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Research and Application of Lightweight Index for Passenger Cars [url=]Jun Li[/url],
 [url=]Ligang Wang[/url],
 [url=]Yunxia Chen[/url],
 [url=]Hongzhou Lu[/url] &
 [url=]Haitao Jiang[/url]
AbstractLightweight is an effective design strategy to conserve energy in automotive vehicles. It is a big challenge to evaluate the level of lightweight for passenger cars. This paper summarizes various evaluation methods for lightweight automotive vehicles. A lightweight index [Lv for internal combustion engine vehicles (ICEVs) and Lev for battery electric vehicles (BEVs)] is proposed to assess the lightweight of passenger cars. The proposed lightweight index is composed of the nominal density, weighttopower ratio, and fuel consumption of footprint area (in the case of ICEVs) or electricity consumption of footprint area (in the case of BEVs). The validity and universality of the proposed lightweight index are demonstrated through a statistical analysis of 7018 ICEV and 326 BEV models. The calculation procedures of the standard partial regression coefficients of statistical multiple regression and elastic coefficients are employed in the proposed method. The results show that either Lv or Lev is most sensitive to the curb mass of the vehicles. The proposed lightweight index can help guide automakers in setting reasonable weight reduction targets during new product development. In addition, the proposed lightweight index can be applied to new hybrid electric vehicles with further efforts, to facilitate the development of lightweight automotive design.
IntroductionWith the increasing demand for performance and function, the number and weight of components in vehicles is increasing along with the average curb mass. In China, based on the fuel consumption rate regulation for passenger cars, the targets for vehicle curb weightbased fuel consumption rate have been specified in a stepped manner, which has had a considerable impact on lightweight strategies [ 1]. Because of the lack of an effective lightweight evaluation system and corresponding industrylevel incentive policies, the average curb mass of passenger cars has increased year on year [ 2]. Therefore, it is necessary to establish evaluation methods to guide the development of lowenergyconsuming components in the automotive industry. With the emergence of domestic doublecredit policy, the market for battery electric vehicles (BEVs) is expanding rapidly. The curb mass of BEVs is at least 10% greater than that of conventional internal combustion engine vehicles (ICEVs) [ 3]. This increase in weight affects the electrical energy consumption and power and braking performances of BEVs. Therefore, it is vital to establish a contemporary evaluation method to guide the future development and lightweight of BEVs. What has been increasingly witnessed in recent years is the research on lightweight evaluation methodologies and related factors in the global automotive industry, such as the car body lightweight index developed by BMW [ 2], the nominal density parameter adopted by Lotus Cars [ 4], and the passenger car lightweight index [ 2, 5, 6]. The car body lightweight index ( Lc), which is an indicator widely used in the automotive industry to evaluate the lightweight level of car body, can be expressed as in Eq. ( 1) [ 2]. <span class="MathJax" id="MathJaxElement1Frame" tabindex="0" datamathml="Lc=mCT⋅A" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">Lc=mCT⋅ALc=mCT⋅A
(1)
where m is the bodyinwhite weight (without four doors and hood), CT is the static torsional stiffness of the car body, and A is the footprint area. To evaluate different types of vehicles, Lotus Cars proposed a lightweight evaluation parameter, namely the density of vehicles ( D) [ 4], which is expressed in Eq. ( 2): <span class="MathJax" id="MathJaxElement2Frame" tabindex="0" datamathml="D=MVL" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">D=MVLD=MVL
(2)
where M is the curb mass, and VL is the vehicle volume defined by Lotus. VL of SUVs and hatchbacks can be calculated using Eqs. ( 3) and ( 4), respectively. <span class="MathJax" id="MathJaxElement3Frame" tabindex="0" datamathml="VLS=[(B×H)]+[(L−B)×0.5×H]×W" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">VLS=[(B×H)]+[(L−B)×0.5×H]×WVLS=[(B×H)]+[(L−B)×0.5×H]×W
(3)
<span class="MathJax" id="MathJaxElement4Frame" tabindex="0" datamathml="VLH={[0.33(L−B)×H]+(B×H)+[0.67×(L−B)×0.5×H]}×W" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">VLH={[0.33(L−B)×H]+(B×H)+[0.67×(L−B)×0.5×H]}×WVLH={[0.33(L−B)×H]+(B×H)+[0.67×(L−B)×0.5×H]}×W
