ANALYSIS OF STABILITY IN BORING OPERATION WITH SECONDARY EFFECTS Materials and Manufacturing Processes

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ANALYSIS OF STABILITY IN BORING OPERATION WITH

SECONDARY EFFECTS

Journal: Materials and Manufacturing Processes

Manuscript ID: LMMP-2011-0790.R2

Manuscript Type: Original Article

Date Submitted by the Author: n/a

Complete List of Authors: Kotaiah, Kalluri; K.L.University, Mechanical Engineering Rao, M. Raja; K.L.University, Mechanical Engineering Reddy, M.B.S.; LBRCE, Mechanical Ratnam, Ch; AU College of Engineering, Mechanical

Keywords: stability, analytical approach, compliance, two-degree model, secondary effects, cutting dynamics, boring, workpiece dynamics

URL: http://mc.manuscriptcentral.com/lmmp Email: [email protected]

Materials and Manufacturing Processes

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Table.1 Major cutting conditions used in experiment

Feed(mm/rev) Depth of cut(mm) Spindle Speed (rpm)

0.2 1.4, 1.5, 1.6, 1.8 120, 350, 450, 770

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ANALYSIS OF STABILITY IN BORING OPERATION WITH

SECONDARY EFFECTS

M.Raja Sekhara Rao1, M.B.S.S.Reddy

2, K.Rama Kotaiah

3, Ch.Ratnam

4

1. Associate Professor, Dept. of Mechanical Engineering, K.L.University, Andhra Pradesh,

India-522502.

2. Associate Professor, Dept. of Mechanical Engineering, LBRCE, Mylavaram, India.

3. Professor, Dept. of Mechanical Engineering, K.L.University, Andhra Pradesh, India-

522502.

4. Professor, Dept. of Mechanical Engineering, AU college of Engineering, Andhra

University, Visakhapatnam, India-530003.

Corresponding Author: K.Rama Kotaiah, Professor, Dept. of Mechanical Engineering,

K.L.University, Andhra Pradesh, India- 522502.

E.Mail : [email protected] ; Fax No: 08645-247249

Acknowledgments

Authors acknowledge Dr. M.K.Tiwri, Professor, IIT Kharagpur and Dr.J.Srinivas,

Professor, NIT Rourkela, ---India for helping the necessary experimental works and

guidance. Authors also thankful to the Management of K.L.University, Vijayawada who had

given financial support to carryout the experimental work.

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ANALYSIS OF STABILITY IN BORING OPERATION WITH SECONDARY

EFFECTS

M.Raja Sekhara Rao1, M.B.S.S.Reddy

2, K.Rama Kotaiah

3, Ch.Ratnam

4

ABSTRACT: In this paper an analytical model is proposed to study the stability

analysis in boring operation. Relevant experiments are carried out to illustrate the effects of

various parameters on stability of boring. In this model, a headstock-supported workpiece is

considered by accounting compliance between the cutting tool insert and workpiece. Here

single degree of freedom spring-mass models are used to represent the cutting tool and

workpiece and the interaction dynamics is derived. The changes in the stability lobe diagrams

are reported. Variations of stability limits with secondary effects i.e. work-piece dimensions,

cutter position as well as the effects of cutting tool dynamics are studied and wherever

possible results are compared with existing models. Experimental analysis is conducted on

headstock supported work-piece to examine the correctness of the proposed stability model.

KEY WORDS: Stability, Analytical approach, Compliance, Two-degree model, Secondary

effects, Cutting dynamics.

