Analysis of vehicle ride comfort applying a 2SPS+SR parallel seat mechanism

Abstract

The violent vibration may cause discomfort to the driver and operation instability in different directions including fore-aft, lateral, and vertical when construction vehicles are driven or operated on off-roads. To improve ride comfort, a novel kind of 2SPS+SR parallel seat mechanism is proposed in this article. First, to verify the motion state of one translation and two rotations, the model of this new seat mechanism was built and analyzed using UG software. Furthermore, the acceleration and power spectrum density between the conventional seat and the 2SPS+SR parallel seat were compared in three directions of vertical, pitching, and rolling when the vehicle was driven on different three-dimensional roads. Then, the comparisons of the weighted vibration level and the root mean square of the total weighted acceleration on different roads were illustrated to denote the ride comfort of the construction vehicle. The results show that this 2SPS+SR parallel seat mechanism could improve the ride comfort of construction vehicles. The results will provide theoretical support for further research on the control of vehicle vibration.

Keywords

Construction vehicle ride comfort 2SPS+SR parallel seat mechanism three-dimensional roads root mean square of the total weighted acceleration

Introduction

Construction vehicles often work on off-roads; thus, vibrations from different directions including the fore-aft, lateral, and vertical will happen. And these vibrations are mostly centered in the range of 0–20 Hz.¹ In addition, the related research studies have shown that the human organs are sensitive to the vibrations whose frequencies are located between 4 and 12.5 Hz. The violent vibrations not only have an effect on the lifespan of mechanical structures of vehicles but also lead to mental and physical exhaustion of drivers, operational instability, and the risk of traffic accidents. So, how to reduce the vibration and improve the ride comfort has become an important issue in the field of construction vehicles.

At present, the ride comfort of various vehicles, including cars, tractors, ambulances, high-speed trains, and so on, has been emphasized.^2–4 For example, Xia et al. evaluated the smoothness of vehicles from different perspectives based on various methods.⁵ Wang et al. conducted a simulation to evaluate the smoothness of the vehicle, and the results show that the comfort of the vehicle is good on the random road and pulse road.⁶ Zhou established a half-car model with eight degrees of freedom and evaluated the ride comfort of the vehicle with the method recommended by ISO 2631-1:1997 (E).⁷ Wang et al. put forward a kind of new mechanical elastic tire used for vehicles and analyzed the structure and ride comfort of vehicles on the new mechanical elastic tire, which shows that the vehicle including the new mechanical elastic wheel meets the comfortable requirements and ride comfort regularity of the pneumatic tire.⁸ Kwon proposed a wheelbase preview active suspension control algorithm with a disturbance-decoupled observer and a wheelbase preview control method to better improve the smoothness of vehicles compared with the feedback control method.⁹ Li et al. studied the ride comfort of a supine patient and driver by the multi-objective genetic algorithm through establishing a 10-degree-of-freedom ambulance model including an ambulance, stretcher, supine patient, and driver.¹⁰ He et al. proposed a ride comfort optimization method based on nonlinear damping of suspension and intelligent algorithms, which could decrease the root mean square (RMS) of dynamic tire load of front and rear wheels and thus improve the ride comfort of passenger cars.¹¹ Gedik et al. investigated the effect of parabolic speed hump profiles on ride comfort and driving safety under variable vehicle speeds, which proved that vehicle speed and parabolic speed hump height were the most important parameters that affect ride comfort and driving safety.¹² The above research studies can provide a good reference for this article, but there are few research studies on the complex and harsh “off-road”, on which the construction vehicles often walk. In addition, most of the existing studies only emphasized that the vertical movements affect ride comfort and driving safety while ignoring the fore-aft and lateral vibrations.

At the same time, because the construction vehicles must have higher request for the load bearing capacity, they generally have larger suspension stiffness. Furthermore, some of them even do not have suspension. Now, it is a more common way to use a certain kind of seat suspension to attenuate the vibration from the cab to the driver. Here, it must be pointed out that the parallel mechanism seats have been used owing to their multidimensional vibration-reducing performance. For example, Zhang et al. constructed a 3-rotating pair, prismatic pair, cylindrical pair parallel mechanism and studied the transfer characteristics of three-axial acceleration and impulse response of the system, which proved that the three-axial resonance frequency can avoid the sensitive frequency of the body and the frequency of vehicle suspension and tires.¹³ Wu et al. designed a 3-prismatic pair, rotating pair, rotating pair, prismatic pair parallel mechanism and demonstrated that it can avoid the sensitive frequency of the human body and make the operators have a better ride comfort by modal analysis.¹⁴ Sajjad et al. built a novel linearly actuated 4-DOF parallel kinematic machine, which had three translational and one rotational motion abilities.¹⁵ Yang built a new vehicle seat with 3-DOF suspension based on the multidimensional movement principle of the parallel mechanism and established a kinematics model to analyze the theory of the displacement of the parallel vehicle seat system, which has a good effort on vibration reduction.¹⁶ Li and Staicu built a (3-PRC) parallel kinematic machine and investigated mainly the dynamics of this parallel mechanism to solve the control of the motion of such a robotic system successfully.¹⁷ However, there are few studies about the influence of the parallel mechanism seats on the driver’s comfort when the vehicles are working on the three-dimensional roads until now.

