Dynamic Simulation of a Hydraulic Excavator to Determine the Joint Reaction Forces of Boom, Stick, Bucket, and Driving Forces of Hydraulic Cylinders

To optimize the dimensions of the boom, stick of the hydraulic excavator and select the suitable hydraulic bucket, stick, and boom cylinders, the designer must determine the joint reaction forces and driving forces. These forces always alter in an excavator's working cycle. They are conventionally calculated by mathematical method. This conventional method is complicated and challenging to determine the maximum reaction forces, which can break the stick and boom. This article builds a 3D model and simulates a working cycle of the hydraulic excavator to find the reaction force diagrams of boom and stick as well as driving forces of hydraulic cylinders by using computer software PTC Creo Parametric. Based on these results, the designer easily calculates the maximum tensions of the dimensions of boom and stick in a working cycle to optimize their dimensions as well as selects suitable hydraulic cylinders.


Introduction
In the first half of the 20th century, because of the strong development of the construction industry, open-pit mining, the first cable generation excavators were born and used widely for digging and loading. In the second half of this century, cable excavator was significantly replaced by a hydraulic excavator. Hydraulic excavators are commonly used in construction, mining, digging and forestry. During working, the excavator driver must pay his attention to digging material parameters, soil-machine interaction conditions. Various manufacturers in Germany, Japan, Italy, France and the United States began to utilize the computer software for designing excavators (Rusiński, E., Czmochowski, J., Moczko, P., Pietrusiak, D, 2017). Like other vehicles, the hydraulic excavator is also divided into several parts (see Fig. 1). To determine the forces on joints of boom and stick, the designer must define working loads of excavator. One of the studies on mini excavator is the single action hydraulic cylinder. The state of the stick against the load in the working environment is monitored by setting up a closed cycle system. This stick of this mini excavator is mathematically modelled and invented for static and dynamic movement (Salcudean, S.S, Tafazoli, S., Lawrence, P.D., Chau, I, 1997).
In order to design the excavator better, the forces between the soil and the machine must be calculated especially during digging (Patel, B. P., Prajapati, J.M, 2011). To reduce the cost of designing and manufacturing, the dimensions and weights of the boom and the stick must be minimized by establishing an optimization model (Korucu, S., Küçük, A. E., Samtaş, G, 2017). Therefore, the maximum tensions of boom and stick must specify in a working cycle of the excavator (Orlemann, E.C, 2003). To determine the reaction forces in a whole working cycle of stick and boom as well as driving forces of hydraulic cylinders, the designer must build an excavator model. Bucket, stick, and boom move during working, hence the reference coordinate system of excavator, the coordinate system of bucket, stick and boom are assigned in their centre of gravity. Based on loads of bucket, stick and boom, the mathematical equations are established to find the forces and reaction forces on joints of stick and boom (Bhaveshkumar P. Patel, J. M. Prajapati, 2014). Paten and Prajapati (Patel, B.P., Prajapati, J.M, 2012) used the mathematical method to calculate the static forces of the bucket, stick and boom.
The mathematical methods were used to develop an excavator's kinematics dynamics and establish the relationship between excavator parameters and the resistive forces from the material formation during the excavation process. By using SIMULATION-X Environment, the trajectory for the bucket tip, driving forces of the boom, stick and bucket cylinder during excavating are calculated and shown in different charts (Alaydi, Juma Yousuf, 2009).
The developed system of differential equations is used to perform a numerical experiment with the inertial and geometrical data for the excavator. The typical digging task simulation demonstrates the applicability of the dynamical model for the study of the excavator motion simulation by Matlab Simulink (Belma Babovic, Almir Osmanovic, Bahrudin Saric, 2017). Enhanced visualization of calculated results, the reaction forces will be plotted on a force/reaction diagram for a working cycle. It makes the designer easy to find out a position with the biggest total of reaction forces (Rosen Mitrev, Dragoslav Janošević, Dragan Marinković, 2017).
The recent developments of dynamic mechanism design broaden mechanism design to include a wide range of motion evaluation functions. When a movement of mechanism is analyzed, it can be observed and recorded the analysis or can be measured quantities such as positions, velocities, accelerations, forces, and graph the measurement. It offers information about creating and working with mechanism models with or without the application of external forces. Simulation lets Submission date: 06-03-2020 | Review date: 22-09-2020 the designer examine how his model will behave in the real world and reduces the need for costly prototype iterations. By using simulation, the 3D excavator model will be created that reflects the loads, materials, and boundary conditions. It also shows how to define and run a wide range of analyses and design studies, review results, and optimize the excavator model (Creo Parametric, 2020). For this reason, this research will design 3D-Cad model of excavator and simulate a working cycle of excavator in PTC Creo to find reaction forces on the joints of boom and stick as well as determine the driving forces in the hydraulic cylinder of the bucket, stick and boom.

