MACHINE TOOL VIBRATION
#1

PRESENTED BY
ROHIT MEHTA

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ABSTRACT
Machining and measuring operations are invariably accompanied by relative vibration between work piece and tool. These vibrations are due to one or more of the following causes: (1) in homogeneities in the work piece material; (2) variation of chip cross section; (3) disturbances in the work piece or tool drives; (4) dynamic loads generated by acceleration/deceleration of massive moving components; (5) vibration transmitted from the environment; (6) self-excited vibration generated by the cutting process or by friction (machine-tool chatter). [3]
The vibration behavior of a machine tool can be improved by a reduction of the intensity of the sources of vibration, by enhancement of the effective static stiffness and damping for the modes of vibration which result in relative displacements between tool and work piece, and by appropriate choice of cutting regimes, tool design, and work piece design.
Industrial vibration analysis is a measurement tool used to identify, predict, and prevent failures in rotating machinery. Implementing vibration analysis on the machines will improve the reliability of the machines and lead to better machine efficiency and reduced down time eliminating mechanical or electrical failures. Vibration analysis programs are used throughout industry worldwide to identify faults in machinery, plan machinery repairs, and keep machinery functioning for as long as possible without failure.
Numerous standards exist to guide or govern vibration monitoring and analysis, including some that establish classifications for machinery vibration, how measurements should be made, and how the acquired data should be analyzed.
ANALYSIS BY USING SOFTWARE
A computer program is developed by using Visual Basic programming language in order to analyze machine tool chatter vibrations. MATLAB and Visual Basic softwares are used interactively for the solution of numerical equations. Since the dynamic equations related to vibration analysis are very complex, these equations are solved numerically. For the solution of these complex equations, some libraries of MATLAB software package are used in Visual Basic program. Fourth order Runge-Kutta method is used for numerical integration of the dynamic equation.
1.INTRODUCTION
Machining and measuring operations are invariably accompanied by relative vibration between workpiece and tool. These vibrations are due to one or more of the following causes:
(1) In homogeneities in the workpiece material;
(2) Variation of chip cross section;
(3) Disturbances in the workpiece or tool drives;
(4) Dynamic loads generated by acceleration/deceleration of massive moving components;
(5) Vibration transmitted from the environment;
(6) Self-excited vibration generated by the cutting process or by friction (machine-tool chatter).
The tolerable level of relative vibration between tool and workpiece, i.e., the maximum amplitude and to some extent the frequency is determined by the required surface finish and machining accuracy as well as by detrimental effects of the vibration on tool life and by the noise which is frequently generated.
2.SOURCES OF VIBRATION [3]
2.1 VIBRATION DUE TO INHOMOGENEITIES IN THE WORKPIECE

