REVIEW ARTICLE ISSN - Integrated Publishing Association ...Two lock nuts are used to give preload....

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011

© Copyright 2010 All rights reserved Integrated Publishing Association

REVIEW ARTICLE ISSN 09764259

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Dynamic and thermal analysis of high speed motorized spindle Syath Abuthakeer.S 1 , Mohanram P.V 1 , Mohan Kumar G 3

1 Department of Mechanical Engineering, PSG College of Technology, Coimbatore 3 Park college of Engineering and Technology, Coimbatore

[email protected]

ABSTRACT

Modern technology to a great extent relieson the use of High speed motorised spindle is a competent technology for significantly everincreasing productivity and plummeting production costs. On the one hand, high precision is essential for the ongoing trend of manufacturing activity, a striking example of which is found in electronics industry, automobile industry and machine tool industry .On the other hand, high precision is essential for leadingedge research. Compared to conventional spindles, motorized spindles are equipped with builtin motors for better energy consumption, balancing to achieve highspeed operation and good quality of product. However, the builtin motor introduces a great amount of heat into the spindle system as well as additional mass to the spindle shaft, thus complicating its thermomechanical dynamic behaviors. This paper presents thermal characteristics and dynamic characteristics of High speed motorized spindle were analyzed experimentally. Numerical analysis was done and results were validated with experimental results.

Keywords: Highspeed motorized spindle,Dynamic –Analysis, Thermal –Analysis.

Nomenclature

F H Heat generation due to friction power − 0 f Factor depends on bearing type and the method of lubrication (Grease2, Oil1.7)

− µ Lubricant kinematic viscosity − m d Searing pitch diameter

− ω Angular velocity − α Contact angle − S F Static equivalent load − S C Basic static load rating − r F Radial load − a F Axial load − 1 f 0.001

− y 0.33 − S X 0.5

− S Y 0.35 − i Q Forces acting on the inner ring − o Q Forces acting on the outer ring




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− i a Contact length of inner ring − o a Contact length of outer ring − a K Load deflection constant

− i δ Axial clearance between inner ring and ball − o δ Axial clearance between outer ring and ball

− S M Spin moment in bearing − S H Heat generation in bearing due to spin moment

− σ Diameter ratio − B Curvature − ε Third elliptical integral − s k Spindle traction factor0.1 − e R Reynolds number − r P Prantle number − o D Diameter of the outer race − r D Diameter of the rotor

− D Diameter of the rotating element

− k Thermal conductivity of fluid medium

− p C Specific heat

− η Absolute viscosity

− v & Flow rate of coolant

− u & Velocity of coolant

− c A Area of coolant passage

− t k 0.9 shear factor − Nu Nusselt number

1. Introduction and literature survey

High speed machining at speed well beyond 10000rpm is growing rapidly in Machine tool industry, automotive, aerospace, die making, electronics and many other industries. To achieve cutting as such high speeds, the technology has advanced in many fronts, including machine tool design, cutting tools and production systems. On the machine tool front, the high speed machining technology requires accurate and superior spindle design. In particular, the dynamic stability of the spindle system against chatter vibration is vital in producing high quality products at high material removal rates. The stability of machine tool is dependent on the dynamic behavior of machine tool is dependent on the dynamic behavior of machine tool structure, which is often expressed in terms of the frequency response function(FRF) (Mohammad R. Movaheedy et.al., 2006).




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Highspeed motorized spindle technology is of great significance to the research and development of highspeed machine tool. The technology of HSM is still relatively new. Although theories of highspeed metal cutting were Reported in the 1930s (C.Salomon, 1981) machine tools capable of achieving these cutting speeds did not exist commercially until the 1980s (M.Kaufeld and Komanduri, 1990, 1985). Only recently, industry has started experimenting with the use of HSM in production. The aircraft industry was first, with the automotive industry and mold and die maker snow following. Because of the lack of experience in this new field, there are still many problems to be solved in the application of HSM. Current problems include issues of tooling, balancing, thermal and dynamic behaviors, and reliability of machine tools. HSM is often associated with high feed rates which require rapid acceleration and deceleration, resulting in drastic changes in cutting conditions. In the aerospace industry the use of long tools to generate deep pockets puts tremendous stress on the spindle and the cutter. Development of highspeed spindle technology is strategically critical to the implementation of HSM.