Based on the above research studies, a new kind of 2SPS+SR parallel seat mechanism is put forward and applied to construction vehicles in order to reduce the vibration of the vehicle from different directions. At first, the vertical-pitching-rolling movements of the designed seat mechanism are verified. Afterward, the vibration-reducing performances in time and frequency domains are analyzed. At last, the total weighted RMS of acceleration and vibration level are calculated in order to grasp the ride comfort of the vehicle. In addition, this study expands the application scope of the parallel mechanism and provides a method to improve the comfort of construction vehicles.

2SPS+SR seat mechanism

Vertical-pitching-rolling movement verification

In order to realize the reduction in vertical-pitching (fore-aft)-rolling (lateral) vibration of the construction vehicles, a new kind of 2SPS+SR seat mechanism is designed. The UG model of the seat mechanism is set up, as shown in Figure 1. The new seat mechanism is composed of a moving platform, a static platform, and three legs. The top of the moving platform is fixed to the bottom of the seat surface. The static platform is fixed to the seat bottom. And the three legs are distributed in an isosceles triangle. The first and second legs are the same, which are formed by a pair of spherical pairs and a moving pair in series, and the spherical pairs are connected to the moving platform and the static platform, respectively. The third is formed by a spherical pair and a rotating pair in series, and the spherical pair is connected to the static platform, while the rotating pair is connected to the moving platform.

Figure 1.

Model of the 2SPS+SR seat mechanism.

During the process of simulation, the loads with y = 20 sint are exerted on the two moving pairs, and the load with y = 10 sint is acted on the rotating pair. Next, the simulation time is set to 100 s, and the number of simulation steps is set to 10,000. Finally, the displacements along the three directions X, Y, and Z and the angular velocities around the X, Y, and Z directions at the center of the moving platform are obtained and shown in Figure 2. From Figure 2(a), it could be seen that the displacements in the X and Y directions start from 0 mm, and the one in the Z direction starts from 347 mm. Besides, the moving platform of the mechanism has a periodic change of about 20 mm in the Z direction, whereas the fluctuation range of the moving platform is very small and can be ignored in the X and Y directions. On the other hand, it can be seen from Figure 2(b) that the angular velocity of the moving platform changes periodically within the range of −0.5 to −0.5 deg/sec in the X direction and also has periodical changes of −0.2 to −0.2 deg/sec in the Y direction. But, the angular velocity of the moving platform is very small in the Z direction which can be ignored.

Figure 2.

Vertical-pitching-rolling movement verification of the 2SPS+SR seat: (a) displacements in three directions; (b) angular velocity in three directions.

To sum up, the proposed seat mechanism can realize the movement along the vertical direction and the rotation of pitching and rolling. Therefore, the 2SPS+SR parallel mechanism can meet our design requirements.

Time-domain analysis

In order to know the effectiveness of the vibration damping of the 2SPS+SR seat mechanism, the seat mechanism model is established in Adams/View as shown in Figure 3. In Figure 3, the first and second legs of the seat mechanism are installed with the damping springs, whose stiffness is 300 N/m and damping coefficient equals to 0.6 N s/m. The third leg does not have the damping spring. Next, according to the literature,¹⁸ the three-dimensional roads E, F, and G and the vehicle model are set up in Adams/Car, which is shown in Figure 4. The vehicle parameters are given in Table 1. Then, all the forces obtained in the above simulation process are applied to the center of the 2SPS+SR parallel seat mechanism for further analysis. The simulation time is set to 10 s, and the simulation steps are set to 1000.

Figure 3.

Seat mechanism using Adams.

Figure 4.

Vehicle model under three-dimensional roads.

Table 1.

Vehicle parameters.

