A Theoretical Model with Which to Safely Optimize the ...

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The safety of trailers as they travel around curves has been analyzed extensively previously. The effect of axle spacing, the load and the height of the center of gravity height on heavy trucks’ stability and handling properties have been studied [ 5 8 ]. Other works [ 9 12 ] have revealed significant influence of loading and suspension stiffness on tractor-semitrailer yaw stability. That revelation involved theoretical models, simulations by computer, and full-scale tests. The theoretical transversal acceleration of a truck as it enters a horizontal curve is commonly calculated as follows [ 13 ]:

g

v

R

k

Withfor the acceleration of gravity,as the truck’s speed,as the radius of the curve, andas the side-slope. However, the equation does not include several other factors that affect the truck in actual operating conditions. These include the force of the wind and the slope of the road. The authors discovered that the lateral acceleration of a 5-axle trailer briefly exceeded the expected values. An earlier study [ 14 ] found that the rollover threshold for various articulated vehicles ranges from 0.33 to 0.54 g, according to the dimensions and weight of the load. Other authors [ 15 ] determined when the vehicle might roll over and developed a dynamic rollover threshold. The critical lateral accelerations that these authors determined range from 0.28 to 0.42 g according to the height of the center of gravity (CoG). These are in agreement with the values that earlier studies have provided [ 14 17 ]. In addition, the British Standard [ 18 ] describes blocking and lashing procedures for securing loads. It established coefficients of 0.8 for forward direction (braking) and 0.5 for backward (acceleration) and sideways (turning) directions. It does not relate these coefficients to the speed or consider the inclination of the road or force of the wind. This means that the coefficients cover all of these phenomena.

F D = 1 2 · ρ · v w 2 · A · C d

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FD

ρ

vw

A

Cd

b

A

The aerodynamic forces on a truck affect the performance in various ways [ 19 21 ]. Forces acting on the side increase the roll instability like the lateral acceleration in curve driving does. Furthermore, the longitudinal force affects the speed and acceleration of the truck and, consequently, its fuel consumption [ 22 ]. When a standard heavy truck drives at a speed of 70 mph, 65% of its fuel consumption, it has been estimated, is used to overcome the aerodynamic force [ 23 ]. Aerodynamic forces usually have a significant effect on the stability of abnormal loads. These forces are caused by the truck’s movement relative to the air. They emanate from the truck’s body, the chassis, the suspension, the axles, the wheels, the trailer, the load, and the space between the truck and trailer or payload. The drag equation below is generally used to calculate the aerodynamic forces:withas the drag force,as the fluid density,as the velocity of the air relative to the truck,as the area that is vertical to the relative motion andas the drag coefficient. The drag coefficient depends on the relative position and geometry of the payload. However, the equation is accurate only for isolated objects. It is normally employed for basic load shapes. The actual truck–trailer configuration can increase the aerodynamic forces. The greatest contributor to the longitudinal aerodynamic force acting in commercial tractor-trailer configurations is the space between tractor and semitrailer [ 22 23 ]. The space is expressed by, a non-dimensional form, in whichis the width of the space (gap) andis the area. The drag force that the gap produces is zero for small gaps. It increases suddenly when, but becomes stable at 0.7 [ 22 23 ]. The other parameter that raises the drag force is the yaw angle, especially in trucks that have sharp-edged cabs. Crosswinds on exposed highways and bridges can cause difficulties in driving in tall and long vehicles and the risk of a serious accident. The force of the crosswind on a conventional truck–trailer in North America as it crosses a bridge was examined by using Computational Fluid Dynamics (CFD) [ 24 ]. The authors validated the model with experimental data that previous studies had provided [ 25 26 ]. The conclusion was that wind pressure can be sufficient to overturn the truck–semitrailer at the wind speeds that were studied.

This paper describes a novel theoretical model that can determine the stability of special transport. The proposed model determines the load on each axle, the tipping angle, and the suspension system’s oil pressure. It was based on modular trailers models that appear in the literature, as well as those in common use within the heavy transport sector [ 27 ]. The model was tested experimentally by a full scale test [ 28 ] in which oil pressure data and output from the model were compared. To conduct the test, a nacelle wind turbine that weighed 42,500 kg and was 5133 × 2650 × 2975 mm in length, width, and height, respectively, was placed at different points within a modular trailer. With the validated theoretical model, a proposed optimization algorithm is capable of determining the optimal CoG of the load, as well as the number of trailers, number of axles, oil pressures, and hydraulic configuration. The theoretical model and optimization algorithm were tested with a cylindrical tank that weighed 108,500 kg and had dimensions of 19,500 × 3200 × 2500 mm. The results showed that the optimization algorithm could safely optimize the configuration of the hydraulic suspension of modular trailers in special road transport, increase the accuracy and reliability of the calculation of the load configuration, save time, simplify the calculation process, and be easily implemented. The theoretical model and the optimization algorithm proposed are able to (1) optimize safely the configuration of modular trailers’ hydraulic suspension in special road transport, (2) improve the reliability and accuracy of load configuration calculations, (3) saves time, (4) simplify the calculation process, and (5) be easily implemented.

 During load-outs, they are often used as vehicle to drive heavy load components from the quay onto the barge. One trailer consists of different modules from 4 or 6 axle lines with a capacity of 36 up to 48 tons per axle line each. SPMT's have the possibility of circle drive around the centre of the trailer or execute "crab moves".

The lifting height of heavy load components is approx. 500 mm.

Due to their variety of combinations, they can lift and move nearly every heavy load component.

 A self-propelled modular transporter or sometimes self-propelled modular trailer (SPMT) is a platform vehicle with a large array of wheels. SPMTs are used for transporting massive objects such as large bridge sections, oil refining equipment, motors and other objects that are too big or heavy for trucks. Trucks can however provide traction and braking for the SPMTs on inclines and descents.

 SPMTs are used in many industry sectors worldwide such as the construction and oil industries, in the shipyard and offshore industry, for road transportation, on plant construction sites and even for moving oil platforms.

A typical SPMT can have a grid of several dozen computer-controlled wheels, all individually controllable, in order to evenly distribute weight and steer accurately. Each individual wheel can swivel independently from the others to allow it to turn, move sideways or even spin in place. Some SPMTs allow the wheels to telescope independently of each other so that the load can be kept flat and evenly distributed while moving over uneven terrain. As SPMTs often carry the world's heaviest loads on wheeled vehicles, they are very slow, often moving at under one mile per hour while fully loaded.

Some SPMTs are controlled by a worker with a hand-held control panel, while others have a driver cabin. In addition, multiple SPMTs can be combined to transport massive building-sized objects.

SPMT Characteristics

1.Stability

Each trailer unit can be separated into 3 and 4 hydraulic fields. Each field can maintain hydraulic pressure to each axle in that field. This allows the trailer to adjust for uneven surfaces increasing stability of the loads.Low loading height & Wide wheel track ensures extreme stability.

2.Loading Capacity

Platforms are torsion-free and bending resistant, designed for direct loading. Platform design and hydraulics allow for a maximum 40,000 kg per axle line.The platform trailer can be equipped with serrated aluminiumplates to cover the track rods.