Dynamic Simulation Study of Hydraulic System for Multi-Joint Parallel Drive of Industrial Rotary Kiln Liner Cleaning Robot

A hydraulic drive system for an industrial rotary kiln lining cleaning robot was designed, and a power bond diagram reflecting the dynamic characteristics of the multi-joint parallel drive hydraulic system was plotted. Based on this, a nonlinear dynamic state equation comprising 11 subsystems was established. Then, a simulation model of the system's dynamic characteristics was constructed according to the input-output relationships between the state variables of each equation. Finally, the equations were solved using the SIMULINK software package, yielding satisfactory simulation results.

In recent years, with the increasingly widespread application of hydraulic technology, the requirements for the reliability, accuracy, and speed of hydraulic components and systems have been continuously increasing, and the analysis and research of the dynamic characteristics of hydraulic systems have received increasing attention. Typically, the dynamic characteristics of hydraulic systems are studied using transfer function analysis based on classical control theory. However, this method is limited to analyzing the stability of linear systems (nonlinear systems require linearization), and is mainly applicable to single-input, single-output systems with zero initial conditions. Subsequently, frequency domain characteristic analysis, which evolved from transfer function analysis, has become more widely used, but this method is based on experiments and is still limited to single-input, single-output linear systems.

With the development of modern control theory and computer applications, computer digital simulation is now widely used. This type of simulation uses state equations to study the dynamic characteristics of a system, known as the state variable method. The power bond graph method, developed over the past 20 years, is an effective modeling tool for describing the dynamic structure of power systems. It consists of a set of two-signal flow graphs composed of a finite number of symbols. Using a series of bonds and simple symbols, it can vividly describe the flow direction and distribution of power in the system's energy network, as well as the collection and conversion of energy. The power bond graph method can quickly derive the system's state equations, abstracting the dynamic characteristics of a realistic and complex nonlinear hydraulic system into a mathematical model. Therefore, power bond graphs can be used to model, solve, and simulate the dynamic characteristics of the hydraulic system of a multi-joint parallel-operating industrial robot.

1. Hydraulic drive system of the kiln cleaning robot

The kiln cleaning robot is an industrial robot used to clean the lining of industrial rotary kilns, a thermal processing equipment used for heating materials. It consists of four main parts: a mechanical system, a control system, a drive system, and an end effector. To improve the system's control accuracy and the robot's flexibility, the robot's hydraulic system employs actuators such as two swing cylinders, two linear cylinders, two hydraulic motors, and a hydraulic impact hammer to achieve the movement of three rotary joints and one locating joint, as well as the robot's walking motion. The working principle of the robot's hydraulic system is shown in Figure 1. Superimposed throttle valves are installed at the inlet of the two cylinders, which are controlled by ordinary solenoid valves, to reduce interference between cylinders and regulate speed. To adapt to different working conditions, the robot control system adopts a two-level control method using a PC and a PLC (S7-200). The control program is written and relevant parameters are set on the upper computer (PC), and then communication is established with the lower computer (PLC) to control the robot system.

2. Establishment of the system dynamics model

Since the same hydraulic component exhibits different dynamic characteristics under different operating conditions, a detailed analysis and appropriate assumptions should be made about each component of the system before establishing a system model, and some minor factors should be reasonably simplified. At the same time, the occurrence of algebraic loops in the power bond diagram should be avoided as much as possible to improve the accuracy and speed of system simulation and reduce accumulated errors.