Parameter description	Unit	Value
Body mass (m_c)	kg	34,000
Tire mass (m_t)	kg	60
Tire stiffness (k_t)	N/m	3.2 × 10⁵
The distance between the shafts (a)	mm	3700
The distance between the tires (b)	mm	2865
Cab mass (m_j)	kg	235
Vehicle suspension stiffness (k_ji)	N/m	4.95 × 10⁴
Vehicle suspension damping (c_ji)	N s/m	2250
Cab length (a_j)	mm	1200
Cab wide (b_j)	mm	1250

When the vehicles are driven at a speed of 10 km/h on the three-dimensional road, the changes of acceleration in the vertical, fore-aft, and lateral of the construction vehicles without and with the 2SPS+SR seat mechanism are shown in Figures 5–7, respectively.

Figure 5.

E-class road: (a) lateral direction; (b) fore-aft direction; (c) vertical direction.

Figure 6.

F-class road: (a) lateral direction; (b) fore-aft direction; (c) vertical direction.

Figure 7.

G-class road: (a) lateral direction; (b) fore-aft direction; (c) vertical direction.

From the solid blue line of Figures 5–7, it could be found that when the construction vehicle without the 2SPS+SR seat mechanism is driven on the E-class road, the peak acceleration in the vertical direction, the lateral direction, and the fore-aft direction are 1.605 m/s², 0.415 m/s², and 0.785 m/s², respectively. In addition, on the F-class road, the peak acceleration of the construction vehicle in the vertical direction is 2.431 m/s², and in the lateral and fore-aft directions, the peak accelerations are 0.709 m/s² and 1.559 m/s², respectively. The peak acceleration of the construction vehicle in the vertical, lateral, and fore-aft directions are 4.835 m/s², 2.206 m/s², and 3.209 m/s², respectively, on the G-class road.

Additionally, from the dotted red line of Figures 5–7, it could be found that the peak accelerations in the vertical, lateral, and fore-aft directions are 0.579 m/s², 8.70 m/s², and 0.0369 m/s², respectively, at the seat center when the vehicle with the 2SPS+SR seat mechanism is driven on the E-class road. On the F-class road, the vertical, lateral, and fore-aft peak accelerations are 0.817 m/s², 0.0104 m/s², and 0.0976 m/s², respectively. And on the G-level road, the peak accelerations in the vertical, lateral, and fore-aft directions are 1.324 m/s², 0.0499 m/s², and 0.389 m/s², respectively.

The above results show that the accelerations of the 2SPS+SR seat mechanism on various roads decrease significantly in all directions. Compared with the accelerations at the center of the conventional seat, the maximum accelerations of the seat with the 2SPS+SR mechanism on the E-, F-, and G-level roads decrease by 63.9%, 66.3%, and 72.6% in the vertical direction, respectively. And in the lateral direction, the maximum accelerations on the E-, F-, and G-level roads decrease by 97.9%, 98.5%, and 97.7%, respectively. About the fore-aft vibration, the maximum accelerations on the E-, F-, and G-class roads decrease by 95.3%, 93.7%, and 92.8%, respectively.

Frequency-domain analysis

In order to further illustrate the vibration damping effect of the seat mechanism, the Fourier transform is used for frequency-domain analysis. The analysis results are shown in Figures 8–10.

Figure 8.

E-class road: (a) lateral direction; (b) fore-aft direction; (c) vertical direction.

Figure 9.

F-class road: (a) lateral direction; (b) fore-aft direction; (c) vertical direction.

Figure 10.

G-class road: (a) lateral direction; (b) fore-aft direction; (c) vertical direction.

From Figures 8–10, it could be found that on the E-class road, the peak of power spectral density with the 2SPS+SR seat mechanism in the vertical direction, the lateral direction, and the fore-aft direction is 0.4 m² s⁻³, 1.7 m² s⁻³, and 50 m² s⁻³, respectively, which is lower than that without the 2SPS+SR seat mechanism (2.8 m² s⁻³, 8 m² s⁻³, and 150 m² s⁻³, respectively). In addition, there is a similar situation on the F-class and G-class roads that the peaks of power spectral density with the 2SPS+SR seat mechanism in three directions are declined compared with that without the seat mechanism.

From the perspective of time domain and frequency domain, the new 2SPS+SR seat mechanism has good vibration-reducing effect on the three-dimensional pavement, and thus very little vibration is transmitted to the drivers’ body. Therefore, the mechanism can improve the ride comfort of the driver.

