Development of mathematical models and online chatter control system in turning AISI 304 stainless steel

Abstract

Chatter is intensive self-excited vibration of the individual components of a Machine-Tool-Fixture-Work (MTFW) system which reduces tool life, accuracy, surface finish quality and productivity. In turning, it manifests itself as bouncing in and out of the tool shank from the flexible work-piece. However, it is a complex process and so no comprehensive theory has yet been developed. Thus, research into the root cause of chatter, its formation mechanism, mathematical modelling and chatter suppression is very important to industry and academia. The prevalent theories on chatter are controversial; often contradicted by experimental evidences. The Regeneration Theory posits that surface waviness left from a previous cut interferes with the next machining pass and leads to chatter. In contrast, the Resonance Theory states that chatter occurs due to resonance when the chip serration frequency coincides with the natural frequencies of the MTFW system. The current research investigated chip serration frequency, cutting force, mode shapes and natural frequencies of the tool shank, and vibration amplitudes during turning of AISI 304 stainless steel under different combinations of primary cutting parameters with the aim to model the responses and gain understanding of chatter. The work material, AISI 304 stainless steel, was turned on an engine lathe using TiN-coated cemented carbide inserts. Small Central Composite Design (CCD) modelling approach in Response Surface Methodology (RSM) was used for designed experiments and resulted in quadratic empirical mathematical models of vibration amplitude and chip serration frequency, and two-factor interaction (2FI) model for cutting force; which were subsequently analysed by ANOVA. It was found that, cutting speed (Vc) and depth of cut (DOC) had quadratic perturbation effect in determining the responses. Next, the postulates of the Resonance Theory of Chatter and energy balance method were used to analytically explain chatter as the consequence of Pmax (vibration energy) at the resonance of tool shank‘s mode shapes. It was found that chatter occurred when chip serrations approached even integer multiples of the two dominant resonant frequencies (transverse and torsional) of the tool shank (fc = 10fn1, 20fn1, 30fn1 and fc = 2fn5, 4fn5, 6fn5) due to mode coupling; resulting in large peak values of cutting force and chatter. The empirical models were numerically and graphically optimised and showed that chatter was more prone to occur for combinations of high cutting speed (near 200 m/min) and large depths of cuts (2 mm or more). Concurrently, an electromagnet-based online chatter control system was developed which was controlled by a closed-loop feedback proportional and integral (PI) controller developed in LabVIEW. This controller detected and minimised chatter amplitude by 46% (on average); treating it as a disturbance in the turning process. The damping was provided by the uniform magnetic field produced by the electromagnet which resisted any movement of the ferromagnetic steel tool shank. This active damper is economical and robust; capable of handling all conditions of cut of the CCD model. Hence, this research developed an in-depth understanding of chatter, modelled it using empirical, statistical and analytical methods which were able to predict stable cutting regions. An economical and effective online chatter control system was successfully developed.