Analyzing the influences of bus driver seat’s suspension system on driver’s comfort level and stability

Abstract

The influences of the seat suspension on the comfort level, and stability of the bus driver are analyzed using a three-degree-of-freedom (3DOF) quarter-vehicle model. The influences are analyzed through the effects of seat suspension damping ratio ξ_se on driver frequency weighted acceleration a_w (m/s²) (comfort level) according to ISO 2631:1-1997 standard, the ratio of driver acceleration and gravitational acceleration a/g (vertical stability). With random excitation according to ISO 8608, considering the same vehicle speed value v (km/h) (in the region of 10 – 20 (km/h)), the decrease of ξ_se increases the a_w value, this result leads to the reduction of comfort level; Considering the same ξ_se value, a_w value decreases as increasing v value. With transient excitation according to IRC 99 – 1988, considering the same v value, the smaller ξ_se creates the larger a/g value; Considering the same ξ_se, the value of a/g increases and reaches the extreme in the vehicle speed range 20 – 30 (km/h), outside this speed range the value of a/g decrease.

Keywords

Bus driver seat nonlinear air spring random excitation transient excitation comfort level

Introduction

Bus drivers work many hours daily, continuously exposed to whole-body vibration while operating vehicles.^1,2 Vibration mostly comes from the uneven road surface, the engine, acceleration and deceleration.^3,4 This vibration affects the driver’s productivity, feelings, and health.^1,2,5,6 The driver seat’s suspension system is an essential structure that directly affects the above factors.^7–10 The suspension system can deform to absorb vibration and improve comfort level. However, this effect decreases the driver’s vertical stability by changing the relative position between the seat surface and the steering wheel.^9,10

Computational simulation models are proposed to optimize the driver seat’s suspension system to ensure effective vibration isolation and stability.^11–15 Optimizing the bus driver seat’s suspension system with a 10DOF whole-vehicle model subjected to harmonic and random excitation signals.¹¹ Improving the driver seat’s suspension system performance using a 1DOF model with a vibration absorber under random excitation signals.¹² Optimizing the behaviour of the driver and the seat suspension system through optimizing the vehicle suspension system with a 3DOF quarter-vehicle model subjected to random excitation signals.¹³ Research to improve comfort and reduce the impact of vibration on driver’s health with a 12DOF bus model.¹⁴ Optimizing the driver acceleration response and relative displacement of the seat suspension system with a decomposed driver model using a 7DOF model under random excitation.¹⁵

The above studies simplify the technical specifications of the elements that make up the driver’s seat suspension system, such as the stiffness of elastic elements and the damping coefficients of dampers in the form of constants. The behaviour of an elastic element, like an air spring, under the effect of external forces is nonlinear and can be determined through experimental measurements.^9,10 Besides, the above studies^11–15 ignore the guiding mechanism’s kinematic influence or set a constant reduction ratio for all working situations.⁹ In reality, the force transmission direction of the elastic and damping elements changes according to the relative displacement of the suspension system through the guiding mechanism, so it is necessary to incorporate the dynamics of the guiding mechanism into the calculation model to achieve high accuracy.

Passive seat suspension systems are commonly used on buses in Vietnam. However, investigating and calculating research to determine optimal technical parameters for specific working cases for seat suspension systems in Vietnam still have not been focused. Most studies use simple models with elastic element - damper acting in the vertical direction only and do not consider the kinematic influences of the guiding mechanism. In addition, the actual nonlinearity in the behaviour of the air spring concerning deformation has not been explored in depth for a specific suspension system. Therefore, this study models a seat suspension system with a nonlinear air spring with technical parameters measured from experiments; the damping force transmission direction change according to the model’s kinematics is combined. From there, the model specifications according to operating cases are clearly analyzed.