Ride comfort analysis

Evaluation method of ride comfort

ISO2361-1997(E) is a universal criterion about vibration.¹⁹ When the vibration crest factor is less than or equal to 9, the basic evaluation method of the weighted RMS should be applied to study the impact of the vehicle vibration on people’s comfort. Because the vibration of the vehicle comes from the three directions X, Y, and Z, the total weighted RMS of acceleration is given as follows^20,21

a_{V} = {[\sum_{i = 1}^{N} {(W_{i} a_{i})}^{2}]}^{1 / 2}

(1)

where a_i (m/s²) is the RMS of the weighted acceleration in each direction. In ISO2361, the weighted coefficient W_i in the X and Y directions is 1.4, and the weighted coefficient W_i in the Z direction is 1. Therefore, equation (1) could be further written as

a_{v} = {[{(1.4 a_{x w})}^{2} + {(1.4 a_{y w})}^{2} + a_{z w}^{2}]}^{1 / 2}

(2)

where a_xw (m/s²) is the RMS of weighted acceleration of the vibration of rolling; a_yw (m/s²) is the RMS of weighted acceleration in the pitching vibration; and a_zw (m/s²) is the RMS of weighted acceleration in the vertical vibration.

The weighted vibration level equation is as follows

L_{a v} = 20 \lg (\frac{a_{v}}{a_{0}})

(3)

where

a_{0} = 10^{- 6} {\frac{m}{s}}^{2}

When the crest factor value of the vehicle vibration is greater than 9, ISO2361-1997 (E) stipulates that the influence of vibration on people is studied by using the auxiliary evaluation method, and the calculation equation is as follows²²

V D V = {[\int_{0}^{T} a^{4} (t) d t]}^{1 / 4}

(4)

where a (t) is the instantaneous frequency-weighted acceleration (m/s²) and T is the duration of the measurements (s).

According to the calculation formula of the crest factor values of the vibration,²³ the crest factor values of the vibration in each axial direction when the vehicle travels on different roads at the speed of 10 km/h are obtained, which is shown in Table 2.

Table 2.

The crest factors of the vibration in each axial under random roads.

Axial	Road
Axial	E	F	G
X	2.4378	2.7134	3.4467
Y	2.3066	3.0051	3.6863
Z	2.5529	2.4139	2.4516

It can be seen from Table 2 that the crest factor values are all less than 9 on the three-dimensional roads E, F, and G. Therefore, this study adopts the basic evaluation method to evaluate the impact of vibration on drivers’ comfort during the vehicle moving on different roads. Table 3 shows the relationship between the RMS of the weighted acceleration given by the ISO2361 standard, the weighted vibration level, and the drivers’ comfort level.

Table 3.

Ride comfort ranges.

The total weighted root mean square of the mass center, a_v (m/s²)	Weighted vibration level, L_av (dB)	Comfort level
<0.315	110	Not uncomfortable
0.315–0.63	110–116	Little uncomfortable
0.5–1.0	114–120	Fairly uncomfortable
0.8–1.6	118–124	Uncomfortable
1.25–2.5	112–128	Very uncomfortable
>2.0	126	Extremely uncomfortable

Ride comfort analysis

In order to further validate the effectiveness of the new seat mechanism, the weighted acceleration RMS of each direction, the total weighted RMS of acceleration, and the weighted vibration level are calculated, respectively. The results are shown in Tables 4 and 5.

Table 4.

The weighted acceleration root mean square and comfort level without the 2SPS+SR seat mechanism.

Road	a_x (mm/s²)	a_y (mm/s²)	a_z (mm/s²)	a_v (m/s²)	L_av (dB)	Comfort level
E	170.4215763	340.2371809	628.8387798	0.8241697172	118.32033	Fairly uncomfortable
F	261.4051718	518.62649	1006.935147	1.294232725	122.240248	Uncomfortable
G	640.1451039	1475.135559	1972.21484	2.992961792	129.522023	Extremely uncomfortable

Table 5.

The weighted acceleration root mean square and comfort level with the 2SPS+SR seat mechanism under different roads.

