Article pubs.acs.org/est
Evaluating the Potential for Secondary Mass Savings in Vehicle Lightweighting Elisa Alonso,† Theresa M. Lee,‡ Catarina Bjelkengren,† Richard Roth,† and Randolph E. Kirchain*,† †
Materials Systems Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Ave., Rm. E38-432, Cambridge, Massachusettes 02139, United States ‡ Chemical Sciences and Materials Systems Laboratory, General Motors Research and Development Center, 30500 Mound Road, Warren, Michigan 48090-9055, United States S Supporting Information *
ABSTRACT: Secondary mass savings are mass reductions that may be achieved in supporting (load-bearing) vehicle parts when the gross vehicle mass (GVM) is reduced. Mass decompounding is the process by which it is possible to identify further reductions when secondary mass savings result in further reduction of GVM. Maximizing secondary mass savings (SMS) is a key tool for maximizing vehicle fuel economy. In today’s industry, the most complex parts, which require significant design detail (and cost), are designed first and frozen while the rest of the development process progresses. This paper presents a tool for estimating SMS potential early in the design process and shows how use of the tool to set SMS targets early, before subsystems become locked in, maximizes mass savings. The potential for SMS in current passenger vehicles is estimated with an empirical model using engineering analysis of vehicle components to determine mass-dependency. Identified mass-dependent components are grouped into subsystems, and linear regression is performed on subsystem mass as a function of GVM. A Monte Carlo simulation is performed to determine the mean and 5th and 95th percentiles for the SMS potential per kilogram of primary mass saved. The model projects that the mean theoretical secondary mass savings potential is 0.95 kg for every 1 kg of primary mass saved, with the 5th percentile at 0.77 kg/kg when all components are available for redesign. The model was used to explore an alternative scenario where realistic manufacturing and design limitations were implemented. In this case study, four key subsystems (of 13 total) were locked-in and this reduced the SMS potential to a mean of 0.12 kg/kg with a 5th percentile of 0.1 kg/kg. Clearly, to maximize the impact of mass reduction, targets need to be established before subsystems become locked in.
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INTRODUCTION It is difficult to find a part of the globe today that is immune to the economic, environmental, and national security issues that derive from the consumption of oil.1 Heightened concern over these impacts continues to affect consumer behavior and government policy. No industry feels this concern more directly than the primary consumer of oil, the transportation industry. However, these trends only emphasize and popularize a fact that automakers have long known: fuel economy is a critical vehicle characteristic. Fuel economy may impact consumer vehicle purchasing,2 vehicle design and manufacturing,3 vehicle lifetime operating costs and greenhouse gas emissions,4 and manufacturer regulatory compliance.5,6 In the light of this importance and in response to today’s changing marketplace, vehicle manufacturers are exploring many strategies to improve fuel economy. Reducing vehicle mass is one such strategy that is being widely considered.7−11 The fundamental driver for this is simple: a lighter vehicle, all else being equal, requires less energy to provide equivalent utility.12,13 A recent example of the potential power of mass reduction comes in a work by Kim et al.,14,15 who reported that reducing © 2012 American Chemical Society
vehicle mass by just under 20% could reduce lifetime vehicle fuel use by more than 10%. Various engineering and design approaches can be used to reduce mass, including materials substitution,11,16 novel processing techniques,17 and design optimization.18,19 A number of authors have noted that all of these mass saving approaches are challenging to implement because it is difficult to estimate their impact on costs16,20,21 and on load path management.22−24 An additional challenge emerges from the nature of the vehicle development process, which is time-constrained and in which subsystems are designed concurrently. As such, to maximize mass savings it is necessary to have sound estimates of the impact of any mass solution, and those estimates must be available early, before key design details are locked in. This paper will focus solely on one aspect of addressing this information challenge for mass reduction engineering: estimating secondary mass savings Received: Revised: Accepted: Published: 2893
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emerging technologies that could reduce the mass of the total vehicle (formally, the gross vehicle mass or GVM). These figures range from 50% to 140% for automobiles.10,15,28−31 (The quoted numbers imply that for every one kilogram of primary mass saved in the vehicle, an additional 0.50−1.4 kg may be saved in secondary mass.) Many of these papers cite industry rule of thumb or expert opinion as the source of the information. While these figures provide useful insights on the potential for SMS, they do not provide sufficient resolutionparticularly at the subsystem or component levelfor mass management during the product development process. Such resolution is important, primarily because it helps guide designers to those subsystems with the most mass savings potential. Second, subsystem-level granularity is needed because real-life design problems are rarely unconstrained. Only certain subsystems may be available for redesign, thus limiting the amount of possible mass reduction. Estimates with subsystem-level granularity and that are specifically sensitive to subsystem constraints are needed. Moreover, the large range in reported SMS potential indicates that