Simulation model and model parameters

Simulation model

DOF quarter-vehicle model

Where:

m_u, m_s, m_d: The mass of the unsuspended part, the vehicle’s body and the total mass of the driver and seat frame (kg), respectively

c_u, c_s, c_d: The damping coefficient of the wheel, the damping elements of the vehicle suspension, and the seat suspension (Ns/m), respectively

k_u, k_s, k_d: The stiffness of the wheel, the elastic elements of the vehicle suspension, and the seat suspension (N/m), respectively

x_u, x_s, x_d: The vertical displacement of the unsuspended part, the vehicle’s body and the driver (m), respectively

${\dot{x}}_{u}, {\dot{x}}_{s}, {\dot{x}}_{d}$ : The vertical velocity of the unsuspended part, the vehicle’s body and the driver (m/s), respectively

${\ddot{x}}_{u}, {\ddot{x}}_{s}, {\ddot{x}}_{d}$ : The vertical acceleration of the unsuspended part, the vehicle’s body and the driver (m/s²), respectively

y (t): The vertical excitation over time (m)

α, φ: The angle between the guide bar, damper, and horizontal (degree), respectively.

g: Gravitational acceleration (m/s²)

μ: Friction coefficient between slider and sliding rails

The 3DOF quarter-vehicle model analyzes the vibration of the driver and the seat suspension system subjected to excitation y (t), as described in Figure 1. The seat suspension system has a scissor-shaped guide mechanism installed on the vehicle floor. The seat suspension system has an elastic element in the form of an air spring with nonlinear stiffness k_d and a damping element in the form of a hydraulic damper with a damping coefficient c_d. This study investigates the influences of c_d through the seat suspension damping ratio ξ_se.

Figure 1.

3DOF quarter-vehicle model with driver seat’s suspension system.

Mathematical model

Equivalent model

The values of α và φ over time can be calculated as eq. (1) and eq. (2).

\dot{α} = \frac{{\dot{x}}_{d} - {\dot{x}}_{s}}{A C \cos α}

(1)

\dot{φ} = \frac{\dot{α} (A K - D L) (K C - D L)}{\cos^{2} α + {(\frac{A K - D L}{K C - D L} \sin α)}^{2}}

(2)

The seat suspension system model with a scissor-shaped guide mechanism has a damper installed on the guide wings at positions K and L and an air spring installed below the seat surface frame at position B. These elements create damping force F_c and elastic force F_bh that prevent the system’s movement. Perform joint separation at the connection positions A, B, C, D, K, and L to obtain a reaction force model, Figure 3.

Where:

F_Ax, F_Ay, F_Bx1, F_By1, F_Bx2, F_By2, F_Cy1, F_Cy2, F_Dy: Reaction force (N) in x and y directions at joints A, B, C and D, respectively

F_msC1, F_msC2, F_msD2: Friction force between slider and sliding rail at joints C, D, respectively

Perform kinematic and dynamic analysis of the model in Figure 2 according to the diagram in Figure 3 to obtain the dynamic differential equation of the seat suspension system eq. (3).

m_{d} {\ddot{x}}_{d} = \frac{1}{μ \tan α - 1} [k_{d} (x_{d} - x_{s}) + . . . + c_{d} v_{K L} . \frac{2 M K}{A C \cos α} (\sin α \cos φ + \sin φ \cos α)]

(3)

Figure 2.

The equivalent seat suspension model with the kinematic conversion factors of the damping and elastic elements U, V.

Figure 3.

Kinematic and dynamic analysis model of the seat suspension system.

The value v_KL is the relative velocity between point K and point L in the direction of KL, calculated as Eq. (4). Both Eq. (3) and Eq. (4) have modelling time’s step based on the step of excitation time y (t) 0.001 (s).

v_{K L} = \dot{α} . \sin α \cos φ . \frac{{(A K - D L)}^{2} + {(K C - D L)}^{2}}{K C - D L}

(4)

The equivalent damping force and elastic force acting on m_d in the vertical direction can be converted from F_c and F_bh with the conversion factors U and V calculated according to Eq. (5)–(7), respectively.

m_{d} {\ddot{x}}_{d} = V k_{d} (x_{d} - x_{s}) + U c_{d} ({\dot{x}}_{d} - {\dot{x}}_{s})

(5)

U = \frac{\tan α \cos φ \sin (α + φ)}{(μ \tan α - 1) \cos α} . . . \frac{2 M K [{(A K - D L)}^{2} + {(K C - D L)}^{2}]}{A C^{2} (K C - D L)}

(6)

V = \frac{1}{μ \tan α - 1}

(7)

System dynamics equation

Applying Newton’s II law according to the force analysis diagram at the mass elements m_u, m_s, and m_d in Figure 4 to obtain the system’s dynamic differential equations Eq. (8):

[M] [\ddot{X}] + [C] [\dot{X}] + [K] [X] = [F]

(8)

Where:

[M], [C], [K] :

