Self Excited Vibratory Drilling
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summer project pal
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15-01-2011, 06:34 PM


Abstract
Drilling assisted by axial vibration at low frequency is a promising machining process because, by naturally fragmenting chips, it can improve both productivity by canceling stripping operations and work piece quality by decreasing negative effects due to chip friction. Based on a theory of self-excited vibrations, a drilling device has been developed which is described in this paper. This technology is very compact and can used on any conventional machine tool. However the experiments on these machine tools are quite difficult and long because the numerous parameters influencing the vibration. Therefore, in order to guide the experiments, a dimensionless approach has been used to choose the cutting conditions and vibratory tool holder properties. This approach permits the number of test to be reduced, since the machining process entirely can be described with only three dimensionless parameters instead of nine physical parameters. This paper presents first experimental results on this new technology. In addition, it shows the way that the dimensionless approach had been applied and validated to guide the experiments.


.rar   Self Excited Vibratory Drilling.rar (Size: 669.52 KB / Downloads: 176)

Introduction
Research on high productivity and quality in machining has been acute problem for a long time. New technologies machining has been emerged over the last few years, making it possible to accelerate the process of cutting and decrease cutting time. Those technologies mainly seek to decrease cutting time by high speed machining or to save the unproductive time by using high feed rate machines. The challenge is to improve simultaneously the productivity of drilling process in two directions by the development of new techniques: low frequency self excited vibratory drilling.
Drilling assisted by axial vibration at low frequency is a promising machining process because by naturally fragmenting chips it can improve both productivity and work piece qualities by canceling stripping operations and by decreasing negative effects due to friction. Based on the theory of self-excited vibration a drilling device has been developed which is described in this paper.
This technology is very compact and can be used on every conventional machine tool. However, experiments on these tools are quite difficult and long because of the numerous parameters influencing the vibration. Therefore, in order to guide the experiments a dimensionless approach has been used to choose the cutting conditions and vibratory tool holder properties. This approach permits the number of tests to be reduced, since the machining process can be entirely described with only three dimensionless parameters instead of nine physical parameters

Objectives
1. To show the benefits of self excited vibratory drilling technology
2. To show how the dimensionless parameters approach makes the setting up of the process easier.
Self excited vibratory drilling
At first glance, it seems that the drilling process is well known and has been mastered for a long time. However, in industrial series it is very difficult to obtain holes with regular geometrical and technological parameters, and to increase the productivity without quality loss. It becomes critical for deep drilling because the chip removal process remains the main obstacle to quality and productivity.
Chip fragmentation is due to axial vibration of drill creating discontinuous cutting. The two main advantages of the process are the following:
1. Chips are naturally fragmented to small pieces implying that there is no need to perform the stripping operations classically used to split up chips.
2. The friction of chip on the manufactured hole surface is limited which leads to improved hole quality.
The idea of assisting the drilling process by low frequency axial vibration has been around for more than 30 years in the world. However, in all studies the vibrations were forced type; they were generated by an external source of energy. [Mechanical excitation, piezoelectric translator etc ]. Such technologies have an advantage in controlling vibrations. However, they are relatively cumbersome and expensive, and are limited in frequency and amplitude. In order to solve this problem a new drilling technology, self-excited drilling was developed based on the mechanism of self-excited vibration. This phenomenon is particularly well known. It was identified as one of the principle causes of chattering. Therefore, studies made on the subject always saw this phenomenon as harmful with the cut and thus sought to identify the cutting conditions without chattering. The step used was reverse the aim was to look at controlling the phenomenon to split chips up.
Self-excited vibratory drilling is a dynamic process extremely difficult to control because of non-linear forces vary in time. The regenerative vibrations naturally appear at certain revolution frequency of drill. These natural axial vibrations are used to fragment chips. The challenge is to keep them stabilized at a suitable frequency and magnitude for good quality cutting.
The mathematical model of self-excited vibratory drilling tried to sole this problem with dimensionless parameters. This model allowed the operating conditions required for the setup to be forecast.
The theoretical study aimed at obtaining the equations governing the creations of work piece surface and making it possible to forecast the operating conditions of the vibratory drilling. This study has been base on specific modeling of drilling. The basic equations are obtained in a dimensionless form in order to decrease significantly the number of parameters of the system for simplicity of study and practical use of this technology.
The equations are solved using analytical method that allows very fast computation of the boundary between vibrating and non-vibrating cutting conditions. However the formations are binary, the system vibrate or does not vibrate. This resolution method thus does not make it possible to know the characteristics of vibration amplitude, frequency etc. in other word certain forms of vibration allows good cutting. Therefore, the determination requires numerous experiments.
The experimental study was carried out with a specific device being developed in the laboratory. The self-vibratory drilling device composed of three main elements.

