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Expanded Human Choice based on Duty/Demand Cycles for In-Wheel Motors in Electric Vehicles.

I. INTRODUCTION

Optimal sizing of IWMs, choice of battery and capacity, development of controllers, and realistic charging scenarios requires a discussion of vehicle duty cycles. In this paper, the demand cycle refers to the individual's driving history and can be described by a speed versus time curve. The duty cycle refers to a vehicle's history of power usage and the manufacturer can use it to design the drive wheel actuator. As a result, the components of the IWM will be sized to meet the selected duty cycle [1, 2].

For instance, an aggressive driver might want 0-60 mph acceleration time in 5 s, but an efficiency-priority driver will want high efficiency instead of the quick 0-60 mph acceleration time. The demand cycle, depending on the customer, will be determined by the driver history's speed versus time curve. Consequently, manufacturers can configure specific driving cycles for each particular customer. Based on their driving cycles, the IWM will be customized to that particular customer. This could lead to a more optimized IWM so that the customer can be best satisfied with their purchase. It is discussed in detail how to evaluate, classify, and satisfy these individual customers. In addition, the expanded choice for the customer can be characterized in terms of two basic operating regimes: drivability and efficiency. It is analytically demonstrated how the selection of the design components of IWMs differs for different types of customers such as an aggressive driver vs. an efficiency-priority driver, and describe design specifications such as different g levels, gear ratio, power rating, weight of the IWM, clutch shift point, efficiency, 0-60 acceleration time etc.

In this paper, the longitudinal vehicle dynamics are presented. Based on that, the customer-oriented duty cycle analysis is developed. After that, simulation results and conclusions are presented.

II. LONGITUDINAL VEHICLE DYNAMICS

A passenger vehicle can be analyzed as a system consisting of one vehicle body (sprung mass) and four wheels (unsprung mass), which are IWMs in this case. The vehicle can be modeled as interactions among five bodies comprising sprung and unsprung masses [3].

As shown in Figure 1. the forces act on a vehicle moving on an inclined road. The equation of motion can be expressed by the following [4]:

[mathematical expression not reproducible] (1)

where [??]

[mathematical expression not reproducible]

The dynamic equation of motion along a vehicle's longitudinal direction is influenced by traction forces, aerodynamic drag resistance, rolling resistance, and grade resistance. The sum of aerodynamic drag resistance ([F.sub.aero]), rolling resistance ([F.sub.rolling]), and grade resistance ([F.sub.grade]) is referred to as "road load," which is a minimal force on a vehicle moving on a road. For example, during cruising (i.e., acceleration [a.sub.x] = 0), traction force ([F.sub.t]) given in terms of the slip between the tire and the road is equal to the road load, which consists of front traction force ([F.sub.xF]) and rear traction force ([F.sub.xR]). Similarly, rolling resistance ([F.sub.rolling]) consists of front rolling resistance ([R.sub.xF]) and rear rolling resistance ([R.sub.xR]).The difference between road loads and the traction force make it possible to accelerate or decelerate the vehicle [4]. The total equivalent mass ([m.sub.eg]) is the sum of vehicle mass ([m.sub.v]) and equivalent mass of the rotating parts of each wheel [5]

From Equation(1), the traction force can be expressed by:

[F.sub.t] = [m.sub.eg][a.sub.car ] + [F.sub.aero] + [F.sub.rolling] + [F.sub.grade] (2)

Given a Electric Vehicle (EV) equipped with four-independent IWMs, the required motor torque can be obtained by [6, 7]:

[mathematical expression not reproducible] (3)

Where [r.sub.w] is the radius of the wheel, [N.sub.w] is the number of wheels, [g.sub.r] is the gear ratio, and [[eta].sub.g] is the gear efficiency. With respect to each IWM, mechanical power from the motor is transmitted through the gear train to the tire. The motor power required to accelerate a vehicle is given by:

[mathematical expression not reproducible] (4)

The Multi-speed hub Drive Wheel (MDW) suggested by the Robotics Research Group at the University of Texas at Austin (UTA) is designed to improve human choice by achieving the desired drivability and efficiency so that customer requirements can be met at the time of purchase for an open architecture EV which would then be assembled on demand. Since the MDW has 4 distinct speeds (two electrical and two mechanical), the g (acceleration) level will have 4 different levels. Four distinct acceleration (g) levels associated with four distinct speed ranges will be [g.sub.1] (0 - 10 mph), [g.sub.2] (11 - 20 mph), [g.sub.3] (21 - 40 mph), and [g.sub.4] (41 mph - 70 mph). The clutch shift occurs at 20 mph from 49-to-1 (for low speed and high torque) to 14-to-1 (for high speed and low torque) for two mechanical speeds [8].

