Ride comfort evaluation for a double-drum vibratory roller with semi-active hydraulic cab mount system

The construction machinery market has required increasingly not only on working capacity but also ride comfort quality, therefore it has required increasing toward researchers and manufacturers. The main objective of this paper proposes and evaluates the performance of semi-active hydraulic cab mount system (SHCMs) of a double-drum vibratory roller in the direction of enhancing vehicle ride comfort under different operating conditions. Firstly, a nonlinear dynamic model of passive hydraulic cab mount system (PHCMs) is established to determine its vertical force which is connected with a dynamic model of vehicle ground surface interaction. And then, a fuzzy logic controller (FLC) is designed to control the value of the damping force of SHCMs. Both the differential equations of motion and FLC are implemented in the MATLAB/Simulink environment. Finally, the ride performance of SHCMs is evaluated under different conditions according to ISO 2631: 1997 (E) standard. The obtained results show that the values of objective functions with SHCMs significantly reduce in comparison with PHCMs under different operating conditions.


Introduction
The earth-moving equipment often operate in harsh environments, sources of vibration are transmitted from the ground deformation, the internal combustion engine as well as the operating mechanism to the cab through cab mount system and driver's seat suspension system. Many research results have shown that driver works for a long time under vibration and shock environment, it can easily cause a series of occupational diseases such as spinal deformities, stomach diseases, etc. Especially, driver exposure for a long time with low frequency and large amplitude vibration which can cause physical discomfort or even diseases [1][2]. The topic of the ride comfort of earth-moving equipment is always of interest to researchers and manufacturers. The auxiliary cab mount system (ACMs) and main cab mount system (MCMs) of a vibratory roller were considered to solve the problem of cab shaking under low frequency excitation and then the design parameters of ACMs were optimized by the finite element method [3,5]. An auxiliary damping mount (ADM) of a vibratory roller was proposed to control the cab shaking based on a half-vehicle dynamics model [4]. The design parameters of rubber cab mount system of a single-drum vibratory roller were optimized by GA (Genetic Algorithm) [6] and NSGA II (Non-dominated Sorting Genetic Algorithm II) [7]. The dynamic characteristics of the vibratory roller and mount cab system were analyzed by both simulation and experimental methods [8]. A hydraulic cab mount system (HCMs) of an earth-moving machinery was proposed and evaluated its ride performance in comparison with the rubber cab mount system using a 3-D dynamic model of the cab with six degrees of freedom(DOF) [9]. The hydraulic cab mount system (HCMs) of a drum vibratory roller was proposed to evaluate the ride performance in comparison with two types of the rubber cab mount system (RCMs) and pneumatic cab mount system (PCMs) using a 3-D nonlinear vehicle dynamics model with eleven degrees of freedom [10]. The hydro pneumatic cab mount system (HPCMs) of a vibratory roller was proposed investigate the ride effectiveness of HPCMs in the direction of enhancing vehicle ride comfort [11]. In order to enhance the off-road vehicle ride comfort, many control methods have been used to control the semi-active or active mount systems of earth-moving equipment. A combination of fuzzy logic controller and PID controller was applied to control the damping coefficient of semi-active cab mount system of vibratory roller using a nonlinear vehicle dynamic model [12]. A fuzzy logic controller (FLC) was designed to control the damping coefficient value of the semi-active hydropneumatic cab mount system of a vibratory roller [13]. Similarly, a fuzzy controller was designed to control a kind of magneto-rheological (MR) damper of a semi-active mount system of vibratory roller using a 2-DOF dynamic model [14]. An optimal fuzzy-PID control method was designed to control for a semi-active hydraulic cab mount system using a three-dimensional nonlinear dynamic model of vibratory roller [15]. The main idea of this paper is to propose a semi-active hydraulic cab mount system (SHCMs) for a double-drum vibratory roller based on the development of the structure of a passive hydraulic cab mount system (PHCMs) with adjustable hydraulic damping force of hydraulic actuator. Firstly, a nonlinear dynamic model of passive hydraulic cab mount system (PHCMs) is established to determine its vertical force which is connected with a dynamic model of vehicle -ground surface interaction. And then, a fuzzy logic controller (FLC) is designed to control the value of the damping force of SHCMs. Finally, the ride performance of SHCMs is evaluated through the root-mean-square (RMS) of acceleration responses (a ws , m/s 2 and a wcphi , rad/s 2 ) based on ISO 2631: 1997 (E) standard [16] when vehicle operates under survey conditions.

Passive hydraulic cab mount (PHCM)
The structural diagram of a passive hydraulic cab mount (PHCM) with the orifices consists of rubber part, two oil chambers such as lower and upper chambers, and the fluid flowing up and down through the orifice derived from the damping plate driven by the bolt, the damping plate and the orifices, as shown in Fig.1(a). A nonlinear dynamics model is established based on the structural diagram of Fig.1(a) to determine its vertical force, as shown in Fig.1 (b), where, m c and m b are vehicle body mass and cab mass, respectively, p 1 and p 2 are the upper liquid chamber and the lower liquid chamber, respectively, z c and z b are the vertical displacements of cab and vehicle body masses, respectively, k r and c r are stiffness and damping coefficients of rubber part, respectively and F c is the total vertical forces of hydraulic cab mount. Based on Fig. 1 (b), the total vertical forces of PHCM could be achieved by where, F r is the vertical force of rubber part which is defined by Eq.(2) and F h is the damping force of the hydraulic actuator with the orifices which is defined by Eq. (7). The damping force of PHCM is determined by where, p is the pressure loss at the orifices, A d is the effective area of the damping plate. Based on the reference [10,17], the pressure loss at the orifices is determined by where, c 0 is the positive constant which is function of the geometry of the orifice and the fluid property, and 0 z is the average flow velocities in the orifices The equation of continuity for the flow through the orifice is written as follows where, A c and A a are the effective area of the chamber and the orifices, respectively, z is the relative velocity between the displacements of the vehicle body and cab masses.
Substitute Eq. (5) into Eq. (4), the pressure loss at the orifices can be achieved by Substitute Eq. (6) into Eq. (4), the vertical damping force of the hydraulic actuator with the fluid flow through the orifices can be achieved by