To achieve highspeed rotation, motorized spindles have been developed. This type of spindle is equipped with a builtin motor as an integrated part of the spindle shaft, eliminating the need for conventional power transmission devices such as gears and belts. This design reduces vibrations, achieves high rotational balance, and enables precise control of rotational accelerations and decelerations. However, the highspeed rotation and the builtin motor also introduce large amounts of heat and rotating mass in to the system, requiring precisely regulated cooling, lubrication, and balancing. As a result, the thermal and mechanical behaviors of highspeed motorized spindles have become very difficult to predict for spindle designers and users. Furthermore, the highspeed rotation also renders many conventional testing techniques unsuccessful at determining spindle behaviors during very highspeed rotation. Only recently, comprehensive thermal characterization of motorized spindles were reported by Bossmanns and Tu (B.Bossmanns, 1999, 2001) to quantify heat sources, heat sinks and the heat transfer mechanism of an entire motorized spindle under the influence of speed and bearing preload. This model is capable of predicting the temperature growth of an entire motorized spindle system, including the rotating components, across a wide speed range. This model is verified on a highspeed machining test bed equipped with a custom built high performance motorized spindle of 32kW and a maximum speed of 25,000 rpm (1.5 million DN). The high speed machining process requests completely new demands for the mechanism of such processing equipment, as due to the process, path speeds exceeding 50m/min can be achieved. In this field, potential capacities of manufacturing processes require a dynamic behavior ten times higher than conventional machine tools and increased accuracy. This can be solved by the systematical evaluation of suitable machine kinematics, by the application of linear direct drives as well as by mass reduction of the axis through light weight components of sheet metal. The requirements of high speed machining and ways to improve the performance of machine tool have been studied (Heisel M Gringel, 1996). The energy flow model of highspeed motorized spindle further, and analyzed the quantitative model reflecting the heating value of spindle (Bernd Bossmanns, 2001). The dynamic effects of the spindle using Timoshenko beam theory were studied (Mohammad R. Movahhedy et.al., 2006).

In this paper, the FEM model of motorized spindle is set up to research on its modal and dynamic characteristics, which is effected by the axial preload on the natural frequency, the




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motorized spindle’s natural frequencies and corresponding vibration shapes, centrifugal forces and gyroscopic moments on the motorized spindle shaft. The mass distribution of rotor, the nonlinearity of bearing rigidity and the whirling motion of spindle are taken into account in modeling. Thermal analysis and its corresponding couple field thermostructural analysis are presented.

2. Structure of the spindle

The spindle parts are supported by two sets of angular contact ceramic ball bearing in front and one set of angular contact ceramic ball bearing in rear which is installed back to back. The motor is set between front second set and rear bearings. As one whole body, the stator and coolant jacket are installed to the shell of spindle. Two lock nuts are used to give preload. One lock nut is positioned at the second set of the front bearing with front preload spacer.

Another one is placed at the rear set of bearings with rear preload spacer. Front and rear bearing housings are placed over the bearing systems. The coolant jacket is placed over the statorrotor system and outer body is placed over the coolant jacket. The main spindle, front and back bearing systems, statorrotor system coolant jacket is shown in figure 1 and the outer body are only considered in the high speed motorized spindle in both dynamic and thermal analysis. The sensor ring and servo controller of the high speed motorized spindle are not included in both the analysis.

Figure 1: Structure of the high speed motorized spindle

3. Experimental modal analysis of High Speed Spindle

The vibration response of the spindle was obtained using impact testing, where an instrumented hammer was used to excite the spindle its free end. The resulting vibration was measured using a low mass accelerometer. The experimental setup consisted of an impact hammer, a charge accelerometer; signal conditioner and data acquisition is shown in figure 2. This experimental setup was used to find the modal characteristics of the motorized spindle.




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The program in LabVIEW 8.2 was developed for measuring the response of spindle for excitation given by the hammer using data acquisition system. The excitation by impact was given to spindle by impact hammer and thus the response was obtained experimentally. The frequency versus acceleration curve was used to determine modal parameters i.e., natural frequency and damping factor. The sample response of spindle was shown in figure 3. The first three Natural frequencies of spindle are shown in table 1.

Table 1: Modal Analysis of High motorized spindle (30,000 rpm) – First 2 Natural Frequencies

Natural Frequencies(Hz) Measurement Location Mode 1 Mode 2

Motorized High Speed Spindle

112 220

Figure 2: Experimental setup

Figure 3: Frequency versus amplitude curve

The mode shapes and damping factors of the structures were calculated using the results of the Fast Fourier Transform of the vibration signals from the accelerometer. By using the half




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power band width method, we can find the damping factor of the spindle from the response curve frome equation 1.

