Investigations on the critical feed rate guaranteeing the effectiveness of rotary ultrasonic machining

doi:10.1016/j.ultras.2016.10.003

Ultrasonics

Volume 74, February 2017, Pages 81-88

https://doi.org/10.1016/j.ultras.2016.10.003 Get rights and content

Highlights

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A critical feed rate guaranteeing the effectiveness of RUM was first reported.
•
When the feed rate exceeds its critical value, the cutting force increases abruptly.
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A model for the critical feed rate was developed.
•
Methods for improving the critical feed rate were proposed.

Abstract

Rotary ultrasonic machining (RUM) is a well-known and efficient method for manufacturing holes in brittle materials. RUM is characterized by improved material removal rates, reduced cutting forces and reduced edge chipping sizes at the hole exit. The aim of this study is to investigate the critical feed rate to guarantee the effectiveness of RUM. Experimental results on quartz glass and sapphire specimens show that when the feed rate exceeds a critical value, the cutting force increases abruptly, accompanied by a significant decrease of ultrasonic amplitude. An analytical model for the prediction of critical feed rates is presented, based on indentation fracture mechanic and the theory of impact of vibrating systems. This model establishes the theoretical relationships between the critical feed rate, idling resonant ultrasonic amplitude and spindle speed. The results predicted by the analytical model were in good agreement with the experimental results.

Introduction

Ultrasonic vibration compound machining technologies show good performance in the processing of difficult-to-machine materials [1], [2]. Rotary ultrasonic machining (RUM) is a novel hybrid machining method which is ideally suited to manufacture holes into brittle materials [3], such as advanced ceramics [4], optical glass [5], ceramic matrix composites [6], and carbon fiber reinforced polymers [7]. It is a hybrid method which combines the material removal mechanism of ultrasonic machining (USM) and conventional diamond grinding (CG) [8]. As shown in Fig. 1, RUM utilizes a special designed diamond core drill vibrating ultrasonically with a tiny amplitude about 5–10 μm along the z direction while it rotates and is fed toward to the workpiece.

RUM preserves the advantages of both USM and CG, and alleviates their disadvantages. Compared with USM, RUM can archive a higher material removal rate due to the help of scratching movement of abrasives that are bonded on the tool surface [9]. Compared with CG, RUM can reduce the cutting force [10], [11], edge chipping size at hole exit [12], tool wear [7], subsurface damage [12], [13] and surface roughness, with the help of ultrasonic vibration. Here, the greatest advantage of RUM is the reduction of the cutting force, which is crucial for the tool life, hole quality and material removal rate.

There are two tool feeding methods for RUM including the method of constant driving force and the method of constant feed rate [3]. At the initial development stage of RUM, a constant driving force was used to feed the tool. This approach was inherited from USM. A major part of early research was thus devoted to the material removal rate for a certain driving force [9]. Various models for the material removal rate in USM and RUM have developed. According to the research by Pei et al., a higher driving force generally results in a higher material removal rate in RUM [14]. What is interesting is that there exists a critical driving force when the material removal rate reaches a maximum value in USM [15]. Astashev et al. have built a theoretical model to explain this phenomenon in USM based on a rheological material model [16]. They found that when the driving force exceeds a critical value, the ultrasonic amplitude decreases resulting in a decrease of the material removal rate [16]. They derived the feed rate as f_r = δf, where f_r is the feed rate, δ is the contact depth between tool and workpiece, and f is the ultrasonic frequency. The major disadvantage of the constant driving force method is its low controllability of material removal rate and low machining quality. Today, the most widely applied feeding method in commercialized RUM machine such as Ultrasonic 50 (DMG, Germany) is the constant feed rate method, that the tool feeds toward the workpiece at a precisely constant feed rate by using a numerical control feed drive system. This leads to the question if a maximum material removal rate exists, when a constant feed rate method is used in RUM. To the authors’ knowledge, no relevant reports on this question can be found in the literature. Also, the developed model for maximum feed in USM such as that by Astashev et al. [16] can’t be applied to RUM directly. This is because of their difference in material removal mechanism and tool feeding method [17].

This paper is devoted to find an answer to the question about the existence of a maximum material removal rate in RUM at constant feed rate by theoretical modeling and experimental exploration. Therefore, an analytical model for the dependency of critical feed rate on the idling ultrasonic amplitude of the RUM machine and the spindle speed is developed. This model offers a quantitative guideline for both the application and manufacturing of RUM machines.

Section snippets

Model development

RUM is a hybrid machining method combining ultrasonic machining and conventional diamond grinding. The movement of the abrasive tool is a combination of ultrasonic vibration, rotation of the spindle and the axial feed motion. The kinematical equation of the tool can be expressed as: $S_{RUM} (t) = [\begin{matrix} R \cos (\frac{2 π S}{60} t) \\ R \sin (\frac{2 π S}{60} t) \\ A \cos (2 π ft) + f_{r} t \end{matrix}] .$ Here S_RUM is the kinematic position of the tool, t is time, R is the radius of drill, S is the spindle speed, A is the ultrasonic amplitude, f is the ultrasonic frequency,

Experimental method

The RUM experiments were conducted on a Ultrasonic 50, DGM (Germany. As shown in Fig. 6, the experiment equipment is composed of an ultrasonic spindle system, a coolant supply system and a cutting force measurement system. The ultrasonic spindle system is the key unit of the RUM machine. It consists of an ultrasonic power supply, a transducer, a concentrator and a diamond core drill. The ultrasonic supply converts the 50 Hz electrical supply to an ultrasonic frequency AC output. The transducer

Obtaining the property V_M0 of a RUM machine

In the model expressed by Eqs. (22), (23), the energy consumption V_M0 is an important parameter. A higher V_M0 is accompanied by a lower Q-factor. To keep the ultrasonic amplitude identical, a RUM machine with a higher V_M0 must consume more power. The value of V_M0 for a certain RUM machine can be obtained by experiments at idling mode.

Fig. 8 demonstrates the dependencies of ultrasonic power and ultrasonic amplitude on frequencies respectively for a specific RUM machine-Ultrasonic 50 with the

Remarks

In this study, the existence of critical federate in RUM of brittle materials at constant feed rate mode was investigated by theoretical modeling and RUM experiments. Based on the findings the following conclusions can be drawn:

(1)
A critical feed rate guaranteeing the effectiveness of the RUM process was reported for the first time. When the feed rate is relatively small, the ultrasonic power/amplitude decreases and the cutting force increases gradually with an increasing feed rate. However, RUM

Conflict of interest

The authors declare that they have no conflict of interest to report.

Acknowledgements

We gratefully acknowledge the financial support for this research from the Beijing Natural Science Foundation (Grant No. 3141001), the National Natural Science Foundation of China (Grant No. 51475260), National Natural Science Foundation of China (Grant No. U1430116).

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View full text

Investigations on the critical feed rate guaranteeing the effectiveness of rotary ultrasonic machining

Highlights

Abstract

Introduction

Section snippets

Model development

Experimental method

Obtaining the property VM0 of a RUM machine

Remarks

Conflict of interest

Acknowledgements

Procedia CIRP

Procedia CIRP

Int. J. Mach. Tools Manuf.

J. Mater. Process. Technol.

Int. J. Mach. Tools Manuf.

Ultrasonics

Phys. Lett. A

Ultrasonics

Process of ultrasonic machining

Rotary ultrasonic machining of dental ceramics

Int. J. Mach. Mach. Mater.

Obtaining the property V_M0 of a RUM machine