1. INTRODUCTION

Many engineering components manufactured using casting, forming and other

processes often require machining as their end operation. To achieve higher accuracy and

productivity, it requires consideration of dynamic instability of cutting process. In order to

obtain chatter-free machining conditions, conservative cutting parameters are to be selected

based on the stability limits. Machine tool operators often select these process parameters

from the stability-lobe diagrams, which are conveniently obtained from the analytical cutting

models. In practice, accurate cutting dynamic models are needed to get the realistic

representation of stability states. The stability lobe diagram depends on many parameters

including tool stiffness, frequency, damping ratio, tool material and geometry, workpiece

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material and its dynamics which are called secondary effects along with the primary cutting

parameters i.e. speed, feed and depth of cut. An analytical prediction of stability limits for

orthogonal cutting is well documented in literature [1–3]. Basically, the boring tool is

represented with a single degree for freedom spring-mass system working over a rigid

workpiece. Atabey et al.[4] and Mei [5] stated that machine tool vibrations may be divided

into the three types i.e. free vibration, forced vibration, and self-excited vibration. These

authors defined self excited vibrations as free vibrations with negative damping.

Chandiramani and Pothala [6] depicted dynamics of chatter with two degrees of freedom

model of cutting tool. Since chatter is due to interaction between tool and work, often the

models in terms of both tool and work are considered. Chern and Liang [7] studied the tool

chatter with boring dynamics using a 3D model. Rama Kotaiah et al. [8] and Ganguli et al.

[9] developed a finite-element beam model of spinning stepped-shaft workpiece to perform

stability analysis using Nyquist criterion. Ganguli et al. [9] showed the effect of active

damping on regenerative chatter instability in boring. Moetakef and Yussefian [10] presented

a spindle speed regulation method to avoid regenerative chatter in boring. Miguelez et al. [11]

pointed out the dimensional deviations occurring during machining of a part due to

workpiece deflections, vibrations of tool, material spring back, etc. Akesson et al. [12]

proposed a method based on variable stiffness in boring bars to suppress chatter. Chen and

Tsao[13] and Sekar et al.[14] presented a dynamic model of cutting tool with and without

tailstock supported workpiece using beam theory and analyzed the stability of the cutting

system in terms of the work-piece length, radius, natural frequency, deflection, slenderness

ratio, cutting point, and material. Ozlu and Budak[15] Kotaiah and Srinivas[16] presented

the stability analysis of boring using one- dimensional, transfer function approach and their

study gives a comparative analysis between one dimensional and multi-dimensional stability

models for boring operations.

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The present paper proposes a compliant two degrees of freedom dynamic cutting

force model by considering the relative motion of workpiece with cutting tool. Tool and

workpiece are modeled as two separate single degree of freedom spring-mass-damper

systems. The model allows selection of different operating conditions without a tailstock

support by accounting the fundamental natural frequency of the workpiece. Effect of

workpiece parameters such as linear and lateral dimensions and cutter positions as well as

influence of flexibility and damping of cutter on the stability is studied.

2. ANALYTICAL MODELS

Stability lobe diagrams indicate the critical operating parameters necessary to avoid

unstable cutting conditions. To draw the stability-lobe diagram involving many cutting states,

it is quite tedious to perform the experiments several times. Analytical models on the other

hand help to obtain the status of stability by incorporating several features in dynamic

equations.

2.1 Compliant Dynamic Model of Cutting Tool and Workpiece

The dynamic stability of a machine tool in the boring process depends essentially on

the compliance of the lathe structure, as well as on the properties of the cutting process. The

main input parameters affecting the machining system vibrations are: work material, work

material geometry, tool material, tool geometry, lathe rigidity, cutting conditions. Basically,

the boring tool is represented with a single degree for freedom spring-mass system working

over a rigid workpiece. Effect of cutting tool position, workpiece dimensions, tool stiffness

and damping on the dynamic stability is presented with the proposed dynamic model.

2.2 Dynamic modeling

In most of the boring operations, workpiece is considered as a rigid member and the

chip thickness is assumed to be affected only by the dynamic parameters of cutting tool. This

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one-dimensional second order orthogonal cutting model shown in Figure.1 is represented

with the following governing equation:

1 1 1m x(t) c x(t) k x(t) F(t) cos t+ + = θ&& & (1)

Here, x(t) is chip thickness (variation in depth of cut) at a time t and the parameters m1,c1 and

k1 are the equivalent mass, damping, and stiffness of the cutting tool and tool holder, θ is a

constant cutting angle and F(t) is cutting force, which is given by:

F(t)=Cbh(t) (2)

Where C is cutting coefficient obtained from experiments and b is depth of cut or chip width.