(4)
where H is the vehicle height, L is the length, B is the wheelbase, and W is the width. To evaluate the level of lightweight for passenger cars, Li et al. [ 6] proposed an index E′ to assess the lightweight level of passenger cars, which is expressed in Eq. ( 5): <span class="MathJax" id="MathJaxElement5Frame" tabindex="0" datamathml="E′=1CT×S×F×MV×QP" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">E′=1CT×S×F×MV×QPE′=1CT×S×F×MV×QP
(5)
where Q is the fuel consumption, F is the firstorder body (twisting) frequency, P is the engine power, S is the ChinaNew Car Assessment Program (CNCAP) star rating, and V is the nominal volume of the vehicle, which can be calculated by Eq. ( 6): <span class="MathJax" id="MathJaxElement6Frame" tabindex="0" datamathml="V=L×B×(H−G)" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">V=L×B×(H−G)V=L×B×(H−G)
(6)
where G is the minimum ground clearance (generally noload). Some variables (such as the body frequency) cannot be easily obtained; therefore, they may be unsuitable for public benchmarking. Moreover, CT, S, and F are process parameters in the development of vehicles; they are not made public. Li et al. [ 6] simplified E′ by Eq. ( 5) to E, as expressed by Eq. ( 7). <span class="MathJax" id="MathJaxElement7Frame" tabindex="0" datamathml="E=MV×QP" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">E=MV×QPE=MV×QP
(7)
There are already some studies on strategies for lightweight assessment, which proposed setting methods to achieve lightweight in the development phase of vehicles [ 7, 8, 9, 10]. Automakers use evaluation parameters to set weight reduction targets during vehicle development. The abovementioned lightweight assessment parameters do not reflect the performance of vehicles nor the challenges in acquiring and characterizing the variables. Therefore, they have not been widely accepted in actual implementations. This paper proposes a novel method to evaluate the lightweight of vehicles using a lightweight index ( Lv for ICEVs and Lev for BEVs), which considers the fuel consumption or electrical energy consumption, weight, and size parameters of vehicles. The lightweight index is mainly used to evaluate the lightweight level of consumeroriented vehicles. The lightweight index is compared with the method proposed by Li et al. [ 6] to demonstrate its reasonability.
Definition and Verification of Lightweight IndexThe lightweight assessment of a consumeroriented automotive product is not the same as that of a part or a subsystem. Consumers have a certain degree of repulsion if a vehicle is characterized to be merely light. Therefore, the lightweight assesment of a vehicle should consider lightweight design, and performance improvement, such as the power and fuel economy owing to weight reduction, which are concerns of consumers. A lightweight design based on the premise of satisfying automotive performance is acceptable to consumers, and the primary performance indicators associated with lightweight is power and fuel economy. In addition, it is necessary to consider the convenience of characterizing the parameters of the evaluation models, and to select the parameters disclosed by the automakers as much as possible, so that the proposed evaluation method can be used widely. In the following section, the relationship between lightweight and vehicle performance is discussed. Lightweight Versus Vehicle PerformanceLightweight refers to the application of modern design methods to optimize the design of automotive products, enhance vehicle performance via new materials and reduce the weight of vehicle components as much as possible. Lightweight does not imply weight minimization, but weight optimization, which helps meet the objectives of the designed performance. Weight reduction has the strongest correlation with the power and fuel economy of ICEVs. Therefore, to evaluate the lightweight level of a vehicle, it is necessary to comprehensively consider the weight reduction, power, and fuel economy as performance indicators. Lightweight has various effects on active and passive safety. The curb mass of a car is strongly correlated with the passive safety. During passive safety tests, the heavier vehicle (with same material and design) performs better in side impact and pole impact crashes. Under specific crash conditions (frontal crash, 40% offsetdeformable barrier (OBD), and 25% offset crash), a lighter vehicle with a low kinetic energy shows better crash performance. Therefore, it is difficult to quantify the relationship between weight and passive