The mass matrix, damping coefficient matrix and stiffness matrix, respectively

[X], [\dot{X}], [\ddot{X}]

: The matrix of state variables of displacement, velocity, and acceleration, respectively

[F]

: The matrix of external force

M = [\begin{array}{c} m_{d} & 0 & 0 \\ 0 & m_{s} & 0 \\ 0 & 0 & m_{u} \end{array}],

[C] = [\begin{array}{c} c_{d} U & - c_{d} U & 0 \\ - c_{d} U & c_{d} U + c_{s} & - c_{s} \\ 0 & - c_{s} & c_{s} + c_{u} \end{array}]

[K] = [\begin{array}{c} V k_{d} & - V k_{d} & 0 \\ - V k_{d} & V k_{d} + k_{s} & - k_{s} \\ 0 & - k_{s} & k_{s} + k_{u} \end{array}], [F] = [\begin{array}{c} 0 \\ 0 \\ c_{u} \dot{y} + k_{u} y \end{array}],

[\ddot{X}] = [\begin{array}{l} {\ddot{x}}_{d} \\ {\ddot{x}}_{s} \\ {\ddot{x}}_{u} \end{array}], [\dot{X}] = [\begin{array}{l} {\dot{x}}_{d} \\ {\dot{x}}_{s} \\ {\dot{x}}_{u} \end{array}], [X] = [\begin{array}{l} x_{d} \\ x_{s} \\ x_{u} \end{array}]

Figure 4.

Free body diagram of the driver, sprung and un-sprung mass elements.

Nonlinear air spring model

Experimental method

The experimental model in Figure 5 with initial parameters shown in Figure 6, such as compression pressure (gauge) P₀ = 1 (bar), volume V₀ = 7.05 × 10⁻⁴ (m³), height h₀ = 0.14 (m), and excitation signal with amplitude A_x = 0.025 (m), excitation frequency f = 0.01 (Hz).

Figure 5.

Experimental model for measuring driver seat’s air spring parameters.

Figure 6.

Frequency weighting filter w_k.²

Air spring stiffness calculation

The air spring reaction force F_bh (N) can be calculated through the pressure (gauge) inside the air spring P (N/m²) and the equivalent area A_ef (m²) as Eq. (9).¹⁶

F_{b h} = A_{e f} . P

(9)

A polytropic process is assumed for the experiment of air spring with polytropic index γ = 1.2.¹⁶ The relationship between the pressure P (N/m²) inside the air spring and the volume V (m³) containing air is calculated according to Eq. (10) with the atmosphere pressure P_at = 10⁵ (N/m²).¹⁶

P + P_{a t} = (P_{0} + P_{a t}) . {(\frac{V_{0}}{V})}^{γ}

(10)

The stiffness of the air spring k_d (N/m) is the derivative of the force F_bh (N) with the deformation z (m), Figure 6, calculated according to Eq. (11).¹⁶

k_{d} = \frac{d F_{b h}}{d z} = \frac{d A_{e f}}{d z} P - \frac{γ (P_{0} + P_{a t}) V_{0}^{γ} A_{e f}}{V^{γ + 1}} \frac{d V}{d z}

(11)

Linear asymmetric damper model

The linear asymmetric damper model describes the reaction behaviour of the damping element of the seat suspension according to relative speed v.¹⁷

The mathematical model describing the characteristics of the damping coefficient of the asymmetric damper is calculated as Eq. (12).¹⁷

c_{d} = {\begin{cases} \frac{2 β c_{0}}{β + 1}, if v_{K D} \geq 0 \\ \frac{2 c_{0}}{β + 1}, if v_{K D} < 0 \end{cases}

(12)

Where:

+ β = 7/3: The damper asymmetric ratio¹⁷

+ c₀: The selected symmetric damping coefficient value (N.s/m), calculated corresponding to the damping ratio ξ_se as Eq. (13).¹⁸

c_{0} = \frac{2 ξ_{s e} \sqrt{m_{d} V k_{d_e q}}}{U_{e q}}

(13)

Where:

k_{d_eq}: Air spring stiffness at the equilibrium position (N/m)

U_eq: Conversion factor at the equilibrium position

Calculation parameters

Input parameters

Table 1 summarises the calculated parameters of the model in Figures 1 and 2.

Table 1.

Model’s parameters.