η= (f2f1)/fr

Where (f2f1) and fr represent the half power band width and the corresponding natural frequency, respectively (Jung Do Suh and Dai Gil Lee, 2008). The damping ratio of the spindle is 0.060.

4. Numerical modal analysis of spindle

The modeling of spindle designs were done in ANSYS is shown in figure 4. The modal analysis was done using Subspace method to find first five natural frequencies and mode shapes (Michael R Hatch, 2011).

4.1 Assumptions made to convert finite element dynamic model

• The spindle is treated as the space spring beam

• The angular contact ceramic ball bearing radial compression spring mass unit

• The rotor, jacket and socket are axial material additional distributing mass.

Figure 4: FEM modelof the High speed motorised high speed spindle

4.2 Element selection

Beam 188 spindle

• Nodes I,J 4.2.1 Degrees of freedom

• 3 translations

• 3 rotations 4.2.2 Special features

• The shearing effects are included by giving stiffness values in the section controls.

A G k k t s * * =




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• It allows gyroscopic effects, includes in mode extraction damped and QR damped methods

• The coriolis is included by giving inertia force in terms of angular velocity. 4.2.3 Combi 214 Bearing

• Nodes – I,J

4.2.4 Degrees of freedom

• 3D radial spring

• K spring constant a. Stiffness of angular contact ball Bearing

r K – Radial stiffness when bearing is in static condition

− rs K Radial stiffness when bearing is in dynamic condition

− P Preload, − Z No of balls. − b D Diameter, − α Contact angle. − n Speed.

b. Section properties for Beam188 and real constants for Combi214

Section properties length, inner radius, outer radial, Area, add mass per unit length, and transverse shear stiffness are given as inputs. Radial stiffness of the bearing is calculated and given in the real constant. Stiffness of the bearing is function of initial preload and thermally induced preload. So it is necessary to estimate the thermally induced preload from the thermal analysis results

c. Thermally induced preload

Details for calculating thermally induced preload in table 2 and temperature difference are calculated for 5000 sec in table 3.

Table 2: Details for calculating thermally induced preload

Co efficient of thermal expansion of bearing steel =1.25*10e5 /K Bearing set

Xb (mm) Dio (mm) Doi (mm) Db (mm) Spring constant I 23.92 127.4 104.18 9.525 9.402*10e9 II 21.89 110 91.3 8.731 10.239*10e9

III 30.16 100 82 7.938 10.639*10e9

o 25 ] 10 92 . 1 1 [ *

* cos * sin * * * 10 * 25 . 1 2

33 . 0 66 . 0 666 . 0 33 . 0 . 7

= − − =

= −

α

α α

for n e K K

D Z p K

rs r

b rs




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( ) ( ) 0 0

1 0 0

0 1 1 T T x T T x s i i i s − − − = ∆ α α

where αs is the linear expansion coefficient of steel which is the material of the shaft and sleeve; xi and xo are the distances of the contact points between the paired bearings of inner and outer rings; Ti

1 and To 1 are the new temperatures of the shaft and housing/spacer

respectively.

The relationship of xi, xo and the distance of the centers of the bearing pair (xb) are

α sin 5 . 0 b b i D x x + =

α sin 5 . 0 b b i D x x − =

( ) 0 1 5 . 0 b b b b b T T D − = ∆ α

( ) ( ) [ ] o or or oi

o ir ir io s r T T D T T D − − − = ∆ 1 1 5 . 0 α

where Dio is the inner diameter of the outer ring, Doi is the outer diameter of inner ring, Tir, is the temperature of the inner ring, and Tor, is the temperature of the outer ring.

Table 3: Temperature difference are calculated for 5000 sec

Temperature difference Bearing set Inner race Outer race Bearing housing Shaft Ball

Front I 16.39 16.34 15.77 16.28 16.82 Front II 17.91 17.11 15.33 17.91 17.55

Rear 23.66 22.3 26.98 23.35 23.61

α α sin cos 1 a r ∆ − ∆ + ∆ = ∆ 5 . 1 ∆ = a t K p

Initial preload and thermally induced preload is shown in table 4.