safety. Moreover, a lighter car shows better active safety. The active security ratio of the CNCAP fivestar rating becomes increasingly important. As per the recommendation [ 11] of the Insurance Institute for Highway Safety (IIHS) for lightweight and safety, the fuel economy can be improved without sacrificing safety. Various technologies can be applied to improving fuel efficiency without reducing the weight. Automakers can also improving fleetwide fuel economy by taking a small amount of weight off their heaviest vehicles without significant safety tradeoffs. In the event of a crash, both the size and weight of a vehicle affect people inside in terms of the force. Table 1 lists the change in the proportion of active safety in terms of the CNCAP scores in it can be observed from past years in China. As listed in Table 1, it can be observed from the 2018 version of CNCAP data that the proportions of active safety, pedestrian protection, and whiplash in the fivestar safety rating results have increased to 30.2%. Active safety is mainly achieved by electronic control systems, which has a low correlation with weight. Hence, safety parameters are not used to evaluate lightweight design. In addition, some aspects, such as durability and NVH, are basic performance indicators of a vehicle, which must be met irrespective of the weight. Table 1 Proportions of safety classifications in the fivestar safety rating of CNCAP
Accordingly, the lightweight index is defined in terms of the nominal density, weight–topower ratio, and fuel consumption of footprint area (or electricity consumption of footprint area). The nominal density is employed to evaluate the weight of the vehicle; the weight–to–power ratio represents the power performance, and fuel consumption of footprint area (or electricity consumption of footprint area) represents the fuel consumption or electrical energy consumption level of the vehicle. The reasons for selecting these parameters are explained in Sect. 4. Definition of the Lightweight Index of Internal Combustion Engine Vehicles (ICEVs)The lightweight index, expressed in Eq. ( 8), is proposed to assess the lightweight level of ICEVs: <span class="MathJax" id="MathJaxElement8Frame" tabindex="0" datamathml="Lv=MV×MP×QA" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">Lv=MV×MP×QALv=MV×MP×QA
(8)
where Lv is the lightweight index for ICEVs. It should be noted that the above parameters can be obtained from early released product information of automotive products and can be measured on the basis of technical standards adopted by relevant countries or industries. The proposed lightweight index (Lv) is composed of three parts: the nominal density (M/V), weight–to–power to ratio (M/P), and fuel consumption of footprint area (Q/A). A smaller value of Lv indicates a higher lightweight level. Because of the different market orientations of automotive products with different grades, a single model should be evaluated by comparing models with similar sizes and product market orientations. Definition of the Lightweight Index of Battery Electric Vehicles (BEVs)Based on the analysis of ICEVs, the lightweight index of BEVs ( Lev) can be expressed by Eq. ( 9). Considering the similarity of the impact of lightweight on vehicle performance and energy saving, the evaluation methodology used for BEVs is analogous to that for ICEVs. <span class="MathJax" id="MathJaxElement9Frame" tabindex="0" datamathml="Lev=MevV×MevPev×YA" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">Lev=MevV×MevPev×YALev=MevV×MevPev×YA
(9)
where Mev is the curb mass, Pev is the peak electric motor power (the sum of the peak powers of all drive electric motors), and Y is the electrical energy consumption. Lev is also composed of three parts: the nominal density (Mev/V), weight–to–power ratio (Mev/Pev), and electricity consumption of footprint area (Y/A). Lev helps evaluate the lightweight level of passenger cars, and can guide automakers in their quest to set reasonable weight reduction targets for their products. It is possible to carry out evaluation and analysis of the lightweight level of different vehicle models from different companies using the lightweight index models. Statistical Verification of the lightweight indexBased on the established evaluation indicators, the curb mass is found to contribute the most to the lightweight index. The sensitivity analysis of the variables is performed. The Lv of 7018 ICEV models are calculated with Eq. ( 8). As the lightweight index is a dependent variable, the five parameters, namely the curb mass, engine power, footprint area, nominal volume, and fuel consumption, are defined as independent variables. Each variable is standardized using Eq. ( 10) [ 12]: <span class="MathJax" id="MathJaxElement10Frame" tabindex="0" datamathml="Xi∗=Xi−Xi¯Si" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">X∗i=Xi−XiˉˉˉˉˉˉSiXi∗=Xi−XiˉSi