Method of study Basic parameters of excavator model:
Standard excavators come in a variety of sizes, from mini excavators that are perfect for tight job sites to large excavators designed for heavy-duty applications. Bucket, stick and boom for standard excavators are also available in different sizes and lengths to tackle a variety of tasks, including digging, trenching, moving debris, hauling heavy materials, and demolishing structures. Standard excavators are useful in construction, landscaping, mining, farming, forestry, and other industries that require excavation (Gregory Poole CAT, 2020). In the scope of this study, a track excavator is selected with the technical specifications in Tab. 1 (Kato works co.,ltd, 2020).

Determination of masse and centre of gravity:
In addition to breakout and digging forces, the weights of bucket, stick, boom, and material in each bucket must be specified and assigned in the excavator model. Mass properties such as area, volume, and the coordinates for the centre of gravity of solids are translated as test properties and saved as parameters in PTC Creo. When the solid models, related to the file formats for CATIA V5, Creo Elements, NX, Solid-Works, Autodesk Inventor and STEP, are imported, model parameters are created for the imported elements. Creo calculates the validation property values and stores the calculated values of the validation properties for geometry and assemblies in the model parameters (Creo Parametric, 2020). Therefore, the designer must not calculate the masses and centre of gravity as well as inertia of bucket, stick, and boom.

Calculation of breakout and digging forces:
Material such as soil, coal, gravel is penetrated to the bucket by the breakout force (F B ) and digging force (F S ).

Determination of bucket capacity:
The capacity of a bucket V S muss be calculated by its measuring dimensions. In this example, it holds the value of 0.8 m3. The excess material capacity is determined by the material to fulfill factor, and it depends on the kind of material (Rusiński, E., Czmochowski, J., Moczko, P., Pietrusiak, D., 2017). In this example, the material is rock, well blasted f f =0.9, and density ρ=1600 kg/m3. Therefore, the weight of material in bucket P=1152 N.

The working cycle of excavator:
Cycle time for the excavator depends on the movements of the swing system, boom, sticker (arm), and bucket. The relative positions of these movements are commonly described in a position-time diagram. In this diagram, the movements will be divided to different phases, the start and end of each position correspond to start and end time of each movement (see an example in Fig. 3 a). Moreover, to determine the driving forces of the boom, stick, and bucket cylinders as well as reaction forces, a loading profile must be shown. According to J.D. Zimmerman (D. Zimmerman, M. Pelosi, C.A. Williamson, 2007), a charging payload holds a value up to 60% working cycle (Fig. 3 b).
A working cycle of excavator is the input reference for the dynamic simulation. The relative positions of bucket, stick and boom are driven by three hydraulic cylinders. The movement of each cylinder decides the working ranges and is   Fig. 4 is used to define these positions/angles. They must ensure the smooth movement of the excavator and are suitable for the working requirements. For this study, the relationship between the positions of the bucket, stick, boom cylinder, as well as the angle of the swing system is shown in Fig. 5.
In this working cycle of the excavator, the stick cylinder moves with a max-stroke 1150 mm at the time of digging material. The bucket cylinder holds a max stroke 780 mm at the time of burrowing and discharging. The max stock value of boom cylinder is 530 mm at the time of discharging material. The swing system rotates 180 degrees from the start position to the discharging material position. The positions of the bucket, stick, boom cylinders, and swing system depend on each other according to the working cycle.

Definition of loads on the bucket:
An operating sequence of the excavator will be simulated according to the cycle time 29.5 s. Weights and direction gravity of the bucket, stick and boom are assigned to them in the whole working cycle. However, the breakout force, digging force only exist in a digging process and depend on the working cycle time. Fig. 6 shows the breakout force, digging force. The loading time takes along 12 s, between 8 s and 20 s. Material on the bucket is determined from the charging time to the discharging time. The gravity of material on the bucket is displayed in Fig. 6.

Simulation results and discussions
Driving forces/moment of the bucket, stick boom cylinders, and swing system: The weights of bucket, stick, boom, and material on the bucket are smaller than the breakout and digging forces. Therefore, the driving forces of bucket, stick, boom cylinders at the time of digging material are much bigger than other time. Their value reaction forces are shown in Fig. 7.
The maximal driving forces of the bucket, stick, boom cylinders are calculated as 564785 N, 353474 N and 1290184 N.
After loading material, the swing system rotates 90 degrees to the discharging position. With full of material on the bucket, the torque of the swing system gets the maximum value of 144670799 Nmm (see Fig. 7).

