Determination and Evaluation of a Three-Wheeled Tilting Vehicle Prototype’s Dynamic Characteristics

Abstract

When a new vehicle is being developed, the parameters of the electric motor, battery modules, and control algorithms have a significant impact on its dynamic characteristics. This paper presents a method of determining the dynamic characteristics of a three-wheeled tilting vehicle created by AKO team. In order to achieve this, the acceleration values in theoretical calculations were determined and were verified by experimental field tests using a three-wheeled vehicle prototype. Theoretical calculations include the determination of speed, dynamic factor, air resistance, and traction force. The theoretical calculation of the above-mentioned dynamic factors also involves the experimental determination of the drag coefficient, which was performed in a wind tunnel using a scaled-down (1:16) three-wheeled vehicle model. Field tests were conducted to determine acceleration data using two accelerometers, one of which was used for the synchronization of the calculated acceleration data with experimentally obtained acceleration data. Obtained data from very sensitive accelerometer were filtered using a Butterworth second-order low-pass filter. Results show compliance between the calculated and measured accelerations, which means that theoretical calculations were verified by experimental measurements.

1. Introduction

Motorized tilting land road vehicles with more than two wheels have been studied and developed since the beginning of the 1950s. There have been many other attempts since the prototype was proposed by Ernst Neumann [1] in 1945–1950.

Later on, in the middle of the 1950s, the Ford Motor Company presented a gyroscopically stabilized two-wheeled lean vehicle (called Gyron) with retractable wheel pods for parking. In the 1960s, the MIT proposed a tilting vehicle similar to a motorcycle but equipped with active roll control. At the beginning of the 1970s, General Motors presented the Lean Machine, characterized by a fixed rear frame and a tilting body module that was controlled by the rider by using foot pedals to balance the tilting body [2].

These projects were confined to the field of research and therefore were far from the stage of mass production. Therefore, the interest in these kinds of vehicles petered out, even though new configuration proposals continued to be made [1].

After a small period of time, innovators focused on this idea again, and some of them were successful. For example, there was a vehicle that was produced and commercialized in the UK by the BSA Company in 1971. The project was then acquired by Honda, which produced the Honda Gyro model at the beginning of the 1980s.

Recently, the problems of pollution, energy consumption, vehicle cost, and traffic congestion and the progress of control system technology has created new interest in narrow commuters for individual mobility [3].

Later, different producers were developing these ideas and created models such as F 300 Life-Jet [4], Clever [5], Carver One [6], and MP3 [7]. Additionally, some of them chose different types of construction but concentrated on the small city vehicle segment Triggo [8]. In this decade, popular examples are NIU TQi-GT [9] and Deliverator [10], created by Arcimoto.

Most of these three-wheeled vehicles can be divided into two groups: those with a front axle consisting of two wheels and those with a front axle consisting of one wheel. There are two groups of tilting technologies: tilting just the front axle or tilting the whole vehicle. However, the main differences affecting the dynamic characteristics are the tilting angle and the steering mechanism.

Mobility is an essential activity in modern society, and it relies on vehicles. Currently, the energy consumed by vehicle transportation accounts for over 25% of the global energy consumption due to the rapid progress of motorization throughout the world [11].

The primary focus of the automobile industry is to develop more efficient, safer, and eco-friendly transportation systems [12,13].

There are few studies that present three-wheeled vehicles using deep research and the determination of dynamic characteristics.

Research conducted by Al-jameel and Abdulamer [14] shows that a particular percentage of three-wheeled vehicles, especially in urban use, can improve traffic flow speed. Therefore, these vehicles should be improved and offered to a wider number of potential users.

Electric vehicles have recently received a lot of attention due to their being classified as zero-emissions vehicles, in addition to having a higher energy efficiency than comparable internal combustion vehicles. It is well known that driving parameters such as harshness of acceleration have an impact on the fuel economy [15,16] and that changes to driving behavior can influence it [17].

Many studies have investigated the acceleration and deceleration of traffic movement based on different types of vehicle, as well as individual models for separate systems analysis [18,19,20,21,22,23]. However, for optimized traffic flow, parallelly extending vehicle types is not only friendly for environment but also provides good dynamic characteristics without sacrificing passenger and pedestrian safety.

Dynamic characteristics are one of the goals where producers of new vehicles are competing. Therefore, there are a lot of different theoretical and experimental methods to determining and evaluating these characteristic [19,20]. These methods, on one hand, are unified, and on the other, they are also evolving. According to this attitude, each vehicle designer and manufacturer is trying to find the best methods for determination and verification.