(10)
where <span class="MathJax" id="MathJaxElement11Frame" tabindex="0" datamathml="Xi∗" role="presentation" style="boxsizing: inherit; display: inline; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: none; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; position: relative;">X∗iXi∗ is the normalized variable, Xi is the raw data of the variable, <span class="MathJax" id="MathJaxElement12Frame" tabindex="0" datamathml="X¯i" role="presentation" style="boxsizing: inherit; display: inline; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: none; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; position: relative;">XˉˉˉˉiXˉi is the sample mean of the variable, and Si is the sample standard deviation. A multiple regression analysis was performed on the processed data lines to obtain standardized partial regression coefficients. A higher coefficient value indicates a greater contribution of the corresponding independent variable to the dependent variable [ 11]. Table 2 lists the standardized regression coefficients of the independent variables and the statistical test values of Lv and E. Table 2 Standardized regression coefficients of variables for ICEVs
As listed in Table 2, the correlation coefficients of Lv and E are 0.903 and 0.846, respectively. The above standardized regression equation is of significance, and the influence of independent variables on the dependent variable is also significant. The above results show that the order of contribution of the respective variables and dependent variables to the Lv of ICEVs is as follows (high to low): the curb mass, maximum power, fuel consumption, nominal volume, and footprint area. However, the maximum power shows the greatest sensitivity to E, followed by fuel consumption and nominal volume; the curb mass is ranked last, contrary to the objective of the work, which is to perform evaluation from a lightweight perspective. The same analysis was conducted on 326 BEV models. Equation ( 7) is only applicable to fuel vehicles. Based on Eqs. ( 8) and ( 9), Eq. ( 7) is extended by replacing Q with Y, and the index E values of the corresponding BEVs are calculated. The data of the variable, sample mean of the variable, and standard deviation of the variable sample were used to normalize the value of the processed variable. Table 3 lists the standardized regression coefficients of the independent variables of Lev and E. Table 3 Standardized regression coefficients of variables for BEVs
As can be seen in Table 3, the correlation coefficients of Lev and E are 0.905 and 0.867, respectively. The curb mass has a greater contribution to Lev than the other independent variables in the case of BEVs. The most sensitive independent variable to E is the maximum power, followed by the nominal volume, and finally the curb mass and electrical energy consumption. Overall, the lightweight index ( Lv or Lev) is more reasonable than E (expressed in Eq. 7) for both ICEVs and BEVs. In addition, the elasticity coefficient of the statistics was used [ 13]. As the elasticity coefficient is dimensionless, it is suitable to explain the sensitivity of varying parameters. The formula for the arc elasticity coefficient is shown in Eq. ( 11). <span class="MathJax" id="MathJaxElement13Frame" tabindex="0" datamathml="ηi=(ΔY/Y¯)/(ΔX/X¯)=βiX¯Y¯" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">ηi=(ΔY/Yˉ)/(ΔX/Xˉ)=βiXˉYˉηi=(ΔY/Yˉ)/(ΔX/Xˉ)=βiXˉYˉ
(11)
where βi is the partial regression coefficient, <span class="MathJax" id="MathJaxElement14Frame" tabindex="0" datamathml="X¯" role="presentation" style="boxsizing: inherit; display: inline; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: none; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; position: relative;">XˉXˉ is the mean independent variable, and <span class="MathJax" id="MathJaxElement15Frame" tabindex="0" datamathml="Y¯" role="presentation" style="boxsizing: inherit; display: inline; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: none; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; position: relative;">YˉYˉ is the mean dependent variable. The elasticity coefficient shows that, in the vicinity of the sample, a change of 1% in an independent variable can cause a percentage change in the dependent