there is no consensus about how much SMS can be achieved and suggests that this figure may be strongly context dependent, possibly varying not just from manufacturer to manufacturer but also among different vehicle types. In fact, Audi’s experiences, with achieved SMS of 23% (A8)10 and 56% (A2),32 is a case of varying SMS for a single manufacturer. Clearly, a reproducible method for estimating SMS potential is needed. There are two basic approaches discussed in the literature to quantify how reductions in GVM affect subsystem mass. They are the use of first principles/physical models and the use of empirical models. Physical modeling covers a range of specific approaches, but all involve the development of mathematical models that comprehend a subset of the architectural details, materials properties, and subsystem inertial requirements to project the mass-dependent interaction forces between subsystems. These forces can then be used to scale the parts and, thereby, estimate GVM. A first principles-based model offers the potential to reveal novel insights that were hidden by the complexity of the interactions. Such studies estimate SMS potentials of between 0.25 and 0.68 for every 1 kg of primary mass saved.33−37 For products like the automobile, however, there are two real limitations to the application of this approach. First, the inertial properties of a vehicle are complex and challenging to compute,38 such that current modeling methods require detailed inputs about the vehicle architecture.39,40 Those studies that estimate SMS potential using physical models are based on only a single sample vehicle design, limiting generalization. Unfortunately, at present, the state of first principles models is therefore insufficient for early stage decision-making when subsystem mass targets are set and design details are scarce. In addition to this issue, there is a real concern that physics-based models may overstate the real potential for SMS because they fail to consider the limitations that confront any real design process. These limitations manifest themselves in the form of parts that are not made available for redesign in a given design cycle, overdesigned parts that are load path constrained, or platformed parts that must meet the demand specifications of an entire product family and the regulatory requirements for various global regions. It is also possible to model the drivers of vehicle or subsystem mass through the use of empirical or statistical analysis.
(SMS) for proposed mass solutions. With a better understanding of SMS potential, vehicle designers should be better able to set early mass targets and analysts should be able to develop better estimates of the life-cycle cost, fuel use, and environmental impact of mass changes. The basic concept of SMS emerges from the realization that the size (and therefore mass) of some components is at least partially determined by the need to bear the mass of other components. As a consequence, if vehicle mass decreases, the mass of some components can also decrease. For example, if vehicle mass were reduced, the brakes of that car could be smaller while still providing the same level of performance and function. SMS can increase the attractiveness of any proposed mass reduction by increasing the realized mass change associated with any significant primary reduction. The implications of this are simple: if vehicle manufacturers underestimate SMS, they are more likely to think that any given mass reduction solution has too little impact, is too costly, or both. Implementing (and therefore estimating) SMS is challenging because of fundamental limitations related to the vehicle development process, use of carryover parts, and component sharing. The vehicle development process lasts 50−60 months before vehicle launch,25,26 and to accommodate the complexity and cost of change, it involves locking in certain vehicle subsystem designs as the process progresses. Once a subsystem is locked, its components are no longer available to realize SMS. Moreover, manufacturers often carry over parts from older vehicle models to avoid having to redesign the entire vehicle every time a new model is introduced.27 Those parts would be unavailable for SMS even before the design process has begun. Finally, manufacturers can produce cars using shared components. As the shared components must satisfy the load and performance criteria of all the vehicles that use it, including the heaviest ones, vehicle mass will not be optimized in the lighter vehicles that use parts from the heavier vehicles. These inherent challenges reinforce the need for sound, early estimates of SMS potential. Given the importance of SMS, its effect factors in almost all analyses of the environmental impact (or cost) of technologies that change mass. Unfortunately, with only a few exceptions noted later, previous papers do not describe or reference a method by which SMS is estimated. This paper attempts to partially fill this gap while providing the most comprehensive assessment to date of SMS for current automobiles. Specifically, this paper aims to extend the fundamental method of empirical estimation of SMS potential by (1) providing a formal statement of the analytical method, (2) developing the methods for quantifying uncertainty in the estimation of SMS potential, (3) characterizing the inherent upper-bound bias of this method, and (4) quantifying the importance of expert classification of data at the component level for managing the impact of mass-independent effects on the analysis. Additionally, by analyzing the largest vehicle data set among available studies, this paper aims to provide a current best estimate of SMS potential for sedans. With this better estimate of SMS potential, it should be possible to make a more informed assessment of the life-cycle environmental impact of alternative vehicle materials, processes, and designs.