Hard spots or a crust in the material being machined impart small shocks to the tool and workpiece, as a result of which free vibrations are set up. If these transients are rapidly damped out, their effect is usually not serious; they simply form part of the general “background noise” encountered in making vibration measurements on machine tools. Cases in which transient disturbances do not decay but build up to vibrations of large amplitudes (as a result of dynamic instability) are of great practical importance. When machining is done under conditions resulting in discontinuous chip removal, the segmentation of chip elements results in a fluctuation of the cutting thrust. If the frequency of these fluctuations coincides with one of the natural frequencies of the structure, forced vibration of appreciable amplitude may be excited. However, in single-edge cutting operations (e.g., turning), it is not clear whether the segmentation of the chip is a primary effect or whether it is produced by other vibration, without which continuous chip flow would be encountered. The breaking away of a built-up edge from the tool face also imparts impulses to the cutting tool which result in vibration. However, marks left by the built-up edge on the machined surface are far more pronounced than those caused by the ensuing vibration; it is probably for this reason that the built-up edge has not been studied from the vibration point of view. The built-up edge frequently accompanies certain types of vibration (chatter), and instances have been known when it disappeared as Soon as the vibration was eliminated.
2.2 VIBRATION DUE TO CROSS-SECTIONAL VARIATION OF REMOVED MATERIAL
Variation in the cross-sectional area of the removed material may be due to the shape of the machined surface (e.g., in turning of a nonround or slotted part) or to the configuration of the tool (e.g., in milling and broaching when cutting tools have multiple cutting edges). In both cases, pulses of appreciable magnitude may be imparted to the tool and to the workpiece, which may lead to undesirable vibration. The pulses have relatively shallow fronts for turning of nonround or eccentric parts, and steep fronts for turning of slotted parts and for milling/broaching. These pulses excite transient vibrations of the frame and of the drive whose intensity depends on the pulse shape and the ratio between the pulse duration and the natural periods of the frame and the drive. If the vibrations are decaying before the next pulse occurs, they can still have a detrimental effect on tool life and leave marks on the machined surface. In cylindrical grinding and turning, when a workpiece which contains a slot is machined, visible marks frequently are observed near the “leaving edge” of the slot or keyway. These are due to a “bouncing” of the grinding wheel or the cutting tool on the machined surface. They may be eliminated or minimized by closing the recess with a plug or with filler. When the transients do not significantly decay between the pulses, dangerous resonance vibrations of the frame and/or the drive can develop with the fundamental and higher harmonics of the pulse sequence. The danger of the resonance increases with higher cutting speeds.
2.3 DISTURBANCES IN THE WORKPIECE AND TOOL DRIVES
Forced vibrations result from rotating unbalanced masses; gear, belt, and chain
drives; bearing irregularities; unbalanced electromagnetic forces in electric motors;
pressure oscillations in hydraulic drives; etc.
2.3.1 Vibration Caused by Rotating Unbalanced Members. Forced vibration induced by rotation of some unbalanced member may affect both surface finish and tool life, especially when its rotational speed falls near one of the natural frequencies of the machine-tool structure. This vibration can be eliminated by self centering due to resilient mounting of bearings. When a new machine is designed, a great deal of trouble can be forestalled by placing rotating components in a position in which the detrimental effect of their unbalance is likely to be relatively small. Motors should not be placed on the top of slender columns, and the plane of their unbalance should preferably be parallel to the plane of cutting. In some cases, vibration resulting from rotating unbalanced members can be eliminated by mounting them using vibration-isolation techniques. Grinding and boring are most sensitive to vibration because of the high surface finish resulting from the operations. In cylindrical grinding, marks resulting from unbalance of the grinding wheel or of some other component are readily recognizable.
2.3.2 The Effect of Vibration on the Wheel Properties. If vibration exists between wheel and workpiece, normal forces are produced which react on the wheel and tend to alter the wheel shape and/or the wheel’s cutting properties. In soft wheels the dominating influence of vibration appears to be inhomogeneous wheel wear, and in hard wheels inhomogeneous loading (i.e., packing of metal chips on and in crevasses between the grits). These effects result in an increased fluctuation of the normal force, which produces further changes in the wheel properties. The overall effect is that a vibration once initiated tends to grow. When successive cuts or passes overlap, the inhomogeneous wear and loading of the wheel may cause a regenerative chatter effect which makes the cutting process dynamically unstable.
2.3.3 Drives. Spindle and feed drives can be important sources of vibration caused by
Motors, power transmission elements (gears, traction drives, belts, screws, etc.), bearings,
and guide ways.
Electric motors can be sources of both rectilinear and torsional vibrations. Rectilinear
vibrations are due to a nonuniform air gap between the stator and rotor, asymmetry of windings, unbalance, bearing irregularities, misalignment with the driven shaft, etc. Torsional vibrations (torque ripple) are due to various electrical irregularities.
Gear-induced vibrations can also be both rectilinear and torsional. They are due
to production irregularities (pitch and profile errors, eccentricities, etc), assembly
errors (eccentric fit on the shaft, key/spline errors, and backlash), or distortion of
mesh caused by deformations of shafts, bearings, and housings under transmitted
loads. All gear faults, eccentricities, pitch errors, profile errors, etc., produce nonuniform rotation, which in some cases adversely affects surface finish, geometry, and possibly tool life.
Belt drives, used in some applications as filters to suppress high-frequency vibrations
(Especially torsional), can induce their own forced vibrations, both torsional and rectilinear. Any variation of the effective belt radius, i.e., the radius of the neutral axis of the belt around the pulley axis, produces a variation of the belt tension and the belt velocity. This causes a variation of the bearing load and of the rotational velocity of the pulley. The effective pulley radius can vary as a result of (1) eccentricity of the pulley or (2) variation of belt profile or inhomogeneity of belt material.
Chain drives have inherent nonuniformity of transmission ratio and are a significant source of vibration, even when used for auxiliary drives.
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#2

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#3

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