variable, which is the change ratio of the variable. Based on the arc elasticity coefficient, the average values of the parameters are presented in Table 4, corresponding to the ICEV and BEV samples. The average values of the corresponding lightweight index ( Lv or Lev) and E, are calculated using Eqs. ( 7), ( 8), and ( 9). The elastic coefficients of the independent variables of lightweight index ( Lv or Lev) for ICEVs and BEVs are calculated using Eq. ( 11), along with the elastic coefficients of E. Table 5 lists the calculated data. Regardless of the vehicle type, the elasticity coefficient of the curb mass in terms of the lightweight index ( Lv or Lev) is greater than that in terms of E. This is mainly because the curb mass in Eqs. ( 8) and ( 9) is a square number, so its elastic coefficient reaches 1.99, making it more sensitive to the dependent variable. The other independent variables as parameters have a corresponding elasticity coefficient of 1, and the elasticity coefficient of the independent variables as denominators is 0.99. Table 4 Average values of the parameters corresponding to ICEV and BEV samples
Table 5 Elasticity coefficients of Lv, Lev and E for different vehicles
In summary, two statistical methods were used in lightweight assessment, and the results show that the curb mass of the ICEVs and BEVs is the most sensitive to the lightweight index (Lv or Lev).
Application of lightweight index to ICEVs and BEVsIn the following sections, the specific implementation process of lightweight assessment is described, and the lightweight level of ICEVs and BEVs from China market (Data source: http://www.autohome.com.cn) is evaluated. ICEVsTable 6 lists the main parameters of 10 ICEV models. The Lv is used to evaluate the lightweight level of the ICEV models. The Lv and other indicators, such as the nominal volume, footprint area, nominal density, weight–to–power ratio, and fuel consumption of footprint area, were calculated using the vehicle parameters. The Lv and E were calculated using Eqs. ( 8) and ( 7), respectively. Table 7 lists the results, along with the ranking of the lightweight levels for each model. Table 6 Parameters of ICEV models
Table 7 The lightweight index (Lv) and calculation parameters of ICEV models
In Table 7, the models are ranked in terms of the Lv, with the ranking based on E included for comparison. When sorting with E, the rankings of Models 5, 1, and 3 are 6, 7, and 5, respectively. As the nominal density and fuel consumption of footprint area are relatively high, Model 3 ranks behind Model 1 in terms of the Lv. However, as the weighting factor for the weight sensitivity is low in terms of E, Model 3 ranks higher than Model 1 in terms of E. Overall, Lv can be used to evaluate the relative weight, energy savings, and power level of a vehicle from multiple dimensions. Compared with E, Lv reflects the overall performance owing to that the evaluation models of lightweight are more comprehensive. BEVsTable 8 lists the parameters of 10 BEV models. The Lev is used to assess the lightweight level of each model. Based on the indicators listed in Table 9, five indicators, namely the nominal volume, footprint area, nominal density, weight–to–power ratio, and electricity consumption of footprint area, are calculated. Equation ( 7) is only applicable to fuel vehicles; Q is replaced with Y in Eq. ( 7) to calculate the index E of the corresponding BEVs accordingly. Table 9 lists the results, along with the ranking of the lightweight levels for each model. Table 8 Parameters of the BEV Models
Table 9 The lightweight index (Lev) and calculation parameters of BEV models
The values of Lev and E of each model were calculated and sorted. From Table 9, it can be found that the overall ranking orders based on Lev and E are the same. Among them, only the orders of Models 2 and 3 have changed. For Model 3, the nominal density is 142.1 kg/m3, whereas that for Model 2, it is only 130.06 kg/m3. When using Lev to assess lightweight level, although the weight–to–power ratio and electricity consumption of footprint area of Model 3 are slightly lower than those of Model 2, the value of its nominal density is higher than that of Model 2; therefore, Model 3 ranks behind Model 2 in terms of the Lev. The automotive lightweight level reflects the comprehensive performance of the model, and a lower weight is only one aspect of the assessment of the lightweight level. The lightweight level of ICEVs and BEVs from various automakers, brands, and grades can be classified and compared in terms of the mean value of Lev reasonably.