In the hydraulic system, a linear cylinder and a swing cylinder are controlled by ordinary solenoid directional valves. To achieve speed control for these two joints, this paper conducts a dynamic simulation of the hydraulic system in which these two cylinders move simultaneously. Based on the design requirements of the power bond diagram, the corresponding power bond diagrams for the hydraulic drive circuits of the swing cylinder and linear cylinder in Figure 1 are drawn, as shown in Figure 2. Here, Sf is the input flow rate of the oil pump, E1 is the pressure loss of the check valve and pressure filter, E2 is the pressure loss of the return oil filter and cooler, Rb is the leakage resistance of the oil pump, Rj is the pipeline resistance, Rbn and Rzn are the viscous damping of the swing cylinder and linear cylinder, RPA and RBo are the two resistances of the electro-hydraulic directional valve, and the other two resistances are approximately zero. Cb, CL/Cbg, and Czg are the fluid capacities of the pump, pipeline, swing cylinder, and linear cylinder cavities, respectively. IL, Ib, and mg are the pipeline fluid inductance, the moment of inertia of the swing cylinder rotor, and the inertial mass of the linear cylinder, respectively, and qt is the displacement of the swing cylinder.

In the power bond diagram shown in Figure 2, the integrals of the independent variables on the action bonds of the volume element C and the inertial element I are taken as the state variables of the system (a total of 11), and the 11th-order nonlinear state equations of the system can be derived:

Where: V2, V8, V15, V16, V23, V24, V37, and V41 are the volumes of the pump, accumulator, swing cylinder inlet pipe, linear cylinder inlet pipe, swing cylinder inlet chamber, linear cylinder inlet chamber, swing cylinder outlet chamber, and linear cylinder outlet chamber, respectively; P10 and P51 are the pressure momentum of the swing cylinder inlet pipe and linear cylinder inlet pipe, respectively; P33 is the momentum of the linear cylinder; G30 is the angular momentum of the swing cylinder rotor. k1, k1′, k2, and k2′ are the conversion modules of the converter.

There are many simulation methods for models. Traditional computer simulations generally obtain discrete numerical solutions and then use plotting statements to draw dynamic characteristic curves. MATLAB's SIMU-LINK is a software package used to model and simulate continuous, discrete, and hybrid linear and nonlinear dynamic systems. SIM-ULINK includes modules such as sink (connection and interface), continuous, discrete, and nonlinear. It also allows the use of submodule encapsulation to build a dialog box containing model parameter inputs for simulation of different parameters. Based on the input-output relationships between the state variables in the 11 equations above (each equation representing a subsystem), a dynamic simulation model of the system is established, as shown in Figure 3. In the figure, the pump flow rate is used as input to calculate the acceleration, velocity, and displacement of the swing cylinder. The displacement of the cylinder is limited by setting the upper and lower limits of the integrator and using a nonlinear element.

4. Implementation of Dynamic Simulation

The simulation was performed using a variable step size ode45, based on the Runge-Kutta fourth-order solver, with a simulation time of 0–3 seconds. The pump's input flow rate Qf = 15 L/min. The simulation was conducted by changing parameters such as pipe length, pipe diameter, throttle valve, load force (torque), and inertia. Here, only the simulation results of changing the load's rotational inertia and inertial mass to obtain the motion velocity and acceleration of the two joints are given, as shown in Figure 4-7.

The simulation curves above show that the increase of mass mg and inertia Ig has little effect on the change of the stable values ​​of velocity and angular velocity, and the time to reach equilibrium does not change much. However, the acceleration of the swing cylinder is smoother in the rising phase, with almost no peaks, and directly reaches the stable value. Furthermore, the increase of mass and inertia actually reduces the acceleration and angular acceleration, which makes the movement of the robot's joints smoother and more suitable for control requirements.

5. Conclusion

(1) The power bond graph method can be used to easily establish a nonlinear dynamic model of the hydraulic drive system of the kiln cleaning robot with multiple joints in parallel drive, and lay a theoretical foundation for the nonlinear dynamic analysis of complex robot systems.

(2) By changing different parameters of the system, simulation can be performed to optimize the hydraulic system design, find the best component matching, and provide some prior knowledge for the design and manufacturing of robots.

(3) The dynamic simulation model of complex system can be easily established by using the MATLAB/SIMULINK model-based graphical dynamic system simulation software package. Its analysis and simulation results are consistent with the actual working conditions of the robot and have high credibility.