The Basic Functionality of Hydraulic Excavator
Discuss about the Mechanism of Hydraulic Excavator and Equipment.
Excavators are useful machines mainly used in construction industry. Their mobility is provided by an undercarriage that has tracks designed to accommodate counterweights which allows safer swings and maneuverability. As described by Patel and Prajapati (2011). The main mechanism that constitutes an excavator includes the undercarriage which includes tracks, track frame, blade, and the final. The final has gears and hydraulic motors that drive the tracks. The counterweights, hydraulic and fuel tanks, and operator’s cabin are attached to the undercarriage hence allows a 3600 swing of the machine. The boom moves up and down, or right to left of the machine. The boom has an arm attached on its ends and it is used for imparting force into the ground. A bucket is fixed at the end of the arm for holding the soil during haulage. Other attachments may be fixed for uses like boring, lifting, and boring. A hydraulic excavator comprises power cylinders and linkages organized systematically to provide a maximum use of power applied to the bucket.
According to Stephen, Harvey, and Turcker (1974). The basic functionality of this machine is such that, a bucket-actuating linkage is supported on a suitable rotatable vehicle mounted on a track undercarriage by means of suitable bearings. The bucket-actuating linkage comprises a boom whose one end is pivotally connected to the frame with a pair of hydraulic lift cylinders for controlling movements of the boom. The cylinders are individually attached to connected to opposite sides of the boom. The bucket linkage includes a stick pivotally connected to the outer end of the boom and movable by a hydraulic crowd jack. The crowd jack is disposed below the boom and offset from the center axis to leave room for a slave cylinder.
The connection of the crowd jack is adjacent to the lower inner end and the outer crowd jack has its end connected to the stick. The lower pivot point is located such that large forces may be applied without causing undesirable bending moments on the boom. The upper end is connected at a position about a third of the distance between the upper and lower pivot to provide an optimum lever arm on the stick and as well allow maximum movement of the lower end when the cylinder is extended.
A bucket is mounted to the lower end of the stick and its movements are controlled by a pair of spaced hydraulic control jacks connected to the boom. The rods of the bucket control jacks are connected to a wrist linkage which connects to the bucket and the stick. The arrangement with the bucket control jacks mounted to the boom gives the bucket cylinder linkage about 30% more force capacity that stick mounted cylinders. The pivot connection of the bucket to the stick is forward to the connection of the bucket jack to the bucket. This allows the bucket to be pulled back on its heel during breakout instead of being lifted off the ground.
Four Bar Linkages used in Hydraulic Excavator Mechanism
The slave cylinder is connected between the frame and the boom and is disposed below the boom and offset from the crowd jack. The rod end of the slave cylinder coordinates with the rod end of the bucket jack The slave cylinder and the jacks must have appropriate volume to enable the desired movement.
The linkages used in an excavator are the four-bar linkage type. The linkages consist of four links connected by four joints in a loop. The joints are designed such that the links are able to move in parallel planes. These planar linkages consist of four links connected by four one-degree-freedom joints. Joints, in this case, are either revolute (hinged) or prismatic (sliding). Any link connected to the ground by means of a hinged joint is referred to as a crank, while a link connected by prismatic joint is called a slider. A link that connects two cranks makes a coupler. A coupler connecting a crank and a slider is referred to as a connecting rod.
Planar four-bar linkages can be either planar quadrilateral linkages, slider-crank linkages, or the double slider. Planar quadrilateral linkages are made up of four links and four revolute joints and consists of two cranks joined by a coupler. Slider-crank linkages are made up of four links connected by three revolute joints and one prismatic joint. This type of linkage can be constructed by connecting a crank to using a connecting rod. Else, it can be made of two cranks with the slider acting as the coupler. On the other hand, the double slider linkage is constructed using two sliders connected by a coupler. If the two sliders move in perpendicular directions, the coupler moves along elliptical trajectories.
The design of the four-bar mechanisms aims at minimizing the cost of producing the desired motion and maximizes efficiency of the machine. Link lengths are determined through dimensional synthesis which involves an iterative method. The four-bar mechanism involves cyclic forward and returns strokes. The time ration of this system measures how fast the forward stroke is as compared to the return stroke. Modern excavators have mechanisms designed to produce symmetrical motion such that the forward stroke and the return stroke can be operated at the same speed. These sort of mechanism have the same amount of force applied in both directions and are referred to as an in-line design.
As described by Patel and Prjapati (2011), the study of link mechanism involving computation of position and orientation of bucket of the backhoe when the joint angles are known, which is referred to as forwarding kinematics. Inverse kinematics involves calculation of possible sets of joint angles, that may be used to attain a given position and orientation of the bucket tip. the kinematic modeling helps in maintaining defined trajectory so that digging function can be executed at the required location by use of proper positioning and orientation of the bucket. Description of the position of an excavator and its mechanism is based on a coordinate system defined by Vaha and Skibniewski in 1993. The Cartesian coordinate system as shown in the figure below defines the local frame for the interconnected links which include the upper structure, arm, boom, and bucket.
Kinematic and Mobility Characteristics of a Hydraulic Excavator
The first link rotates on the supporting base about the vertical axis while the rotational axes for the other joints are horizontal. Structural kinematic parameters are defined for determining the transformation matrices for the rotating joints. This kinematic model allows computation for investigating the machine behavior and may serve as a basis for simulation during the design of the excavator.
