Abstract
Given the crossing-obstacle problems of wheeled vehicle on soft beaches, the changing rules with driving speeds of the crossing-obstacle ability of wheeled vehicle, soil moisture content, and soil type on soft beach ground were innovatively studied in this paper, with the hook traction force taken as the evaluating index. It showed that the RMS values of wheeled vehicle hook traction force, which was 9484N at 5 km/h and 8859N at 20 km/h, decreased with the increase in driving speed when the wheeled vehicle crossed the horizontal ditch. It collected soft beach ground soil samples and tested the parameters of mechanical properties. By considering specific structural parameters of the wheeled vehicle, this paper constructed the simulating model of the crossing obstacle ability of wheeled vehicle on the soft beach, analyzed the differences between the simulation and test result through full-scale vehicle tests. It discussed the influential factors of the crossing obstacle ability of wheeled vehicle on soft beach ground, indicated that the crossing obstacle ability of wheeled vehicle on soft beach increased with the increase of equipment’s driving speed and soil moisture content. This paper creatively proposed a method to evaluate the equipment’s off-road trafficability based on the combination of soil in-situ collection, soil tank test, dynamic simulation and experimental verification, and proposed the influencing factors and changing rules of equipment’s off-road trafficability on soft beach ground, which laid a theoretical foundation for the research on the off-road trafficability of wheeled vehicle.
1. Introduction
When wheeled equipment drives on the soft beach ground, the wheels are constantly embed and ejected in the beach soil. The research on the crossing obstacle ability of wheeled vehicle on soft beach ground involves complex influence factors such as vehicle structural parameters, ground topography and terrain, soil mechanical characteristics, the coupling relationship between wheel and ground, coupled with the high moisture content of beach ground and complex mechanical characteristics of beach soil, has become one of the hot spots and difficulties in vehicle ground mechanics.
Irani et al. (2011) studied the subsidence process of the dentate rigid wheel in soft sandy soil and analyzed the distribution of soil stress under the rigid tooth wheel when the wheel run on the soft sandy soil and construct the dynamic pressure-bearing model of sandy soil. Jayakumar et al. (2018), according to the soil bearing problem on soft ground, developed a soil pressure-settlement test platform, constructed the Bekker pressure correction model based on the experimental data. Feng et al. (2020) analyzed the influential rules of platen size, moisture content, soil density, and other factors on the pressure-settlement curve in the platen test, constructed the soil pressure bearing model suitable for the soft clay by fitting the experimental data. By considering the resistance theory of soil mechanics, Li et al. (2021), Zhang et al. (2020), Zheng et al. (2019) built the static pressure-bearing characteristics model of planetary soil, analyzed the flow form of satellite soil particles in the wheel dynamic subsidence process, and established the time-varying fitting model of dynamic and the prediction model of satellite soil subsidence. Lv et al. (2019), Yang et al. (2019), and Zhu et al. (2020), by studying the influence of loading speed, soil moisture content, and repeat load times on deformable soil bearing characteristics by simulating analysis and laboratory tests, constructed the soil dynamic bearing pressure and dynamic shear empirical model. Based on the soil trough experiment method, Yang et al. (2020), proposed a theoretical model of the relationship between soil subsidence and mechanical property parameters, soil moisture content, and repeated loading times. Golub et al. (2019), based on wheel-rail coupling relationship simulation and test results, constructed the theoretical calculation model of wheel subsidence. Sitkei et al. (2019) summarized the experimental data of soil mechanical properties by dimensional analysis and proposed a soil mechanics model with wide applicability. Becker et al. (2020) investigated the different methods used to measure motion resistance on tires with large lugs. They concluded that some basic considerations that need to be taken into account are the very low longitudinal forces that need to be measured compared to the large vertical load carried by the tire and tire operating condition. Dallas et al. (2020) proposed a parameter evaluating method of reduced order nonlinear soil dynamic bearing model and construct an online terrain parameter evaluation system for the deformable ground of the unmanned vehicle. Karpman et al. (2020) analyzed the dynamic coupling relationship between wheel and ground by discrete element method and took the amount of soil settlement as the evaluation index, evaluating the error between simulation and test results. Wesołowski et al. (2020) studied the coupling effect between aircraft tire and ground by combining theoretical analysis and experimental verification, analyzed the deformation and stress of ground soil under different loads.
