Elsevier

Measurement

Volume 45, Issue 6, July 2012, Pages 1380-1386
Measurement

Decomposition of process damping ratios and verification of process damping model for chatter vibration

https://doi.org/10.1016/j.measurement.2012.03.028Get rights and content

Abstract

In the previous study, by the same authors, titled “A new process damping model (PDM) for chatter vibration (Measurement, 44 (8) (2011) 1342–1348)”, a new approach has been presented for obtaining process damping ratios (PDRs). This PDM has been constituted on the basis of the shear angle (φ) oscillations of the cutting tool and the alteration of the penetration forces when they penetrate into the wavy surface. Variation and quantity of PDR are predicted by reverse running analytical calculation procedure of traditional Stability Lobe Diagrams (SLDs). In this study, firstly, how the PDM in previous study results with different materials such as AISI-1050 and Al-7075 are examined. Then, two problems are solved: how much of the total PDR of cutting system is caused by the tool penetration and how much is caused by (φ) oscillation? Finally, verification of PDR values and PDM are performed by energy equations.

Highlights

► A new analytical process damping model is developed. ► Process damping ratios (PDRs) are determined using this model. ► Total PDRs ratio of cutting system caused by the tool penetration is determined. ► Total PDRs ratio of cutting system caused by (φ) oscillation is determined. ► Quantity of PDRs is predicted using reverse running analytical calculation procedure.

Introduction

To obtain the final shapes of mechanical parts by turning operations are very important in present-day manufacturing. Examples of this metal cutting process can be found in the automotive, aerospace, and the mold and die industries [1]. However, one of the main factors limiting productivity in milling is the vibration of the system machine tool, spindle, tool holder, and tool, mainly due to a lack of dynamic stiffness. Regenerative chatter, a self excited vibration in operations where the tool cuts a previously machined surface, is the most common problem. The consequences are poor surface quality, inaccuracy, loud noise, excessive tool wear, machine tool damage, increased costs in terms of time, materials, and energy, and the environmental and economic impact of sanding marks, dumping non-valid final parts or repeating the metal removal operation [2].

Early research on chatter started with Taylor [3], Arnold [4] and Hahn [5] in the early part of the 20th century. Chatter was thought by some to be negative damping in the machining process [6] whilst others have more recently claimed that in the case of titanium milling the oscillation in forces as the result of segmented chip formation can initiate chatter [7], but is widely understood to be a function of the system dynamics and the cutting parameters [6], [8].

A simple way to avoid regenerative chatter in machining is to select stable cutting conditions. A stability map can be generated, to show the combinations of width of cut and cutting speed where stable cutting conditions are found. Another successful strategy involves mitigation of chatter at lower surface speeds, utilizing process damping by tool–workpiece contact [9]. Most machining operations are conducted in low speeds (typically less than 300 m/min) range for hard materials, for instance titanium and nickel alloys. Certain operations take place in this range for softer materials also, e.g. grooving for carbon steels. When the tool or workpiece vibrates during cutting, waves are generated on the workpiece surface as a result [10].

Process damping force occurs in a section between tool cutting edge and wavy surface during the dynamic cutting. However, as it is not linear, the modeling of the process is still arduous and the basic subject matter has not fully been comprehended though it is recognized why and how this force is produced. The main subject of analytical calculation of process damping for chatter vibration is to research how and why the process damping occurs in chatter vibrations under low cutting speed conditions. Answers to those questions could not be found in the former research available in literature [11], [12], [13], [14]. Since how the process damping affects the orthogonal cutting is not clearly understood, the additional effect of the process damping to the cutting system’s structural damping could not be determined as well. In our previous study [15], a complex dynamic system is modeled prior to the orthogonal cutting which forms a mechanical cutting basis for all cutting processes in general. The complex dynamic system consists of dynamic cutting system force model which is based on the shear angle (φ) oscillations and the penetration forces which are caused by the tool flank contact with the wavy surface. Static and Dynamic Cutting Force Coefficients (DCFCs) are obtained by using the dynamic cutting force model. Using these coefficients in the motion equations derived for the stability analysis increased the total PDR of the system. The complex PDM is developed through considering that it is derived from the shear angle (φ) oscillations of dynamic cutting system and the penetration of tool to the wavy surface. PDR of the available cutting system are can be obtained by this complex PDM for different workpiece materials and cutting tools. Obtaining of the PDR values is achieved for the stability analysis in turning and milling conversely. Additionally the verification of PDM is analyzed after having found the total PDR with this procedure and how much is caused by tool penetration and how much by the alteration of cutting angle is found [15], [16]. In this study, primarily the results of PDM with diversified materials such as AISI-1050 and Al-7075. The reason is to investigate according to what features of workpiece material the PDR changes.

Section snippets

Process damping investigation from experimental results

In this study, a system of orthogonal cutting was dealt with as a SDOF. Analytical modeling of this system and investigation of its stability were conducted in two different forms. The movement of the tool in dominant direction for SDOF system was considered because the natural frequency of the tool in another direction was very low in relation to the dominant direction. For this reason, it was accepted that the movement in this direction had no effect on stability limit of orthogonal cutting.

Decomposition of process damping ratios

PDR for stable spindle speeds and cutting depths of the cutting tests are total process damping ratios (ζsT) values of the dynamic cutting system. These (ζsT) values contain two different types of PDRs which occur by change of the shear angle (φ) of cutting system and penetration volume (Vh) of tool. Table 3 gives (ζsT) values for workpieces with AISI-1050 and Al-7075 materials. These (ζsT) values have been obtained from the PDM in [15], [16].

If the total PDR (ζsT) values in Table 3 contain two

Verification of process damping ratios

The verification of PDR also means the verification of (ζsT) and PDM used for obtaining (ζ) and (ζsb) values that constitutes the total process damping. This verification process could be achieved through the verification of (C) in Eq. (6) of [15]. The (C) value is used for obtaining static and dynamic coefficients in [15], [16]. Also, verification of specific cutting resistance constant (fsp) could be investigated by Eq. (26) of [15]. By this way both of the operation procedures that affect

Conclusions

When investigating the results of this study firstly, Table 2 shows that (alim) values decreases by decrease of spindle speed and increase of attach length of cutting tool (L). Additionally, it shows that (alim) values increase by decrease hardness of the work pieces. After, total PDR values (ζT) for various attach length of cutting tool and cutting speeds are obtained by reverse running analytical calculation procedure of traditional SLD. Table 3 shows that (ζT) increases through increase of

References (17)

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