III. CUSTOMER-ORIENTED DUTY CYCLE ANALYSIS

It is demonstrated how the selection of IWM matches to the driver whose driving cycles are UDDS and US06. These driving cycles would be based on an average driving style. The individual demand cycle can be defined as the driving cycle associated with a particular customer[9]. Customer's demand cycle is critical for their desired drivability and efficiency. The question arises: how to measure a customer? how to classify a customer?, and how to satisfy a customer?.

To address these problems, an automobile company might provide a customer with smart phone application to obtain the individual demand cycles. The customer runs the application on his phone when he drives his current vehicle for a period of day for two weeks. Whenever he drives, the app records the velocity and acceleration of the car. After that, a third-party "software application" analyzes specific duty cycle for that driver. Consequently, the resulting customer's duty cycle can be used to predict what the customer wants, and thus the EV will be customized to suit the customer's demand style, so that the customer can be best satisfied with their purchase [8].

Since, at this time, the individual demand cycles are not available, assumption is that the standard duty cycle is given by: Urban Dynamometer Driving Schedule (UDDS) and Aggressive Driver (US06). In this paper, the maximum vehicle speed is determined by the maximum speed of the traction motor. Therefore, in this design the maximum speed of the IWM is constrained by 70 mph (i.e., Switched Reluctance Motor (SRM) motor speed 13000 ~ 15000 RPM). According to this constraint [10], if the motor operates above 15000 RPM (which can be regarded as high speed), it is important to evaluate the effects of hoop stress, inertia, and critical speed.

A. Standard Duty Cycles

The duty cycles are used to assess vehicle fuel economy and emissions. Moreover, in order to develop the automotive power trains, they are used as a valuable design evaluation tool. EPA dynamometer driving schedules list 17 types of road driving cycles [11]. Two driving cycles are selected to simulate the vehicle performance such as UDDS and US06, assuming that each cycle corresponds to efficiency-driver and aggressive-driver, as shown in Figure 2 (a) and (b), respectively

Figure 2 shows the existing duty cycles. The UDDS is called "LA4" or the "city test", and represents a city duty cycle with continuous stop-start operation. The US06 represents a high acceleration driving schedule which can be used for an aggressive driver. Assuming

B. Total Wheel Torque and Power

The total wheel power required to accelerate a vehicle is the product of the wheel speed ([[omega].sub.w]) and total wheel torque ([[tau].sub.tw]) given by:

[P.sub.tw] = [[omega].sub.w] x [[tau].sub.tw] = (2[pi]n/60) x ([F.sub.t][r.sub.w]) (5)

After substituting traction force ([F.sub.t]) from Equation (1) into (5), the above equation becomes:

[P.sub.tw] = (2[pi]n/60) x ([m.sub.eg][a.sub.car] + [F.sub.aero] + [F.sub.rolling] + [F.sub.grade]) [r.sub.w] (6)

The total wheel power required is simulated given Equation (6)

Figure 3 (a)-(d) shows wheel speed, normalized acceleration, total wheel torque, and total wheel power, respectively. From the relation between normalized acceleration and corresponding total wheel torque/power, it is concluded that the peak torque and power are strongly associated with acceleration events.

A US06 duty cycle is translated into wheel speed, normalized acceleration, total wheel torque, and total wheel power requirement, as shown in Figure 4 (a) - (d) respectively. The maximum normalized acceleration is around 0.35 g. Clearly, it is evident that the instantaneous torque and power are strongly dependent on acceleration events. The variation of total wheel torque and power shows how the aggressive driver behaves and what he / she expects (wants).

C. Speed-Acceleration Frequency Distribution

The required information about the time proportions of individual duty cycles can be obtained from the Speed-Acceleration Frequency Distribution (SAFD) [1]. In addition, this plot provides a visual picture of each duty cycle, and hence, this 3D map can illustrate whether the duty cycle is biased in terms of speed or acceleration regions.

Figure 5 (a) and (b) show 3D maps of speed-acceleration frequency distribution with respect to normalized acceleration level and velocity in terms of UDDS and US06. This map helps us to understand how the duty cycle is biased. In other words, this map describes the range and distribution of time spent at different speeds and acceleration. For instance, duty cycles regarding urban driving conditions represent a city cycle with continuous stop-go operation. With regard to UDDS, it is apparent that there is a bias around 0 kph due to a city cycle with continuous stop-start operation, around 40 and 80 kph. The peak acceleration and deceleration are around 0.15 g, as shown in Figure 5 (a). Compared to UDDS, Figure 5 (b) US06 has much higher rates of acceleration and deceleration. Peak acceleration and deceleration is around 0.35 g and a peak deceleration of 0.3 g, respectively. This is a characteristic of an aggressive driver. In addition, each operating points are shown in Figure 6 (a) and (c) in detail.