It has been predicted that the prevailing COVID-19 situation will result in an increased demand for personal vehicles. There is a renewed interest in three-wheeled vehicles for short urban mobility in Western countries due to their inherent cost advantages, which will make it affordable for the common person [24].

A problem for electric and hybrid vehicles is powertrain control, which is focused on the major challenge of power distribution among the energy sources, i.e., the energy management strategy. Many advanced techniques have been published concerning this challenging issue [25,26].

There are technical safety requirements that are presented in SAE technical papers. If they are achieved, then three-wheeled vehicles can offer safe alternatives to four-wheeled vehicles [27].

The present research discusses the optimal control of hybrid electric vehicles [28]. One of initial conditions is to accurately determine vehicle acceleration, which later can be corrected to fit the best performance not only for the fastest acceleration but also for best comfort for drivers and passengers.

Previous studies show that using the rational design of energy optimization strategies, the working points of the main power components can be optimized, thus enhancing energy efficiency when driving vehicles [29,30,31]. Therefore, all vehicles should be precisely tested in each phase of project, especially safety and driving properties.

He, Cao, and Cui in 2020 [32] presented vehicle acceleration strategies based on the optimization of energy consumption. The results of the case study show that energy consumption in the acceleration process can be effectively reduced using the strategy’s control and with the acceleration time being extended within an appropriate range. Energy-saving potential is better, especially under low target-velocity conditions. The strategies obtained by the two algorithms can achieve almost the same energy-saving potential.

Research shows that when the electric vehicle (EV) accelerates on a good road, energy consumption and battery capacity loss mainly depend on acceleration and vehicle velocity, vehicle velocity can be expressed by acceleration and acceleration time, and then acceleration and acceleration time can be characterized by the acceleration curve. Therefore, finding a suitable acceleration curve is extremely important in order to reduce EV energy consumption and extend battery life [33].

Acceleration is one of most important parameters of a vehicle’s dynamic characteristics of its driving cycle; it affects not only traffic flow speed and pollution, but also battery discharging level [34]. Basically, with optimized acceleration parameters (including the driver factor), the vehicle can reach cruising speed faster, which leads to the best performance in terms of traffic flow.

According to research, different age groups choose different levels of acceleration. Higher acceleration does not always lead to more accidents, but sometimes can solve traffic jam problems [35]. We also should not forget that improvements in vehicle quality have enabled the use of emotional satisfaction as an important criterion for vehicle selection as a dynamic characteristic [36].

In sum, three-wheeled vehicles, like other vehicles other must go through long stages of improvement. To do this, many optimization processes must be completed, such as optimal determination of the vehicle’s dynamic characteristics. Additionally, each step must be verified with experimental tests. Therefore, this paper presents unified theoretical and experiment methodologies and their results.

2. Three-Wheeled Vehicle Description

The Lithuanian EV startup AKO presented new type of three-wheeled tilting vehicle in 2020 (Figure 1) [37].

This two-seater electric three-wheeled tilting vehicle is now at the second-generation prototype stage and features a novel tilting mechanism. Turning the steering wheel also turns the two front wheels, which is sufficient for turns at slow speed. At higher speeds, the driver can lean the steering column from side to side, which causes the entire trike to lean to each side by 30° during turns, similarly to a typical motorcycle. The tilting mechanism was designed by the AKO team and is currently patent-pending [37].

2.1. Theoretical Determination of Acceleration

The goal of this paper is to obtain theoretical acceleration results and verify them with experimental results using the prototype model MVP, which was built by the AKO team. According to this information, parameters for the electric motor and battery control module are chosen to optimize the three-wheeled tilting vehicle’s dynamic characteristics. The first step is to acquire parameters of the electric motor (HPM-2000) (power and torque) using manufacturers’ data (Figure 2) and three-wheeled tilting vehicle characteristics (body dimensions, weight, etc.) (

Table 1. Three-wheeled vehicle characteristics.

Nr.	Parameter	Symbol	Dimension	Value
1.	Gear ratio	ipp	-	4.365
2.	Transmission efficiency coefficient	ηtr	-	0.93
3.	Three-wheeled tilting vehicle mass with driver	Ga	kg	486
3.1.	Mass to drive axle	G2	kg	212
4.	Three-wheeled vehicle mass without driver	G0	kg	406
4.1.	Mass to drive axle	G02	kg	177
5.	Front axle wheel base	Ba	m	0.892
6.	Height	Ha	m	1.6
7.	Wheels dimensions	B–d	-	R17 170/60

).

