7.5.1 Excavator Model executing a digging cycle with boom, arm and bucket
On analysis of results presented in the previous section, it is evident that the pump model is capable of reproducing actual conditions. Thus the model was extended to include the valve blocks and the kinematics as depicted in Figure 11 and described in section 2.3. The complete system was subjected to a duty cycle as described in Table.3.
The values from Table.3 were used to control the valve opening for respective implements. The pump’s maximum displacement used for this simulation was 84 cm3/rev and the engine speed was set at 1000 r/min. Figure 7.34 describes the initial condition of the excavator in the simulation model. Figure 7.34 describes the forces on the implements and the effects of these forces can be seen in Figures 7.34 in pressure terms on the boom, arm and bucket actuators. Figure 7.34 describes the pressures across the FC, as it can be seen the LS pressure is the instantaneous maximum pressure
194 of the system derived from the actuators and the pump pressure is the instantaneous system pressure. Figure 7.34 describes the differential pressure across the FC, which is equal to the pump margin set to about 17 bar. Figures 7.34 describe the spool displacements of the PC and FC respectively: the FC provides a flow path through the spool when the displacement is greater than 3.90 mm and the PC when the displacement is greater than 2.10mm. Figure 7.34 describes the pump swash angle controlled by the flow across the FC and PC spools.
Table. 7.10. Duty cycle – Control Signals to Valve Block for Boom, Arm, Bucket Motion Implement
Name
Time [s] Valve Opening [%] Actuator Action
Boom 0 - 2 0 – 30 (ramp) Retraction
2 - 7 0 -
7 - 10 0 – 30 (ramp) Extension
10 - 13 0 -
Arm 0 - 2.5 0 -
2.5 - 7.5 100 – 50 (ramp) Extension 7.5 - 10 0 – 50 (ramp) Retraction
10 - 13 0 -
Bucket 0 - 2.5 0 -
2.5 - 7.5 100 Extension
7.5 - 10 0 -
10 - 13 0 – 50 Retraction
5.
6.
7.
8.
9.
Figure 7.34 a. Initial position of the Excavator
195 Figure 7.34 b. Actuator Forces
Figure 7.34 c. Pressure in Boom Actuator
Figure 7.34 d. Pressure in Arm Actuator
196 Figure 7.34 e. Pressure in Bucket Actuator
Figure 7.34 f. Pressure Across the FC
Figure 7.34 g. Differential pressure across the FC
197 Figure 7.34 h. Displacement of the FC
Figure 7.34 i. Displacement of the PC
Figure 7.34 j. Swash Angle
198
Conclusion
The document has presented the analysis of an excavator control system. The model has been developed with the objective of creating a fast simulation model. The model is described by the models of a: hydraulic grey box model of the LS variable displacement axial pump, detailed model of the LS flow sharing valve block and a 2D kinematic model to simulate the excavator's body elements.
The detailed hydraulic model described is that of the main hydraulic pump, which has been conceived as a grey box model; where the flow and pressure compensators have been modeled as white box models and the actual flow characteristics of the pump as a black box model. The black box model to obtain the swash plate positions has been developed using a relation between the control piston pressure and the net torque acting on the swash plate through the system pressure. A linear relation between these pressure characteristics were derived from experimental results and was used to simulate the functioning of the pump. This methodology has the advantage of being easily applicable to pumps of different types and sizes, by changing the gain values and the constants of the linear equation. The model of the variable displacement pump has been validated on the basis of a preliminary set of experimental data collected at particular operating conditions. It has permitted the necessary verification of the interaction between the hydraulic and structural linkage/mechanical model.
A detailed model of the LS flow sharing valve block has been developed. This model owing to its complexity and non linearity has been developed as a white box model. This approach has been adopted owing to the complexity of the orifices integrated into the central section of the main orifice and the meter out orifices of the main spool. The pressure compensator of the valve block has a very complex function of being integrated
199 with a piston check valve, to force close the pressure compensator when the bridge pressure rises. There is another fuction where the sensed LS pressure if greater than a section, will cause the pressure compensator to close and the piston check to return to its home position. This offers a great modelling complexity as there occurs a situation of mechanical contact or fluid contact. Creating this discontinuity in the model has been a fair challenge. This has finally been integrated with the use of a special air gap damper spring arrangement, where the spring properties have been changed to rigid links and the air gap to recreate the fluid contact situation. The valve model requires complex verification of displacements, pressures and flow characaterisitcs. This has lead to an extensive validation campaing to carry out the complete verification of the valve.
A 2D kinematic/mechanical model has been developed to simulate the body elements of the excavator. This would reproduce the motion of the boom, arm and bucket. The kinematic model also includes a developed soil interaction model, which has been used to study and effect the soil interaction properties on the excavator implements in the course of an excavation cycle. This has assisted the model development in the creation of a unique simulation environmen where the hydraulic models can be loaded with realistic load characteristics on the systems from the implements.
The model has been validated completely in terms of the pump characteristics and the pumps response and behaviour in a complete excavator. These tests of the pumps behaviour have been carried out and verified using field tests on an excavator. Tests and verification of the characteristics of the LS flow sharing valve have been carried out. There is a good amount of confidence in the models capabilities of recreating the flow characteristics of the flow sharing valve.
This study has been a very interesting and challenging one, where the capabilities and potential of the completely developed autonomous model are paramount. It offers a futuristic approach to studying the complete excavator. The fact that there is a mix of modelling approaches used in the recreation of the system model offers the capability of the development of a complete fast model. Where the model can be used to study complete excavation cycles and the systems performance during the process.
Dott. Ing. Alvin Anthony