Dynamic Analysis of Slender Shaft in Twin-Spindle Turning

Abstract

Machining slender workpiece is still a technical difficulty. This paper investigates the dynamic behavior of a slender shaft subject to constant feedrate moving cutting forces in twin-spindle turning process. The Euler-Bernoulli theory is used to model the rotating shaft. A dynamic cutting force model is formulated considering the flexibility of workpiece and rigid machine tool. The modal analysis method is employed to solve the dynamic response of the shaft. The parametric influence to the response and natural frequencies of shaft is discussed. Finally, the results are presented and compared between constant cutting forces and deflection-dependent force model introduced in this paper. It is found that there exists a stiffening effect due to the cutting process.

Optimization of Machining Parameters in Turning Processes by Dynamic Programming

“…As one future direction was pointed out in [5], incorporating the time as a variable in prediction and optimization needs to be addressed in machining processes. This is similar to the conclusion in [6,7] that the tool-work cutting model is a time-variant dynamic system essentially. To the best of the authors' knowledge, the restrictive conditions on the decision variables, such as the bounds of the cutting parameters and the maximum cutting force, are generally defined as invariants without considering the time-variant property of the tool-work cutting system in references.…”

“…It implies that the larger depth of cut for the last cutting passes could cause chatter vibrations more easily. In reference [7], the response of the workpiece is directly proportional to the cutting force and the biquadratic of the / ratio, respectively. Based on handbook recommendations or the empirical experience, Hinduja et al [8] defined smaller bounds of depth of cut and feedrate in the last cutting pass, that is, finishing pass, than those adopted in roughing passes.…”

“…But the depth of 3.5 mm obviously needs to be further divided. By the use of backward tracking, the subdivision information on (4,7) gives (4,6) + (10,1), representing the depth of cut 3 mm should be cut first and then 0.5 mm. It is observed that both of the two smaller depths of cut are not required further division.…”

“…The stability charts that can give the boundary between stable and unstable regions with respect to the spindle speed and width or depth of cut are evaluated analytically. In another our work [7], the dynamic behavior of a slender shaft in turning process was investigated, and the influence of the length-to-diameter ( / ) ratio of workpiece, cutting parameters, as well as fixturing conditions to the dynamics was discussed respectively. Based on the results of these two previous researches, the goal of this paper is to optimize the machining parameters to control the vibration and deformation at the lowest cost.…”

A reconfigurable system of chatter stability evaluation and monitoring for industrial machining processes

“…With the machining operations going, the length-to-diameter ratio of the workpiece is becoming greater, which leads to the low stiffness of the workpiece. And the different cutting position along the workpiece has the different stiffness (Lu et al, 2011a), the varying stiffness may result in quasi-harmonic or self-excited vibrations in machining processes (Rivin, 1999).…”