Performance of the combined hydropneumatic isolations on improving vibration of vibratory roller cab: Experiment and simulation

Abstract

This study, based on preeminent characteristics of both the pneumatic and hydraulic isolations, combined hydropneumatic isolations (CHPIs), is proposed for improving the cab ride quality of the vibratory rollers in low-frequency domain. A 3D dynamic model and mathematical model of the cab isolations and the vibratory rollers are established to simulate CHPI’s characteristics under the excitations of the off-road terrain and vibratory drum at 28 Hz and 35 Hz. To enhance the reliability of research results, vehicle’s mathematical models are also verified via the experimental investigation. The effectiveness of CHPIs on ameliorating the cab’s ride quality is then analyzed via two indicators of the power spectral density (PSD) acceleration on the frequency region and root-mean-square (RMS) acceleration on the time domain of the cab and operator seat. It is found that with the combination of the high-elastic stiffness parameter and high nonlinear damping coefficient of CHPIs using for the vehicle’s cab isolations, the results of the cab’s ride quality are greatly improved compared with other cab isolations in the well-known existing works.

Keywords

Vibratory rollers hydropneumatic isolation ride comfort low frequency region off-road terrain

Introduction

Under the working conditions of vibrating rollers on deformed terrains, the generated vibration sources from the interaction between the vibrator drum/tires and terrains had been directly transmitted to the operator through the cabin isolation mounts and operator’s seat suspension.^1-4 Moreover, excitation vibrations under low frequencies of 0.5–10 Hz caused by off-road soil surface roughness severely influenced the operator’s physical health.^5-6 Thus, the operator’s ride quality was greatly affected by deformable soil grounds.

To reduce the influence of off-road terrains on the operator’s ride quality, cab isolations were thus particularly interested. Traditional rubber isolations (TRIs) mainly used in cab isolations of vibratory rollers^4,7 were optimized to ameliorate the ride quality.^{4, 8} The scholars indicated that the optimized TRI was also very arduous to ensure the ride quality under low-vibration excitation frequencies due to the TRI’s low damping characteristic. Especially, the vibrations of the vertical operator and cab angles were very large under different operating conditions. To solve this problem, the hydraulic isolations (HIs) with high nonlinear damping characteristic^9-10 were added in the TRI³. Three cab isolations including TRI,¹¹ HI,¹² and pneumatic isolation (PI) had been applied to evaluate on the isolation performance of the vibratory roller cab.¹³ Based on optimal fuzzy PID controllers, HI’s damper forces were then optimized and controlled to enhance the cab’s ride quality.^{8, 14} It was found that the vehicle’s vibrations were significantly improved under both domains of frequency and time. However, research studies also indicated that power spectral density(PSD) acceleration responses of cab’s pitching angle and operator’s seat heave were still high under low-excitation frequencies, especially below 4 Hz. Thus, the operator’s health and safety were seriously affected under off-road terrains.

The PI with its nonlinear damping parameters and high-elastic/static stiffness parameters were widely employed on the cabin’s suspension systems of vehicles to ameliorate the ride quality and decrease noise.^15-17 A hybrid suspension system of the hydropneumatic suspensions (HPSs) was used for dump trucks and agricultural tractors to ameliorate the ride quality and reduce the energy.^18-19 The results revealed that the operator’s ride quality was remarkably increased with HPSs. Although the impact of off-road terrains on vehicle’s ride quality with HPSs had not yet been analyzed, however, the result of HPSs was an obvious basis to apply for cab isolations of vibratory rollers.

In this research, based on advantages of the HI and PI, a combined hydropneumatic isolations combined by hydro and pneumatic isolations is proposed for ameliorating the cab’s ride quality. A mathematical model of vibratory rollers working on off-road ground terrains and excited by the vibratory drum at 28 Hz and 35 Hz is established; concurrently, its mathematical model is also verified via the experimental investigation with the TRI. The PSD acceleration in the frequency region and root-mean-square(RMS) acceleration in time domain of the cab and operator seat are objective studies. The research results are then compared with the TRI to evaluate the CHPI’s effectiveness.

This study’s innovation is that using a 3D dynamic model of vibratory rollers to fully assess the cab’s pitching and rolling vibrations under off-road terrains. The CHPI with characteristics of high-elastic stiffness and nonlinear damping are proposed and studied to enhance the cab’s ride quality in low-frequency domain. Two indexes of RMS and PSD accelerations are concurrently used to assess the influence of vibrations on the ride quality, health, and safety of the operator.