Based on the complex coupling between tires and soil, Beregi et al. (2020) analyzed the tire's nonlinear dynamics and constructed the theoretical model of tire traction force. Cutini et al. (2020) analyzed the construction of NG-NRMM from military requirements, modeling methods, the randomness of path planning, and mobility requirements of intelligent vehicles and proposed the evaluation method of vehicles' traction force running on snow and icy roads. McCullough et al. (2021) analyzed the construction of NG-NRMM from military requirements, modeling methods, the randomness of path planning, and mobility requirements of intelligent vehicles and present a prediction and evaluation method for off-road vehicle mobility in a wide area. For the low gravity on the lunar surface, Yao et al. (2016), Huang et al. (2019) established the modified soil pressure model and study a single wheel's pressure characteristics and traction passability under light load conditions. Based on the ground elevation error and the randomness of soil mechanical properties, Gonzalez et al. (2021) proposed a random migration algorithm for off-road vehicles and analyzed the probability distribution of vehicle cross-country passability. Based on the coupling relationship between track and ground, Nicolini et al. (2018) constructed the tracked vehicle-ground multibody dynamics simulation model focusing on the ground mechanical properties. Rybansky et al. (2020) studied the characterization method of micro-terrain and the passability of vehicles under different terrain microstructures and constructed the vehicle passing and mobility map based on micro terrain. Suzuki et al. (2020) studied the theory of wavy geomorphology formed by wind-blown sand in multiple stages and presented an evaluation method of wheel passability under complex terrain based on resistance theory.
In conclusion, the scholars were mainly concentrated on the fields of the model construction of soil dynamic bearing, the subsidence prediction, the traffic ability and mobility characteristic evaluation of vehicles under hard ground conditions, the wheel-ground coupling relationship, and shear slip failure mechanism of soil under pressure, but the research of the equipment traffic ability on high moisture content and geological soft beach ground was rarely involved. This paper takes the crossing obstacle ability of wheeled vehicle on soft beach ground as the research object, attempting to obtain the typical soil mechanical properties of beach soil, analyzing the evaluating index and test verification technology of crossing obstacle ability of wheeled vehicle on soft beach ground, discussing the influential factors of the wheeled vehicle's crossing obstacle ability on soft beach ground, providing technical support for the trafficability characteristic research of beach ground.
2. Mechanical properties of beach soil
To study the effect of soil on wheel resistance and settlement, scholars have used different bearing models to describe the relationship between vertical deformation and normal stress of soft ground: Bekker, Reece, and Korchunov’s pressure-bearing models and the pure exponential pressure-bearing model, etc., among which Bekker’s pressure-bearing model is the most widely used. In Bekker’s pressure-bearing model under the pressure force of a press plate used to describe the pressure-bearing characteristics of soil, the deformation relationship between vertical load and ground soil can be expressed as follows
To ensure the consistency between laboratory soil samples and field soil properties, on-site sampling was used to collect the soil on the beach, and the conic index of soil was taken as the evaluating index.
This paper selected the circular pressure plate with a radius of 70 mm and 90 mm, respectively, to replace the actual wheels, obtained the mechanical properties of the Bekker model by testing the pressure displacement curve of the pressure plate of the soil. It adopted the high-precision electronic universal testing machine to carry out the indoor pressure plate test of the beach ground soil, as shown in Figure 1(a), measured the settlement and load amount when the pressure reached 75kPa. The loading rate of the bearing characteristic test was 50 mm/min, and the applied vertical loads were 1900N (90 mm radius platen) and 1200N (70 mm radius platen). By processing the test data, we obtained the pressure characteristic parameters of the soil samples on the beach ground, as shown in Table 1. The mechanical properties experiments of soil samples. (a) Pressure characteristic experiment (b) Shear characteristic experiment. Bearing characteristic parameters of the Yellow River beach samples.