Discussion on Parameter SelectionsNominal DensityThe primary objective of lightweight is to reduce the weight of a vehicle as much as possible while ensuring its performance. Under the assumption that a smaller value of Lv (or Lev) corresponds to a lower curb mass of the vehicle, the curb mass is set as the numerator of the lightweight index and the size parameter of the vehicle as the denominator. Approximately 8000 models in the Chinese passenger car market were statistically analyzed [ 6]. Table 10 presents the linear correlation coefficient between the curb mass and the vehicle size parameters. The curb mass shows a better linear relationship with the nominal volume than the footprint area. Table 10 Linear Size parameter between the curb mass and individual vehicle size parameter
The projected area, designated as Ap, can be calculated by Eq. ( 12). <span class="MathJax" id="MathJaxElement16Frame" tabindex="0" datamathml="Ap=L×W" role="presentation" style="boxsizing: inherit; lineheight: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: 100%; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; overflow: auto hidden; position: relative; display: block !important;">Ap=L×WAp=L×W
(12)
The lightweight index reflects the amount of space that can be created by a certain weight of material while ensuring the performance of the automotive product and customer requirements. This increase in space is conducive to ensuring enough provision for safety measures, providing a comfortable driving space for the drivers, and meeting loading–space requirements. Weight–to–Power RatioThe vehiclespecific power (VSP with a unit in kW/kg) [ 14] is a parameter that correlates to vehicle weight and power state, and is closely related to the power performance, braking performance, and energy consumption of the vehicle. The reciprocal of the VSP, i.e., the weight–to–power ratio (unit in kg/kW), is introduced to understand the VSP more intuitively. The weight–to–power ratio indicates how much mass of a material is in motion. A smaller weight–to–power ratio means better power performance and low energy consumption. Figures 1 and 2 show the relationships between the acceleration performance and the weight–to–power ratio of ICEVs and BEVs, respectively. The vehicle parameters were obtained by authors from the Chinese vehicle market [ 2]. The linear correlation coefficients are 0.89 and 0.97, respectively, which are greater than 0.75 and indicate strong correlations. As presented in Fig. 2, the electric motor power is the basis of the acceleration performance of the BEVs, ensuring both weight reduction and performance. Fig. 1
[size=1.6]Relationship between weight–power–to ratio and acceleration performance of ICEVs
Fig. 2
[size=1.6]Relationship between the weight–to–power ratio and acceleration performance of BEVs
Regardless of the new technologies, the engine power is important for the acceleration performance of ICEVs. Improving the performance of the vehicle requires improving the fuel efficiency and engine power. The main power that can be in BEVs is generated by an electric motor. The maximum power that can be generated by an electric motor is the most important parameter dominating the acceleration performance of BEVs. Therefore, the total power of an electric motor is selected as the denominator of the formula, which suggests that a higher total electric motor power improves the power performance of BEVs. The same effect as reducing the weight of a vehicle can be achieved by increasing the power of the electric motor, namely, both result in decreasing Lev. Fuel (Electricity) Consumption of Footprint AreaWith the official release of the domestic fifthphase fuel consumption regulation GB 279992019 [ 15], the linear fuel consumption evaluation system has been mandated. Hao et al. [ 1] reported that the stepped targets have prevented automakers from applying lightweight technologies. Smooth targets should be considered in the next phase of regulations. The fuel economy standards based on the footprint area has not been adopted in GB 27999–2019 considering the standard regulatory system with continuity. Therefore, eliminating the stepwise evaluation method facilitates lightweight