Material and method

Mathematical model of off-road vibratory rollers

The vibratory roller’s structure mainly consists by operator’s seat, cabin, vehicle bodies, drum, and wheels. The cabin floor is isolated from the rear vehicle frame through four vibration isolations, as shown in Figure 1. Thus, a 3D dynamic model of the vehicles has been built for simulating cab isolations, as seen in Figure 2 where m_χ is the mass of operator seat, cabin, rear frame and engine, front frame, and drum (χ = s, c, rf, ff, and d), respectively. z_s is the vertical operator seat vibration. z_c, φ_c, and θ_c are the vertical, pitching, rolling vibrations of the cabin. z_rf, φ_rf, and θ_rf are the vertical vibration, pitching, and rolling angles of the rear frame, respectively. z_d, θ_d and z_ff, θ_ff are the vibration heave and roll of drum and front vehicle body. c_s, k_s and c_dj, k_dj are coefficients of damping and stiffness of operator seat suspension system and drum’s rubber isolations. l_α and b_β are distances of vehicle’s horizontal and width. q_tj are excitations of off-road terrain under wheels (α = 1, 2, ..., 8, β = 1, 2 ,..., 5, j = 1, 2).

Figure 1.

Schematic of an actual vibratory roller.

Figure 2.

Mathematical model of the vehicle.

From the mathematical models of the vehicle and cab shown in Figure 2, their motion equations are written based on Newton’s II law as follows

\begin{array}{l} m_{s} {\ddot{z}}_{s} = - F_{s} \\ m_{c} {\ddot{z}}_{c} = - \sum_{i = 1}^{4} F_{c i} + F_{s} \\ I_{c y} {\ddot{ϕ}}_{c} = \sum_{i = 1}^{2} F_{c i} l_{2} - \sum_{i = 3}^{4} F_{c i} l_{3} + F_{s} l_{1} \\ I_{c x} {\ddot{θ}}_{c} = \sum_{i = 1}^{4} {(- 1)}^{i + 1} F_{c i} b + F_{s} b_{1} \\ m_{f f} {\ddot{z}}_{f f} = \sum_{j = 1}^{2} F_{d j} \\ I_{f f x} {\ddot{θ}}_{f f} = \sum_{j = 1}^{2} {(- 1)}^{j + 1} F_{d j} l_{j + 3} \\ m_{r f} {\ddot{z}}_{r f} = - F_{a} - \sum_{j = 1}^{2} F_{t j} + \sum_{i = 1}^{4} F_{c i} \\ I_{r f y} {\ddot{ϕ}}_{r f} = F_{a} l_{6} + \sum_{i = 1}^{4} δ F_{c i} l - \sum_{j = 1}^{2} F_{t j} l_{7} + M_{a y} \\ I_{r f x} {\ddot{θ}}_{r f} = \sum_{i = 1}^{4} {(- 1)}^{i} F_{c i} b + \sum_{j = 1}^{2} {(- 1)}^{j + 1} F_{t j} b_{j + 5} - M_{a x} \end{array}

(1)

where F_a = F_d1 + F_d2, M_ay = F_al₈, and M_ax = F_d1b₄ + F_d2b₅ are the vertical force and the rotation moments of pitching and rolling axes at the articulated-frame steered, respectively

w h e n {\begin{cases} i = 1,2 \\ i = 3,4 \end{cases} t h e n {\begin{cases} δ = - 1, l = l_{5}, a n d b = b_{i + 1} \\ δ = + 1, l = l_{4}, a n d b = b_{i - 1} \end{cases}

The vertical force responses in equation (1) including F_s, F_ci, F_dj, and F_tj are, respectively, determined as follows

The dynamic force F_s of the operator’s seat suspension is written as follows

F_{s} = c_{s} ({\dot{z}}_{s} - {\dot{z}}_{c} - l_{1} {\dot{ϕ}}_{c} - b_{1} {\dot{θ}}_{c}) + k_{s} (z_{s} - z_{c} - l_{1} ϕ_{c} - b_{1} θ_{c})

(2)

