Research on Ultrasonic Machining Gap Control Based on Fuzzy Self-tuning PID Parameters Technology

. The working principle and measurement of ultrasonic machining gap is analyzed in this paper. A stable machining gap between the tool and workpiece must be maintained for improving processing accuracy and efficiency. Therefore, a fuzzy self-tuning PID parameters controller for ultrasonic machining tool feed system is designed, by means of using Matlab /Simulink simulation experiment, in this paper.


Formulation of issues
Onf the major concerns in any kinds of processing method is the producing proficiency. Ultrasonic machining is a method which process material by suspension abrasive material under the condition of a high-frequency vibration of the tool, thus, it is one of the most effective methods in processing hard and brittle materials such as glass and ceramics. Tool vibration amplitude and frequency, machining gap (that is, workpiece feed pressure produced by the tool) between the tool and the workpiece, abrasive suspensions, materials of the tool are the main factors that affect the processing speed. With other conditions remain unchanged, when the machining gap is too big, the impact of machining abrasive on the workpiece will decrease, resulting in decreased processing speed and reduced efficiency; when machining gap is too small, machining abrasive will be squeezed out, reducing the amount of abrasives, also resulting in decreased processing speed and reduced efficiency. To ensure accuracy and efficiency, we must maintain a stable machining gap (usually slightly larger than the average diameter of abrasive) between the tool and the workpiece. Therefore, under certain conditions, the controlling ultrasonic machining gap is a critical issue to improve ultrasonic machining productivity. In this paper, we mainly discuss the ultrasonic machining gap control based on fuzzy self-tuning PID parameter technology.

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Basic principle of ultrasonic machining Ultrasonic machining is a forming processing method in which the end face of an ultrasonic machine tool (Fig:1) is made ultrasonic vibration, by use of abrasive suspension to process brittle materials. Ultrasonic generator produces more than 16000 Hz high frequency AC power supplied to the ultrasonic transducer to generate ultrasonic Vibrations, and the amplitude is amplified up to about 0.05 ~ 0.1mm by means of the horn, so that the lower end of the tool horn generates strong vibration. The suspension, containing water and an abrasive material, driven by the Tool, also produces a strong vibration, impacting the surface of the workpiece. When machining, the tool puts a tiny pressure on the workpiece and the abrasive surface, continuously impacted by abrasive material with great speed and accelerated velocity, is crushed into small particles, falling down from the surface. The tool continuous feeds and the processing goes on until finally the desired size is reached and the shape of the tool is "Copied" on the workpiece. Ultrasonic resonance principle can be used to measure the gap between the tool and the work piece. Figure 2 is an ultrasonic machining gap measure and control system illustrative diagram.When machining, the ultrasonic is transformed into mechanical oscillation by machining transducer, then amplified by the horn and passed to tools.In order to improve the processing precision and efficiency,we expect the gap between tool and workpiece to be maintained at the set valuee = λ / 2(λ is ultrasonic propagation wavelength measured in the abrasive suspension). When measured, pulse excitation transducer converts signal into measured ultrasound and launched and spread to abrasive suspension by the horn.Part of the ultrasonic waves are reflected at the interface, others pass through the suspension and reach the surface of the work piece, resulting in reflection and transmission. When the gap between the workpiece and the tool is λ / 2, or nλ / 2 (n is an integer), the ultrasonic waves and its reflected waves transmitback and forthin the suspension and interfere with each other precisely in the same phase.According to the principle of resonance, as the ultrasound energy transmitted from the horn to abrasive suspension is reduced, ultrasonic amplitude is reduced accordingly. Based on the circuit feedback signal, CNC system then decideswhether the gap between the workpiece and the tool is equal to λ / 2 or nλ / 2.If it is equal to λ / 2 or nλ / 2, the gap information will be sent back to CNC system;if it is not equal to λ / 2 or nλ / 2, the feed structure will keep feeding until the machining gap is equal to λ / 2 or nλ / 2.

Design
Conventional PID control is simple in principle and easy to use, but its control methods are mostly to be fixed a set of adjustable parameters under certain performance requirements. Such controls cannot often give attention to both static and dynamic performance, therefore the control of the system is not optimal. As to the fuzzy control, in which the mathematical model of the controlled objectis not necessarily to be known, it is easy to implement the control on uncertain or nonlinear systems and has a strong robustness to the parameters of the controlled objects, also it has strong suppression to external interference, and other similar characters. We, in this paper, try to combine the advantages of PID fuzzy control and design the fuzzy self-tuning PID parameters controller, with the function of identifying fuzzy relations between the three parameters, scale factor, integration constant and differential constant, and the error as well as error rate of change. It also keeps detecting error and error rate of change, and then revises the three parameters according to the fuzzy control principle, to meet the requirements of errors and error rate of change to the three parameters, thus the control system processes good dynamic and static performance.

Structure
The fuzzy self-tuning PID parameters controller consists of PID controller in which the parameters are adjustable and fuzzy controller. The fuzzy controller takes the deviation e and deviation rate of change ec of the ultrasonic machining gap as input value, the three parameters Kp , Ki , Kd of the conventional controller as output value, and then conducts real-time adjustments to Kp , Ki , Kd with fuzzy inference methods so as to meet the requirements of deviation e and deviation rate of change to PID parameters in different time.The structure of the composition of the controller is shown in Fig.3.   Fig. 3. Structure of Fuzzy Self-Turning PID Parameters Controller

Design of fuzzy control
The design of fuzzy control system employs two inputs  Figure 4 andthe membership function profiles of △ Kp, △ Ki, △ Kd is shown in Figure 5.The control rules of parameters△ Kp , △ Ki , △ Kd are shown in Table 1, Table 2 and Table  3.The control rules of fuzzy PID parameter self-tuning controller is shown in Figure 6.

Simulation experiment based on simulink simulation
In order to verify the control effect of fuzzy self-tuning PID parameters controller, and for comparison, we apply the software Mtlab/Simulink to conduct the simulation experiment and analysis on conventional PID control and fuzzy self-tuning PID control. The common second order delay in actual control tasks is selected as the control object. Suppose the transfer function is:

Conventional PID control system simulation experiment
Conventional PID control system simulation model shown in Figure 7. In the role of unit step signal, we take sampling time T=0.1 seconds, the simulation time t = 60 second, PID controller parameters Kp=0.1, Ki=0.12, Kd=0.01, then we get the output waveform of the system shown in Figure 8, system deviation e and deviation change rate e care shown in Figure 9 and Figure 10, respectively, andthe curve of the PID controller output u changes in pace with time t is shown in Figure 11.   Figure 12. The simulation result of the system in the role of unit step signal is shown in Figure 13.
To compare the simulation results in Fingure 8 and Figure 13, we can see that the fuzzy PID parameter selftuning controller discussed in this article can be well used to control machining gap, to improve processing quality and efficiency, at same time free of such shortcomings as large overshoot amount and long time for adjustment that exist in conventional PID controlling.

Conclusion
Machining gap is a critical parameter in ultrasonic CNC machining. This article puts forward that fuzzy selftuning PID parameters controller is used to control the feed system of ultrasonic CNC machine tool to ensure a stable machining gap between the tool and the workpiece. Matlab/Simulink simulation software is applied to conduct the experiment on the designed system, and proved to have good results for it achieves an on-line control of the process.