The battery consists of two series-connected LG Electronics LiMM-C.F/LGE (Model Name: Vista 2.0 Cell Module Assembly) modules with a rated energy capacity of 5.94 KW h and a rated voltage of 36 V each. The motor controller and other used parts and their solutions, as well as their parameters, are not presented by the AKO team in terms of a unique construction.

For the theoretical determination of acceleration, a classical methodology presented by Gillespie [39] was used.

The three-wheeled tilting vehicle speed is calculated as follows:

$$v_a=\frac{w_e·r_r}{i_{pp}};$$

(1)

where w_e—engine rotations, rad/s;

r_r—radius of rotating wheel, m.

i_pp—gear ratio.

In our case, the radius of rotating wheel (r_r) is 0.2579 m and tire deformation coefficient λ = 0.93.

The traction force of the three-wheeled vehicle is calculated as follows (N):

$$F_r=\frac{M_e·i_{pp}·i_{pd}·{\eta }_{tr}}{r_r};$$

(2)

where M_e—engine torque, Nm;

i_pd—transmission gear ratio (i_pd = 1);

η_tr—transmission efficiency coefficient.

The radius of rotating wheel diameter is calculated (r_r = 0.2579).

The equation of traction balance is as follows:

$$F_r=F_f\pm F_i+F_o+F_j;$$

(3)

where F_f—rolling resistance force, N;

F_i—uphill resistance force, N;

F_o—air resistance force, N;

F_j—acceleration resistance force, N.

If we are analyzing a case in which the three-wheeled tilting vehicle moves at a constant speed on a horizontal surface, then the equation of the traction balance is:

$$F_r=F_f+F_o;$$

(4)

Rolling resistance force:

$$F_f=G_a·f;$$

(5)

where f—rolling resistance coefficient depending on the road surface.

In our case, a hard asphalt-concrete surface was chosen (f = 0.016). Air resistance force:

$$F_o=K·S·V_a^2;$$

(6)

where K—drag coefficient;

S—front part surface area, m².

Front parts’ surface area:

$$S=0.6·B_a·H_a;$$

(7)

where B_a—front axle wheel base, m;

H_a—height, m.

The drag coefficient is usually determined by vehicle producers, but in this case, the design is created by an AKO team, and coefficient (K) should be determined experimentally. For this solution wind tunnel were used (Figure 3).

The test chamber is the most important part of the wind tunnel. The dimensions of the square-shaped test chamber are 0.5 × 0.5 m and 1 m in length, with walls made of 2 mm high-quality clear polycarbonate and a bottom made of 5 mm organic glass. Two weight scales, mounted at the bottom of the test chamber, were used for measuring vehicle air resistance and the clamping force of the three-wheeled vehicle, which is expressed in units of weight (grams). The maximum measured weight of these scales is 0.3 kg, with an accuracy of ±0.01 g. The chamber has a built-in air flow speed and temperature sensor. The diffuser is the part connecting the test chamber and the fan. Its shape varies from square to round (Ø0.720 m).

The air flow rate in the diffuser decreases, and the pressure increases. The speed in the diffuser must decrease in order to minimize the energy losses. Due to the minimal energy losses the maximum pressure being guaranteed. The blower fan is mounted at the end of the wind tunnel. Its impeller is rotated by an electric motor. The electric motor power is 1.8 kW, and it is controlled by a frequency converter with frequencies from 0 Hz to 70 Hz. The maximum generated airflow rate is approximately 22 m/s. The fan flow at 60 Hz is 19,000 m³/h, and the impeller speed is 1715 min⁻¹.

During the experimental testing, the scaled-down (1:16) model of the three-wheeled tilting vehicle (Figure 4) was placed in the test chamber to identify the air resistance. During the tests, the data were recorded at 9 frequency values, with different, increasing fan speeds from 30 Hz to 70 Hz. During the tests, the air flow rate (m/s), temperature (°C), three-wheeled air resistance force (N), and clamping force (N) were recorded. For more accurate results, the experiments were repeated for 4 cycles. The obtained data are presented in

Table 2. Air resistance measurements results.