2. The vertical force responses F_ci of cab isolations are calculated in Section 2.2.

Loading phase and drum-hop phase

3. The excitation forces F_dj of the rigid drum-elastoplastic soil interaction (RD-ESI).

According to the study of Adam and Kop,² the elastoplastic soil (ES) was characterized by the elastic damping constant c_se and plastic and elastic stiffness constants k_sp and k_se. Thus, the RD-ESI model is established to determine F_dj, as shown in Figure 3, where m_e and m are the mass of rotating eccentric and total mass of the vibrator drum and front vehicle body, respectively. z_d and z_se are displacements of drum and elastic soil deformation in the vertical direction. F_g is the reaction force of plastic deformation generated by the soil layer. F_e = m_eω²e sinωt is the force heave of the eccentric mass in the rotating direction. ω and e are rotational speed and eccentricity of m_e. l_a is the static equilibrium line. g is the gravitational acceleration.

Figure 3.

Model of the rigid drum-elastoplastic soil interaction.

During soil compaction, over each cycle of the RD-ESI, the drum motion on a soil patch may appear in two or three phases of loading phase, unloading phase, and drum-hop phase. To determine z_d and F_dj, the vibration equation of the RD-ESI ^4,20 is described as follows

{\begin{cases} ε γ m_{d} {\overset{⃛}{z}}_{d} + m_{d} {\ddot{z}}_{d} = ε γ {\dot{F}}_{d} + F_{d} - ε c_{s e} {\dot{z}}_{d} + (ε - 1) k_{s p} z_{d} \\ + ε γ m e e ω^{3} \cos ω t + m_{e} e ω^{2} \sin ω t \\ F_{d} = \sum_{j = 1}^{2} F_{d j} = \sum_{j = 1}^{2} [c_{d j} ({\dot{z}}_{f f j} - {\dot{z}}_{d j}) + k_{d j} (z_{f f j} - z_{d j})] \end{cases}

(3)

m_{d} {\ddot{z}}_{d} = F_{d} - c_{s e} {\dot{z}}_{d} + m_{e} e ω^{2} \sin ω t

(4)

m_{d} {\ddot{z}}_{d} = F_{d} + m g + m_{e} e ω^{2} \sin ω t

(5)

where

γ = c_{s e} / k_{s p}

and

ε = k_{s p} / (k_{s p} + k_{s e})

are the soil damping and plasticity factors, respectively.

Equations (3)–(5) are then applied to calculate the parameters of z_d and F_d.

4. Excitation forces F_tj of the elastic tire-deformable soil contact (ET-DSC).

The contact of the elastic tires and off-road terrain with the random surface also yields vibrations; thus, the ET-DSC model shown in Figure 4 is used to determine F_tj.

Figure 4.

Model of the elastic tire-deformable soil contact .

When the tire travels on off-road terrains with roughness surface q_(t), the soil ground is sunk by z_oa due to the impact of the tire dynamic and static load of vehicle. Two deformable characteristics including one of the tire-soil deformation (c’oc-region) and another one of the unique soil (ca-region) are thus described as in Figure 4. In the deformable regions of c’oc and ca, both the generated pressure p_x and shear stress τ_x impact on the tire. F_g generated by off-road terrain and tire interaction is written as follows

F_{g} = B_{t} r_{t} \int_{0}^{θ_{a} (t)} (p_{x} \cos θ + τ_{x} \sin θ) d θ

(6)

where B_t and r_t are the tire width and radius and θ_a(t) is the angle of the ET-DSC generally changed according to the terrain surface roughness.

Both τ_x and p_x determined in ¹ are given as

{\begin{cases} p_{x} = (k_{c} / b + k_{φ}) z_{x}^{n} \\ τ_{x} = (C + p_{x} \tan φ) (1 - e^{- (j / K)}) \end{cases}

(7)

Herein, k_ϕ and k_c are stiffness constants of soil. b is the smaller value between the contact patch and tire width. C is the cohesion constant of soil. n is the sinkage exponent.

Assuming that an average line l_a is representative of the roughness surface of terrain, so the sunk solid z_x is determined by

z_{x} = z_{o a} - z_{o x} + q_{(t)} = z_{t} - z_{0} - z_{o x} + q_{(t)}

(8)

where z_t and z₀ are displacements of tire and static sinkage. z_ox is soil sinking in the deformable region of cx.

