CHAPTER 2: LITERATURE REVIEW
2.4 Identification of a Research Direction Based on Prior Work
This literature review shows that a cutting force model has yet to be developed to predict chatter in turning that simultaneously and accurately captures the two most important mechanisms during dynamic cutting: the regenerative effect and the interference between the cutting tool and the workpiece. This work seeks to develop a fully comprehensive dynamic cutting force model for turning by using physical insight and extending orthogonal models used in quasi-static cutting force modeling to the current application of predicting chatter. The model will also consider material property effects such as the strain, strain rate and temperature dependence on the flow stress of the workpiece material during machining.
This work is written from an engineer’s perspective, not an applied mathematician’s. Consequently, there is no treatment of topics such as chaos, bifurcations, or perturbation solution techniques. These types of investigations are still important, since regenerative chatter is a good real- world example of a system with pure delays that exhibits chaos. However, the field has seen an explosion of these papers in recent years and needs to become more rigorous from a first-principles point of view. This is what will ultimately help the machining community to better understand why chatter occurs and to advance process monitoring and control.
Because of the geometric complexity of the current approach, a decision was made to only consider machining conditions where the nose of the cutting tool is engaged in the workpiece. In other words, the model cannot immediately deal with larger depths of cut that have both the tool nose and the side cutting edge in contact with the workpiece. It is not to say that this effect cannot be incorporated, but since it introduces a cutting edge that cannot be described by a smooth function with a finite number of terms, the equations needed would become considerably more complicated
and greater in number. The author feels that this increase in complexity to an already geometrically rigorous methodology would preclude the contribution of the present approach without contributing any new fundamental understanding. In addition the commanded feed rate, f, nominal cutting velocity, VC, and commanded depth of cut, dc, are all assumed to be held constant. Once again, the model could be modified to deal with these parameters if they were time varying; however it would just add complexity to the proposed approach and is not necessary in determining its validity. Finally, owing to the nature of the dynamic properties inherent to the workpiece used in the experimental validation portion of this work in Chapter 8, vibration along the axis of the workpiece is neglected.
Two dynamic cutting force models will be presented in this dissertation. One termed the “simplified cutting force model”, resolves the cutting condition at every time step of a dynamic simulation into a single equivalent orthogonal cutting scenario and solves for the forces in closed- form. The other approach derives the cutting forces in a more precise manner by using a geometrically rigorous representation with some elements that cannot be evaluated in closed-form and is termed the “refined cutting force model.”
It should be noted that there is nothing inherently “chatter specific” about the following approach. The subject of chatter is just an obvious context to demonstrate the validity of the proposed modeling methods. The experimental system under study is a compliant workpiece machined by a relatively rigid cutting tool (assumed rigid for modeling purposes). Therefore in Equation (2.2) y tt( ) will always be zero in this analysis. However, all subsequent equations are developed around the use of RTWDs, which would facilitate modeling a vibrating cutting tool as well.
It is the author’s opinion that in order to make a truly accurate dynamic cutting force model that is used to predict chatter the following components must be incorporated:
• Forces due to chip formation along the undeformed chip area, taking into account influence of relative tool workpiece vibration at the current time, and at previous times, t−τ, t−2τ,…
• Plowing forces
• Forces caused by interference between the machined workpiece surface and the clearance face of the cutting tool
• For a chattering workpiece in a turning operation, a model with at least two degrees of freedom is required (recommended for a chattering tool holder as well)
The necessity of the aforementioned components will be substantiated in later chapters. With a truly accurate model for chatter, the following four items should be able to be predicted:
•
Frequency content of chatter vibration•
Stability lobe diagrams with increased stability at lower cutting velocities•
Chatter amplitude vibration growth over time•
Machined surface topography (chatter marks)These four aspects are arranged in increasing level of difficultly since each successive one requires a more accurate model. To the author’s knowledge the last two items, chatter amplitude growth and machined surface topography, have never been compared with experimental measurements in turning. The most rigorous method of comparison would be a combination of the third and fourth objectives, since if they are predicted adequately the model is able to reproduce both the amplitude and the nature of the growth of vibrations during chatter. It is the goal of this thesis to accurately predict all four of these aspects from a physics-based dynamic cutting force model that excites a model of the workpiece.