He concentration result in a straight line for the first 2000s where concentrations are reasonably above the detection limit. The gradient of this straight line is directly the air exchange rate, thus V C3 =V. Its inverse is the above discussed air exchange overall model. A known amount of helium (or hydrogen) can be released either in one moment as above or repeatedly if ARTICLE IN PRESS INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 33 (2008) 863–869 867 mediately and its concentration was measured subsequently, while external ventilation was closed but internal circulation was on, allowed the chamber volume to be estimated from the dilution ratio. The value was found to be 256m 3 with a standard deviation of 8m 3 . 0 500 1000 1500 2000 2500 3000 0 10 20 30 40 50 Helium concentration in air exchange test He [ppm] 3.1. Determination of chamber volume Estimating the air volume in the chamber by geometrical means is quite difficult, since the volumes of car, ventilators, and ventilation are small. Realistic examples are given in the next section, where both the different methods (Eqs.(11), (13) and (15)) and different sampling intervals are applied to the same test data to highlight how accuracy depends on the different parameters of the system. 3. Example and sensitivity analysis The test examples described here were conducted in the climatic cell chassis dynamometer of Empa. All numeric time [s] Fig. 3 – Determination of air exchange ra equipment allows and the calculus (Eqs. (11), (13) or (15)) using measured values must give the amount released. This was repeatedly checked. 3.3. Evaporation test and accuracy analysis Real hydrogen system emission tests were conducted with a hydrogen vehicle. The test shown here included a parking phase from 1 to 2523s, then a test ride up to 3842s, where another parking phase is monitored up to 7100s (Fig. 4). The left plot in Fig. 4 shows the hydrogen concentration measured with a 2min interval. On the right side the emissions of the car for each time interval are displayed. 0 500 1000 1500 2000 2500 3000 -4 -2 0 2 4 log(He - He ambient ) He [ppm] time constant V C3 =V, and if one of the chamber volume or ventilation volume flow is known the other can be deter- mined. Here, with the given chamber volume the volume flow is found to be 0:5605m 3 =s with a standard deviation of 0:005m 3 =s. The volume flow was found to depend on ambient pressure, and this identification should thus be repeated on the day of the evaporation tests. In addition, if the volume flow of the ventilation is known by measurement, similar tests can be used to validate the time [s] te by helium injection experiment. difference of two measured values. These errors are, however, ARTICLE IN PRESS because 0 2000 4000 6000 8000 -0.05 0 0.05 0.1 0.15 Mass H 2 [g] time [s] Fig. 5 – Cumulative hydrogen emissions. OG They are calculated applying the different methods and assumptions, i.e. Eqs. (9), (11), (13) and (15). For the given situation with a chamber volume of 256m 3 ,a ventilationvolume flow of 0:5605m 3 =s (giving an air exchange time constant of 463s or 7.72min) and a sampling rate of 2min, the accuracy results are as follows: The approximate formula (9) and the accurate formula (15), both assuming that the vehicle emissions are constant over one sampling interval differ less than 0.5% from each other. The values calculated by the worst case equations (11) and (13), assuming short emission peaks at the beginning or end of the sampling intervals, produce errors of 14% and C012%. As can be seen from the overall characteristic of the mass emission curve (Fig. 4, right), however, it is very implausible that the emissions of the vehicles are peak-like and those peaks exactly synchronised with the sampling. Thus, the real accuracy locally, when emissions start or stop, may be as uncertain as C012% to 14%. The overall or aggregated emis- sions, however (as displayed in Fig. 5), will show a much higher accuracy in all practical cases. 0 2000 4000 6000 8000 600 800 1000 1200 1400 1600 1800 2000 Hydrogen concentration Conc (H 2 ) [ppb] time [s] Fig. 4 – Evaporation test: left: chamber concentration, right: calcula left and right curve appears similar, the right one is sharper INTERNATIONALJOURNALOFHYDR868 From Figs. 4 and 5 it can be readily seen that this vehicle shows rather small system emissions while running, i.e. 0.0046g after a 21min ride (3842s). Conversely they rise remarkably after system stop. The maximal gas flow reaches 4.32mg/min some 20min (1200s) after engine stop and decreases slightly afterwards. Obviously some parts of the hydrogen system leak after system stop until they are exhausted. Note that all variables such as ventilation flow and ambient concentrations are considered to be constant within each time step. If they vary slowly and their values are measured, this methodology is also applicable with the same accuracy. 3.4. Sensitivity analysis The sensitivity to measurement errors of this method can be analysed by standard error propagation methods [12].It shows that random errors in the measurement of the chamber concentration have a considerable impact on the quality of step by step results, caused by building the 0 2000 4000 6000 8000 -2 0 2 4 6 8 x 10 -5 Massflow of hydrogen form car Massflow H 2 [g/s] time [s] equ. (9) equ. (15) equ. (11) equ. (13) ted emission mass flow. Note: Although the shape of the it includes the derivative of the left curve. 0.2 Cumulated hydrogen emissions ENENERGY33 (2008) 863–869 compensated when the integral emission is built. A systematic error of the concentration values, i.e. a bias between the chamber values and the ambient (or inflow) values would result in an incorrect linear trend underlying the integral signal. Such a trend can be detected easily, if the tested vehicle shows phases with assured zero emissions, such as after being stationary overnight. Alternatively, such bias can be reduced by using the same sensor for ambient (intake) and chamber concentration measurements, what is recommended. In addition this method is sensitive to the ratio of sampling rate and air exchange rate. This sensitivity is highlighted by just neglecting intermedi- ate data points in the above example. In this way, the sampling rate can easily be simulated to be a multiple of the original sampling of 2min. It can be seen in Table 1 that with increased sampling time the range of theoretical uncertainty increases. When the sampling time reaches similar values to the air exchange time constant of 7.72min, i.e. 6 or 8min, then the maximal uncertainty rises above 50%, and the values of single steps thus become somewhat ARTICLE IN PRESS Table 1 – Error between methods as a function of OGEN Sampling time interval 2min