D. Wheel Torque-Speed

Torque-speed characteristics play an important role in designing the proper motor power rating, which is the primary consideration with respect to performance specifications. Figure 6 (a) and (b) show the total wheel torque vs. speed scatter plot and the number of occurrence vs. total wheel torque histogram, respectively, for the UDDS driving cycle. As can be seen in Figure 6 (a), each circle is the operating point associated with the UDDS duty cycle. As seen at symbol 'A and 'B' in Figure 6 (a), two significant findings are highlighted. First, the symbol 'A' (40 kph (25 mph)) represents characteristics of downtown driving (i.e., stop and go operation). The second, symbol 'B' (80 kph (50 mph)) indicates that the operating points move away from the center due to the quadratic aerodynamic drag force as wheel speed increases. In order to find the continuous torque and peak torque specifications, it is necessary to obtain a histogram in terms of the number of occurrences vs. total wheel torque, as shown in Figure 6 (b). The majority of the energy consumed corresponds to those occurrences that occur at low torque levels between 0 and 100 N-m. Given four-independent drive wheels, the total continuous wheel torque is 400 N-m (i.e., 100 N-m per wheel) and total peak wheel torque is 1000 N-m (i.e., 250 N-m per wheel) [12, 13].

Regarding the US06 driving cycle, Figure 6 (c) and (d) show the total wheel torque-speed scatter plot and the number of occurrences vs. total wheel torque histogram, respectively. As seen at symbols 'C, 'D', and 'E' in Figure 6 (c), three significant findings are highlighted. First, symbol 'C indicates that high acceleration levels for the aggressive driver occur at low speed, and are relatively short in duration. Second, symbol 'D' indicates that high deceleration levels for the aggressive driver also occur at low speeds. Third, the symbol 'E' indicates that the operating points move away from the center due to the aerodynamic drag force. In other words, during steady state speed, it required the minimum wheel torque. As shown in Figure 6 (d), the majority of the energy consumed occurs at low torque levels between 0 and 400 N-m wheel torque. Given four independent drive wheels, the total continuous wheel torque is 1600 N-m (i.e., 400 N-m per wheel) and total peak wheel torque is 2400 N-m (i.e., 600 N-m per wheel). The peak wheel torque is limited by the power rating of the IWM.

E. Motor Output Torque and Power

The IWM designed by UTA has four distinct speeds (two electrical and two mechanical) in order to improve efficiency and enhance drivability such as acceleration, braking, and climbing a hill on the command of the operator. One controller configuration operates the [g.sub.1] and [g.sub.3] regimes at low power while the other controller configuration operates the [g.sub.2] and [g.sub.4] regimes at higher power for the two electrical speeds. Hence, the IWM has four choices regarding efficiency and drivability. [8].

Assuming four independent IWMs, the motor characteristics can be determined in terms of motor speed, torque, and power of the IWM of an EV. It is discussed regarding the motor speed, torque, and power in terms of the 4 operating regimes of the IWM.

With regard to the IWM, the first and second speed ranges would be 0-20 mph, and the third and fourth speed ranges would be 21-70 mph. The IWM operates from 0 to 13,726 RPM in the first/second motor speed range based on the first gear ratio of 49-to-1 (for low speed and high torque). After a changeover due to clutch shift at 20 mph, the MDW operates from 4,118 to 13,726 RPM corresponding to 21 to 70 mph (for high speed and low torque).

Figure 7 (a)-(d) shows motor output speed, acceleration, torque, and power derived from Figure 3 considering the four-independent IWM, respectively. The motor speed required to produce the wheel speed is given by:

[n.sub.m1] = [n.sub.w1] x [g.sub.r1]

[n.sub.m2] = [n.sub.w2] x [g.sub.r2] (7)

Where [n.sub.w1] and [n.sub.m1] are the wheel speed (RPM) and motor speed (RPM) associated with a gear ratio of [g.sub.r1] (49:1), and [n.sub.w2] and [n.sub.m2] are the wheel and motor speed related to a gear ratio of [g.sub.r2] (14:1). As seen at symbol 'A' in Figure 7 (a), a sudden peak speed occurs before the clutch shift. At that time, the wheel speed is 280 RPM (20 mph) and the motor speed is 13726 RPM with an acceleration of 0.15 g as shown in Figure 7 (b). As can be seen in Figure 7 (c) and (d), the motor output torque and power can be obtained from the total wheel torque and power divided by the number of wheels as follow:

[mathematical expression not reproducible] (8)

From Equation (8). [[tau].sub.m1] and [P.sub.m1] are the motor output speed and motor output power (kw) associated with a gear ratio of [g.sub.r1] (49:1), and [[tau].sub.m2] and [P.sub.m2] are the motor output speed and motor output power related to a gear ratio of [g.sub.r2] (14:1). As seen at symbol 'A' in Figure 7 (b) it is concluded that the peak torque and power are strongly associated with acceleration events.

Figure 8 shows motor output speed, normalized acceleration, torque, and power derived from Figure 4 considering the four-independent drive wheels. As seen at symbol 'A' shown in Figure 8 (a), the motor speed is rapidly accelerated from 0 to 6000 RPM (30 mph) through the clutch shift at 20 mph. This behavior indicates characteristics of an aggressive driver. The normalized acceleration is around 0.3 g. At that time, peak motor output torque and power associated with each wheel are around 27 N-m and 16 kw. The 27 N-m is from 1557 N-m divided by gear ratio (14:1) and four wheels. The 16 kw is from 64 kw divided by four wheels. The sudden spike of motor torque and power shows how the aggressive driver wants to operate.

F. Motor Power Demand

Depending on the specific duty cycles, it is essential to evaluate what the power demands are on the IWMs. The motor input power demand can be obtained from the motor output power divided by motor efficiency as follows[14]:

[P.sub.m-in] = ([[tau].sub.m] x [[omega].sub.m])/ [[eta].sub.m] (9)

This indicates that the electrical power is larger than the mechanical output power. Regarding regenerative power which is negative power, the efficiency works in the opposite sense. The electrical power required is decreased, so that the equation becomes [6]:

[P.sub.m-in] = ([[tau].sub.m] x [[omega].sub.m]) x [[eta].sub.m] (10)

Using Equation (9) and (10). Figure 9 (d) results from the product of motor output torque and motor output speed through the motor efficiency, as shown in Figure 9 (a) (b). and (c). respectively.

RRG research[14] presented the mapping output requirements to prospective input requirements. Figure 9 shows the process of how to obtain motor input power demand from motor output torque and speed through the overall efficiency of an IWM. Figure 9 (c) shows the efficiency map of a motor at different operation points. The below numbers indicate the efficiency percent. This map describes how efficiency varies with respect to motor torque and motor speed. The motor efficiency can be defined as the ratio given by[6, 15]:

[mathematical expression not reproducible] (11)

The motor efficiency is the ratio of the power output to the input power. The copper losses are caused by electrical resistance of the wires of the motor, resulting in heating ([I.sup.2]R). This is proportional to the torque ([k.sub.c][[tau].sup.2]). The constant [k.sub.c] is selected as 16. The iron losses are caused by magnetic effects in the iron of the motor. It is proportional to the frequency with which magnetic field changes relative to the speed of the rotor ([k.sub.t][[omega].sub.m]). The constant [k.sub.t] is selected as 0.005. The windage losses increase with the increased speed of the rotor ([k.sub.w][[omega].sup.3]). The constant of [k.sub.w] is dependent on the size and shape of the rotor. It is selected as 1.0 x [10.sup.-11]. Finally, the constant loss coefficient (C) is chosen as 0.2. Even though this efficiency equation can be used for determining the efficiency of a brushed DC motor, this equation is true for all types of motors to obtain a good approximation, which allows us to predict the expected motor losses [6]. In this research, this efficiency equation was for a switched reluctance motor (SRM). Negative motor torque to the driven wheels is due to the regenerative braking system which utilizes the electric motor, converting kinetic energy to electrical energy for recharging the battery [16].

IV. METHODOLOGY TO DERIVE IWM SPECIFICATION

Based on this previous analysis, it is discussed what IWM specification is suitable for duty cycles UDDS and US06. The MDW user choice specifications will be different g levels, 0-60 acceleration time, power rating, IWM size, optimal gear ratio, and clutch shift point.

A. UDDS - How to Maximize Efficiency in Terms of an IWM?

Figure 10 shows the wheel torque-speed curve of the IWM in correspondence with the speed ranges of the first and second stages. Each number indicates the efficiency percent. In this case, the wheel torque-speed curve is defined as the design envelope for the given constraints, which are different g levels: [g.sub.1] = 0.3, [g.sub.2] = 0.3, [g.sub.3] = 0.15, [g.sub.4] = 0.15. Figure 10 (a) is plotted based on these different g levels.

