Whole body vibration and rider comfort determination of an electric two-wheeler test rig

Introduction

In India, the major mode of transportation is two-wheeled vehicles.¹ About 15 million two-wheeled vehicles were sold in India over the last 10 years on yearly basis.² Professionals like the food and goods delivery partners, low-wage employees, and post-delivery persons mainly use two-wheelers for their daily transportation.³ Two-wheeled vehicles, owing to limited size and mass are prone to vibration when compared to four-wheeled vehicles.⁴ Whole-body vibration (WBV) mainly affects these people who are in continuous exposure to noise and vibration throughout the day.^5,6 Truck drivers, drill operators, heavy machinery workers, and forklift drivers are the victims of these vibrations.⁷ High risks of lower back pain, motion sickness, and digestive system problems have been reported due to WBV when exposed for a longer period.^8,9

The whole body vibration of the vehicle is dangerous not only to the rider but also to the vehicle as well.¹⁰ In a vehicle exposed to different terrain conditions, the driving scenario is subjected to vibration, and these are transmitted to the human body through the seat, handlebar, and footrest in the case of two-wheelers.¹¹ These vibrations transferred to the human body cause different health issues in long run.^12,13 Some researchers are working on reducing these vibrations to effectively increase rider comfort.^14–17

A vehicle's comfort is influenced by many factors such as the seat design,¹⁸ driving posture¹⁹ and environmental factors,²⁰ road condition, and suspension system to name a few. In a two-wheeler, the rider’s comfort plays a very important role, as the rider has continuous exposure to these influencing factors. Both the static and dynamic condition of the vehicle are important in predicting the rider’s comfort.²¹ Different kinds of shock absorbers,²² and damping techniques²³ play a vital role in improving the rider’s comfort. Two-wheelers especially in the Indian scenario are very much subjected to vibration due to the condition of roads even in the cities.²⁴ The comfort level is greatly influenced by potholes, humps, cracks, and riding speed, and some study work has assisted in recognizing the potholes for safe driving.²⁵

The measurement of whole-body vibration in terms of human health and comfort, perception probabilities, and motion sickness occurrence is studied with the help of ISO 2631-1 standard.²⁶ It provides guidance on measurement techniques for periodic, random, and transient whole-body vibrations.²⁷ By getting the Frequency Response Function (FRF) at critical vibrational points, variable acceleration values at multiple spots were identified. The rider's comfort depends on these values of acceleration. The higher the value of acceleration lowers the rider's comfort. ISO 2631-1 standard provides different levels of comfort faced by riders depending on the acceleration values. Table 1 gives the detailed classification of the rider’s comfort level as per ISO 2631-1.

The present study involves finding the strategic locations of vibration and evaluation of rider comfort on an electric two-wheeler (E2W) test rig. Different points at the test rig are evaluated for their acceleration values in different running conditions. The points (locations on the body of test rig) at which the amplitude of vibration is higher than other locations are considered strategic points of vibration. The vibration at the strategic points is high enough to cause discomfort to the rider. The impact hammer test²⁸ is conducted using the PCB (Pico Coulomb) Piezotronics made impact hammer of sensitivity 10.1 mV/g and data acquisition by using NI LabVIEW.

Methods

Development of state space model

The electric two-wheeler test rig is modeled as a state space model for finding its natural frequencies. Performing the impact hammer test on the setup, the natural frequencies are obtained. The details of the work carried out are discussed in this section.

Test setup

The test setup is an electric vehicle two-wheeler test rig, which uses a 1.5 kW, brushless direct current (BLDC) traction motor powered by a 25AH LiFePO₄ battery. Figure 1 shows the photograph of different parts of the Electric two-wheeler (E2W) test rig (components sourced from Artis Technologies) and Table 2 gives the nomenclature.

Figure 1. Electric two-wheeler test rig.

Table 2. E2W test rig nomenclature.

Number	Part name
1	Electric panel
2	Wheel and the loading area
3	Traction motor
4	RPM sensor
5	Desktop with Sync sols EV lab Software
6	25 Ah Battery
7	Battery Modulator
8	NI Data Acquisition system
9	Suspension
10	Loading area
11	Base mount

Using the laboratory's setup, the E2W test rig is modeled as state space model.²⁹ However, to build a similar model, two considerations were made, which are briefly discussed here. The first thing to consider is the cylindrical steel roller of approximately 40 mm diameter and 200 mm in length beneath the test rig's wheel is used to simulate a real-life road surface. The roller used is a hard plastic material In this case, however, unlike the road and wheel, the roller causes a small vertical displacement to the wheel. As a consequence, the vertical displacement of the roller concerning the vertical displacement of sprung and un-sprung masses is estimated to be near zero or zero.^28,30 The second subject of consideration concerns the sprung and un-sprung masses. Sprung mass is the percentage of the vehicle's overall mass that is supported by the suspension. Un-sprung mass refers to the mass of the suspension, wheels, and other components that are directly connected to them. This implies that a vehicle's sprung mass is typically the vehicle's kerb weight, the weight of the driver, and in certain cases, the weight of the engine.³¹ A state space model of the E2W test rig is shown in Figure 2.³² The model nomenclature is indicated in Table 3. The acceleration values are measured by the PCB Piezotronics made accelerometers of 101.1 mV/g sensitivity and data acquisition is carried out through National Instrument’s LabVIEW software. (MyOpenLab is an open source alternative that can carry out a similar function). Three trials were conducted and the average values are considered for analysis.