Parameter	Value	Unit
m _d	100	kg
m _s	4500	kg
m _u	500	kg
k _s	300,000	N/m
k _u	1,600,000	N/m
c _u	150	Ns/m
c _s	20,000	Ns/m
ξ _se	0.1÷0.8	—
μ	0.08	—

Excitation signal

Random excitation signal

The random excitation signal (C class) y (t) (m) is simulated according to ISO 8608 standard¹⁹ with the mathematical model Eq. (14).

y (t) = \sum_{1}^{N} A_{i} \sin (Ω_{i} \cdot v \cdot t - ψ_{i})

(14)

Where:

$A_{i} = \sqrt{2 Φ (Ω_{i}) Δ Ω}$ : The ith sine wave amplitude (m)

Ω_i: The wavenumbers that are chosen to lie at N equal intervals $Δ Ω$ (rad/m)

ψ_i: The different sets of uniformly distributed phase angles in the range between 0 and 2π (rad)

Φ (Ω_{i}) = Φ_{0} {(\frac{Ω_{i}}{Ω_{0}})}^{- w}

(15)

With:

Φ₀: the value of the power spectral density at the reference wavenumber Ω₀ = 1 (rad/m)

w = 2: the drop in magnitude

Transient excitation signal

The transient excitation signal y (t) (m) is simulated according to IRC 99-1988 standard²⁰ with the mathematical model Eq. (16), where d₁ = 3.7 (m), d₂ = 0.1 (m) and vehicle’s velocity v (km/h).

y (t) = {\begin{array}{c} d_{2} \sin^{2} \frac{π v}{d_{1}} t; & 0 \leq t < \frac{d_{1}}{v} \\ 0; & t < 0, t \geq \frac{d_{1}}{v} \end{array}

(16)

Assessment standards

Comfort level

ISO 2631:1-1997 standard² outlines a primary vibration assessment method using the time-frequency weighted mean square (RMS) acceleration a_w (m/s²) as Eq. (17), calculated according to driver frequency weighted acceleration over time a_w (t) (m/s²) and measuring duration T (s) Table 2.

a_{w} = \sqrt{\frac{1}{T} \int_{0}^{T} a_{w}^{2} (t) d t}

(17)

Table 2.

Driver comfort estimation under different acceleration intensities.²

Acceleration intensity a_w (m/s²)	Comfort estimation
a_w < 0.315	Not uncomfortable
0.315 < a_w < 0.63	A little uncomfortable
0.5 < a_w < 1	Fairly uncomfortable
0.8 < a_w < 1.6	Uncomfortable

The value of the weighting filter w_k at frequency f (Hz) can be calculated as Eq. (18)²:

w_{k} = | H_{h} (p) | \cdot | H_{l} (p) | \cdot | H_{t} (p) | \cdot | H_{s} (p) |

(18)

Where:

$| H_{h} (p) |$ : High-pass filter (Butterworth characteristics)

$| H_{l} (p) |$ : Low-pass filter (Butterworth characteristics)

$| H_{t} (p) |$ : Acceleration-velocity transition filter

$| H_{s} (p) |$ : Upward step filter

Stability

The driver’s vertical stability under transient excitation can be assessed through a/g, calculated as Eq. (19).

\frac{a}{g} = \frac{{\ddot{x}}_{d} (t)}{g}

(19)

The condition to ensure that the driver can be stable in the sitting position is that the a/g value does not exceed 1.

Results and discussion

Experiment’s results

The experimental results of measuring the air spring parameters according to the measurement process in Figure 5 are shown in Figure 7. The change of air spring pressure P (N/m²), Figure 7(a), according to the deformation z (m), is a nonlinear curve with a magnitude varying from 1 (bar) at the beginning to approximately 3 (bar) at the end of the measurement. Besides, with z (m) value in the range 0–0.025 (m), the P (N/m²) value changes less (approximately 0.75 (bar)) than with z (m) value in the range 0.025 – 0.05 (m). In this range, the P (N/m²) value changes more significantly (about 1.25 (bar)). The fact that the air spring pressure P (N/m²) changes nonlinearly with the deformation z (m) shows that calculating and simulating the vibration of the seat suspension system with the air spring requires combining experimental data to achieve high accuracy. The change of P (N/m²) according to z (m) in Figure 10 is digitized using a third-order polynomial mathematical model with “Matlab Toolbox Fitting.”