Reaction forces on the joints of boom and stick:
The boom rotates on the pin Joint B_4, the stick rotates on the pin Joint B_1. The double effect hydraulic cylinder allows to raise and lower the boom. The boom motion around Joint B_4 can be related to the variation of angle (Eugenio Leati, Roberto Paoluzzi, 2010). The boom of excavator contains 4 joints and are shown in Fig. 8. The joint B_3, and B_4 connect to the boom cylinder and upper structure. Therefore, the reaction forces of these joints are the same value. The Joint B_2 connects to stick cylinder, the Joint B_1 links to the stick. The curve of these reaction forces on B_1 is similar to the curve of B_2. During a digging material, the joint reaction forces hold the maximum values and are calculated as S_1 = 1289928.334 N, S_2 = 1290584.244 N, S_3 = 353425.518 N and S_4 = 351038.93 N.
The stick rotates on the pin Joint S_4, and bucket linkage goes around on the pin Joint S_1. Stick cylinder allows to extend and retract the stick, while the bucket cylinder allows to open and close the bucket. The stick of excavator links to the bucket and stick cylinders. It comprises five joints S_1 to  Fig. 9).
H_Link joins the bucket cylinder by H_Link_1 and bucket by H_Link_2. The curves of reaction forces are similar, but the values of H_Link_1 are little bigger (see Fig. 10). Reaction forces on these joints alter in a working cycle. The values of the reaction force of each time of H_Link_1 are bigger than H_Link_2.
In a working cycle, the reaction forces not only alter the magnitudes but also charge the directions. The Fig. 8 to Fig.  10 show all of reaction force magnitudes of each joint of the boom, stick and H_Link. However, to determine the stress of them by using FEM (Finite Element Method), it requires to define all directions of reaction forces according to the working cycle. It means, the equilibrium condition of the boom, stick and H_Link muss be established for every position in the working cycle. The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero (XiaoboYang, PeijunXu, 2012).
By utilizing the method of equilibrium condition to find the directions of reaction forces, it takes a lot of time. Hence, dynamic simulation is applied to find them quicker. Fig. 11 shows the directions of reaction forces of joints S_1 to S_5 of stick at the beginning position as an example, which are indicated by blue arrows. At this position, gravities of the bucket, stick and driving forces of the stick and boom cylinder influence these joints. Based on Fig. 11, the designer can fix the direction and magnitude of the reaction force and then calculate stress.
Creo parametric is used in this paper to establish the 3D-CAD model and calculate the driving and joint reaction forces of the hydraulic excavator. In order to improve the simulation accuracy, users have to accurately define the links and joints, external forces acting on the excavator in a working cy-cle. In the study of Šalinić (S. Šalinić, G. Bošković, M. Nikolić, 2014), they used the mathematical method to determine the forces in the bucket, stick and boom cylinders. It is taken that the time interval of the considered digging task reads 0 ≤ t ≤ 3 s, the digging force varies and gets the max value of 20.5 kN. The driving forces of the hydraulic bucket, stick, and boom cylinders also alter according to this time interval and hold the max values of 120 kN, 150 kN and 200 kN. In this study, the breakout and digging forces are five times bigger than the above example. Therefore, the driving forces are approximately bigger than five times.

Conclusions and proposals
A working cycle of excavator consists of multiple movements of the bucket, stick, boom cylinders and swing system. The values of driving forces and reaction forces depend on the positions of drive elements. The driving/reaction forces as well as the acceleration, velocity typically can be calculated by analytic geometry and mathematical method. However, it is complex and takes a lot of time. In this study, the position-time diagram is used to describe the motions of excavator in a working cycle, then the external loads (gravities, break out and digging forces) are declared and assigned them to components of the excavator.
Based on the 3D-Cad model, the design parameters such as the masses, moments of inertial and dimensions of the boom, stick, bucket, swing system are quickly determined as well as the input parameters are defined. 3D modeller reduces project cost margins for machinery maker.
Dynamic simulation in PTC Creo is applied to calculate and plot the driving forces/moment and joint reaction forces. On the grounds of the diagrams, the designer can easily find out the maximum value on each joint and required driving forces/moment of drive components.
Dynamic simulation can be used not only for the design of track excavator but also for the design of any machine or equipment and reduce the time from the first idea to the delivered device.