assessment. In the US, the footprint area is treated as an independent variable on the basis of the corporate average fuel economy (CAFE) of light vehicles [ 16]. The fuel economy varies with the footprint area. A smaller footprint area indicates a longer traveling distance per gallon of fuel. The fuel economy target values at both ends of the footprint area are distributed horizontally. This distribution structure serves to encourage small cars and restrict large cars [ 1, 16]. Fuel economy standards based on the footprint area are more inclined to encourage weight reduction [ 17]. There is less risk of “gaming” (artificial manipulation of an attribute to achieve a more favorable target) by increasing the footprint under footprintbased standards than by increasing vehicle weight by weightbased standards, and it is relatively easy for an automaker to add/remove enough weight, as compared to changing a vehicle’s footprint. To change the footprint area of a vehicle, manufacturers need to redesign the chassis, and changes of many components are required as well [ 16]. According to the US Environmental Protection Agency and National Highway Traffic Safety Administration light vehicle emission and fuel consumption regulations [ 16], the vehicle footprint is mainly considered when deciding the development platform. This parameter is relatively fixed, and the cost of changing the footprint is expensive. Therefore, applying the footprint in developing a parameter for fuel economy is more conducive for the stable implementation of the regulations. Fuel consumption regulation based on the footprint area can promote lightweight design, while making it difficult for opportunistic companies to meet the standards. Overall, it is reasonable to introduce the footprint fuel consumption (Q/A) index to reflect the contribution of lightweight to fuel economy. For BEVs, the electricity consumption of footprint area (Y/A) is employed instead of Q/A. The proposed lightweight index shows the core objectives of vehicle lightweight. Emission reduction and green design can be achieved by improving fuel economy and reducing the weight. The proposed lightweight index can be used to assess the lightweight level more comprehensively than the existing evaluation indicators at present. A mathematical method is developed to reflect the requirements and future direction of automotive lightweight requirements, consistent with the trends pertaining to the original index.
ConclusionsA new lightweight index was proposed to assess the lightweight level of passenger cars, which comprises the product of nominal density, weight–to–power ratio, and fuel consumption of footprint area/electricity consumption of footprint area (for ICEVs/BEVs). The practicality of the proposed lightweight index was discussed by comparing with other methods. The following conclusions can be drawn: 1. The standardized partial regression coefficients of multiple regression and the elasticity coefficient are used to analyze the sensitivity of the variables in the model. The results show that the curb mass has the greatest influence on proposed lightweight index. 2. The proposed lightweight index is effectively applied to the lightweight assessment of ICEVs and BEVs, and can be used to guide automakers in setting reasonable weight reduction targets for product development and promote benchmarking analysis for automotive development.
The proposed lightweight index can be adopted by industry authorities to make policies on evaluating lightweight automotive products comprehensively by incorporating adjustment factors if necessary. Further research and analysis are required for the implementation of incentive policies, and the new hybrid electric vehicles. As the understanding of automotive lightweight design continues, it is believed that the proposed lightweight index can be used to help design new vehicles.
AbbreviationsBEVs:Battery electric vehicles CNCAP:ChinaNew Car Assessment Program ICEVs:Internal combustion engine vehicles VSP:Vehiclespecific power
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AcknowledgementsThis research is funded by National Key Research and Development Program of China (Grant No. 2016YFB0101605).