The excitation q_(t) is calculated as follows.

Based on ISO/TC108/SC2/WG4 N57²¹ of deformable terrain surfaces, their spectral densities are given by

G (m) = G (m_{0}) {(\frac{m}{m_{0}})}^{- ω_{0}}, {\begin{cases} m > m_{0}, ω_{0} = 3 \\ m \leq m_{0}, ω_{0} = 2.25 \end{cases}

(9)

where the value G(m₀) is a measured soil roughness at a reference frequency of m₀ = 1/2π (cycle m⁻¹).

At a constant speed v₀ of the vehicle traveling, the terrain surface roughness is simulated as follows

q_{(t)} = \sum_{i = 1}^{N} \sqrt{2 G (i Δ m) Δ m} \sin (i Δ ω t + δ_{i})

(10)

Herein, the random phase δ_i is uniformly distributed from 0 to 2π. The fundamental temporal frequency is Δω = Δmv₀.

The different values of G(m) for unpaved off-road levels including levels from very good to poor were given by Mitschke.²² Thus, q_(t) in equation (10) is created by selecting a value G(m) of Mitschke. From the mathematical model of the vehicle shown in Figure 2 and ET-DSC model shown in Figure 4, the excitation forces F_tj are given by

{\begin{cases} F_{g j} = m_{t j} g + F_{t j} \\ F_{t j} = c_{t j} ({\dot{z}}_{t j} - {\dot{z}}_{x j}) + k_{t j} (z_{t j} - z_{x j}) \end{cases}

(11)

where m_tj is the vehicle mass at a wheel.

Model of cab isolation systems

With the design and optimization of TRI^{2-4, 8} in Figures 5(a) and (b) and its mathematical model with the linear damping and stiffness coefficients (c_r and k_r) shown in Figure 5(c), the TRI’s vertical dynamic force is described by

F_{T R I} = k_{r} z + c_{r} \dot{z}

(12)

Figure 5.

Structure and model of cab isolations. (a) Traditional rubber isolations, (b) optimal rubber isolation, and (c) its mathematical model.

Because of the TRI’s effectiveness on improving the cab’s ride quality was very low,^2-4 this study proposes the CHPI based on advantages of the HI and the PI^{9-10, 12, 15} to further ameliorate the cab’s ride quality of vibratory roller. The CHPI’s structure includes the airbag and air reservoir connected by the air pipe system, a fluid chamber, and a damping plate in fluid chamber driven by the bolt. The liquid flows in upper/lower chambers are led by the damper plate’s transfer via both the orifices and the annular orifice in the HI. Thus, the structure and dynamic model of CHPI are described in Figures 6(b), where c_h is the HI’s nonlinear damping constant, k_e and k_v are the PI’s static and viscous stiffness coefficients, and M and c_β are the mass and nonlinear viscous damper coefficient of the airbag.

Figure 6.

(a) Combined hydropneumatic isolation structure and (b) its mathematical model.

Based on the calculation result of the HI in ^8–10, its liquid damping force is given by

F_{h} = c_{h} | \dot{z} | \dot{z}

(13)

Similarly, with the PI, the airbag is assumed to deform only in the z-direction, and the initial volumes of the airbag and reservoir are V_b0 and V_r0, respectively; therefore, the reservoir and airbag volumes after deformation are defined by

{\begin{cases} V_{r} = V_{r 0} - A_{s} ζ \\ V_{b} = V_{b 0} + A_{s} ζ - A_{e} z \end{cases}

(14)

where ζ is the air displacement in the pipe and A_e and A_s are the effective and pipeline’s cross-sectional area, respectively.

Based on the calculation result of the dynamic parameters of the airbag in ¹⁵, the parameters k_e, k_v, and M, respectively, are determined as follows

k_{e} = \frac{λ A_{e}^{2} p_{0}}{V_{r 0} + V_{b 0}}, k_{v} = \frac{V_{r 0} k_{e}}{V_{b 0}} and M = A_{s} l_{s} ρ Γ^{2}

(15)

where λ and p₀ are the polytropic rate and initial pressure of the airbag. ρ and l_s are the air density and the surge pipe length, respectively, and Γ = [V_r0/(V_r0+V_b0)] × (A_e/A_s).