Figure 7.

Change according to the deformation z (m) of: (a) the air spring pressure P (N/m²), (b) the stiffness k_d (N/m).

Similar to the results in Figure 7(a) and(b) shows that the air spring stiffness k_d (N/m) changes nonlinearly with the air spring deformation z (m). With z (m) deformation of 0–0.015 (m), the air spring stiffness, with an initial value at the compression starting point of k_d = 30,000 (N/m), decreases and reaches a minimum k_dmin = 11,000 (N/m) at the deformation of z = 0.015 (m). As the deformation z (m) increases from 0.015 (m) to 0.05 (m), the air spring stiffness k_d (N/m) gradually increases and reaches its maximum k_dmax = 90,000 (N/m).

Responses in the time domain

Random excitation

Figure 8(a) shows that with the same value of damping ratio ξ_se = 0.4, vehicle speed v = 10 (km/h), the driver’s acceleration value a_w (m/s²) has a higher fluctuation amplitude than when the vehicle moves at a speed of v = 40 (km/h). The driver’s level of feeling with v = 40 (km/h) is evaluated according to a_w1 = 0.140 (m/s²), which is in the comfortable zone. In contrast, the driver’s level of feeling with v = 10 (km/h) evaluated by a_w2 = 0.475 (m/s²) is 3.3 times larger than a_w1, which creates a slightly uncomfortable feeling. The acceleration value a_w at low-speed v = 10 (km/h) is more significant than at high-speed v = 40 (km/h), considering the same value ξ_se = 0.4, is due to the seat suspension system at low speed is affected by low-frequency vibrations more than high frequencies, and this is combined with the fact that the natural frequency of the passive seat suspension system is in the small region of 1.5 – 4 (Hz),^8,9 specifically with the suspension system considered in this research is 1.5 – 2 (Hz) according to Figure 9, should cause vibrational resonance at low frequencies.

Figure 8.

Driver’s frequency weighted acceleration a_w (t) over time (a) with ξ_se = 0.4, v = 10 (km/h) and v = 40 (km/h), (b) with v = 10 (km/h), ξ_se = 0.1 and ξ_se = 0.4.

Figure 9.

Gain response of seat acceleration.

Figure 8(b) shows that, when considering the same vehicle speed v = 10 (km/h), the driver acceleration value a_w (t) over time with damping ratio ξ_se = 0.1 has higher fluctuation amplitude than ξ_se = 0.4. This result occurs because the damping ratio ξ_se varies linearly with the value of the damping coefficient c_d according to Eq. (12) and Eq. (13). The difference in damping coefficient causes a slight difference in the natural frequency of the seat suspension system. However, it has a considerable influence on the vibration amplitude of the system,¹³ Figure 9. According to the results of Figure 9, with ξ_se = 0.4, the amplitude around the resonance frequency 1 – 3 (Hz) is cut down more than with ξ_se = 0.1. From there, the amplitude value with ξ_se = 0.4 in Figure 8(b) is also cut down more when the excitation frequency is in a low range, as moving at a speed of v = 10 (km/h). Specifically, with ξ_se = 0.1, the driver’s acceleration a_w1 = 0.955 (m/s²) causes an uncomfortable feeling and is larger than the driver’s acceleration a_w2 = 0.475 (m/s²) with ξ_se = 0.4 approximately 2.01 times.

Transient excitation

Figure 10(a) shows that, with the same damping ratio ξ_se = 0.4, the value a (t)/g in two cases of vehicle speed v = 10 (km/h) and v = 40 (km/h) does not exceed 1, this means the driver is stable in the seat and does not bounce off the seat surface. Besides, the vehicle moves over a bump at the speed of v = 40 (km/h), causing driver acceleration larger fluctuation amplitude than the speed v = 10 (km/h). This result can be explained by the fact that when exposed to bump at high-speed v = 40 (km/h), the vehicle body and floor surface move vertically faster than v = 10 (km/h). This process causes the seat suspension system’s damper to deform at a higher speed with v = 40 (km/h), which in turn causes a more significant damping force acting on the system and creates greater acceleration, according to Eq. (5). At speed v = 10 (km/h), the most significant value a (t)/g is less than 0.025, Figure 10(a), this means the driver’s acceleration in the vertical direction does not exceed 2.5% of the gravitational acceleration g. Similarly, when the vehicle moves over a bump at a speed of v = 40 (km/h), the most significant value of a (t)/g is less than 0.1 (approximately four times higher than when v = 10 (km/h)) or the driver’s vertical acceleration does not exceed 10% of the gravitational acceleration g.