Cycle	Test Number	Hz	Wind Speed, m/s	Air Temperature, °C	Clamping Force, N	Air Resistance Force (Fo), N
1	1	30	10.6	15.6	1.2	20.2
	2	35	11.9	15.6	6.8	27.1
	3	40	13.3	15.6	7.8	33.6
	4	45	14.7	15.3	9.5	38.8
	5	50	15.9	15.1	10.6	51.9
	6	55	16.1	15.6	12.8	56.9
	7	60	16.9	15.7	23.6	60.9
	8	65	17.6	15.5	26.4	62.6
	9	70	18.3	15.6	27.8	64.5
2	1	30	9.2	15.4	5.8	11.9
	2	35	11.3	14.5	2.2	17.4
	3	40	12.9	13.6	7.5	24.2
	4	45	13.4	13.3	15.8	33.4
	5	50	15.3	13.1	13.6	38.5
	6	55	15.9	12.9	20.7	47.6
	7	60	16.7	12.7	24.6	56.2
	8	65	17.2	12.6	26.3	64.4
	9	70	17.4	12.7	25.8	66.7
3	1	30	9.3	13	4.8	12.1
	2	35	10.9	12.9	9.1	19.3
	3	40	12.4	13	11.3	26.4
	4	45	14.1	13	9.8	34.8
	5	50	15	12.4	14.5	41.8
	6	55	15.7	12.3	22.4	49.5
	7	60	17	12.6	24.8	57.4
	8	65	17.3	12.5	26	62.8
	9	70	18,5	14.7	28	64.4
4	1	30	9.7	14.3	8.5	12.9
	2	35	11	14.3	9.5	17
	3	40	12.3	15	10.6	24.4
	4	45	13.6	14.6	14.2	29.6
	5	50	14.6	14.6	13.3	40.9
	6	55	15.9	15.5	23.5	43.6
	7	60	17.2	14.2	22.9	56.6
	8	65	17.6	14.4	26.9	60.6
	9	70	18.1	14.9	29.8	62.5

.

Using Formula (6), the drag coefficient (K) was calculated at different speeds in the wind tunnel: 50 Hz—0.0968; 55 Hz—0.100; 60 Hz—0.103; 65 Hz—0.106; 70 Hz—0.102. The average of the drag coefficient is 0.102, which was used for the following calculations.

The dynamic characteristic of a vehicle is called the graphical dependence between the dynamic factor (D) and the speed (v_a) of the vehicle. The dynamic factor is calculated according to the formula:

$$D=\frac{F_r-F_o}{G_a};$$

(8)

The acceleration of the vehicle (m/s²) is calculated, assuming that the vehicle with the driver accelerates on a horizontal road (i = 0) with a hard asphalt–concrete surface (f = 0.016) in the absence of wheel slip, according to the formula:

$$j=\frac{D-f}{\delta }·g;$$

(9)

where g—gravity acceleration, 9.81 m/s²;

δ—coefficient estimating the rotating masses of vehicle.

$$\delta =1.05+0.07·i_{pd}^2;$$

(10)

In our case, the internal combustion engine is changed in an electric motor, so we must use δ = 1.

All previous dynamic parameters are calculated according to Formulas (1)–(10) and are presented in

Table 3. Calculated three-wheeled tilting vehicle theoretical dynamic characteristics.

Parameter	Values
va, m/s	3.55	7.09	10.64	14.19	17.74	21.28	24.83
Fr, N	1142.66	1142.66	1142.66	1142.66	1127.625	962.24	902.1
Fo, N	1.22	4.88	10.98	19.50	30.48	43.90	59.73
D	0.2394	0.2386	0.2374	0.2356	0.2301	0.1926	0.1767
j, m/s2	2.19	2.18	2.17	2.15	2.10	1.73	1.58

.

2.2. Experimental Determination of Acceleration

An aircraft runway was chosen to conduct the experimental field tests. To determine the acceleration, two different accelerometers (Dragy GP Meter and Vernier Wireless Dynamic Sensor), which were mounted on a three-wheeled vehicle center part were used. Measurements were performed while the vehicle was accelerating with two acceleration measurement devices; one of them was used for filming and measuring (Dragy GP Meter), and the Vernier Wireless Dynamic Sensor was used for measuring and using data for analysis. Obtained acceleration data are presented in Figure 5 and Figure 6, which presents a test drive for acceleration measurements. Filtered data were obtained using the Butterworth second-order low-pass filter, which is usually used for the filtering of electric signals. The noise in the obtained data is related to the sensitivity of the measuring equipment, which was used for the determination of the three-wheeled vehicle acceleration (Figure 5 and Figure 6).