Therefore, the airbag’s viscous and static forces in the z-direction are calculated by²³

{\begin{cases} F_{v} = c_{β} {| \dot{ζ} |}^{β} sign (\dot{ζ}) + M \ddot{ζ} \\ F_{e} = k_{e} z \end{cases}

(16)

The vertical airbag’s dynamic force F_b from equation (16) is then inferred by

F_{b} = k_{e} z + c_{β} {| \dot{ζ} |}^{β} sign (\dot{ζ}) + M \ddot{ζ}

(17)

By combining Equations (13) and (17) of the HI and PI, the CHPI’s dynamic force is written as follows

F_{C H P I} = c_{h} | \dot{z} | \dot{z} + k_{e} z + c_{β} {| \dot{ζ} |}^{β} sign (\dot{ζ}) + M \ddot{ζ}

(18)

At each mount i of cab isolations, the dynamic force F_ci can be rewritten as follows

F_{c i} = {\begin{cases} c_{r i} {\dot{z}}_{i} + k_{r i} z_{i} \\ c_{h i} | {\dot{z}}_{i} | {\dot{z}}_{i} + k_{e i} z_{i} + c_{β_{i}} {| {\dot{ζ}}_{i} |}^{β_{i}} sign ({\dot{ζ}}_{i}) + M_{i} {\ddot{ζ}}_{i} \end{cases} \begin{matrix} T R I \\ C H P I \end{matrix}

(19)

where z_i and its derivatives are the vibration heaves and their speeds on floors of the cabin and vehicle at each mount i. Their equations are determined by

{\begin{cases} z_{i} = z_{c} - z_{r f} + {(- 1)}^{ν} l_{ν} ϕ_{c} - l ϕ_{r f} + {(- 1)}^{i} b (θ_{c} - θ_{r f}) \\ {\dot{z}}_{i} = {\dot{z}}_{c} - {\dot{z}}_{r f} + {(- 1)}^{ν} l_{ν} {\dot{ϕ}}_{c} - l {\dot{ϕ}}_{r f} + {(- 1)}^{i} b ({\dot{θ}}_{c} - {\dot{θ}}_{r f}) \end{cases}

(20)

w h e n {\begin{cases} i = 1,2 \\ i = 3,4 \end{cases} t h e n {\begin{cases} ν = 2, l = l_{5}, a n d b = b_{i + 1} \\ ν = 3, l = l_{4}, a n d b = b_{i - 1} \end{cases}

Simulation and analysis of results

Efficiency indicators

The isolation effectiveness of suspension systems was mainly assessed via three indexes working space, ride quality, and road friendliness, in which the ride quality index assessed via RMS acceleration was one of the most important indexes.^{8, 24} On the other hand, according to ISO 2631,²⁵ PSD acceleration is given to evaluate human’s endurance that confines under excitation vibrations at low frequencies. ISO-2631-1 emphasized that the operator’s safety and health were greatly affected by the vibrations at a frequency range below 10 Hz.

Consequently, this study, the CHPI’s effectiveness at the low-frequency region is compared with TRI through the values of PSD and RMS of operator’s seat, cab pitching angle, and rolling angle. Both smaller values of PSD and RMS with corresponding isolations mean that its vibration isolation effectiveness is better, and RMS accelerations are described as follows

a_{w} = {[\frac{1}{T} \int_{0}^{T} {(a_{w} (t))}^{2} d t]}^{0.5}

(21)

where a_w(t) is the vertical, pitching, and rolling accelerations of operator’s seat and cab, respectively. T is the time of the numerical simulation.

Experiment of vibratory roller

In order to evaluate the CHPI’s effectiveness on isolating the cab vibrations, cab isolations used by TRIs are tested to confirm the accuracy of the mathematical model. In the compaction condition of the vibrator drum on the off-road terrain, the low and high frequencies at 28 Hz/35 Hz of the vibrator drum could generate the maximum compaction force.^{1, 4} Based on operation parameters of the vehicle equipped with TRI, as listed in Tables 1–2, the experiment and simulation of the vehicle are made in condition of the vehicle traveling at 3 km h⁻¹ and compacting on high-density soil and poor surface roughness of the ES at a frequency 35 Hz of the vibrator drum. The ES’s parameters are listed in Tables 3–4,^{2, 4, 22} and its test process is detailed as follows.

Table 1.

Operation parameters of vibratory roller.