Given four-independent IWMs, the power rating of each wheel is selected as 16 hp. The clutch shift occurs at 20 mph (280 RPM). Before the clutch shift, given the gear ratio (49:1), the design envelope of 350 N-m as shown in Figure 10 (a), which is in the wheel domain, is translated into the design envelope of 7.14 N-m in the motor domain, as shown in Figure 10 (b). The Negative motor torque to the driven wheels is due to the regenerative braking system. After the clutch shift, given the gear ratio (14:1), the design envelope of 179 N-m in the wheel domain is translated into the design envelope of 12.5 N-m in the motor domain, as shown in Figure 10 (c).

Figure 10 (b) and (c) show mapping of the wheel torque into motor torque with respect to the speed range of the first stage and the second stage. That is, two maps, which are the motor efficiency map and scatter map superimposed. As shown in Figure 10 (b), the scatter map in the motor domain is transformed from Figure 6 (a) in the wheel domain. In other words, the wheel torque - wheel speed (0 - 280 RPM) is transformed into motor torque - motor speed (0-13726 RPM) through the gear ratio (49:1).

Assuming that the controller efficiency equals 1, the motor efficiency is transformed from Figure 9 (c). In the same manner, as shown in Figure 10 (c), the wheel torque - wheel speed (280 - 1000 RPM) is transformed into motor torque - motor speed(4118 - 13726 RPM) through the gear ratio (14:1). The corresponding motor efficiency map is transformed from Figure 9 (c).

From the design point of view, the question arises: does the MDW's design envelope cover the desired operating points? How do we find the optimal gear ratio and clutch shift point?. The symbol 'A' in Figure 10 (c) indicates the IWM's design envelop. As seen at symbol 'B', some scattered operating points of the HDDS exceed the IWM's capability. That is, the IWM design somewhat fails to satisfy the customer. For the purpose of analysis, even though this is acceptable through the maximum power rating for a short period of time, the IWM design should be modified to cover all reasonable operating points. We will demonstrate how the selection of the design components of IWMs matches to the driver whose duty cycle is the HDDS.

As can be seen in Figure 10 (b) and (c), each operating point has a corresponding efficiency. The overall efficiency can be obtained from the sum of all operating points divided by the number of operating points. The overall efficiency including the speed ranges of the first and second stages is around 88.6%. Also, regarding the clutch operation to the speed range of the second stage, the total number of clutch shift events on a given HDDS is around 40 events, corresponding to sudden peaks at motor speed vs. time plot as shown in Figure 7 (a).

How to Maximize Efficiency in Terms of the IWM?

Ren develops and predicts EV energy consumption with a variable and fixed ratio gearbox over a standard driving cycle to obtain useful efficiency estimates [13]. In order to maximize the efficiency, the IWM should be optimized for the highest efficiency. As seen at symbol 'C shown in Figure 10 (c), the driving operating points between 20 and 35 mph occur frequently.

To cover these operating points, the clutch shift point of an IWM should be redesigned. After the IWM redesign, Figure 11 shows the configuration of the IWM optimized for maximizing efficiency by choosing the first stage gear ratio (28:1) and second stage gear ratio (14:1). In addition, the clutch shift point of the MDW is chosen as 35 mph (i.e., motor speed = 13720 RPM). These MDW parameters will be chosen by the customer who prefers efficiency as his priority. As seen at symbol 'A' shown in Figure 11 (c), the design envelope now covers all operating points. Each number indicates the efficiency percent.

Consequently, the overall efficiency including the speed ranges of the first and second stage is around 88.7% which is slightly higher than the previous efficiency (88.6%). Furthermore, regarding the clutch operation to the speed range of the second stage, the total number of clutch shift events on a given HDDS is around 7 events, which is 5 times less than previous IWM design (40 events). This leads to decreasing the energy consumption and improving the MDW's durability because the clutch actuator is used less. Despite a minor difference of efficiency, it is necessary to pursue this reduced need to shift. In addition, the paper [17] confirms that an energy management strategy based on optimal driving torque distribution improves the efficiency by 27.4%, given four-independent IWM. The work by Qian and Xu show that additional efficiency benefits occur by managing in real time the actual traction forces on each independently controlled IWM. This result adds to the importance of the present work, especially for those cases where traction varies a great deal or is uncertain.