Test drive took 9.5–10 s, because the main goal was to determine the acceleration values of the three-wheeled tilting vehicle and use them for verification of the theoretical calculation.

The obtained acceleration data (Figure 5 and Figure 6) show similar results in both tests: the maximum accelerations are in the time period from 1.4 s to 4.5 s, after which it varies from 2.18 m/s² to 2.4 m/s². To precisely analyze these accelerations, we need to eliminate the 1.3 s (beginning) and 1.4 s (end) time periods, which were when the three-wheeled tilting vehicle started and ended acceleration process, because measuring devices are very sensitive and since it takes 1.3 s at the beginning to reaching the acceleration. The same is true at the end, when the three-wheeled vehicle is not accelerating. Another aspect is that when acceleration measurements were filtered, we also eliminated the maximum values at 4.2 s, when it reached more than 7 m/s² (Figure 5) and more than −2 m/s². These discrepancies were found in both experimental results and were possibly caused by the accelerometer being too sensitive, which in the same place gave values of acceleration that were different and too big.

Comparing the experimental and calculated acceleration results shows that the maximum range of accelerations at the beginning, from 1.3 s to approximately 4.5 s, were similar (Figure 7 and Figure 8). The calculated accelerations values (Table 3) were synchronized with driving speed data obtained from the Dragy GP Meter accelerometer. In this synchronizing stage, the time periods were converted from the driving speed range presented in Table 3 and the data obtained from the Dragy GP Meter accelerometer.

The calculated accelerations, presented in Figure 7 and Figure 8, were converted similarly for these time periods as those mentioned above according to the synchronized data: 1.31–2.34 s—2.19 m/s²; 2.35–3.38 s—2.18 m/s²; 3.39–4.42 s—2.17 m/s²; 4.43–5.46 s—2.15 m/s²; 5.47–6.50 s—2.1 m/s²; 6.51–7.54 s—1.73 m/s²; 7.55–8.58 s—1.58 m/s².

The time period after 4.5 s is visible; according to the compared data, the difference between the calculated and the measured data is growing, and experiment on the test drive should be repeated, or accepted, because the difference between the measured and calculated data is approximately 0.5 m/s².

3. Results and Discussion

The presented determination and evaluation of the three-wheeled tilting vehicle made by the AKO team reveals dynamic characteristics that can help to improve future versions of it, especially versions using other electric motors and a control algorithm.

Using a three-wheeled vehicle scaled-down model (1:16) and a wind tunnel, the drag coefficient (K = 0.102) was determined experimentally, which was used for the dynamic calculations.

The vehicle max speed (v_max = 24.83 m/s) and range of acceleration, which varied from 2.19 m/s² to 1.58 m/s², were obtained according to three-wheeled tilting vehicle body’s dimensions and the electric motor (HPM-2000) used.

The case was analyzed in which the three-wheeled vehicle moved at constant speed on a horizontal surface with traction force (F_r) varying from 1142.66 N to 902.1 N and an air resistance force (F_o) of 1.22 N–59.73 N, when the speed changed accordingly from 3.55 m/s to 24.83 m/s.

The calculated accelerations values, which were synchronized with driving speed data obtained from the Dragy GP Meter accelerometer and compared with experimentally obtained acceleration results, show that the max acceleration range at the beginning, from 1.3 s to approximately 4.5 s, was similar (difference in all the ranges is smaller than 0.5 m/s²).

By comparing the time period after 4.5 s, it is determined that, according to the compared data, the difference between the calculated and the measured data is growing, and experiment of the test drive should be repeated or accepted because the difference between the measured and calculated results differs by no more than 0.5 m/s². This difference might be affected by the fact that accelerometer data are too sensitive and by the used second-order low-pass Butterworth filter that was used, which, after 4.5 s needed to filter a wide range of acceleration data.

4. Conclusions and Future Research

The obtained results show that this method of determining dynamic characteristics is accurate enough for validating and performing the selection of powertrain components for the three-wheeled tilting trike being developed. The powertrain components of the new P150 model prototype were selected according to this method.

The next step for the research will be to determine the aerodynamic three-wheeled vehicle’s dynamic characteristics using other (more powerful) electric motors and by combining control algorithms to reach better dynamic characteristics such as acceleration, top max speed, etc. Another study should include experimental driving tests and calculations involving tilting the three-wheeled tilting vehicle at different angles.