The shear strength of the soil on the beach ground was described by Moore–Coulomb strength theory, which was expressed as follows
In this paper, the ZJ strain-controlled direct shear apparatus was used to test the experimental shear curve of soil samples, as shown in Figure 1(b). The corresponding shear characteristic parameters were determined by using the Moore-Coulomb formula. When conducting the direct shear test of soil samples, the applied vertical pressure grade was 25kPa, 50kPa, 75kPa, and 100kPa, and the pressure was still for 2 mins. When the soil samples reach equilibrium, the direct shear test was conducted at a shear rate of 2.4 mm/min, and the shear-stress displacement relationship curve of the soil samples was obtained, as shown in Figure 2. Shear stress-displacement relation curve of soil samples.
We took the peak point on the shear stress-displacement curve of the beach ground soil as the shearing strength and obtained the shearing strength of the beach ground soil under different vertical pressures as shown in Figure 3. Through the analysis of the test data, we get the cohesion force c = 12.69kPa and internal friction Angle φ = 21.63 of the beach ground soil of Moore–Coulomb model. Shear strength under different vertical pressures.
3. Evaluating index of crossing obstacle ability of wheeled vehicle
Structural parameters of wheel-equipment.
The hook traction force, the difference between the maximum traction force and driving resistance of wheeled vehicle in the forward direction, is an important index to evaluate the ability of wheeled vehicle to surmount obstacles on the beach, shown as follows
When the wheeled vehicle was running on the beach because the beach was a typical soft ground, the tire of the wheeled vehicle can be calculated as a rigid wheel; it was assumed that the soil deformation under the action of the rigid wheel cannot be restored; that is, the soil pressure bearing characteristics under the action of the rigid wheel followed the Bekker pressure bearing model. The coupling relationship between the wheel and the ground was shown in Figure 4, then the hook traction force of the wheeled vehicle can be expressed as follows The coupling relationship between the wheel and the ground.
4. Analysis and test verification of the equipment's surmounting obstacle ability
In order to know the surmounting obstacle capability of wheeled vehicle, this paper used the method of combining simulating analysis with experimental verification to study the change law of the hook traction force of wheeled vehicle when it crossed a horizontal trench with a width of 0.275 m and depth of 0.3 m on the soft beach ground at a speed of 5 km/h. With the help of the simulating model of the surmounting obstacle ability of the wheeled vehicle, we obtained the change of the vertical displacement of the tire center of mass when the wheeled vehicle passed through the horizontal ditch, as shown in Figure 5. The vertical displacement variation of tire centroid.
According to Figure 5, when the wheeled vehicle was running on the beach's soft ground, each tire will sink under the action of the equipment load. The subsidence values of the front wheels were about 25.3 mm on the flat beach; when the tire passed through the horizontal ditch of the beach, the vertical displacement of their center of mass will change significantly, and their subsidence value will drop from 25.3 mm to 69.8 mm, and then their displacement value will oscillate; they approximately obeyed the law of harmonic motion with smaller and smaller amplitude until their amplitude return to 25.3 mm when the beach was flat. Compared with the vertical displacement of the front wheels, the rear wheels crossed the trench slightly later for the existence of the wheelbase, and the vertical displacement of the rear wheels tire's center of mass on the flat beach was also slightly larger than that of the front wheels, which was 27.1 mm. When the tire passed through the horizontal trench, their subsidence value decreased from 27.1 mm to 69.8 mm, and then their displacement value oscillated; they also approximately obeyed the law of simple harmonic motion with smaller and smaller amplitude until their amplitude return to 27.1 mm when the beach was flat. The main reason was that when the tire crossed the horizontal ditch at high speed, it bounced under the action of the horizontal ditch and then gradually tended to flatten. When the rear wheels moved under the rut of the front wheels, their subsidence will slightly increase compared with the front wheels, but the impact they receive when crossing the ditch will relatively decrease.