Parameter	Value	Parameter	Value
m_s/kg	85	l₈/m	1.5
m_c/kg	891	b₁/m	0.55
m_ff/kg	2822	b₂/m	0.7
m_fr/kg	4464	b₃/m	0.68
m_d/kg	4378	b₄/m	0.945
l₁/m	0.383	b₅/m	0.945
l₂/m	0.1	k_s/kN m⁻¹	12
l₃/m	0.524	k_d1,2/kN m⁻¹	3900
l₄/m	0.136	k_t1,2/kN m⁻¹	500
l₅/m	0.76	c_s/kNs m⁻¹	0.12
l₆/m	0.9	c_d1,2/kNs m⁻¹	2.9
l₇/m	0.6	c_t1,2/kNs m⁻¹	4.0

Table 2.

Operation parameters of cab isolation systems.

Isolation	Parameter	Value	Parameter	Value
TRI	k_r1,2/kN m⁻¹	910	c_r1,2/Ns m⁻¹	218
TRI	k_r3,4/kN m⁻¹	120	c_r3,4/Ns m⁻¹	29
CHPI	k_e1,2/kN m⁻¹	910	c_β1,2/kNs² m⁻²	12.4
	k_e3,4/kN m⁻¹	120	c_β3,4/kNs² m⁻²	10.7
	k_v1,2/kN m⁻¹	1530	c_h1,2/kNs² m⁻²	20
	k_v3,4/kN m⁻¹	201	c_h3,4/kNs² m⁻²	4.5
	M_1,2/kg	98	M_3,4/kg	33

Note: TRI: traditional rubber isolation; CHPI: combined hydropneumatic isolation.

Table 3.

Operation parameters of elastoplastic soil with high-density soil.

Parameter	Value	Parameter	Value
k_sp/kN m⁻¹	283000	ɛ	0.87
k_se/kN m⁻¹	42300	c_se/kNs m⁻¹	37.1

Table 4.

Operation parameters of a deformable soil ground of the poor Grenville loam.

Parameter	Value	Parameter	Value
N	1.01	c/kPa	3.1
k_c/kN m⁻⁽ⁿ⁺¹⁾	0.06	ω ₀	2.14
k_ϕ/kN m⁻⁽ⁿ⁺²⁾	5880	G(m₀)/km³ cyc⁻¹	3782500

The ICP acceleration sensors in three directions are used to measure accelerations at four positions of isolations on the cabin floor (a_c1-4) and operator’s seat (a_z), as shown in Figure 7(a) and (b). Through the LMS dynamic test and analysis system of the signal processor, datum is calculated and given in the same Figure 7(c), and the acceleration responses of the cab and operator’s seat are then displayed.

Figure 7.

Experimental arrangement of vibratory roller. (a) Cab floor accelerometer at four positions of isolations, (b) operator’s seat accelerometer, and (c) display measurement results.

To determine the pitch and roll accelerations of the cab based on the measured accelerations in the vertical direction at four tested positions of cab isolations, it is assumed that the angular deformations of the cabin floor are very small and have negligible effect; therefore, the angular accelerations of the cab via its kinematic relations are calculated as follows ^{11, 13}

a_{ϕ c} = \frac{a_{c 1} - a_{c 3}}{l_{2} + l_{3}} and a_{θ c} = \frac{a_{c 1} - a_{c 2}}{b_{2} + b_{3}}

(22)

where a_c1-4 are the measured accelerations in the vertical direction at four tested positions. l_2,3 and b_2,3 are the horizontal and width distances between the tested points.

The experimental PSD results of operator’s seat heave, cab’s pitching angle, and cab’s rolling angle are then compared with the simulated results, as illustrated in Figures 8(a–c).

Figure 8.

Result of frequency responses. (a) Operator’s seat heave, (b) cab’s pitching angle, and (c) cab’s rolling angle.

Observing Figure 8, it is found that the measured values are almost similar to the numerical simulation values under the same operating condition. A small change between the results of the experiment and simulation is also shown in the same Figure 8. These changes are ascribed to the dimension error of the vehicle and effect of the engine excitation in experimental process. However, the result error between the experiment and simulation is negligible. Therefore, the vibratory roller model with its operation parameters and deformable terrain can be relied upon to evaluate the CHPI’s effectiveness on ameliorating the cab’s ride quality.

