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This is an extension of simple fuel consumption modeling toward HEV. Previous work showed that in urban driving the overhead of running an ICEV engine can use as much fuel as the traction work. The bidirectional character and high efficiency of electric motors enables HEVs to run as a BEV at negative and low traction powers, with no net input from the small battery. The ICE provides the net work at higher traction powers where it is most efficient. Whereas the network reduction is the total negative work times the system round-trip efficiency, the reduction in engine running time requires knowledge of the distribution of traction power levels. The traction power histogram, and the work histogram derived from it, provide the required drive cycle description. The traction power is normalized by vehicle mass, so that the drive trace component becomes invariant, and the road load component nearly invariant to vehicle mass.

The previously developed power-based fuel consumption theory for Internal Combustion Engine Vehicles (ICEV) is extended to Battery Electric Vehicles (BEV). The main difference between the BEV model structure and the ICEV is the bi-directional character of traction motors and batteries. A traction motor model was developed as a bi-linear function of positive and negative traction power. Another difference is that the accessories and cabin heating are powered directly from the battery, and not from the powertrain. The resulting unified model for ICEV and BEV energy consumption has linear terms proportional to positive and negative traction power, accessory power, and overhead, in varying proportions. Compared to the ICEV, the BEV powertrain has a high marginal efficiency and low overhead. As a result, BEV energy consumption data under a wide range of driving conditions are mainly proportional to net traction power, with only a small offset.

Fuel power consumption for light duty vehicles has previously been shown to be proportional to vehicle traction power, with an offset for overhead and accessory losses. This allows the fuel consumption for an individual powertrain to be projected across different vehicles, missions, and drive cycles. This work applies the power-based model to commercial vehicles and demonstrates its usefulness for projecting fuel consumption on both regulatory and customer use cycles. The ability to project fuel consumption to different missions is particularly useful for commercial vehicles, as they are used in a wide range of applications and with customized designs. Specific cases are investigated for Light and Medium Heavy- Duty work trucks. The average power required by a vehicle to drive the regulatory cycles varies by nearly a factor 10 between the Class 4 vehicle on the ARB Transient cycle and the loaded Class 7 vehicle at 65 mph on grade.

Previously fuel consumption on a drive cycle has been shown to be proportional to traction work, with an offset for powertrain losses. This model had different transfer functions for different drive cycles, performance levels, and applied powertrain technologies. Following Soltic it is shown that if fuel usage and traction work are both expressed in terms of cycle average power, a wide range of drive cycles collapse to a single transfer function, where cycle average traction power captures the drive cycle and the vehicle size. If this transfer function is then normalized by weight, i.e. by working in cycle average power/weight (P/W), a linear model is obtained where the offset is mainly a function of rated performance and applied technology. A final normalization by rated power/weight as the primary performance metric further collapses the data to express the cycle average fuel power/rated power ratio as a function of cycle average traction power/rated power ratio.

Medium duty vehicles come in many design variations, which makes testing them all for CO2 impractical. As a result there are multiple ways of reporting CO2 emissions. Actual tests may be performed, data substitution may be used, or CO2 values may be estimated using an analytical correction. The correction accounts for variations in road load force coefficients (f0, f1, f2), weight, and axle ratio. The EPA Analytically Derived CO2 equation (EPA ADC) was defined using a limited set of historical data. The prediction error is shown to be ±130 g/mile and the sensitivities to design variables are found to be incorrect. Since the absolute CO2 is between 500 and 1,000 g/mi, the equation has limited usefulness. Previous work on light duty vehicles has demonstrated a linear relationship between vehicle fuel consumption, powertrain properties and total vehicle work. This relationship improves the accuracy and avoids co-linearity and non-orthogonality of the input variables.

The fuel consumption of a vehicle is shown to be linearly proportional to (1) total vehicle work required to drive the cycle due to mass and acceleration, tire friction, and aerodynamic drag and (2) the powertrain (PT) mechanical losses, which are approximately proportional to the engine displaced volume per unit distance travelled (displacement time gearing). The fuel usage increases linearly with work and displacement over a wide range of applications, and the rate of increase is inversely proportional to the marginal efficiency of the engine. The theoretical basis for these predictions is reviewed. Examples from current applications are discussed, where a single PT is used across several vehicles. A full vehicle cycle simulation model also predicts a linear relationship between fuel consumption, vehicle work, and displacement time gearing and agrees well with the application data.

Vehicle certification data are used to study the effectiveness of the major powertrain technologies used by car manufacturers to reduce fuel consumption. Methods for differentiating vehicles effectively were developed by leveraging theoretical models of engine and vehicle fuel consumption. One approach normalizes by displacement per unit distance, which puts both fuel used and vehicle work in mean effective pressure units, and is useful when comparing engine technologies. The other normalizes by engine rated power, a customer-relevant output metric. The normalized work/power is proportional to weight/power, the most fundamental performance metric. Certification data for 2016 and 2017 U.S. vehicles with different powertrain technologies are compared to baseline vehicles with port fuel injection (PFI) naturally aspirated engines and six-speed automatic transmissions.

The drive cycle average powertrain efficiency of current US vehicles is studied by applying a first principles model to the EPA Test Car List database. The largest group of vehicles has naturally aspirated engines and six speed planetary automatic transmissions, and defines the base technology level. For this group the best cycle average powertrain efficiency is independent of vehicle size and is achieved by the lowest power-to-weight vehicles. For all segments of the EPA test, the fuel required per unit of vehicle work (the inverse of powertrain efficiency), is found to increase linearly with a basic powertrain matching parameter. The parameter is (D/M)(n/V), where D is engine displacement, M vehicle mass, and (n/V) the top gear engine speed over the vehicle speed. The fuel consumption penalties in the City segments due to powertrain warm-up, aftertreatment warm-up, stop-and-go operation, and power-off operation are estimated.

An analytic model of powertrain efficiency on a drive cycle was developed and evaluated using hundreds of cars and trucks from the US EPA ‘Test Car Lists’. The efficiency properties of naturally aspirated and downsized turbocharged engines were compared for vehicles with automatic transmissions on the US cycles. The resulting powertrain cycle efficiency model is proportional to the powertrain marginal energy conversion efficiency K, which is also its upper limit. It decreases as the powertrain matching parameters, the displacement-to-mass ratio (D/M) and the gearing ratio (n/V), increase. The inputs are the powertrain fuel consumption, the vehicle road load, and the cycle work requirement. They could be modeled simply with only minor approximations through the use of absolute inputs and outputs, and systematic use of scaling. On the Highway test, conventional automatic transmission vehicles of moderate performance achieve between 25% and 30% powertrain efficiency.

A normalized analytical vehicle fuel consumption model is developed based on an input/output description of engine fuel consumption and transmission losses. Engine properties and fuel consumption are expressed in mean effective pressure (mep) units, while vehicle road load, acceleration and grade are expressed in acceleration units. The engine model concentrates on the low rpm operation. The fuel mep is approximately independent of speed and is a linear function of load, as long as the engine is not knock limited. A linear, two-constant engine model then covers the speed/load range of interest. The model constants are a function of well-known engine properties. Examples are discussed for naturally aspirated and turbocharged SI engines and for Diesel engines. A similar model is developed for the transmission where the offset reflects the spin and pump losses, and the slope is the gear efficiency.