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PREVIOUS WORK Generally, the SMS potential is expressed as a percentage of secondary to primary mass saved. There are many publications that report SMS potential in the execution of case studies of 2894
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analysis reveals only correlation. For the topic at hand, the existence of unresolved, highly correlated codeterminants of mass change (e.g., vehicle projected area, vehicle luxury class) means that an empirical analysis will inherently provide an upper bound to any estimate of SMS potential. Additionally, the effectiveness of empirical analysis methods is limited by the quality of the data, which in this case is dispersed. Finally, empirical approaches are inherently limited to projecting only future behaviors that are consistent with those of the past. For the case at hand, the most significant departure from this would be the introduction of novel technologies for mass reduction, unconventional architectures, and powertrains. Still, the impact of this is not catastrophic, if those novel changes are the source of the primary mass change rather than a component within the SMS. Despite these important shortcomings, empirical analysis provides valuable insight for characterizing SMS potential. A critical benefit of empirical analysis is that by reflecting the observed behavior of only actual production vehicles, it captures many of the real world constraints that limit the realization of SMS. For example, there are limits in manufacturing processes for reducing gage. Along a similar vein, the variation in mass data provides an important reminder of the uncertainty in realizing SMS in a resource-constrained development environment. Finally, empirical approaches are computationally inexpensive and rely on relatively available data. As such, these methods are scalable and easily applied to a variety of firm specific cases. General Framing. The specific method developed for this paper builds off of the method described in ref 49 and in the thesis of one of the authors.50 The following is a mathematical description of the empirical analysis presented here. The symbols used in the description are defined as follows: N = number of subsystems, N = 13 Si = mass of the ith subsystem, where i ranges from 1 to N Mi = number of components per subsystem i Cij = mass of the jth component in the ith subsystem, where j ranges from 1 to Mi GVM = gross vehicle mass SMS = secondary mass savings mij = jth component in the ith subsystem, determined to be GVM-dependent m̅ ij = jth component in the ith subsystem, determined to be GVM-independent Ξ = Functional characteristics of the vehicle, not including GVM γi = mass influence coefficient of the ith subsystem; equivalent to β1i γt = mass influence coefficient of the total vehicle Γi = mass decompounding coefficient of the ith subsystem Γt = mass decompounding coefficient of the total vehicle The fundamental goal is to characterize the potential SMS in response to some “primary” weight savings, Δ. To develop this relationship, we assume that the magnitude of SMS is proportional to Δ such that the total change in GVM can be described as
It is useful here to break down the set of empirical work on vehicle mass into two further categories: those that derive mass from other performance characteristics and those that explicitly examine the role of mass in determining mass. In the former category, there are a number of case-related papers that have examined how performance or design characteristics drive the mass of aerospace vehicles,41−43 ships, and automobiles.44,45 The primary focus of these models is to inform performance benchmarking, initial mass target setting, or project management. With the notable exception of mapping the relationship between payload mass and the mass of the required fuel and craft, these documents do not generally explore the impact of mass on mass. Given the goals of this work, these methods are not directly applicable and will not be explored further. Instead, the approach selected here is empirical analysis to determine how the different subsystem masses are affected given a change in the overall mass of the vehicle. Only a few papers exist that fall into this category and have applied empirical methods to explicitly deduce SMS potential within the automobile. From a methodological perspective, these papers differ primarily in the way that mass data was aggregated, partitioned (i.e., parts of the data excluded from analysis), and adjusted (or not) in an effort to exclude