In this case, two torque-speed regions based on the mechanical clutch operation were considered. On the other hand, with a reconfigurable power controller, the IWM would have higher efficiency over its entire torque-speed profile by spreading out the efficiency sweet spot. In other words, by choosing appropriate controller components, the overall efficiency can be further improved to meet the customer requirements for different purposes of the system in real time. The electric motor would be driven under two controller configurations, resulting in two additional speed domains. Hence, four distinct operational regimes are created (with a mechanical clutch shift) [8].

In order to understand visually in the wheel domain instead of the motor domain, it is essential to visualize the efficiency map with respect to wheel torque and wheel speed. Figure 12 (a) shows the overall efficiency map of the MDW as a function of wheel torque and wheel speed. This visual performance maps can be used to aide decision making[18, 19]. Also, Figure 12 (b) shows overall efficiency map of the MDW in a 2D contour plot. The symbol 'A' shown in Figure 12 (b) indicates the design envelope in the wheel domain. The contour lines represent efficiency values at different wheel torques and speeds in terms of the speed ranges of the first and second stage. The scatter points are the operating points associated with the urban duty cycle (UDDS). Each number indicates the efficiency percent.

Clearly, it can be seen that the IWM design capacity covers all operating points. In addition, it is more efficient because it is possible to keep the IWM within the most efficient RPM range. Therefore, we can now suggest the IWM specifications which are appropriate to the driver (UDDS). Given four-independent IWMs, the power rating of the IWM will be 16 hp. Total effective power utilization rating of the EVs is 64 hp. The different g levels become [g.sub.1] = 0.3, [g.sub.2] = 0.3, [g.sub.3] = 0.15, and [g.sub.4] = 0.15. The 0-60 mph acceleration time becomes 15.2s. The weight of the IWM is estimated at 75 lb[8]. The optimal clutch shift point will be 35 mph.

In this case, we assume that the design envelope ('A') is related to the maximum torque, and the second quadrant (generator mode) is mirrored by the first quadrant (motor mode)[5]. Furthermore, the efficiency of controller and gear train is assumed to be one. For the purpose of analysis, the design envelope should cover all scattered operating points. In practice, for a short period of time, electric motors can be operated at higher than their designed power rating. According to [20], overload torque and power are acceptable for a couple of minutes and are limited by the inverter and battery maximum ratings. That is, the maximum torque is determined by the inverter current, and the maximum power is limited by the battery unless we also use a super capacitor.

B. US06 - How to Maximize Drivability in Terms of an IWM?

With the same scenario, the simulation results are shown in Figure 13 (a) regarding the wheel torque-speed curve of the MDW in correspondence with the speed range of the first and second stages. In the same manner, the design envelope is generated by different g levels: [g.sub.1] = 0.3, [g.sub.2] = 0.3, [g.sub.3] = 0.15, [g.sub.4] = 0.15. As seen at symbol 'A in Figure 13 (c), the scattered operating points exceed the MDW design capacity. Since the US06 represents the aggressive driver, the MDW design should focus on drivability such as acceleration, resulting in a higher power rating. In the next section, we show how to maximize drivability to meet the customer (US06) needs.

How to Maximize Drivability in Terms of the IWM?

In order to maximize drivability to meet the aggressive customer needs, the power rating of the IWM should be increased. Given the power rating of 32 hp with different g levels, simulation results are shown in Figure 14 to cover all operating points. Figure 14 (a) shows the wheel torque-speed curve of the MDW in correspondence with the speed ranges of the first and second stages. The clutch shift occurs at 20 mph (280 RPM). Before the clutch shift, given the gear ratio (49:1), the design envelope of 933 N-m in the wheel domain is translated into the design envelope of 19 N-m in the motor domain, as shown in Figure 14 (b). After the clutch shift, given the gear ratio (14:1), the design envelope of 408 N-m in the wheel domain is translated into the design envelope of 29.2 N-m in the motor domain, as shown in Figure 14 (c).

The curves seen at symbol 'B' represent the constant power region. Figure 14 (b) and (c) show the mapping of the wheel torque into motor torque with respect to the speed range of the first and second stage. In brief, compared to Figure 13, the power rating required increases from 16 hp to 32 hp. The different g levels become [g.sub.1] = 0.8, [g.sub.2] = 0.8, [g.sub.3] = 0.35, and [g.sub.4] = 0.35. The 0-60 mph acceleration time becomes 7 s. The overall efficiency is around 86.6%. It is apparent that US06 duty cycle has a lower efficiency than the UDDS duty cycle.