Semi-active hydraulic cab mount (SHCM)
A control model for a semi-active hydraulic cab mount (SHCM) is developed from a model of passive hydraulic cab mount (PHCM) in Fig.1(b) with adjustable hydraulic damping force of hydraulic actuator, as shown in Fig.2 where, F r is the vertical force of rubber part which is defined by Eq. (2), F h is the damping force of the hydraulic actuator with the orifices which is defined by Eq. (7) and f is the adjustable damping force of the hydraulic actuator which is defined by fuzzy logic controller. The controller design for a semi-active hydraulic cab mount (SHCM) of a double-drum vibratory roller will be presented below  Table 2.

Half-vehicle Dynamic Model
A structure diagram of a double-drum vibratory roller is selected for the ride performance evaluation of a semi-active hydraulic cab mount system (SHCMs) which consists of the mount and suspension systems such as the dynamic drum mount systems, the cab mount system and driver's seat suspension system, as shown in Fig.3. A dynamic model of vehicle -ground surface interaction is developed from the structure of a double-drum vibratory roller in Fig.3, as shown in Fig.4 where Fcs and m c , respectively; k si , k di , k s and c si , c di , c s are the stiffness and damping coefficients of elastic road surfaces, front and rear mount systems of drums and driver's seat suspension system, respectively; z di , z b , z c and z s are the vertical displacements of the front and rear drums, vehicle body, cab and driver's seat, respectively;  b and  c are the pitch angle displacements of vehicle body and cab, respectively; q i are the front and rear drum absolute hard road excitations, respectively; l j are the distances; F ei =F 0i sin( i t) are the force excitations of the dynamic drums; F 0i are the amplitude of force excitations;  i are the angular frequencies of the vibrators; F ci are the vertical forces of cab mount system and v is the vehicle speed (i=1÷2, j=1÷6).
where, F ci is the total vertical forces of cab mount system which is is defined by Eq. (12). 0 The vibration equations of the vertical and pitching vehicle body are written as follows 2 2 ( 1) where, F di are the vertical forces of front and rear mount systems of dynamic drums which could be determined through two cases. Case 1: Vehicle operates in the workshop Condition1: When both front and rear drums compact on the original place, the differential equations describing the vertical vibrations of dynamic drums are written as follows  describing the vertical vibrations of front or rear dynamic drums is determined by Eq. (15) or Eq. (16) and the vertical force of rear or front dynamic drum mount system is determined by Eq. (18) or Eq. (17).

Case 2: Vehicle moves into the workshop
Vehicle moves on a variety of ground surfaces such as the absolute hard and deformed ground surfaces. The dynamic drums move on the absolute hard road surface. The vertical forces of front and rear mount systems of dynamic drums are defined as where, q 1 and q 2 are the front -rear drum absolute hard road excitations according to the International Standards Organization (ISO 8608) [23].

Results and Discussion
To solve the equations describing the vibrations in Fig.4 and design the fuzzy logic controller (FLC) for the ride performance evaluation of a semi-active hydraulic cab mount system (SHCMs) compared to the passive hydraulic cab mount system (PHCMs), Matlab /Simulink environment software is applied to simulate and control with a set of parameters of the vehicle, the PHCMs, the elastic soil ground and road surface roughness in the references [19,20].  The comparison results in Fig.5 show that the peak amplitude values of a s and a cphi with SHCMs respectively decrease compared to the PHCMs. Furthermore, we could be determined the values of a ws and a wcphi through Eq. (19) as a ws = 1.2865 m/s 2 , a wcphi = 1.6970 rad/s 2 with PHCMs and a ws = 1.0305 m/s 2 , a wcphi = 1.3393 rad/s 2 with SHCMs. The obtained results show that the a ws and a wcphi values with SHCMs respectively improve by 24.84% and 26.71% compared to PHCMs. The values of a ws and a wphi according to ISO standard 2631-1:1997 [16] are chosen as the objective functions which are defined by the formula below   Fig.9. The comparison results in Fig.8   Similarly, the comparison results in Fig.9 show that the values of a ws and a wcphi with SHCMs significantly decrease compared to PHCMs when ground surface conditions become bad. The results reflect that vehicle ride comfort with SHCMs is better than the PHCMs results as indicated by a ws and a wcphi values. Thus, the ride performance of SHCMs with FLC has significantly improved vehicle ride comfort compared to PHCMs under low excitation frequencies and large amplitudes of road surface.

Conclusions
In this paper, a semi-active hydraulic cab mount system (SHCMs) of a double-drum vibratory roller was proposed on the basis of the development of the structure of a passive hydraulic cab mount system (PHCMs) with adjustable damping force of hydraulic actuator.