1. Drill holder: fix the drill and enable axial movements to be made
2. The leaf spring: it is the dynamic cutting fixture provides a magnitude and frequency adaptation to good quality control.
3. The body: it connects the device to the machine spindle.


Dynamic drilling models

Modeling of Self-excited vibratory drilling

The model of self-excited vibratory drilling is shown in figure. The governing equation of the system is
mώ(t) + cώ(t) + kώ(t) = Tc ————————————1
Where m, c, k are the mass of the drill holder, the damping and the stiffness of its connection with the body respectively. ώ(t) is the instantaneous axial position of the vibrating part and Tc is the axial cutting force. The value of m and k can be measured directly while damping c is obtained by modal analysis.
The axial cutting force law is empirical according to
Tc = Z.R.Kc.hq. ——————————————2
Where Z = number of lips of the drill, R is the drill radius, Kc and q are mathematical constants depending on the tool geometry and the work piece material, h is the uncut chip thickness.

Basis of the theory of self-excited vibratory drilling
In conventional drilling, the uncut chip thickness measured in the spindle axis direction is equal to the number of lips (Z) divided by the feed rate (h0)
i.e. h0/2
In vibratory drilling this thickness is modified by the deflection of the drill holder. Assuming that the amplitude of vibratory deflection is small and does not produce discontinuous cutting the uncut chip thickness is equal to the distance between the current positions of the cutting edge occupying the same angular position.
Therefore the dynamic uncut chip thickness,

h = h0/2 + ώ(t) – ώ(t – 1/fz¬) ———————————————3
Where fz¬ is the passing frequency of the lips given by
fz¬ = N.Z / 60 ————————————————4
Substitute the equation 2 and 3 in equation 1 gives the mathematical model of the dynamic drilling with a self-excited vibratory mechanism according to

mώ(t) + cώ(t) + kώ(t) = Z.kc.R [h0/2 + ώ(t) – ώ(t – 1/fz¬)]q —————5

The equation has a constant solution corresponding to continuous cutting given by
ώ0 = kc/k. Z1-q R h0q ————————————————————6

The vibratory cutting condition corresponds to the condition for which constant solution asymptotically constant unstable. This study is made by first method of Lyapunov.
Assuming that the cut is continuous, the solution of the equation 5 is the sum of the constant solution ώ0 and a perturbation Δώ namely

ώ = ώ0 + Δώ ———————————————————7
The first method of Lyapunov permits the stability of the non disturbed solution to be studied using the linear form of equation 5.which is given by,

mΔώ(t) + cΔώ(t) + kΔώ(t) = Z2-qkc.q.R.h0q-1[Δώ(t) – Δώ(t – 1/fz¬)]—8
Applying laplace transform,

D(s) = ms2 + cs + k - Z2-qkc.q.R.h0q-1[1-exp( -s/fs)]———————9
The stability limit correspond to the solution of equation 9 for the imaginary value of s. in parametric form limit satisfies the condition
Re [D(s)] = 0
Im [D(s)] = 0
The diagram shows the stability limits for a set of physical parameters in a spring stiffness Vs spindle speed diagram. The zone below the limits corresponds to continuous machining, because it does not provide energy sufficient for realizing vibratory drilling. The zone above the limit covers the vibratory field of instability.