Figure 15 (a) shows overall efficiency map of the MDW as a function of wheel torque and wheel speed. Also, Figure 15 (b) shows the overall efficiency map of the IWM in a 2D contour plot. The symbol A' shown in Figure 15 (b) indicates the design envelope in the wheel domain. The contour lines represent an efficiency value at different wheel torques and speeds in terms of the speed range of the first and second stages. The scatter points are the operating points associated with the duty cycle (US06).

Clearly, it can be seen that the IWM design capacity covers all operating points. Therefore, we can suggest the MDW specifications which are appropriate to the driver (US06). Given four-independent IWMs, the power rating of the IWM will be 32 hp. Total effective power utilization rating of the EVs is 128 hp. The different g levels become [g.sub.1] = 0.8, [g.sub.2] = 0.8, [g.sub.3] = 0.35, and [g.sub.4] = 0.35. The 0-60 mph acceleration time becomes 7.4 s. The weight of each IWM becomes is estimated to be 110 lb.

V. Simulation Results

It is analytically demonstrated how the selection of the design components of the IWMs differs for different types of customers such as an aggressive driver vs. an efficiency-priority driver, and describe design specifications such as different g levels, gear ratio, clutch shift point, power rating etc. Comparison of an efficiency-priority driver and an aggressive driver is tabulated in Table 1.

Based on the customer-oriented duty cycle analysis, it is suggested that the IWM specifications are appropriate to the particular drivers such as an efficiency-priority driver and an aggressive driver as shown in Table 1.

Figure 16 shows the flow chart illustrating the visual approach to duty cycle analysis. Given the individual demand cycles for the particular customer, total wheel torque / speed / power are calculated. Depending on the customer's choice of two-wheels or four-wheels, motor output torque / speed / power are calculated. Knowing the efficiency map of the SRM based on copper, iron, windage, constant losses, we are able to obtain the motor input power demand. This leads to determining the battery size / super capacitor, controller technology which is left here as future work.

Given the Speed-Acceleration Frequency Distribution (SAFD), wheel torque-speed scatter and histogram, we do the mapping of the wheel torque into motor torque with respect to the speed range of the first stage and the second stage. In addition, the motor efficiency map is transformed into the needed speed range based on the rated power, different g levels, gear ratio, and clutch shift point.

The first decision question related to drivability is: 'is the design envelope covered?' The second decision question related to efficiency is: 'is the resulting efficiency acceptable?' If these two decision questions are satisfied, then we can make suggestions to the customer regarding the IWM specifications such as different g levels, gear ratio, rated power etc.

VI. Conclusions

The customer-oriented duty cycle analysis based on customer's individual demand cycle was proposed to describe the IWM specifications such as power ratings, weight of the IWM, g levels, gear ratio, clutch shift point, efficiency, 0-60 acceleration time, etc. The expanded choice for the customer can be characterized in terms of two basic operating regimes: drivability and efficiency. The IWM design procedure of how to maximize efficiency and drivability was developed and demonstrated to respond to the customer such as an efficiency-priority driver and an aggressive driver.

Once customers choose the EV equipped four-independent IWMs based on the individual demand cycle, the EV can be tailored to meet the needs of a particular customer, which leads to expanded human choice. In addition, this result in more optimized IWMs so that the customer can be best satisfied with their purchase.

In addition, by comparison with a single speed IWM, the MDW offers a 1.9x reduction in fuel losses for duty cycle US06 and a 2.2x reduction for UDDS by using a reconfigurable controller which expands and raises the efficiency sweet spot. Combined with the enhanced customer choices outlined in this paper, the MDW shows exceptional commercial promise. Lastly, the future work is to determine how to factor occasional use into the customer needs for the IWM such as occasional towing and moving from flat to hilly area. In addition, from the fault tolerance point of view, it gives a significant option when a partial failure occurs. The effects of the total/partial failure on performance criteria and operational decision making is to be analyzed in terms of the IWM [21].

REFERENCES

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Nomenclature

[m.sub.eg] - Total equivalent mass

[m.sub.v] - Sum of vehicle mass

[a.sub.x] - Longitudinal acceleration

[F.sub.aero] - Aerodynamic drag resistance

[F.sub.rolling] - Rolling resistance

[F.sub.grade] - Grade resistance

[F.sub.t] - Traction force

[F.sub.xi] - Traction force at i-th wheel (Front, Rear)

[R.sub.xF] - Rolling force at i-th wheel (Front, Rear)

