Chatter – Origin and Suppression• Definition of chatter• Types of chatter• Origins of chatter• Methods of suppression

- M Brij Bhushan

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Chatter• Chatter, in grinding, is the undesirable vibration during

the grinding process, which results in marks on the surface of the work-piece or wheel or both called chatter marks.

• Basically caused due to two types of vibration:▫ Forced vibration ▫ Self Excited Vibration

Ref.: Inasaki, Karpuschewski, Lee – Grinding Chatter – Origin and Suppression, CIRP Annals, 2001.

Chatter Marks on a crankshaft journal

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Quantification of chatter• Chatter is caused due to vibrations at a

particular frequency, being impinged on the work-piece by the wheel.

• Thus, if work speed is (rpm) and we count the number of chatter marks on the component to be (marks/rev.); then the frequency that may be causing the chatter is:▫ (Hz)

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Forced Vibration• External (to the grinding zone) source of vibration which induced vibration

into the grinding zone with a large enough amplitude causing chatter marks on the work-piece.

• Main causes:▫ Unbalance and eccentricity of the grinding wheel

• How to check:▫ Wheel unbalance:

Count the number of chatter marks on the work-piece for a given wheel speed Change wheel speed, again count the number of chatter marks. If the no. of chatter marks corresponds to the ratio of wheel rpm/work rpm in both the

cases, i.e. it has changed according to the change in wheel speed, then it is most likely due to wheel unbalance.

If the no. of chatter marks is the same, then it is mostly due to regenerative chatter.▫ It can also be due to other rotating components such as pulley wheel, motor,

rotary dresser, external vibrations (due to improper mounting), etc.▫ Best way to find out the cause is to run the machine in free running condition

and check for the vibration at different locations in the machine. If any vibration we get corresponds to the chatter frequency, then it may be the cause of the chatter.

• Other tips:▫ Avoid integer ratios of wheel speed to work speed. ▫ True and balance in succession, multiple times:

True, balance, true and final balance (for example)

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Self-Excited Vibration• Regenerative Chatter:

▫ Considered to be a major cause of self-excited vibration in grinding.▫ Due to rotational motion of work-piece during grinding, waves are generated on

the work-piece surface created by the relative vibration between the grinding wheel and the work-piece.

▫ This results in a change of depth of cut after 1 revolution of the work-piece.▫ The phase shift between the surface waves (outer modulation) and current relative

vibration (inner modulation) makes the process unstable when a certain condition is reached.

▫ Regenerative effect affects both the work-piece and the grinding wheel surfaces. Because of the regenerative nature of these vibrations, the waves generated on the

work-piece grow quite rapidly. This is a limitation when selecting the grinding set-up parameters. If the work-piece speed is high or the chatter frequency is low, vibration with large

amplitudes can be observed at the beginning of the grinding process even if a newly dressed grinding wheel is used.

Chatter marks are significantly visible on the work-piece. If work-piece speed is reduced or the chatter frequency is high, then the vibration

amplitude is low at the beginning of grinding, but gradually increases as grinding time advances.

The waves generated on the grinding wheel surface grow slowly due to higher wear resistance. This type of chatter effects the wheel life. Always present, but growth rate is critical. Waves can be removed by truing and dressing.

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Regenerative Chatter

Ref.: Rowe B., Principles of Modern Grinding Technology, 2009, Elsevier

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Regenerative Chatter:•Depends on many factors:

▫Geometrical interference between the grinding wheel and the work-piece

▫Vibration behaviour of various grinding operations

▫Grinding stiffness and grinding damping▫Contact stiffness▫Dynamic compliance of the mechanical

system

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Geometrical interference between the grinding wheel and the work-piece• Waves generated on the work-piece as well as on the grinding wheel surfaces

envelop the relative vibration between them.• Work-piece waves:

▫ For amplitude of relative vibration () and the amplitude of waves generated on the work-piece surface () to be identical, conditions to be met: Low vibration frequency Small relative amplitude Low work-piece velocity

▫ Once, the critical limit is exceeded, the amplitude of waves on the work-piece surface becomes smaller than that of the relative vibration, i.e. the envelope begins to have a node.

• The geometrical interference ():

▫Here, is the work-piece speed; is the angular chatter frequency; is the equivalent diameter.

▫ for wheel replace with

▫ For chatter to occur, therefore,▫ For chatter, Thus, waves with large amplitude and high chatter frequency frequency

cannot be generated on the work-piece as the critical amplitude () becomes small.

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Vibration behaviour of various grinding operations • Internal and Surface Grinding:

▫ Chatter frequency in most cases is related to the natural frequency of the grinding wheel spindle system. Dynamic stiffness of these parts is lower than that of the work-piece system.

▫ Chatter vibration caused by regenerative effect on work-piece surface is difficult in surface grinding. Phase shift between inner and outer modulation is not necessarily constant

due to uncertainties in the work-piece’s reciprocating motions.

• Cylindrical Grinding:▫ Chatter frequency in most cases is related to the natural frequency of

the work-piece and its associated system. Dynamic stiffness of these parts are generally lower than that of the grinding

wheel spindle system.