Limits of the theory to predict optimal vibratory conditions
Not all the vibratory conditions are optimal only some make it possible to have satisfactory regular vibrations for the drilling process. However, these favorable zones cannot be obtained by theory because
• The use of linear solving method does not make it possible to describe strongly the non-linear vibratory motion that exists in the unstable field.
• The ploughing phenomenon, which occurs near the centre of drill, is not taken into account, which acts like damper of vibration, when the vibration frequency becomes increasingly important in front of rotational frequency.

During drilling, it was observed that this phenomenon was very strong and the cutting conditions chosen below the first lobe the variations do no appear.
Because of the limits of the theory, it is impossible to obtain with certainty the best vibratory cutting conditions for drilling. Therefore, search for these conditions are most experimental. However, at this stage it becomes too expensive to carry out a great number of test and methods for the nine physical parameters kc, q, h0, Z, k, c and fz that control the drilling process.

Dimensionless approach
The field of investigation has been reduced by grouping all the physical parameters into three dimensionless parameters
Dimensionless stiffness k
Dimensionless frequency f
Damping ratio z,
Using the theory of similarities. According to this theory of similarities, these three parameters are sufficient to characterize the process entirely and to describe the motions (vibratory motions). A single set of dimensionless parameter corresponds to a multitude of sets of physical parameters. Therefore, these sets all produce identical vibratory motion. Thus if a set makes it to have good vibratory cutting conditions any other set corresponds to the same dimensionless parameter will vibrate in a similar way and will be satisfactory for the cut. Thus, the advantages of dimensionless approach are-
• It allows starting from an identified satisfactory set, the new characteristics of the vibratory drill holder for a new diameter, a new spindle speed, or a new material to be determined quickly.
• Moreover, this approach is only slightly affected by imperfections or gaps in the model.


Experimental setup






The experimental setup as composed of the following elements:
1. ‘Hermle’ machine tool five axes, Nmax 15000 r/min
2. Self vibratory drilling device
3. Leaf spring
4. A tool holder vibrating part
5. Surface or reference for measuring displacements
6. Sensor holder
7. Displacement sensor measuring the axial position of 5
8. Work piece
9. A Kistler device for measuring the cutting force
10. Acquisition system
11. Computer
The vibratory device 2 is held in the machine tool spindle equipped with a position sensor 7 maintaining by a fixed holder. The disc 5, which is screwed on the tool holder 4, is used as a reference surface. The work piece is put on the machine table fixed on a Kistler cutting force measuring device 9. Because of the configuration, it is possible to record the displacements of the vibrating part and the axial cutting force during drilling.

Experimental measurement of model parameters
Drill holder parameters k,m,З
The tool holder can be used with various springs and various masses the value of which are measured directly.
Damping depends on the friction in the ball guides and m and k for each couple (m,k) used in the experiments. The values of З was measured by model analysis

Parameters kc and q of the model of the axial cutting force.
The values of these parameters of axial force during conventional drilling carried out at various feed rates. These parameters are also obtained by fitting experimental forces. The identification was made with the same drill for two materials used.
Then to calculate the stability of lobes by solving the equation for a particular limit of З. To conduct the test by testing several spindle speed and spring stiffness. Then calculate the best dimensionless parameter corresponding to this best configuration.
Here the experimental results highlights
• Interest in self-excited vibratory drilling compared with conventional drilling.
• The influence of parameter k and F on vibration.
• The modification of tool holder properties keeping k constant for drilling at different spindle speed.
• The modification of tool holder properties keeping k and f constant for drilling in a new material with different diameter.

Experimental comparison of vibratory drilling and conventional drilling
The comparison is made in test 1 and test 2. For the two tests the measured axial cutting force over the duration of test and in detail over a few revolution and chip, photographs are shown.