When the wheeled vehicle crossed the horizontal trench on the soft ground of the beach, the driving resistance of each tire changed with the change in driving distance, as shown in Figure 6. The changes in tire running resistance.
From Figure 6, we can see that when the wheeled vehicle was running on the beach's soft ground, the driving resistance of the tire will arise for the subsidence and friction resistance of the soft ground; the driving resistance of the front wheels were about 102N, while the driving resistance of the rear wheels were about 62N, significantly lower than the front wheels. It was mainly because the front wheels need to overcome the bulldozing resistance caused by soil settlement and overcome the friction resistance when the wheeled vehicle runs on the beach's soft ground. When the wheeled vehicle crossed the horizontal ditch, the driving resistance of the tire changed obviously for the impact of the horizontal ditch. When the front wheels passed the horizontal ditch, the driving resistance of the front wheels changed the most, from 102N to 1420N, and then decreased with the increase in driving distance. When the rear wheels passed the horizontal ditch, the driving resistance of the front wheels reached a peak value of 1002N, then their amplitude approximately obeyed the simple harmonic law of decreasing amplitude until their driving resistance become 102N; when the front wheels crossed the ditch, the driving resistance of the rear wheels increased from 62N to 681N, and then decreased with the increase of driving distance. When the rear wheels crossed the ditch, the rear wheels’ driving resistance value increased to 1288N. Then their amplitude approximately obeyed the simple harmonic law of decreasing amplitude until the rear wheels’ driving resistance value become 62N. It was mainly because the tires must overcome the sizeable earth-moving resistance for the impact and subsidence of the ditch on the wheels when the front and rear wheels of the wheeled vehicle passed through the horizontal ditch, respectively.
It can be seen from Formula (3) that the hook traction of wheeled vehicle was the difference between the maximum traction of the equipment in the forward direction and the sum of all driving resistances; the maximum tractive force of wheeled vehicle in the forward direction on the soft beach ground can be expressed as The changes in wheel equipment's hook traction force.
According to Figure 7, when the wheeled vehicle crossed the horizontal trench on the soft beach ground, its hook traction force changed with the change of driving resistance. When the wheeled vehicle run on a flat soft beach, its hook traction force was about 10550N. When the equipment passed through a horizontal ditch, its hook traction force changed significantly, and its RMS value was about 9180N. When the wheeled vehicle crossed the horizontal trench, its hook traction force RMS value was far greater than zero. Hence, the wheeled vehicle could pass the horizontal trench on the soft beach ground when the hook traction force was taken as the evaluating index.
The vehicle traction performance test was used to measure the change of driving resistance to verify the reliability of the simulated results when the wheeled vehicle crossed the horizontal trench on the soft beach ground. The winch device pulled the wheeled vehicle through the horizontal trench on the soft beach at a constant speed of 5 km/h, and the change of its driving resistance was read out by the tension pressure sensor installed between the winch and the wheeled vehicle. Since the weight of the wheeled vehicle was 15,000N, the ratio of the driving resistance of the wheeled vehicle to the full load weight was taken as the resistance coefficient, and the driving resistance coefficient tested result and simulation result of the wheeled vehicle were shown in Figure 8. The test and simulating results of driving resistance.
Figure 8 showed a slight deviation between the test and the simulation result of the driving resistance coefficient of the wheeled vehicle; that is, the test result of the driving resistance coefficient of the wheeled vehicle was slightly larger than the simulation ones. It was mainly because of the test process. However, the wheeled vehicle was placed in neutral gear, it still had part of the transmission resistance and friction force, but the changing trend of the test simulating result was the same. The error was within 10%, which meet the needs of equipment surmounting obstacle ability research.