Simulation results

Cab’s isolations equipped with CHPI for the vibratory roller is then simulated under the same experimental condition of TRI at low-/high-excitation frequencies 28 Hz/35 Hz of drum, and CHPI’s operation parameters have been listed in the same Table 2. Herein, the parameter k_ei of CHPI has been equivalently calculated with the parameter k_ri of TRI, while other parameters of CHPI have been calculated via the structure of CHPI, and the coefficient of c_hi is referenced in ⁸. Both the maximum values of the PSD values and RMS values of operator’s seat heave, cab’s pitching angle, and cab’s rolling angle are used to evaluate CHPI’s effectiveness under the low-excitation frequencies.

Result in the frequency region

The PSD results at different excitations 28 Hz and 35 Hz of drum are plotted in Figures 9 and 10. Concurrently, their resonance frequencies are given in Table 5. The comparison results between TRI and CHPI in Figures 9 and 10 and Table 5 revealed that the PSD value of operator’s seat heave, cab’s pitching angle, and cab’s rolling angle with TRI has shown more peaks of the resonance than that of CHPI. Thereby, the high-density soil of the ES seriously impacts the operator’s health via the TRI. Conversely, the resonance peaks of PSD accelerations by using CHPI are reduced in comparison with TRI, particularly at resonance frequencies of 2.49 Hz, 5.69 Hz, 8.59 Hz, and 18.09 Hz. Besides, the resonance frequencies with the CHPI are changed compared with TRI in all directions. This is due to the change of coefficients V_b, M, and ρ of the air in airbag.

Figure 9.

Frequency responses at 28 Hz of drum. (a) Operator’s seat heave, (b) cab’s pitching angle, and (c) cab’s rolling angle.

Figure 10.

Frequency responses at 35 Hz of drum. (a) Operator’s seat heave, (b) cab’s pitching angle, and (c) cab’s rolling angle.

Table 5.

Resonance frequency with cab isolations.

Resonance frequency, Hz	At 28 Hz		At 35 Hz
Resonance frequency, Hz	TRI	CHPI	TRI	CHPI
ƒ₁	1.69		1.69
ƒ₂	1.89	1.7	1.89	1.7
ƒ₃	2.09	2.1	2.09	2.1
ƒ₄	2.49	2.2	2.49	2.2
ƒ₅	5.69		5.69
ƒ₆	8.59		8.59
ƒ₇	18.09		18.09
ƒ₈	28.18	26.6	35.18	29.1

Under vibration excitations from 0.5 to 10 Hz, the PSD’s resonance peaks with CHPI are remarkably decreased at both the low and high frequencies 28 Hz and 35 Hz of the vibrator drum in all directions, especially at excitation frequencies below 4 Hz. The maximum values of PSD accelerations of operator’s seat heave, cab’s pitching angle, and cab’s rolling angle with CHPI are lower than that of TRI by 47.1%, 57.1%, and 56.2% at 28 Hz, and by 38.8%, 59.5%, and 64.8% at 35 Hz of the vibrator drum, respectively. These results can be due to the impact of CHPI damper forces $F_{h i} = c_{h i} | {\dot{z}}_{i} | {\dot{z}}_{i}$ and $F_{β i} = c_{β i} {| {\dot{ζ}}_{i} |}^{β_{i}} sign {(\ddot{ζ})}_{i}$ . Thus, the CHPI could significantly ameliorate the operator’s health in the low-frequency region and under various excitations 28 Hz and 35 Hz of the vibrator drum.

With the vibration excitations above 10 Hz, the PSD’s resonance peaks are also shown in the same Figures 9 and 10. The resonance frequencies with TRI also appear at 28.18 Hz under a low excitation and 35.18 Hz under a high excitation of drum. This has been ascribed to the influence of resonances at various excitations 28 Hz and 35 Hz of the excitation drum. Meanwhile, the PSD’s resonance peaks with the CHPI occur at 26.6 Hz and 29.1 Hz instead of at 28 Hz and 35 Hz of the excitation drum; concurrently, the PSD accelerations are slightly increased in comparison with the TRI. This particularity may also ascribe the impact of the parameter k_e of airbags. However, the operator’s health is insignificantly affected in this frequency range. Therefore, it can conclude that the operator’s safety and health are remarkably ameliorated by using the CHPI under low frequencies in the condition of the vibratory roller traveling and compacting on the ES.

