Dynamic simulation analysis of working equipment of small backhoe hydraulic excavator

To further improve the performance of a company’s excavator, reduce the production cost, and simplify the complex process of dynamic modeling, a 13-ton small backhoe hydraulic excavator working device was taken as the research object, and a virtual prototype was established by using Pro/E and ADAMS software. The excavation resistance was calculated and the STEP function was defined, the dynamic simulation analysis was carried out during the working process of the excavator, and the stress change curve of the hinge point was obtained, which reduced the calculation amount, and provided a reference for the finite element analysis and optimization design of the working device of the excavator.


Introduction
At present, the development mode of small hydraulic excavators in China is to introduce first, and then imitate, and the introduced machine lacks systematic understanding.Virtual prototyping technology can be used to conduct detailed research from the system level, track the design idea of the prototype, and guide the design [1].Zhong et al. used Sim-Mechanics to quickly model the excavator, thereby replacing the kinematics model to obtain the excavator mechanism model [2].Chen et al. simulated bucket excavation conditions with Adams to obtain the stress curve of each articulated point of the bucket [3].Drissa et al. carried out the bucket rod design of a virtual prototype through CAD to improve the excavator's mobility [4].
This paper takes the hinged points of the boom and bucket rod of excavator working equipment as the research object.First, the 3D model of the working equipment is created by using Pro/E software, and then it is imported into ADAMS software to establish a virtual prototype.The STEP function is used to drive the movement of each cylinder to simulate the loading and unloading process of the external load of the working device.Through dynamic simulation analysis, the stress curves of each hinge point of the boom and bucket rod are obtained.The goal of this study is to provide a feasible solution for the subsequent optimization of the design to save costs and reduce workload.

Establishment of the virtual prototype model
In a 3D model built by using Pro/E, if there are more parts, more constraints will need to be added to import the model into ADAMS.Therefore, the model is simplified, such as simplifying the fuselage and the chamfer and cutting the weld shaft.The flowchart is shown in Figure 1. Figure 2. 3D model of excavator working device.

Pro/E 3D modeling
The construction of a virtual prototype mainly relies on 3D software Pro/E and simulation software ADAMS.Because the ADAMS software is relatively complex in model creation, we first used the professional modeling software Pro/E to accurately model the various components of the backhoe hydraulic excavator working device, and assembled them into a complete 3D model of the working device, as shown in Figure 2.
The main working size of the working device is by the stroke of the hydraulic cylinder [5], and the parameters of the hydraulic cylinder are shown in Table 1.
Table1.The main parameters of hydraulic cylinder.

ADAMS virtual prototype modeling
The 3D model created in Pro/E is stored in the form of a Parasolid, that is, *.x_t format file, and then imports the saved Parasolid file in ADAMS.The input model needs to rebuild the constraint relationship in ADAMS, rename each part, and set properties such as color and quality [6].Mark points are established at each constraint pair and motion pair, which makes it easier to proceed with subsequent steps.The constraints and drivers are shown in Table 2.The virtual prototype model that has been created is shown in Figure 3.   Through the establishment of a virtual prototype and the verification of the ADAMS model, the results show that the prototype does not have redundant constraints and its degree of freedom is 0, indicating that the model is established correctly.Model validation is shown in Figure 4.

Theoretical excavation resistance and material gravity calculation
In most cases, the excavation action is completed by the combination of bucket rod and bucket working at the same time [7], so the simulation analysis in this paper adopts the combination action mining method.
When excavators cut soil, the external load is the main factor affecting the reliability and digging ability of excavators and is also the main source of stress on the hinged points of excavators' working devices [8].Therefore, it is necessary to conduct an in-depth analysis of the external load on excavators.Without considering the soil resistance and friction force, tangential excavation resistance 1 W , normal excavation resistance 2 W , and the gravity of loading soil G in the bucket exist in the excavation process.W can be approximated as the operation point at the tip of the bucket teeth, and their directions are along the tangential direction and normal direction of the bucket tooth tip motion track line respectively.Their empirical calculation formula is as follows [9] : where 0 K is the specific resistance of excavation.The test value is shown in Table 3, and the unit is N/cm 2 .In this paper, the excavator excavates under the Ⅲ grade soil, which can be selected as 0 K =19.5 N/cm 2 according to Table 3; b is the cutting width (unit: cm), according to the model b =82 cm; h is the cutting depth (unit: cm), generally taken as h =0.2 cm and b =16.4 cm;  is the coefficient of excavation resistance, optionally taken as  =0.4.At the end of the excavation, the gravity of the soil filled in the bucket can be calculated by the following formula: where V represents the soil volume when the bucket can be filled with soil, according to the design value V =0.5 m 3 ;  indicates the soil density (generally Ⅲ soil), and the density is  =1.8×10 3 kg/m 3 ; g indicates the acceleration of gravity, usually taken as g =9.8 m/s 2 .The specific value of the selected parameters into the formula Vg G   aims to calculate the gravity of the soil loaded in the bucket G =8, 820 N. The application point of gravity is usually chosen at the center of mass of the bucket, and the direction of action is always vertically downward.