5. Analysis of influential factors of crossing obstacle ability of wheeled vehicle
When the wheeled vehicle run on the soft beach, the tires interact with the ground, and the soil deformation went through subsidence, shearing, sliding, destruction, etc. The surmounting obstacle ability of the wheeled vehicle depends not only on the obstacle's geometric shape and the equipment's structural parameters but also on the driving speed of the equipment, soil type, soil moisture content, and other factors. Studying the influential factors of wheeled vehicle’s surmounting obstacle ability and analyzing the influential rules of each factor on the equipment’s surmounting obstacle ability can provide technical support for the design, development, optimization, and upgrading of wheeled vehicle.
5.1. Driving speed of wheeled vehicle
In order to study the influence of driving speed on the surmounting obstacle ability of wheeled vehicle on the beach soft ground, the coupler traction force was taken as the research object to analyze the change of the coupler traction force when wheeled vehicle crossed the horizontal trench on the soft beach with 10% moisture content at speeds of 5 km/h, 10 km/h, 15 km/h, and 20 km/h respectively. The change of the coupler traction force under different driving speeds was obtained, as shown in Figure 9(a). The variation of hook traction with driving speeds. (a) The hook traction at different speeds (b) The hook traction variation rules with driving speeds.
The driving speed of the wheeled vehicle was taken as the abscissa, the hook traction force on flat ground and the RMS value of the hook traction force as the ordinate when the vehicle crossed the ditch, the variation curve of the traction force of the hook with the driving speed was shown in Figure 9(b).
According to the above analysis, when the wheeled vehicle run on the soft beach at different speeds, the drawbar traction force will change significantly with the change in driving speeds. When the driving speed of the wheeled vehicle gradually increased from 5 km/h to 20 km/h, the drawbar traction of the wheeled vehicle on the flat ground increased from 9883N to 10807N; that is, the driving resistance of the wheeled vehicle on the flat beach gradually decreased with the increase of the driving speed, which was mainly attributed to the fact that when the wheeled vehicle was running on the flat ground, its driving resistance consisted of two parts: the dynamic friction force between the tire and the ground and the deformation resistance when the soil deformation was overcome. With the increased driving speed, the tire had already passed over the ground before the soil deformed, so its deformation resistance decreased with increased driving speed. When the driving speed of the wheeled vehicle gradually increased from 5 km/h to 20 km/h, the RMS value of the hook traction force of the wheeled vehicle decreased from 9484N to 8859N when the equipment crossed the trench; that is, with the increase of the driving speed, the hook traction force gradually decreased. It was because the impact load caused by the equipment increased with the driving speed when the equipment crossed the horizontal trench, increasing the driving resistance value. Therefore, the minimum traction force of the trench crossing hook decreased with the increase in driving speed.
5.2. Soil moisture content
In order to know the influence of soil moisture content on the ability of wheeled vehicle to surmount obstacles on the soft beach, the drawbar traction was taken as the evaluating index to analyze the change of the hook traction force of wheeled vehicle when the equipment crossed the horizontal trenches on the soft beach with a moisture content of 5%, 7%, and 10% at a speed of 5 km/h. Through the preparation of soil samples in the laboratory and the compression and shear characteristic tests of soil samples, the mechanical characteristic parameters of three kinds of soil with different water content were obtained.
When the wheeled vehicle crossed the horizontal trench on the soft surface with a water content of 5%, 7%, and 10% at a speed of 5 km/h, the variations of the hook traction force were shown in Figure 10(a). The variation of hook traction with moisture content. (a) The hook traction with different moisture content (b) The variation of hook traction with moisture content.
The soil moisture content of the soft beach ground was taken as the abscissa, the hook traction force of the flat ground and the RMS value of the hook traction force as the ordinate when the equipment crossed the trench, the change curve of the hook traction force with the soil moisture content was obtained as shown in Figure 10(b).