When digging at a certain point on the excavation trajectory, the crawler and the rotational bodies are stationary so that the kinematic model is reduced to 3 degrees of freedom. The kinematic solution of the arm is accomplished in the form of homogeneous transformation matrix by using Denavit-Hartenberg (D-H) notation whose joint displacement variables and the coordinate frames and (D-H) parameters are as shown in Table 1below.
|
Link |
Θ |
α |
a |
d |
|
Crawler Superstructure |
0 q1 |
900 0 |
qc a0 |
0 0 |
|
Arm boom Arm stick Bucket |
q1 q2 q3 |
0 0 0 |
a1 a2 a3 |
0 0 0 |
Table 1: Denavit-Hartenberg parameters
The forward kinematic transformation matrices of the boom, stick, and bucket, converts the coordinates in the bucket frame into the fixed superstructure frame. The cognitive force control prevents excessive forces by converting the control of the ram-forces into the modification of the digging. Cartesian coordinates are assigned to the links of the excavator as illustrated in figure 2 above. With known lengths of actuators or joint angles, the positions and orientation of the bucket are computed using forward kinematics equations. Else, if the position of the bucket is defined, corresponding joint angles and lengths of actuators are computed through inverse kinematic equations. The velocity relations corresponding to the determined positions and orientation are derived.
When designing a boom, a digging position with the highest strain is chosen because the boom is at most times subjected to large forces of loadings. Uzer (2008) mentions that the geometry of the boom is defined in terms of points, angles, radii, and lengths. There are numerous possibilities of resultant forces exerted at the bucket tip due to movements of the arm and bucket cylinders. The force at bucket tip is given by the function
The arm breakout force occurs when the arm cylinder acts on the arm at 900. An arm cylinder length should be set at about 73% of the total arm in order to maintain maximum breakout force. On account of the effect of torsional and lateral forces experienced when the excavator turns for loading. The lateral force is determined as F = m. a where a is the acceleration for a loader bucket and m represents the sum mass of the bucket and load. The basic mass function of a boom is given by;
Fx = m(x,p)
where x is the vector of the design variables and p is the density of the material used to make the boom.
Input Force of a Hydraulic Excavator
The input force required for excavation process using a hydraulic excavator relies on soil-tool interaction, soil parameters and digging force (Kim, Kang, Ha, Kim, Kim, Baek, & Park, 2017). Soil parameters and soil-tool interaction are theoretical parameters defined to optimize design and performance of an excavator. The force involved in excavator operations is determined through inverse dynamics of workload. This involves the determination of torque, velocity, and acceleration of each joint.
The dynamics formula is stated as;
Where M: is the mass matrix which is constituted as a moment of inertia and mass. C implies centripetal and Coriolis forces.
JT F is the external force of excavator which is the constraint force for compensating virtual open chain.
γ is the joint moment
q is the configuration matrix.
To determine the inverse dynamics during digging, digging force is applied to the equation in the form of; Mq + C = T + JtF
The aim is to obtain cylinder force T. F is the digging force applied on the bucket tip and can be calculated using soil-tool interaction model which accounts for soil weight, soil-tool friction, and soil moments.
In lifting operations, the soil volume is obtained by integration on the digging path. Density and volume of the soil determine the of the soil imposed on the lifting bucket. The loading effect is comprised of the weight of the soil and the weight of the bucket. The dynamic function of the lifting operation is given as;
Mq + C = T
where M is the sum of the mass of soil and bucket. T represents the cylinder force required to perform the lifting function.
During dumping operation, the volume of the soil is considered to be decreasing linearly as the angle of the bucket increases. The dynamic function of this operation is given by;
M(α)q + C = T
where M(α) represents the mass matrix and α the angle of the dumping bucket.
The least cylinder forces required for the above functions is attained when the torque in the system is at minimal. The objective function for minimum torque is given as;
The excavators during motions with no loading keep the arm inner so as to save swing torque. The computed motions tend to linear movement to approach the goal in the minimum time possible. This is meant to minimize time spent in performing the digging, lifting and dumping functions. Additionally, operating at minimum torque reduces cylinder force that actuates the system. There are many local minima and hence the optimal time solution is determined using a line search to avoid settling at some local minima. The resultant function defines a stable motion which allows operation of the machine with less vibration.
References
Kim, Y., Kang, H., Ha, J., Kim, M., Kim, P., Baek, S., & Park, J. (2017). A Study on the Virtual Digging Simulation of a Hydraulic Excavator. Construction Equipment Research Department, Hyundai Heavy Industries, Ulsan, Korea
Patel, B. & Prajapati, J. (2011). A Review on Kinematics of Hydraulic Excavator’s Backhoe. International Journal of Engineering Science and Technology. Vol. 3(3). pp.1990-1997. ISSN:0975-462
Stephen, H., Harvey, A., & Turcker, J. (1974). Shovel Linkage for a Hydraulic Excavator. Cate Corp. of DE. ILLINIOS
Uzer, C. (2008). Shape Optimization of an Excavator Using Genetic Algorithm. Masters Dissertation Paper. Middle East Technical University.
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