The instantaneous chip thickness h(t) can be written from Figure.1 as:

h(t)= h0-x(t)+x(t- τ) (3)

here, x (t−τ) is chip thickness in previous cut ; h0 is nominal chip thickness resulting from

feed mechanism and the term x(t)−x(t−τ) represents the regenerative chatter. Time delay τ

represents the period for successive passages of tool, which is equal to time required for one

revolution of workpiece in boring. Substituting Eqs.(2) and (3) in Eq.(1) and taking Laplace

transforms on both sides, the dynamic equation in Laplacian(s) domain becomes:

2 s

1 1 1 0(m s c s k )X(s) Cb(H (s) X(s) e X(s))− τ+ + = − + (4)

Thus the overall transfer function becomes

)e1)(s(bCG1

)s(bCG

)s(H

)s(Xs

0

τ−−+=

(5)

where 2

1 1 1

c o sG (s )

m s c s k

θ=

+ + (6)

In practice, operating spindle speeds are well below the natural frequency of workpiece.

Hence, in the flexibility considerations, the first mode of vibration is considered as significant

and the workpiece is represented as another single degree of freedom spring mass damper

system. For this combined system, the equations of motion can be written in terms of tool and

workpiece deformations x1(t) and x2(t) at a time t as follows:

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m1 1x (t)&& + c1 1x (t)& + k1x1(t) = –F(t) cos θ (7)

m2 2x (t)&& + c2 2x (t)& + k2x2(t) = F(t) cos θ (8)

Here m2, c2, and k2 respectively represent mass, damping coefficient, and stiffness of the

workpiece. F(t) is dynamic feed force which can be expressed in terms of the present and

previous relative motion of cutting tool with respect to work-piece: (x1(t) − x2(t)) and (x1(t −

τ) − x2(t − τ)). That is force

F(t) = Cbh0 – (x1(t) – x2(t)) + (x1(t – τ) – x2(t – τ)) (9)

When the above force term F(t) in Eq.(9) is substituted in Eqs.(7) and (8) and writing k1/m1 =

ω2n1 , k2/m2 = ω

2n2, c1/m1 = 2ξ1 ωn1 , c2/m2 = 2ξ2 ωn2 , these two equations become coupled

dynamic equations in terms of the variables x1 and x2 as follows.

2

1 1 n1 1 n1 1 0 1 2 1 2

1

Cb cosx (t) 2 x (t) x (t) h (x (t) x (t)) (x (t ) x (t ))

m

θ+ ξ ω + ω = − − − + − τ − − τ&& &

(10)

2

2 2 n2 2 n2 2 0 1 2 1 2

2

Cb cosx (t) 2 x (t) x (t) h (x (t) x (t)) (x (t ) x (t ))

m

θ+ ξ ω + ω = − − − + − τ − − τ&& &

(11)

Here ωn1,ωn2 and ξ1,ξ2 are natural frequencies and damping ratios of the cutter and work piece,

respectively.

2.3 Stability analysis

The stability can be analyzed by considering the characteristic equation of the system

and studying the relationship between the spindle speed N and chip width b. For rigid work-

piece analysis from Eq.(5) the characteristic equation is obtained by equating denominator to

zero. That is :

s

2

1 1 1

(1e ) cos1 bC 0

m s c s k

−τ θ+ =

+ + (12)

Substituting s = jω, separating real and imaginary terms, and solving for τ and b yields the

following critical values:

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* 1

2

1 1

c2(n 1/ 2) a tan

m k

ω τ = + π+ ω ω −

(13)

where n = 0,1,2…….