Figure 2. Model of the E2W test rig.

Table 3. Test rig model nomenclature.

Variables	Description
M1	Un-sprung mass (tyre mass) – (kg)
M2	Sprung mass (Mass of test rig - Tyre mass) – (kg)
X1	Vertical displacement of M1 – (m)
X2	Vertical displacement of M2 – (m)
K1	Tyre stiffness – (N/m)
K2	Spring stiffness of vehicle suspension – (N/m)
C	Damping coefficient of the vehicle suspension – (Ns/m)
U	Vertical displacement of the roller – (m)

The free body and Laplace equations of the state space model derived are as indicated below in equations 1, 2 and 3, 4 respectively:

(1)

$${\mathrm{m}}_2{\ddot{x}}_2+\mathrm{c}\left({\dot{x}}_2–{\dot{x}}_1\right)+{\mathrm{k}}_2\left({\mathrm{x}}_2–{\mathrm{x}}_1\right)=0$$

(2)

$${\mathrm{m}}_1{\ddot{x}}_1+\mathrm{c}\left({\dot{x}}_1–{\dot{x}}_2\right)+{\mathrm{k}}_2\left({\mathrm{x}}_1–{\mathrm{x}}_2\right)+{\mathrm{k}}_1\left({\mathrm{x}}_1-\mathrm{U}\right)=0$$

Laplace equations

(3)

$${\mathrm{X}}_2\left(\mathrm{s}\right)\left[{\mathrm{M}}_2{\mathrm{S}}^2+\mathrm{CS}+{\mathrm{K}}_2\right]={\mathrm{X}}_1\left(\mathrm{s}\right)\left[\mathrm{CS}+{\mathrm{K}}_1\right]$$

(4)

$${\mathrm{X}}_1\left(\mathrm{s}\right)\left[{\mathrm{M}}_1{\mathrm{S}}^2+\mathrm{CS}+{\mathrm{K}}_2+{\mathrm{K}}_1\right]={\mathrm{X}}_2\left(\mathrm{s}\right)\left[\mathrm{CS}+{\mathrm{K}}_2\right]+\mathrm{U}\left(\mathrm{s}\right)\left[{\mathrm{K}}_1\right]$$

Figure 2 shows the state space model of the E2W test rig and the corresponding notations as indicated in the figure. Here, the governing system equation of the test rig (1 & 2) are derived to get the Laplace equations (3 & 4).

Figure 3 shows the magnitude vs frequency plots of the impact hammer test conducted on the E2W test rig. The plot obtained from the NI LabVIEW, 2016³³ shows the natural frequency of the test rig as obtained at two strategic points on the test rig as shown in Figure 3. The peaks in the graphs indicated the natural frequency of the rig. The average of the natural frequency obtained is shown in Table 4.

Figure 3. Impact hammer test on E2W test rig (a,b,c,d - Loading area- left back, right back, left front, right front), (e,f,g,h – Base mount – left back, right back, left front, right front).

Table 4. Average of natural frequencies.

Frequency (Hz)	Magnitude (g)
180.225	6.338
575.36	11.37
786.942	7.03

Obtaining acceleration using LabVIEW

National Instruments’ LabVIEW 2016 (64-bit) software is used to extract the acceleration values through accelerometers along with conversion of raw acceleration values into RMS acceleration. Some open software like ‘MyOpenLab’ or PyLab_Works can be used for data acquisition as well. Fast Fourier transform (FFT)³⁴ is used to obtain the root mean square (RMS) acceleration values at the strategic locations. Using LabVIEW, the RMS acceleration is obtained using spectral analysis provided in the software.

The test setup is tested under different loading conditions such as kerb load, 5 kg load, and 10 kg load. This type of loading makes a machine or a material get stiffer as the load increases.³⁵ PCB Piezotronics made accelerometers are mounted at four strategic locations of vibration as indicated in Figure 1; the loading area, traction motor, suspension and the base mount of the rig. RMS acceleration, at these strategic locations, is recorded using LabVIEW programming. These values are then sorted using MS Excel to find the peak values at each interval and graphs are plotted to show the RMS acceleration vs frequency characteristics as shown in Figure 5.