Vibratory drilling conventional drilling

The comparison of chips highlights two advantages:
• Good fragmentation of chips
• Low heating of the cutting force
The chips are regular with very reduced in size and do not present any indication of excessive heating contrary to those obtained in conventional drilling which are long and burnt.
The analysis of efforts explains these observations:
• In conventional drilling the effort is relatively constant for a medium value
tc-M=251 N, but it increases at the end to reach maximum value tc-M=532 N, which explains the heating.
• In vibratory drilling, the effort is periodic and the intermittency of cut, which cause the chip fragmentation, appears because of null effort during the part of revolution.
The cutting rate is Cr, which is the ratio of the cut to the duration of revolution. In this case, the ratio is about 0.54, which means that 0.46 revolutions, the lips do not cut because the vibrations take them off from the material. In the case of conventional drilling, it is seen that the ratio is one.
Considering the value of forces it can be seen that the maximum effort
tc-M =696 N is higher than value of 457 N, predicted by model analysis. On the other hand the average effort which reveals the cutting power is much lower tc-M =241 N cutting power, which is less than that obtained in a conventional drilling, for a feed rate nearly half that in the vibratory drilling. This explains, why even at high speeds the chips are not burnt since less heat is dissipated for the same chip volume.
Another characteristic parameter of the vibration is the ratio Fr that is the ratio of vibration frequency to the rotational frequency. Because of the effective range of Fr in the self-excited vibratory drilling, the influence of this is not very strong.
These parameters will be used here to validate the dimensionless approach.

Influence of the parameter F on the vibration profile
The set of experiments was carried out in five drilling test 3 to 7 operated at under similar conditions and only the cutting speed was varied. Consequently the dimensionless parameter F characterized by the cutting speed, increased progressively from test 3 to 7. Indeed the parameter k remains identical for all sets of experiments.
Below N=5000 r/min F>0.55 the system vibrate irregularly as in test 5 and 6 or does not vibrate in test 7. This is explained by the fact that at these frequencies when the system vibrates the frequency ratio Fr is important so that he axial vibration speed can be important, as the cutting speed with equal amplitude ploughung is stronger and can damp vibration.
When F is sufficiently small (F<0.4) the vibrations becomes regular. In this zone it appears that the more F decreases the more the cutting rate increases. This involves reduction in the maximum effort, which may require not breaking the drill. On the other hand average effort increases in heating. Therefore, determination of the optimal cutting condition is based on a compromise.

Use of the dimensionless theory to change the spindle speed
Suppose the characteristics of the vibration in test 4 with F=0.4 seems very interesting but it is desired to increase the spindle speed in order to increase productivity.
For that we have to change the mass in order to preserve the value of F. this step was applied in 8.
A general comparison of efforts shows that the vibratory models are very close. There is a peak effort at 1005 N (instead of 1010 N) then the effort is stabilized. The value of average forces and Cr are also very close to those of test 4 108 N and 0.3 (Instead of 115 N and 0.3 respectively). This shows that the dimensionless approach validate this case.

Use of dimensionless theory to drill a new material with a different diameter
In test 9 the objective was to reproduce the vibration of test 4, preserving the values of parameters F and k for a hole of large diameter in stainless steel Z6 CNT 18. once the coefficients kc and q of the force model are measured for this material the first stage consists in calculating new values of spring stiffness k to preserve k calculation gives kc = 1510 N/mm. however as no spring of this stiffness was available a spring with stiffness of 1618 N/mm which corresponds to k=2.29 was used. In addition, a choice was adopted to preserve the mass of test. Therefore the new spindle speed = 8450 r/min. from the results it is noted that the cutting rate Cr=0.33 and the frequency Fr=1.60are very close to those obtained in test 4 and test 8, 0.3 and 1.61 and 0.3 and 1.62 respectively. Thus, it can be concluded that except for the transient phase the vibrations are similar to those of the other test.