changes in mass that are not made in response to change in overall GVM (mass-independent changes). The earliest set of work in this space comes from two separate groups from Chrysler Corp., who estimated a SMS potential of 53.9% and 130%, respectively.46,47 In these studies, regression methods are used to deduce a correlation between GVM and subsystem mass. These estimates are based on data aggregated at the subsystem level. One subsystem is acknowledged to be mass-independent (i.e., the upper body structure) and is omitted (partitioned) from the analysis. Other subsystems may have been partitioned similarly but are not explicitly reported. Kato and Shiroi48 also use statistical regression techniques as well as first principles based analysis to estimate the impact of mass on mass. They report SMS potentials of 147% and 123% for these methods, respectively. However, no details are provided as to how to convert specific regression information into SMS potential. More recently, Malen et al. examined mass behavior in a set of 35 vehicles including sedans, SUVs, vans, and pickups, which were subdivided into 13 subsystems.49 Data was aggregated and partitioned at the subsystem level, excluding the nonstructure subsystem and those subsystems with low coefficient of determination (R2). They estimated the SMS potential deterministically as 128%. These studies lay an important foundation for exploring mass interdependency within the vehicle. One clear issue is the broad range of reported estimates (72%−210%). We propose that one driver of this variability is the convolution of mass driven and strongly correlated but mass-independent mass changes across the sets of vehicles that have been analyzed. This variability can be managed through expert-based data partitioning, although, as noted, these papers differ in their approach to partitioning. Moreover, none have explored the importance of those approaches or examined uncertainty.
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METHODOLOGY The methodological approach applied here is empirical analysis of existing vehicles to infer how subsystem masses change in response to a change in GVM. An empirical analysis of this form is limited in several ways. Most fundamentally, an empirical
ΔGVM = Δ + SMS = Δ(1 + Γt)
(1)
To develop an analytical relationship for Γt, the mass decompounding coefficient of the vehicle, we assume that a vehicle comprises N subsystems (indexed on i) of mass Si and 2895
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Figure 1. Graphical representation of mass decompounding in a vehicle with three subsystems. One subsystem (c) in which primary mass savings, Δ, are implemented and two (a and b) that are wholly GVM-dependent and, therefore, candidates for secondary mass savings.
wholly GVM-dependent, and c, which is wholly GVMindependent. Assume that a new technology allows for a primary mass saving of Δ′ in c. This change would enable a corresponding mass reduction of γaΔ′ in a and γbΔ′ in b. These two mass reductions translate into a total secondary change of GVM of Δ″ = (γa + γb)Δ′. If the above assumptions hold true, this change in GVM (Δ″), however, would enable further savings of Δ‴ = (γa + γb)Δ″. In principle, this hypothetical progressive process continues indefinitely (see Figure 1). The mathematical representation of overall secondary mass savings can be generalized from this hypothetical example. Summing over all SMS from a two-subsystem vehicle with γa for subsystem a, γb for subsystem b, gives γt = γa + γb. Allowing n to represent the number of progressive “iterations” of mass savings yields the following expression for SMS potential in subsystem a:
that each of these subsystems is composed of an exclusive set of Mi components (indexed on j) of mass Cij. Given these definitions, the gross vehicle mass (GVM) equals the sum of the masses of the subsystems, the passengers, the cargo, and the fluids. ⎛N ⎞ N M ⎜ ⎟ GVM = ⎜ ∑ Si = ∑ ∑ Cij⎟ + passenger mass ⎜ ⎟ i=1 j=1 ⎠ ⎝i = 1 + cargo mass + fluids mass
(2)
We further assume that the mass of each component is a function of GVM and other functional characteristics of the vehicle (Ξ), such as horsepower. The components within each subsystem can be further classified as belonging to one of two exclusive subsets: GVM-dependent (mij) or GVM-independent (m̅ ij) such that Mi ∪ {mij,m̅ ij}. A GVM-independent component is one whose mass does not change in direct response to a change in overall GVM [i.e., δCij/δ(GVM) = 0].47 This paper will explore the validity and implications of a linear relationship among these drivers of mass. Specifically, this relationship would be of the form: Si = f (GVM, Ξ) = β0i + β1i × GVM + β2iΞ