Road	a_x (mm/s²)	a_y (mm/s²)	a_z (mm/s²)	a_v (m/s²)	L_av (dB)	Comfort level
E	2.112349554	2.112349554	175.9834669	0.1761974837	104.919994	Not uncomfortable
F	2.599478437	11.74386728	293.6198113	0.2941022917	109.369968	Not uncomfortable
G	7.518614874	30.41494723	379.7699982	0.3822946309	111.662758	Little uncomfortable

Table 4 describes the RMS of the total weighted acceleration, the weighted vibration level, and the driver’s ride comfort without the new seat mechanism on different roads. It can be clearly concluded that the road level and ride comfort are negatively correlated and the road vibration contributes to the drivers’ uncomfortableness. Particularly, with the increase of the road level, the acceleration of each direction becomes larger, and the total weighted acceleration and the weighted vibration levels gradually increase. It means that the ride comfort of vehicles gradually decreases with deterioration of the roads. And the total accelerations a_w are all greater than 0.315 m/s², and the weighted vibration levels L_av are all greater than 110 dB.

Table 5 gives the total weighted acceleration, the weighted vibration level at the seat center with the 2SPS+SR seat mechanism, and the ride comfort of the driver on the three kinds of roads. As can be seen from it, no matter the construction vehicle is driven on the E-class road or the F-class road at a speed of 10 m/s, the total RMS values of the weighted acceleration are within 0.315 m/s², and the weighted vibration level is less than 110 dB. However, when the vehicle is driven on the G-class road, the total weighted acceleration and weighted vibration level are slightly higher than 0.315 m/s² and 110 dB.

Through comparing Tables 4 and 2, it could be seen that the RMS values of the total weighted acceleration and the weighted vibration levels surpass the limited range stipulated by international standards. And with the deterioration of the road, people’s subjective feelings become more and more uncomfortable, not to meet the driver’s requirements for comfort.

The comparison between Tables 5 and 2 shows that the ride comfort of the vehicle is good, and the subjective feeling of the driver is not uncomfortable. When the vehicle with the 2SPS+SR seat mechanism is driven on the G-class road, the total weighted acceleration RMS at the seat center is between 0.315 and 0.63, and the weighted vibration level is between 110 dB and 116 dB. So, the drivers may feel uncomfortable, but the overall uncomfortable degree is much lower than the original one. Therefore, the parallel mechanism improves the stability and ride comfort of the construction vehicle on the E-class and F-class roads.

Tables 4 and 5 show that the total RMS of the weighted acceleration decreases by 78.6%, 77.3%, and 87.2%, respectively, and the weighted vibration level decreases by 12.4%, 10.5%, and 13.8% at the center of the new seat on E, F, and G-class roads, respectively, compared with those of the conventional seat. Furthermore, on the same road, the weighted acceleration RMS values in all directions at the seat center decrease significantly, meaning that the proposed seat mechanism in the article can significantly improve the ride comfort of the vehicle.

Through the comparison of Tables 2, 4, and 5, it is further illustrated that the new seat mechanism is significantly effective in improving the operating stability and ride comfort of the vehicle.

Conclusions

In this article, a 2SPS+SR parallel seat mechanism is proposed to reduce the violent vibration of construction vehicles and improve the driver’s comfort. Through the analysis, the main conclusions are given as follows:

The model of the new seat mechanism is built using UG software, and it could realize the motion state of one translation and two rotations. Therefore, the proposed seat structure could satisfy the design requirement of reducing vertical-pitching-rolling vibration.

The vehicle and three-dimensional road model are built in Adams for vibration analysis. The results show that with the deterioration of the road, the vibration gradually increases when the construction vehicles with the conventional seat are driven on the roads. And the RMS of the weighted acceleration is more than 0.8, and the weighted vibration level is more than 118. So, the driver feels obvious discomfort, which affects the driver’s physical and mental health and operational stability.

The total RMS of the weighted acceleration decreases by 78.6%, 77.3%, and 87.2%, respectively, and the weighted vibration level decreases by 12.4%, 10.5%, and 13.8% at the center of the new seat on E, F, and G-class roads, respectively, compared with those of the conventional seat. When the construction vehicle with the 2SPS+SR parallel seat mechanism is driven on the E- and F-level roads, the weighted accelerations at the seat center are less than 0.3, and the weighted vibration levels are less than 110, which conform to the standard of ISO2631-1997 (E). However, the driver will feel slight discomfort when the vehicles are driven on the G-class road, but the overall discomfort is greatly reduced. Therefore, the 2SPS+SR parallel seat mechanism plays a good role in improving the ride comfort of vehicles.

The results of this article could provide a solution for ride discomfort of vehicles and lay a foundation for the control research of the parallel mechanism.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project is sponsored by the fund from the Natural Science Foundation of Shanxi (Grant No. 201901D111238), the Major Scientific and Technological Projects of Shanxi Province (Grant No.20181101017), and the Natural Science Foundation of China (Grant No. 51405323).

ORCID iD

Jie Zhang

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