[[rho].sub.a] - Air density

[A.sub.f] - Aera

[C.sub.d] - Aerodynamic coefficient

[v.sub.v] - Vehicle velocity

[v.sub.w] - Wind velocity

[C.sub.r] - Rolling coefficient

[N.sub.w] - Number of wheels

[I.sub.w] - Moment of inertia of the wheel

[I.sub.m] - Moment of inertia of the Motor

[r.sub.w] - Radius of the wheel

[g.sub.r] - Gear ratio

[[eta].sub.g] - Efficiency of the gear train

[[eta].sub.m] - Efficiency of the motor

[[tau].sub.m] - Motor torque

[n.sub.w] - Wheel rpm

[P.sub.m] - Motor power

[P.sub.tw] - Wheel torque

[[omega].sub.i] - Speed(rpm, m:motor, w:wheel)

[g.sub.r1] - Gearratio (49:1)

[g.sub.r2] - Gear ratio (14:1)

[n.sub.m1] - Motor speed associated with gear ratio [g.sub.r1]

[n.sub.m2] - Motor speed associated with gear ratio [g.sub.r2]

[n.sub.w1] - Wheel speed associated with gear ratio [g.sub.r1]

[n.sub.w2] - Wheel speed associated with gear ratio [g.sub.r2]

[P.sub.m1] - Motor power associated with gear ratio [g.sub.r1]

[P.sub.m2] - Motor power associated with gear ratio [g.sub.r2]

[[tau].sub.m1] - Motor torque associated with gear ratio [g.sub.r1]

[k.sub.c] - Copper loss coefficient

[k.sub.1] - Current loss coefficient

[k.sub.w] - Windage loss coefficient

[g.sub.i] - Normalized acceleration level at ith range

Hoon Lee

Hyundai Motor Company

Delbert Tesar

Univ of Texas-Austin

Pradeepkumar Ashok

University of Texas-Austin

CONTACT INFORMATION

Hoon Lee received his B.S. in Mechanical Engineering at the Chosun University, Korea, in 1998. After serving a military service as an ROTC officer, he worked as a maintenance engineer at Hyundai-Kia Motors for six years before joining the University of Mchigan at Ann Arbor. He then received his M.S.E. in Mechanical Engineering from University of Michigan at Ann Arbor, in 2008. After that, he received his Ph.D degree in Mechanical Engineering from the University of Texas at Austin, in 2012. He is currently working for Hyundai Motors in Korea.

Pradeepkumar Ashok received his B.Tech degree in production engineering and management from N.I.T, Kozhikode, India, in 1998. He received his M.S., 2002 and Ph.D. degree, 2007 in mechanical engineering from the University of Texas at Austin. He worked in

T.E.L.C.O., Pune, India, an automotive manufacturing company from 1998-1999. He currently specializes in system intelligence. He is the chief scientist and the program manager of the Robotics Research Group at the University of Texas at Austin.

Delbert Tesar has been active in robotics for some 45+ years. At the University of Texas at Austin, he has led the largest robotics research group in mechanical engineering at a United States university. To date, Dr. Tesar's program has generated 64 Ph.Ds and 158 Masters of Science, and he has written 90 position papers, 215 refereed conference and journal papers, and given more than 600 invited lectures. He also holds several U.S patents. Tesar has established a unique open architecture for robots and manufacturing cells to be assembled on demand using standardized actuators as building blocks on one universal system software to operate all assembled systems. He has shown a true commitment to national service as well, having served on various National Boards (AF, Army, NASA, etc.) for 30 years. Dr. Tesar's research has focused on the need to produce higher performance open architecture machines at lower costs for value added manufacturing to create new opportunities for U.S business development and employment. He is now Editor-in-Chief of the Intl. Journal of Actuators.
Table 1. Comparison of IWMs in terms of an efficiency-priority driver
and an aggressive driver

                         Efficiency-priority   Aggressive
                              driver             driver

Power ratings              12 kw(16hp)        24 kw (32 hp)
(Four-independent IWM)     48 kw (64 hp)      96 kw(128hp)
Weight of IWM              34 kgf (75 1b)     50 kgf (110lb)
g levels([g.sub.1]=         0.3, 0.15          0.8, 0.35
[g.sub.2],[g.sub.3]=
[g.sub.4])
Gear ratio ([g.sub.r1],    28:1, 14:1         49:1, 14:1
[g.sub.r2])
Clutch shift point         56kph (35 mph)     32kph(20mph)
Efficiency                 88.7%              86.6%
0-60 accel. time           15.2 s              7.4 s
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Author:Lee, Hoon; Tesar, Delbert; Ashok, Pradeepkumar
Publication:SAE International Journal of Passenger Cars - Mechanical Systems
Article Type:Report
Date:Apr 1, 2017
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