The impact deformation amount caused by equipment crossing the trench increased with soil moisture content, and the more considerable deformation value reduced the contact impact force between the equipment and the trench. The above analysis showed that the hook traction force will change significantly with the change of soil moisture content when the wheeled vehicle was running on a soft beach with different moisture content. When the soil moisture content on the beach surface gradually increased from 5% to 10%, the hook traction force of the wheeled vehicle on the flat ground decreased from 10070N to 9883N; that is, the driving resistance of the wheeled vehicle on the flat surface increased with the increase of the soil moisture content. It was because when the wheeled vehicle run on the beach surface with significant moisture content, its soil will have large settlement deformation. Then its deformation resistance will increase accordingly. When the wheeled vehicle crossed ditches with a soil moisture content of 5%, 7%, and 10%, respectively, the RMS value of its hook traction force decreased from 9544N to 9511N and 9484N; that is, with the increase of soil moisture content, the RMS value of its hook traction force gradually decreased.
5.3. Soil type
The mechanical properties of different soil types.
When the wheeled vehicle crossed the horizontal trench of the beach's clay, gravel, and sandy soft ground with 10% moisture content at 5 km/h, the change of its hook traction force was shown in Figure 11. The variation of hook traction with the change of soil types.
The hook traction under different soil types.
According to Table 4, when the wheeled vehicle run on the soft beach of different soil types, the traction force of the hook changed significantly with the change of soil types, among which, when the wheeled vehicle run on the flat sandy soft ground, its hook traction force was the smallest, 9883N; when the wheeled vehicle run on the clay flat soft ground, its hook traction force was the largest, 9970N; when the wheeled vehicle crossed the horizontal trenches of sandy soil, clay and soft sandy ground, the RMS value of the hook traction forces were 9484N, 9557N, and 9520N, respectively. In other words, when the wheeled vehicle crossed the horizontal trench of sandy ground, the driving resistance was the largest, and when the wheeled vehicle crossed the trench of clay ground, the driving resistance was the smallest. It was attributed to the complex mechanical properties of sandy soil, clay soil, and sandy soil.
6. Conclusion
This paper studied the surmounting obstacle ability of wheeled vehicle on the soft beach and its influential factors. Based on the experiment of mechanical properties of the beach soil and the structural parameters of wheeled vehicle, a simulating model of the surmounting obstacle ability of wheeled vehicle on the beach was constructed. The hook traction force was taken as the evaluating index, and the surmounting ditch ability of wheeled vehicle on the beach ground was analyzed. The rationality of the simulating model was verified through actual vehicle tests; the influential factors of surmounting obstacle ability of wheeled vehicle were discussed. The research results of this paper wound lay foundation for the construction of the equipment’s off-road trafficability assessment modal, which including the key information of equipment, ground, and equipment ground coupling system in the future. The conclusions of this paper were as follows: (1) With the increase in driving speed, the RMS value of the hook traction force of the wheeled vehicle decreased from 9484N at 5 km/h to 8859N at 20 km/h when the equipment crossed the horizontal ditch; that is, the crossing obstacle ability of the wheeled vehicle on the beach decreased with the increase of driving speed. (2) When the wheeled vehicle crossed the horizontal ditch, with the increase of the soil moisture content, the RMS value of the hook traction force gradually decreased from 9544N to 9484N when the soil moisture content varied from 5% to 10%; that is, the surmounting obstacle ability of the wheeled vehicle on the beach ground decreases with the increase of the soil moisture content. (3) When the wheeled vehicle drove on different types of beach surfaces, the RMS values of the hook traction forces crossing the horizontal ditch also had noticeable changed, among which the RMS values were 9484N and 9557N on the sandy and clay surface, respectively.
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) received no financial support for the research, authorship, and/or publication of this article.