Result in the time region

The accelerations of the operator’s seat heave, cab’s pitching angle, and cab’s rolling angle are also illustrated in Figures 11 and 12, respectively. The comparison results between TRI and CHPI in both Figures 11 and 12 indicate that the accelerations with the CHPI are smaller than that with the TRI at various excitations 28 Hz and 35 Hz of the vibrator drum at high-density soil of the ES.

Figure 11.

Acceleration responses at 28 Hz of drum. (a) Operator’s seat heave, (b) cab’s pitching angle, and (c) cab’s rolling angle.

Figure 12.

Acceleration responses at 35 Hz of drum. (a) Operator’s seat heave, (b) cab’s pitching angle, and (c) cab’s rolling angle.

Additionally, the compared RMS values of operator’s seat heave, cab’s pitching angle, and cab’s rolling angle between TRI and CHPI in Figures 13(a) and (b) also revealed that their RMS values with CHPI are lower than that of TRI by 31.9%, 43.1%, and 49.2% at a low excitation of 28 Hz, and by 34.8%, 41.0%, and 52.2% at a high excitation of 35 Hz. It can be due to the influence of damper forces F_hi and F_βi of CHPI. Thus, the cab’s ride quality of vibratory roller can be ameliorated by using the CHPI.

Figure 13.

Root-mean-square accelerations of operator’s seat vibration and cab shaking. (a) At 28 Hz and (b) at 35 Hz of the excitation drum.

Besides, the CHPI’s effectiveness is not only compared with the TRI via the RMS and PSD values but also compared with the different cab isolations in many previous studies including the TRI,¹¹ HI,¹³ and RI with an auxiliary hydraulic damper (RAH),³ and semi-HI.^{8, 14} The comparison values of the operator’s seat heave and cabin’s pitching angle employed by the various cab isolations are presented as in Table 6. It can be seen that RMS accelerations are lower than other isolations of the TRI, HI, and RAH. Also, the results with the CHPI are insignificantly higher than the semi-HI. Based on the analysis results, the operator’s ride quality and health have been remarkably enhanced with CHPI under both calculation domains of frequency and time. Consequently, the CHPI has an obvious effect on providing a good ride quality for the off-road vibratory roller cab under low-vibration excitation frequencies.

Table 6.

Comparison of RMS values with the different cab isolations at 28 Hz of the vibrator drum.

RMS value	TRI	HI	RAH	Semi-HI	CHPI
a_wz/(m/s²)	0.71	0.65	0.58	0.43	0.48
a_wφc/(rad/s²)	0.39	0.31	0.21	0.17	0.22

Note: HI: hydraulic isolation; RMS: root-mean-square; TRI: traditional rubber isolation; CHPI: combined hydropneumatic isolation.

Conclusions

The mathematical models of the vehicle and cab equipped with TRI are also tested under the same simulation conditions. The CHPI’s effectiveness is then simulated and assessed via two indexes of PSD and RMS accelerations of the operator’s seat vibration and the cabin shaking. The research results can be summarized as follows.

The results of PSD accelerations in the frequency domain and acceleration responses in the time domain with CHPI are lower than that of TRI under various conditions of low-/high-excitation frequencies 28 Hz/35 Hz of drum and the ES. Especially, the maximum value of PSD and RMS accelerations of operator’s seat, cab’s pitching angle, and cab’s rolling angle have been greatly reduced by 38.8%, 59.5%, and 64.8% and by 34.8%, 41.0%, and 52.2% at 35 Hz of the excitation drum, respectively.

The research results indicate that the CHPI with the properties of the high static stiffness and nonlinear damping obviously isolate the vibration under low frequencies and control cab’s pitching angle of the vehicle. Additionally, nonlinear damping parameters c_hi of the CHPI can be controlled to further enhance the isolation effectiveness of the CHPI.

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 work has been supported by the Science and Technology Research Project of Education Department of Hubei Province, China (No. B2020199), Teaching and Research Project of Hubei Polytechnic University, China (No. 2020C21), and Open Fund Project of Hubei Key Laboratory of Intelligent Transportation Technology and Device, Hubei Polytechnic University (No. 2020XY105).

ORCID iD

Vanliem Nguyen

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