Excavation resistance loading
To facilitate the analysis, the digging resistance is defined as two concentrated forces acting on the middle of the tip of the bucket teeth.One follows the tangential direction of the bucket tooth tip track, and the other follows the normal direction of the bucket tooth tip track and sets its relevant coordinate system in the middle of the bucket edge, whose direction always changes with the bucket.The two forces increased first and then decreased.The tangential mining resistance change is shown by the dotted line in Figure 5, and the corresponding STEP function is as follows: STEP (TIME, 6, 0, 9, 26.223) +STEP (TIME, 9, 0, 11, -26.223).The change of normal mining resistance is shown in the solid line in Figure 5, and the corresponding STEP function is as follows: STEP (TIME, 6, 0, 9, 10.490) +STEP (TIME, 9, 0, 11, -10.490)During the excavation process, the material gravity gradually increases until it reaches the theoretical maximum.After unloading, the material's gravity quickly drops to zero.According to the actual situation, the maximum gravity of the material is 8.82 KN.The material gravity is defined as a single concentrated force, fixed in direction and applied to the center of the bucket .The change curve is shown by the midpoint line in Figure 5, and the corresponding STEP function is as follows: STEP (TIME, 6, 0, 11, 8.8200) +STEP (TIME, 11, 0, 16, -8.8200)As can be seen from Figure 5, the loading process mining load and the motion simulation process show a corresponding relationship in time, which reflects that the theoretical load in the mining process conforms to the practical application.

Dynamic simulation analysis
This study mainly focuses on the stress of 8 hinged points on the bucket rod and boom when the excavator is combined digging under the working condition of the maximum digging radius.In the simulation process, first, the working device needs to be accurately adjusted to a specific attitude, and then the excavator starts to carry out compound excavation work [10].After the bucket is fully loaded, MATMA-2023 Journal of Physics: Conference Series 2691 (2024) 012007 the working device is unloaded, the boom cylinder is extended, and the bucket and rod cylinder are contracted.We set the simulation time to 20 seconds for simulation.The STEP functions added in the mining process are as follows: Boom cylinder drive function: STEP (TIME, 0, 0, 3, 136) +STEP (TIME, 3, 0, 6, -490) + STEP (TIME, 16, 0, 21, 500) Bucket rod cylinder drive function: STEP (TIME, 0, 0, 3, 322) +STEP (TIME, 6, 0, 11, -1, 005) +STEP (TIME, 11, 0, 16, 1, 005) Bucket cylinder drive function: STEP (TIME, 0, 0, 3, -885) +STEP (TIME, 6, 0, 11, 700) +STEP (TIME, 11, 0, 16, -700) After the simulation is completed, we enter the post-processing module of ADAMS, select relevant parameters, and obtain the stress change curve of each hinge point on the boom and bucket rod, as shown in Figures 6 and 7.
In Figure 6, the solid line represents the stress change curve of the hinge point between the boom and the upper frame; the dashed line represents the force change curve of the hinge point between the boom and the boom cylinder piston rod; the point line represents the force change curve of the hinge point between the boom and the bucket rod; the point line represents the stress change curve of the hinge point between the boom and the bucket rod cylinder.In Figure 7, the solid line represents the stress curve of the articulation point between the bucket rod and the bucket rod cylinder piston rod; the dashed line indicates the stress change curve of the articulation point between the bucket rod and the bucket cylinder; the point line represents the stress change curve of the articulation point between the bucket rod and the connecting rod; the dotted line represents the force change curve of the articulation point between the bucket rod and the bucket.By observing Figures 6 and 7, it can be found that the changing trend of each hinge point is roughly the same.In 0-6 s, the device is in the preparation stage, and the hinged points are subjected to small fluctuating loads.With the beginning of excavation work, the external load increases, resulting in a gradual increase in the force of each hinge point.At about 9 s, the excavation resistance reaches the maximum, and each hinge point also reaches the maximum stress state one after another.Among the hinge points of the boom, the maximum force of the hinge point between the boom and the boom cylinder reaches 317 KN.In each articulated point of the bucket rod, the maximum force between the bucket rod and the bucket rod cylinder is 170 KN.At 11 s, the excavation operation ends and the unloading process begins.Currently, the working device only bears the material and its gravity, and each hinge point is subject to a small force.It can be concluded from the above that the stress conditions of the hinged points on the hydraulic excavator arm and bucket rod change with the change of tangential and normal resistance, and the maximum value is consistent with the peak value of tangential and normal resistance.The force change of the hinge point between the boom and boom cylinder and the hinge point between the bucket rod and bucket rod cylinder is the most prominent.Therefore, when designing a hydraulic excavator, measures such as increasing the diameter of the connecting pin and thickening the steel plate at the connection can be targeted to improve the bearing capacity of the hinged point to ensure stability and safety in the excavation process.

Conclusions
(1) The 3D model of the excavator's working device is established by Pro/E, which is transformed into a kinematics simulation model by ADAMS, and the hinge point of the working device is analyzed by simulation.This can quickly modify and evaluate the design scheme, improve design efficiency, and reduce the cost and cycle of actual manufacturing.
(2) Through dynamic simulation, the stress change curve of the key hinge point of the backhoe hydraulic excavator working device is obtained, which can more intuitively reflect the stress situation of each hinge point, and can be targeted to select materials and design the working device, to improve the reliability and durability of the working device.

Figure 5 .
Figure 5. External load of excavator working device.

Figure 6 .
Figure 6.Force on the boom hinge point.

Figure 7 .
Figure 7.The force on the hinge point of the bucket rod.

Table 2 .
Restraint pair and drive.