Figure 10.

Ratio of driver acceleration and gravitational acceleration over time a (t)/g over time (a) with ξ_se = 0.4, , v = 10 (km/h) and v = 40 (km/h), (b) with v = 40 (km/h), ξ_se = 0,1 and ξ_se = 0.4.

Figure 10(b) shows that, when considering the same vehicle speed v = 40 (km/h), the a (t)/g with the damping ratio ξ_se = 0.1 has a higher amplitude fluctuation than with ξ_se = 0.4. This result happens when the vehicle, in the two circumstances, exposes a bump at the same speed; the circumstance with a greater ξ_se has the system’s energy dissipated more, leading to being stable faster. Specifically, with ξ_se = 0.1, the most significant ratio a (t)/g value reaches a_max1/g = 0.23 and is larger than the case of ξ_se = 0.4 with the largest a (t)/g reaching a_max2/g = 0.1, nearly 2.3 times.

Responses in the velocity domain

Random excitation

Driver acceleration and relative displacement of the seat suspension system were expanded and investigated throughout the vehicle speed range v 10 – 80 (km/h), corresponding to the vehicle’s actual working speed. The RMS of driver frequency weighted acceleration according to ISO 2631 standard a_w (m/s²) corresponding to each vehicle speed value is summarized in Figure 11.

Figure 11.

RMS of driver frequency weighted acceleration a_w (m/s²) in velocity domain v (km/h).

When considering the same vehicle speed, corresponding to ξ_se = 0.1, ξ_se = 0.4 and ξ_se = 0.8, in the speed range 10 – 40 (km/h), the a_w value, Figure 11, gradually decreases. In the speed range 40 – 80 (km/h), the difference between a_w values in three cases of ξ_se = 0.1, ξ_se = 0.4 and ξ_se = 0.8 is very small. Besides, when considering the same seat suspension damping ratio value ξ_se, the a_w value reach it’s maximum at v = 10 (km/h) and gradually decreases with increasing vehicle speed. The most significant decrease occurs in the speed range 10 – 20 (km/h).

The deviation between the driver’s acceleration value a_w and the standard value 0.315 (m/s²) at ξ_se = 0.1, ξ_se = 0.4 is at least 50% larger than the standard value 0.315 (m/s²) (especially with ξ_se = 0.1 the deviation reaches 203 (%)) and 0% at ξ_se = 0.8. This deviation shows that, with ξ_se = 0.1, ξ_se = 0.4, when the vehicle moves at a slow speed (<10 (km/h)) in the city on road class C, it can easily cause discomfort compared to ξ_se = 0.8. On the contrary, when vehicle’s speed v = 20 (km/h), the driver always feels comfortable because the deviation is less than 0%, and the best performance is at ξ_se = 0.8 with −30.2%.

Transient excitation

Figure 12 shows that, when considering the same vehicle speed (for all speed values in the range 10 – 80 (km/h)), the value a_max/g gradually decreases, respectively, to ξ_se = 0.1, ξ_se = 0.4 and ξ_se = 0.8. When considering the same damping ratio value ξ_se, a_max/g value increases as increasing the vehicle speed in the range 10 – 30 (km/h) and reach it’s maximum value at [a_max/g]_max,. In the speed range of 30 – 80 (km/h), the a_max/g value decreases as increasing vehicle speed.

Figure 12.

Maximum ratio of driver acceleration and gravitational acceleration a_max/g (m/s²) in velocity domain v (km/h).

Corresponding to the cases ξ_se = 0.1, ξ_se = 0.4, and ξ_se = 0.8, the values of a_max/g reach their maximum in the vehicle speed range 20 – 30 (km/h). However, the driver is always guaranteed to sit stably and not be separated from the seat surface vertically as [a_max/g]_max is at least 75% smaller than 1 at all vehicle speed values. The best performance is at ξ_se = 0.8 for the driver’s vertical stability.