No load condition of the electric two-wheeler test rig is conducted without adding any payload. This condition reveals the strategic location of the test rig and allows identifying the major vibration amplitude regions. Adding payload of 5 kg and 10 kg the mechanical vibration characteristics of the test rig changes showing different vibration patterns. This pattern of vibrations is studied in order to obtain the dangerous frequencies and amplitudes. Strategic locations especially the loading area, corresponds to rider’s seat in an actual two-wheeler and hence ISO 2631 standard is compared in this study.

Drive cycle

The drive cycle used for the study is shown in Figure 4. Different scenarios like idling, acceleration, steady speed, and deceleration are shown in the graph. The drive cycle runs each of these scenarios for a particular time duration. The cycle begins with a preparation speed-up period of 5 seconds, followed by 20 seconds of idling, 18 seconds of acceleration, and 2 seconds of steady speed. The cycle then decelerates for the next 11 seconds, a combination of acceleration and steady speed for the next 7 seconds, decelerates for the next 30 seconds, idles for the next 11 seconds, and ends with 3 seconds of halting. The values of acceleration are recorded at the strategic locations during this cycle.

Figure 4. Drive Cycle.

Results and discussion

In this study, major strategic locations of vibrations in an electric two-wheeler test rig are found. The vibration response from the strategic locations indicates the rider’s comfort through RMS acceleration values. As compared to ISO 2631, the results obtained are discussed in detail in this section.

Observing, the RMS acceleration at the loading area as shown in Figure 5, it is noted that the vibration amplitudes are higher at no load condition when compared to loading condition viz. 5 kg and 10 kg. This is due to the shift of frequency observed in the loading area. Figure 6 indicates the frequency shift occurred at the loading area. Addition of loads caused changes in the dynamic characteristics of the system and resulted in mismatch between the excitation frequency and system’s natural frequency. This mismatch has caused the decrease in the vibration amplitudes.

Figure 5. RMS Acceleration at the strategic locations.

Figure 6. Effect of loading on RMS accelerations.

However, at the traction motor, suspension and base mount of the test rig it is found that, the vibration amplitudes increased slightly with loading. This is due to the reason that, the added mass has changed the natural frequency of the system and allowed the system to oscillate in the new oscillation frequency. The change in stiffness of the system has caused this increase in vibration.

Observing, the maximum RMS acceleration values as shown in figure 6, at the loading area, as the frequency shifted from 224 Hz to 85 Hz on loading, the vibration amplitude decreased to about 93 % from 3.28 to 0.22 m/s². On further loading the system with 10 kg, the frequency changed to 69 Hz with an amplitude of 0.165 m/s². Hence, comparing these values with ISO 2631 as given in table 1, the comfort category has moved to comfortable region from extremely uncomfortable region after loading.

At traction motor, the vibration amplitude increased to about 27 % and 34 % on addition of 5 kg and 10 kg respectively. Whereas, the frequency shift was not very much pronounced. Comparing with table 1 this strategic location is safe and falls under not uncomfortable region.

At the suspension, about 33 % of increase in the vibration amplitude from 0.78 m/s² to 1.04 m/s² is observed after loading the test rig with 5 kg. And further increased to 1.31 m/s² at the load of 10 kg. Comparing the results with the ISO 2631 standard, this location falls under uncomfortable region.

At the base mount of the test rig, about 6 % increase in the vibration amplitude is observed on addition of 5 kg on the test rig and about 19 % on addition of 10 kg of weight. However, the peak frequency was found to be same throughout. Fairly uncomfortable vibration intensity is observed at this location when the values are compared with ISO 2631 standard.

Conclusions

A detailed experimental analysis of finding the strategic locations of vibration is discussed in this paper. The acceleration values play an important role in deciding the rider’s comfort. Electric two-wheeler, even though a cost-effective mode of transportation, require further research in improving rider comfort. Observing the different strategic locations of vibration at the test rig the following conclusions are drawn from this study.

At the loading area, no load vibration is found to be extremely uncomfortable and further these vibrations reduced after the addition of weights at the test rig. This phenomenon is observed due to the shift of excitation frequency from the working frequency of the system. The traction motor vibrations are found to be safe at the operating region at no load as well as loading conditions. The suspension and the base mount of the test rig is found to be uncomfortable. Further, comparing the natural frequency of the test rig from table 4, the operating frequency at base mount of the test rig which is 181 Hz, is close to the natural frequency (180 Hz). This indicates a necessity of incorporation of a suitable damping technique at these locations.

As the speed increases, the vibration intensity increased as well. This is due to the wheels running on the roller support, which simulates an actual road scenario. Hence, it can be concluded that in the actual driving scenario of a two-wheeler the vibration increases as the speed of the vehicle is increased. Further, the condition of the road is again an influencing factor, which increases the vibration intensity.

Overall study indicates that the electric two-wheeler is subjected to vibrations is an important area to be considered for further research work and this can be reduced by using suitable damping techniques at the strategic locations of vibrations.