Conclusion
The contribution of this paper is two fold
It presents the first experimental results of a new drilling technology assisted with low frequency vibration.
It shows an interesting use of a dimensionless approach to guide the experimentation and to determine the best vibratory conditions.
Concerning this new technology of vibrating and drilling the interest lies in the discontinuity of cut. The experiments show that in addition to very good fragmentation this technology makes it possible to reduce the cutting force 30 to 50% compared with conventional drilling. Moreover, the power of cut is lower and limits the heating of the drill, which makes it possible to increase the cutting speed without burning.
With regards to the use of dimensionless formulation,
It allows insufficiencies in the current modeling of self-excited drilling to be compensated.
It makes it possible to extrapolate for one drilling configuration to other drilling configuration.

References
Poduraev V N: “Cutting with Vibration”
Gouskov A M, Voronov S A and Batzer S A: “Chatter synchronization in vibratory drilling”
V P Singh, Dhanpath Rai and Co, “Mechanical Vibration”
S K Hajra Chowdhary, “Elements of Workshop Technology”- Volume 2
Dr. P N Modi, Dr S M Seth, “Hydraulics and Fluid Mechanics”
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summer project pal
Active In SP
**

Posts: 308
Joined: Jan 2011
#2
15-01-2011, 06:44 PM

SELF-EXCITED VIBRATORY DRILLING : A DIMENSIONLESS PARAMETER APPROACH FOR GUIDING EXPERIMENTS
Sameer Salim
Roll No: 44
S7 Mechanical


.ppt   SELF-EXCITED VIBRATORY DRILLING.ppt (Size: 1.84 MB / Downloads: 136)

Introduction
This technology is very compact and can be used on every conventional machine tool
In order to guide the experiments a dimensionless approach has been used to choose the cutting conditions and vibratory tool holder properties.
This approach permits the number of tests to be reduced, since the machining process can be entirely described with only three dimensionless parameters instead of nine physical parameters
Objectives
To show the benefits of self excited vibratory drilling technology
To show how the dimensionless parameters approach makes the setting up of the process easier.
Self excited vibratory drilling
Chips are naturally fragmented to small pieces implying that there is no need to perform the stripping operations classically used to split up chips.
The friction of chip on the manufactured hole surface is limited which leads to improved hole quality.
Self-Excited vibratory drilling device
Dynamic drilling models
Basis of the theory of self-excited vibratory drilling
In conventional drilling, the uncut chip thickness measured in the spindle axis direction is equal to the feed rate (h0) divided by number of lips (Z) i.e. h0/Z

In vibratory drilling this thickness is modified by the deflection of the drill holder

h = h0/2 + ώ(t) – ώ(t – 1/fz­) ………….3

mώ(t) + cώ(t) + kώ(t) = Z.kc.R [h0/2 + ώ(t) – ώ(t – 1/fz­)]q …………………………………4

ώ0 = kc/k. Z1-q R h0q ………………….5
Limits of the theory to predict optimal vibratory conditions
The use of linear solving method does not make it possible to describe strongly the non-linear vibratory motion that exists in the unstable field.
The ploughing phenomenon, which occurs near the centre of drill, is not taken into account, which acts like damper of vibration, when the vibration frequency becomes increasingly important in front of rotational frequency.

Dimensionless approach
The field of investigation has been reduced by grouping all the physical parameters into three dimensionless parameters

Dimensionless stiffness K=kc/k
Dimensionless frequency F=f0/fz
Damping ratio Z=2c/√km
Advantages of Dimensionless Approach
It allows starting from an identified satisfactory set, the new characteristics of the vibratory drill holder for a new diameter, a new spindle speed, or a new material to be determined quickly.
Moreover, this approach is only slightly affected by imperfections or gaps in the model.
Experimental setup
Experimental results highlights
Interest in self-excited vibratory drilling compared with conventional drilling.
The influence of parameter k and F on vibration.
The modification of tool holder properties keeping k constant for drilling at different spindle speed.
The modification of tool holder properties keeping k and f constant for drilling in a new material with different diameter.
Experimental comparison of vibratory drilling and conventional drilling


Conclusion
The contribution of this paper is two fold

It presents the first experimental results of a new drilling technology assisted with low frequency vibration.
It shows an interesting use of a dimensionless approach to guide the experimentation and to determine the best vibratory conditions.

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