Conclusions

Through experimental measurements, the technical parameters of the air spring were determined, and the influences of the seat suspension damping ratio ξ_se on the level of comfort, vertical stability, and safety under random and transient excitation were analyzed with a 3DOF quarter-vehicle model. The results show that:

+ The vehicle moves on class C road according to ISO 8608 standard: In the speed range v 10 – 20 (km/h), when considering the same speed value v (km/h), the increase of damping ratio ξ_se creates the decrease of driver’s acceleration a_w (m/s²), and this result leads to the improvement of the comfort level. With the same damping ratio ξ_se, as increasing vehicle speed v (km/h), driver acceleration a_w decreases. These effects help improve comfort level.

+ The vehicle moves through a bump (transient excitation) according to IRC 99-1988 standard: When considering the same vehicle speed v (km/h), the decrease of the damping ratio ξ_se creates larger a_max/g values, these effects lead to the reduction of vertical stability. When considering the same value of damping ratio ξ_se, in the vehicle speed range v 10 – 30 (km/h), the values of a_max/g increase as increasing v; with v 30 – 80 (km/h), the values of a_max/g decrease as increasing v.

Footnotes

Acknowledgement

We acknowledge Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for supporting this study.

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) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Dai Pham Ngoc

References

Griffin

. Handbook of human vibration. 1st ed. London, UK: Academic Press, 1996.

International Organization for Standardization. ISO 2631-1: 1997 . Mechanical vibration and shock - evaluation of human exposure to whole-body vibration. Part 1: general requirements. Geneva, Switzerland: ISO, 1997.

Nahvi

Fouladi

Nor

. Evaluation of whole-body vibration and ride comfort in a passenger car. Int J Acoust Vib 2009; 14: 143–149.

MdSah

Taha

Ismail

. Lightweight vehicle and driver’s whole-body models for vibration analysis. IOP Conf Ser Mater Sci Eng 2018; 318: 012069.

Bhuiyan

Fard

Robinson

. Effects of whole-body vibration on driver drowsiness: a review. J Saf Res 2022; 81: 175–189.

Voicu

Stoica

Vilău

, et al. Frequency analysis of vibrations in terms of human exposure while driving military armoured personnel carriers and logistic transportation vehicles. Electronics 2023; 12: 1–18.

Zhang

. Vibration control of vehicle seat integrating with chassis suspension and driver body model. Adv Struct Eng 2013; 16: 1–9.

Heidarian

Wang

. Review on seat suspension system technology development. Appl Sci 2019; 9: 1–20.

Maciejewski

Meyer

Krzyzynski

. Modelling and multi-criteria optimisation of passive seat suspension vibro-isolating properties. J Sound Vib 2009; 324: 520–538.

10.

Igor

Tomasz

. Application of the pareto-optimal approach for selecting dynamic characteristics of seat suspension systems. Veh Syst Dyn: Intern J of Veh Mech and Mob 2011; 49: 1929–1950.

11.

Rezazadeh

Moradi

. Design of optimum vibration absorbers for a bus vehicle to suppress unwanted vibrations against harmonic and random road excitations. Scientia Iranica, Transactions B: Mech Eng 2021; 28: 241–254.

12.

Segla

Trišović

. Modeling and optimization of passive seat suspension. Am J Mech Eng 2013; 1: 407–411.

13.

Sekulic

Dedović

. The effect of stiffness and damping of the suspension system elements on the optimisation of the vibrational behaviour of a bus. Int J Traffic Transport Eng 2011; 1: 231–244.

14.

Sekulic

Vlastimir

Rusov

, et al. Analysis of vibration effects on the comfort of intercity bus users by oscillatory model with ten degrees of freedom. Appl Math Model 2013; 37: 18–19.

15.

Nagarkar

Bhalerao

Patil

, et al. Multi-objective optimization of nonlinear quarter car suspension system – PID and LQR control. Procedia Manuf 2018; 20: 420–427.

16.

Beater

. Pneumatic drives: system design modelling and control. Berlin, Germany: Springer, 2007.

17.

Dixon

. The shock absorber handbook. Hoboken, NJ: John Wiley & Son, 2007.

18.

Gillespie

. Fundamentals of vehicle dynamics. 1st ed. New York, NY: SEA, 1992.

19.

International Organization for Standardization (ISO) . Mechanical vibration – road surface profiles – reporting of measured data. Geneva, Switzerland: ISO, 2016. Standard No. ISO 8608.

20.

The Indian Roads Congress . IRC-99-1988, tentative guidelines on the provision of speed breakers for control of vehicular speeds on minor roads.