Stability analysis of machine tool spindle under uncertainty

Abstract

Chatter is a harmful machining vibration that occurs between the workpiece and the cutting tool, usually resulting in irregular flaw streaks on the finished surface and severe tool wear. Stability lobe diagrams could predict chatter by providing graphical representations of the stable combinations of the axial depth of the cut and spindle speed. In this article, the analytical model of a spindle system is constructed, including a Timoshenko beam rotating shaft model and double sets of angular contact ball bearings with 5 degrees of freedom. Then, the stability lobe diagram of the model is developed according to its dynamic properties. The Monte Carlo method is applied to analyse the bearing preload influence on the system stability with uncertainty taken into account.

Research on Vibration Characteristics of a Ceramic Spindle Based on the Reverse Magnetic Effect

“…To study the e ects of the reverse magnetic e ect and bearing Hertz contact force on spindle dynamics, we combine every shaft segment of the Timoshenko beam unit with the bearing motion formulas and magnetic eld formulas of spindle. Formulas (9) and (23) are substituted in formula (4) to obtain the dynamic formula (24) under the action of the bearing contact force and electromagnetic radial force. e dynamic formula of the spindle is solved by an iterative method.…”

“…e dynamic formula of the spindle is solved by an iterative method. Formulas (9), (23), and (24) of the ceramic spindle model show that there is a direct relationship between the vibration and speed of the spindle, centrifugal force of the bearing, pretension force, gyroscopic moment, air gap, electromagnetic radial force, and magnetic field density. e structural parameters of spindle and the length of the rotating shaft discrete system, respectively, are shown in Tables 1 and 2.…”

“…Effect. According to formulas (8) and (9) for raceway control theory of a spindlebearing system, the bearing correction coefficient is adjusted for the characteristics of a ceramic Si 3 N 4 bearing to establish a ceramic bearing model and a metal bearing model, respectively. e conditions of simulation are radial dynamic stiffness, gyroscopic moment, and inner and outer ring contact angles of the bearing calculated under the working conditions of a preload force of 300-500 N and speed of 3000-30000 rpm.…”

“…e model can not perform the vibration accurately in some extreme cases. Some papers [8][9][10] proposed speed-dependent FRF (Frequency Response Function) spindle model. e coupled spindle model based on Timoshenko beam can be predicted.…”

A prediction model of the surface topography due to the unbalance of the spindle system in ultra-precision fly-cutting machining

“…Chen et al 18 pointed out that tool geometry, material-related factors, and original surface characteristics might have some influence on the error frequency components on the machined surface as well as the error magnitude. Dou et al 19 pointed out that chatter was a harmful machining vibration that occurred between the workpiece and the cutting tool, usually resulting in irregular flaw streaks on the finished surface and severe tool wear, and constructed the analytical model of a spindle system to predict chatter. The spindle of the ultra-precision machine tool is usually aerostatic or hydrostatic, which is more complex than the fluid movement in the bearings.…”