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Grinding Stiffness and Grinding Damping• On the basis of a simple grinding force model,

• Grinding Stiffness:

• Grinding Damping:

Here, : constant, : exponent, : grinding width, : wheel depth of cut, : work-piece speed, : wheel speed, is the equivalent diameter.

• Generally, as grinding stiffness increases, the system becomes less stable (more vibration) and as the grinding damping increases, the system become more stable.

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Contact Stiffness• This is concerned with the elastic deformation of the grinding wheel.

• Grinding wheel deformation:

where, < 1 is the Normal Force.

• Normal Force:

parameter description

• Contact Stiffness:

▫ Non-linear, similar to a hard spring.

• Grinding wheel wear stiffness is a more practical parameter for the grinding wheel regenerative chatter. Generally, wear stiffness is much higher than the contact stiffness.

• Conclusions:▫ An increase in speed-ratio increases the contact stiffness.▫ An increase in the depth of cut () increases the contact stiffness.▫ A friable wheel will have lower and hence lower grinding stiffness, which will result in a

more stable operation and hence, lower the amplitude of vibrations.

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Dynamic Compliance of the Mechanical System • This depends on a large number of parameters such as:

▫ Static compliance of the machine▫ The orientation factor, comprising of an interplay between:

The direction of the natural frequency mode of the mechanical system

The direction of the depth of cut The direction of the resultant grinding force

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Stability Issues:• Absolute stability in terms of work-piece regenerative chatter can

be attained if the work-piece speed is sufficiently low.• The wheel regenerative chatter has a large instability range, and

thus, most practical grinding conditions exist in the unstable region.▫ Thus, the rate of increase of vibration amplitude becomes most

important for chatter due to this effect.• The increase rate of vibration amplitude for wheel regenerative

chatter is much slower than work-piece regeneration type vibration amplitude.

• Chatter frequency is always higher than the natural frequency of the mechanical system.

• To avoid waviness, an integral speed ratio () must be avoided.• For work-piece regenerative chatter:

▫ The process tends to be unstable under the condition of lower traverse speed, higher work-piece speed, larger grinding wheel width, and smaller depth of cut.

▫ Chatter frequency increases with increases of traverse speed, grinding wheel width, depth of cut, and work-piece speed.

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Suppression of self-excited chatter vibrations

• Three strategies:▫ Modification of grinding conditions▫ Increase in dynamic stiffness of the mechanical system▫ Disturbing Regenerative effects

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Suppression of self-excited chatter vibrations• Stability analysis based on the 3 strategies can be depicted as:

• The dynamic compliances of the mechanical systems are represented by the vector loci on the complex planes, while straight lines parallel to the imaginary axes represent the material removal process.

• Instability occurs when both the lines have intersections.

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Methods for suppressing regenerative chatter vibration1. Modifications of grinding conditions

a) Reduce work-piece speedb) Reduce grinding widthc) Use a more friable wheel

2. Increase the dynamic stiffness of the mechanical system:a) Increase the static stiffnessb) Decrease the orientation factorc) Increase the damping (active and passive damping)

3. Shifting the vector locus of the dynamic compliance to the positive real part

a) Decrease the contact stiffness of the grinding wheel

4. Disturbing regenerative effectsa) Vary the rotational speed of work-piece (reduce work-piece

regenerative chatter) or grinding wheel (reduce wheel regenerative chatter) periodically.

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Methods of suppressing regenerative chatter vibration

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Methods of suppressing regenerative chatter vibration

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Grinding Tests• To describe the process behaviour, the vibration analysis results as well as the

surface profile measurements of the grinding wheels and work-pieces are taken into account.

• Visible chatter marks on the work-piece lead to a first estimation of the frequency.

• In the case of regenerative chatter in the work-piece, the grinding wheel usually retains its circumferential round shape.

• External excitations may lead to development of waviness pattern if the excitation frequency is an integral multiple of the rotational frequency.• Any change in grinding conditions will have an impact on the dynamic cutting stiffness as well as on the static cutting force.

• Both quantities are directly proportional to the width of the grinding wheel. (reduce width to reduce chatter)

• Increase in grinding wheel compliance can be achieved by:▫ Small E-modulus of grinding wheel▫ A soft bond▫ Small cutting forces

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References1. I. Inasaki, B. Karpiszewski, H.S. Lee: Grinding chatter – origin and

suppression. Annals of the CIRP, 50(2001)2.2. W. Brian Rowe, Principles of Modern Grinding Technology, Elsevier,

20093. Handbook of Machining with Grinding Wheels: Ioan D. Marinescu,

University of Toledo, Ohio, USA; Mike Hitchiner, Saint-Gobain Abrasives, Romulus, Michigan, USA; Eckart Uhlmann, Institute for Machine Tools & Factory Management, Berlin Uni; W. Brian Rowe, LJMU, Liverpool, UK; Ichiro Inasaki, Keio University, Yokohama, Japan. Hardback - Published Dec 21, 2006