Δ[γa + γa(γa + γb) + γa(γa + γb)2 + ... + γa(γa + γb)n ] = Δγa[1 + γt + γt 2 + ... + γt n]
Assuming that γt is less than 1 and letting n approach infinity, the above equation converges to
(3)
⎛ γ ⎞ Δ⎜⎜ a ⎟⎟ = ΔΓa ⎝ 1 − γt ⎠
Furthermore, let the mass influence coefficient be defined as the rate of change in subsystem mass per change in GVM, such that ∂Si β1i = γi ≡ ∂(GVM)
(7)
where Γa is defined as the mass decompounding coefficient specific to subsystem a. This coefficient can be calculated for each vehicle subsystem as Γi: γi Γi = (1 − γt) (8)
(4)
By definition, the GVM-independent mass does not change with GVM and so γi will be defined more precisely as γi =
(6)
m m m ∂(∑i i Cij + ∑i i Cij) ∂(∑i i Cij) ∂Si = = ∂(GVM) ∂(GVM) ∂(GVM)
The sum of the subsystem mass decompounding coefficients is the vehicle mass decompounding coefficient (Γt), which quantifies the total SMS potential in response to a given primary mass reduction.
(5)
The sum of the subsystem mass influence coefficients (γi) is the vehicle mass influence coefficient (γt = ∑iγi) and is an estimate of SMS potential assuming subsystems are affected by a change in GVM in isolation, with no influence on each other or their own mass. However, several authors have suggested that it is reasonable to expect that the mass of individual subsystems is influenced by the mass of other subsystems.46,47,51 To understand this interrelationship, it is useful to envision a hypothetical set of events in the development process of a product with only three subsystems: a and b, both of which are
Γt =
∑ Γi i
(9)
At this point, it is worth emphasizing that while the underlying logic for the calculation of Γt was described as relying on an iterative process of redesign, such iteration is not necessary in a real world design context. If mass targets are set early on the basis of a realistic expectation of SMS, it is possible for all subsystems to be designed to an ultimate (lower) mass that takes into account SMS, without having to proceed 2896
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load path management requirements. In limiting the vehicle set to current vehicles, the tool is designed to estimate secondary mass savings potential while still ensuring that all parts can still carry the required loads. This also limits the range of vehicle lightweighting applicable for analysis by the model. The range of GVM for the vehicles in the data set is 1290−2360 kg with 90% of vehicles falling within the 1650−2250 kg range. At the very least, the predicted mass after primary and secondary mass change has taken effect should be within the range of the GVM of the data set used.49 Moreover, the model applicability is limited to the boundary of the linear behavior observed in the regression of each of the subsystems. The mass data for each vehicle was broken up into over 1000 parts and categorized into 200 components, which were further categorized into 13 major subsystems in a consistent manner across all vehicles. The subsystem categories are shown in Table 1. The mass data were collected by vehicle teardown centers, where automakers reverse engineer vehicles in order to discover design details.54 To understand the magnitude of uncertainty associated with an estimate of SMS, the significance of non-GVM driven mass change, and the value of expert data classification and partitioning to address both of these issues, several analytical approaches to SMS estimation were compared. The base case analysis reflects the methods description presented so far in this paper, mass-dependency determined through engineering analysis and GVM-independent mass partitioned from SMS analysis at the component level. This analysis will be referred to as engineering analysis/component-level GVM-dependency. The base case was compared with three alternative empirical methods. The first examined the mass decompounding coefficient where GVMdependency was not identified and all components were included: wholly GVM-dependent. The second assumed that GVM-dependency could be determined when components’ mass correlated to GVM: mathematical analysis/component-level GVMdependency. The third analysis attempts to reflect the approach reported in49 which GVM-dependency was only assessed and data partitioned at the subsystem level. Both statistical analysis and engineering analysis were used to determine GVMdependency. This fourth approach will be labeled engineering and mathematical analysis/subsystem-level GVM-dependency.