* 1

*

cb

C cos sin

ω= −

θ ω τ (14)

Here ω is the chatter frequency. Spindle speed in revolution per second is computed as N =

1/τ*. It can be seen that Eq. (13) has multiple solutions due to different values of n. Thus, Esq.

(13) and (14) define the stability limits of this system.

3. EXPERIMENTAL ANALYSIS

In order to verify the analytical models, several tests are conducted to collect the

required data through measurements which are done before, during and after the cutting tests.

In machining practice cutting force signals carry good amount of information regarding

dynamics of cutting. When stability is lost, the feedback between the displacement and

cutting forces begins, which results in an erratic cutting force histories. These cutting force

histories are often recorded by means of lab-view equipped tool post dynamometers. Fig.2

illustrates the arrangement for dynamic cutting force measurement using lathe tool-

dynamometer. For testing the effects of work flexibility and compliance between work and

tool, a series of cutting experiments are conducted on a 7.5 KW engine lathe with headstock

supported work-pieces. The cutting tools are carbide inserts and cutting is performed

orthogonally. Work material is AISI 1045 steel. The cutting variables like depth of cut and

spindle RPM are varied and cutting force histories are obtained. The major cutting conditions

employed are depicted in Table.1.

In order to measure output forces Kistler-9121 three-component piezoelectric

dynamometer is employed. There is an associated 5070 multi-channel charge amplifier

connected to PC employing Kistler Dynoware force measurement post processing software.

The measured cutting forces are digitized and saved in the post processor files. This time

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domain data can be translated into a text file and time histories are drawn using EXCEL or

MATLAB so as to obtain the corresponding FFT spectrums. Prior to the cutting force

measurements, modal data of cutting tool and work-piece and stiffness of tool and work-piece

are obtained from impact hammer testing, as the natural frequencies and damping ratios of

work-piece and tool are required first. Work-pieces of 100 mm external diameter and 70 mm

internal diameter and set-over length of 200 mm are used under various operating conditions.

Fig.3 shows the experimental set-up used for measurement of modal parameters along with

the dynamometer arrangement.

4. RESULTS AND DISCUSSION

This section presents the results of various analytical models proposed in the work

along with the experimental validations wherever necessary. Initially, the output stability

results of multi-degree of freedom tool and work compliance model are described.

4.1 Effect of work-piece dynamics

When cutting force deflects the work-piece, the effect of work deflections on stability

of cutting process are shown in Figure 4. This figure shows the relationship between the

critical chip width and the spindle speeds for work-pieces of length 0.7 m and internal radius

0.035 m. For comparison purpose, the results for both the rigid (dashed line) and flexible

work-piece cases (solid line) are presented. It is seen that critical chip-width at higher spindle

speeds is considerably larger when the work-flexibility is considered. The results reveal that

for a constant spindle speed, the critical chip width is consistently higher when the work-

piece deformation is taken into consideration. Figure 5 shows variation of percentage

difference in the critical chip-width as a function of spindle speed for four different work-

pieces of constant length with different radii. A single lobe at higher speeds is only shown for

clarity. As noticed from earlier works, here also the percentage difference of chip-width

decreases progressively with increase in radius. Figure 6 shows the variation of percentage

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difference in critical chip-width as a function of spindle speed for two work-pieces of

constant radius 0.035 m, with two different lengths. From the diagram it can be observed that

larger work-piece has more deflection and critical chip-width. In all the above cases, the

position of cutting tool is considered at L1=0.6L. The damping ratio for all work-piece

conditions is taken as 0.025, since it normally varies from 0.01 to 0.05. Figure 7 shows the

influence of cutter position on chatter stability. Here a work-piece of 0.5m length and 0.03m

radius is subjected to different tool forces at points: L1=0.2L,0.4L, 0.6L and 0.8L. These

analytical results suggest that the magnitude of the critical chip-width difference should

decrease as the force is applied successively at 0.2, 0.4.0.6 and 0.8L respectively.