through the intermediary design stages with their intermediary masses. Estimating the Mass Influence Coefficients. Following the hypothesis stated in eq 3, the mass influence coefficient is estimated as the slope of the linear regression of subsystem mass as a function of GVM. For this paper, this regression was performed using the method of least-squares. Conventional statistical tests were used to identify data outliers52 and high leverage points. Such data points were evaluated for data errors such as misclassification of parts, and once identified, these errors were corrected. Residuals and t-statistics were evaluated to determine the model adequacy for all subsystems. A key goal of this work has been to understand the magnitude and drivers of uncertainty surrounding estimates of SMS. To accomplish this, the mean (μγi) and standard error of each γi were determined. Using these values, the γi values were modeled following a normal distribution (evaluated with standard normal quantile−quantile plots50) within a Monte Carlo simulation (executed for 1000 samples). The simulation was employed to calculate the mean, standard deviation, and the 5th and 95th percentiles of the mass decompounding coefficients (Γi). Simulation was necessary because Γi, representing the quotient of two normally distributed variables, γi and γt (see eq 8), is necessarily non-normally distributed.53 The observed skewness gives rise to an expected value of Γi that is higher than that calculated deterministically from μγi. Previous literature used a deterministic calculation for computing Γ. Later in the paper, such deterministic calculations are presented simply for comparison with the values reported in earlier studies. Determining Mass Dependency through ExpertBased Partitioning. As described mathematically in eq 3, component mass, Cij, is a function of GVM and other vehicle characteristics. Conventionally, the influence of these factors would be resolved using multivariable regression methods. Unfortunately, the strongly correlated nature of GVM and other mass determinant characteristics (see Supporting Information) precludes the independent estimation of their influence. Because these quantities are positively correlated, the quantitative estimates derived here are upper-bound estimates of the influence of GVM on component mass and, therefore, of SMS. To accommodate these facts and minimize this upper bias, component mass data was partitioned into two sets: GVMdependent (mij) and GVM-independent (m̅ ij). The goal was to include only GVM-dependent components in the analysis. This level of detail is an important addition to previous work on SMS.48,49 A team of mass engineers from a major North American automaker evaluated the individual components to determine if the mass of each part would change due to a change in GVM. Parts that supported load paths, structure, and propulsion (i.e., engine, fuel, and exhaust) components were considered mass-dependent. This method of partitioning GVMdependent parts using engineering-based expertise and at the component level is compared to methods that partition using mathematical correlation at the component and subsystem level. Data and Scenarios. The analysis uses data from 77 current passenger vehicles sold in North America or Europe (2007− 2009 sedans and crossovers, 13 different manufacturers). Data on 21 other vehicles were available but were excluded because they were sold exclusively in world markets requiring an alternative architecture and, therefore, had significantly different
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MODELING THE SMS POTENTIAL OF SEDANS Table 1 shows the results derived from the base case analysis. The largest γi are for the suspensions and structure subsystems. These values indicate that a 1 kg change in GVM has been observed to correlate with a change of 0.128 and 0.110 kg, respectively, in these subsystems. While p-values across all of the subsystems indicate that the correlation between GVM and subsystem mass were statistically significant, R2 are generally low. Several issues drive unexplained variation in the data. Most importantly, the data is from actual vehicles that may not be optimized for mass because of the need to accommodate variants within a product platform, the use of carry-over parts from previous products, and the fundamental time and resource constraints within the design process. For the base case analysis, γt is estimated to be 0.47. This value is very close to the most common value cited based on expert opinion, 0.50. It is worth noting that γt could also be thought of as the amount of mass savings that would occur if mass reductions were realized iteratively with only one round of feedback in the development process. Given these facts, it is 2897
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Table 1. Results for Approach 1 (Base Case) Analysis mass decompounding coefficient, Γ
mass influence coefficient γ
std error
R2
p-value
mean
SD
5th
95th
GVM-dependent subsystem mass as a fraction of GVM
fraction of subsystem mass that is GVM-dependent
suspensions structure transmission engine fuel and exhaust tires and wheels hvac steering and brakes exterior closures electrical info and controls interior
0.128 0.110 0.070 0.067 0.036 0.035 0.018 0.013 0.008
0.014 0.017 0.010 0.013 0.005 0.004 0.003 0.003 0.002
0.516 0.348 0.389 0.246 0.375 0.485 0.397 0.178 0.189