4.2 Effect of cutting tool dynamics

Fig. 8 shows the chatter stability limits, when cutting tool stiffness k1 changes from 0.5×107

N/m to 2×107 N/m at constant values of work-piece length L=0.7 m and radius r=0.05 m.

From the diagram it is observed that as the tool becomes more flexible, critical chip width

increases. Fig.9 shows the effect of cutter-damping on the chatter stability for a cutter

stiffness k1=0.5×107 N/m, along with work-piece dimensions: L=0.7m and r=0.5m. When

damping increases in the cutter the stable depths of cut increase at the same spindle speeds.

4.3 Experimental Results

The modal parameters namely, natural frequencies and damping ratios of work and tool are

obtained from the conventional impact hammer test. Initially, the force and corresponding

acceleration histories are directly recorded in the analyzer and the data is further employed to

obtain the frequency response curves using a MATLAB program. The Fourier transforms

gives the frequency spectrum. As seen from the amplitudes of the spectra, the fundamental

natural frequency of the tool as 2560 Hz while the work-piece is around 612 Hz. The cutting

force coefficient (C) calculated from orthogonal data of AISI 1045 steel work-piece using

shear stress, shear angle and friction angle with orthogonal transformations and it is found to

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be 700 MPa. In this test, AISI 1045 steel work-pieces are used. That is Z-component. Hence

the dynamic component of the main cutting force is expected to be relatively large in

amplitude among the three components. Also the amplitude of this force is expected to be

larger than the amplitude of the same component force with continuous chip formation. In

such cases, X and Y components (thrust and feed force) would be relatively large. Fig. 10 (a)

and (b) shows the dynamic components of three cutting forces in two different cutting states

for stable state. As seen, the stable cutting is characterized by the lower amplitudes of

dynamic component Fz and stable process has small amplitude variation in all force

components. From these figures it can be seen that there is no high frequency variations in

the force plots. For example in the force spectrum plot a significant energy occurs at 465 Hz

and 520 Hz in the Fx signal, 490 Hz in Fy signal and 490 Hz in Fz signal. The frequency-

domain plots show constant energy through out all the three force signals. The operation can

be considered as stable. Unstable boring operation is shown in Fig. 11 (a) and (b). Here high

frequency variations are evident. The frequency spectra show a significant energy in all the

three force signals at 430 Hz. In these cases chatter instability is present. In addition, they

have smaller peaks surrounding the extreme one. Finally some of the experimental states at a

cutting speed of 770 RPM are superimposed over the analytical lobe diagram and it can be

seen that the predicted experimental states are in excellent agreement with the proposed

analytical model.

5. CONCLUSIONS

In this work, stability analysis in boring process has been presented with coupled

dynamic model of cutting tool and workpiece. Here while studying the compliance between

the workpiece and cutting tool, the spring mass models have been employed and the relative

deformations were considered in cutting force expressions. The methodology was presented

with headstock supported workpiece operated with cutting tool in orthogonal boring

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operation. Effect of secondary parameters that is cutting position, workpiece dimensions,

cutter flexibility, and cutter damping on the dynamic stability have been presented with the

proposed dynamic model. The deviations of stable depths of cut measured by present model

and existing one-dimensional rigid workpiece model have been found to be in close

agreement with available work in literature. The experimental chatter predictions have

revealed that the proposed compliance model establishes the stable states accurately in rough

boring operations.

REFERENCES

1. Tobias, S.A.; Fishwick, W. The chatter on lathe tools under orthogonal cutting

conditions. Trans. ASME 1958, 80, 1079–1088.

2. Jean, F.R.; Cristina, P.; Claude, B. A Model for Simulation of Vibrations During

Boring Operations of Complex Surfaces. CIRP Ann.- Manufacturing Technology

1998, 47, 51-54.

3. Ismail, L.; Fuat, A.; Yusuf, A. Dynamics of boring processes: Part III-time domain

modeling. International journal of Machine Tools and Manufacture 2002, 42, 1567-

1576.

4. Atabey, F.; Lazoglu, I.; Altintas, Y. Mechanics of boring processes—Part I.

International journal of Machine Tools and Manufacture 2003, 43, 463-476.

5. Mei, C. Active regenerative chatter suppression during boring manufacturing process.

J. Robotics and Computer-Integrated Manufacturing 2005, 21, 153-158.

6. Chandiramani, N.K.; Pothala, T. Dynamics of 2-DOF regenerative chatter during

turning. J. of Sound Vibration 2006, 290, 448–464.

7. Chern, G.L.; Liang, J.M. Study on boring and drilling with vibration cutting.

International journal of Machine Tools and Manufacture 2007, 47, 133-140.

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8. Rama Kotaiah, K.; Srinivas, J.; Babu, K.J.; Srinivas,K. Prediction of optimal cutting

states during inward turning –An experimental approach. Journal of Materials and

Manufacturing processes 2010, 25, 432-441.

9. Ganguli, A.; Deraemaeker, A.; Preumont, A. Regenerative chatter reduction by active

damping control. J. of Sound and Vibration 2007, 300, 847-862.

10. Moetakef, I.B.; Yussefian, N.Z. Dynamic simulation of boring process. International

journal of Machine Tools and Manufacture 2009, 49, 1096-1103.

11. Miguelez, M. H.; Rubio, L.; Loya, J.A.; Fernandez, S.J. Improvement of chatter

stability in boring operations with passive vibration absorbers. International journal of

Mechanical Sciences 2010, DOI:10.1016/j.ijmecsci.2010.07.003.

12. Akesson, H.; Smirnova, T.; Hakansson, L. Analysis of dynamic properties of boring

bars concerning different clamping conditions. J. of Mechanical Systems and Signal

Processing, 2009, 23, 2629-2647.

13. Chen, C.K.; Tsao, Y.M. A stability analysis of turning tailstock supported flexible

work-piece. International journal of Machine Tools and Manufacture 2006, 46, 18–25.

14. Sekar, M.; Srinivas, J.; Kotaiah, R.K.; Yang, S.H. Stability analysis of turning process

with tailstock-supported workpiece. International Journal of Advanced Manufacturing

Technology 2008, 45, 331-342.

15. Ozlu, E.; Budak, E. Analytical Modeling of Chatter Stability in Turning and Boring

Operations- part-I: Model development. J. of Manufacturing Science and

Engineering, Trans. ASME 2007, 129, 726-731.

16. Kotaiah, R.K.; Srinivas, J. Dynamic analysis of a turning tool with a discrete model of

the workpiece. Proc. IMechE, Part B: J. Engineering Manufacture 2010, 224, 207-

215.

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Fig.1 Cutting tool model with rigid workpiece

Fig. 2 Arrangement for dynamic force measurement

Fig. 3 Experimental set-up for finding modal data

k1

c1

m1

F(t)

θ

x

y

Ω

h(t) x(t)

h0(t) x(t-τ)

Previous cut

surface

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Fig.4 Comparative lobe diagram for rigid and flexible work-pieces

Fig. 5 Variation of percentage difference in chip-width

as a function of radius

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Fig. 6 Percentage difference in chip-width versus speed for

work-piece of constant radius

Fig. 7 Effect of position of cutting in headstock supported work-piece

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Fig. 8 Effect of stiffness of cutting tool at high speeds

Fig. 9 Variation of chip-thickness as a function of damping ratio of tool

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(a) Time-domain

(b) Frequency domain

Fig.10 Experimentally obtained dynamic cutting forces in stable state

(a) Time-domain

(b) Frequency domain

Fig.11 Experimentally obtained dynamic cutting forces in unstable state.

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ANALYSIS OF STABILITY IN BORING OPERATION WITH SECONDARY EFFECTS Materials and Manufacturing Processes

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