Table 4: Initial preload an thermally induced preload

Bearing set

Axial thermal deflection

Initial preload Thermally induced preload Total preload

I 8.90E07 146 7.59 153.59 II 1.14E06 123 12.42 135.42 III 2.15E06 50 33.53 83.53

The stiffness of the bearing is greatly affects natural frequencies. Actually, it increases the natural frequencies. The thermally induced preload is estimated for 10000rpm speed.




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d. Modal analysis

Table 5 shows the natural frequencies including centrifugal and gyroscopic effects of spindle bearing system without including thermally induced preload.

The model has been created using beam 188 and combi214. The sections are created to give dimensional properties for beam188 and stiffness is given to combi214. The coriolis is included by giving inertia force in terms of angular velocity to include the effect of centrifugal effects. Gyroscopic effect included by extracting by QR damped method Campbell diagram extracted damped frequencies.

Table 5: Natural frequencies including centrifugal and gyroscopic effects of spindle

Natural frequencies (Hz) Speed

Mode I Mode II Mode III

Gyroscopic Gyroscopic Gyroscopic

Forward Forward Forward Effects Centrifugal

Backward

Centrifugal

Backward

Centrifugal

Backward 122.67 225.392 632.02 10000 122 121.71

224 222.43

625 619.80

91.781 172.86 645.24 50000 89.4

86.763 163

155.58 613

583.24

Table 6: is the critical speed by including all the effects

Natural frequencies (Hz) Speed Mode I Mode II Mode III

Gyroscopic Gyroscopic Gyroscopic

Forward Forward Forward Effects Centrifugal

Backward

Centrifugal

Backward

Centrifugal

Backward 132.15 229.392 633.02 10000 131 131.3

228 226.43

627.6 621.58

Critica l speed 7870 13573 37294




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a: I mode shape for 122 Hz b: II mode shape for 224 Hz

c: III mode shape for 625Hz d: IV e mode shape for 1428Hz

Figure 5: Mode shape of High motorized spindle

5. Analysis of heat transfer through motorized spindle

Motorized spindle is equipped with a builtin motor, equally add a heat source in it. The heat generated in motor mainly is the heat generated due to copper loss in stator winding and iron loss in rotor, and the heat generated due to copper loss in stator winding almost has 2/3 among total heating value. In addition, for high speed rotation of rotor, the air in the inner of spindle shell will also generate heat. The heat mainly radiate through spindle and its shell, so the heat in a measure will transfer to bearings through spindle, that will reduce the lifetime of bearing and elongate spindle, finally the machining accuracy will decreased. In addition to heat generated from motor, heat generated from spindle bearings also cannot be neglected.

A lot of complex factors cause the heat, include many kinds of friction, and those various frictions will become severe along with the increase of spindle’s rotate speed, the heating value will also increase. When the temperaturerise increases, the pretightening value will be more, accordingly more heat will be generated from bearings, and considering the heat radiation and transfer, the spindle bearings must be lubricated and cooled down correctly, otherwise, it cannot ensure that motorized spindle runs at high speed. In order to improve thermal characteristics of motorized spindle, it is necessary to cool down motor. The main adopted measure is to design circulating cooling water jacket on the place where motor stator joints shell. Figure1 shows the structure of motorized spindle.




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Affected by various heat sources, the temperature of motorized spindle’s each part changes, and heat always transfers from hightemperature place to lowtemperature place. The heat exchange between motorized spindle and surroundings mainly depends on heat conduction, convection and radiation. Figure 6 shows the heat transfers. Part of heat generated from stator is absorbed by cooling liquid and then disappears, another part transfers to air by convection and radiation. Part of heat generated from rotor transfers to spindle and bearings directly by heat conduction, another part transfers to stator by convection and radiation, and the heat exchange between surface of highspeed motorized spindle and ambient air is also done by it.

5.1 Finite Element Selection

Assumptions made to convert finite element dynamic model

• The model is considered as axisymmetric structure. • Only half of its crosssection is needed to modeling.

Figure 6: .FEM model of the high speed spindle

Element selection Plane55

• 4 node I, J,K, L

• Degrees of freedom temperature at each node

Material properties • K conductivity, Density, Specific heat and Enthalpy

Load • Convection

• Heat generation

5.2 Heat generation in the motor

Heat generation in the motor has been calculated from power loss. The 25000 rpm gives power losses of 3.34 KW. The heat generation in the stator is equal to the 2/3 of the power loss and heat generation in the rotor is equal to 1/3 of the power loss.

Power loss of the motor = 3340 W Heat generation in the stator = 2226 W

Heat generation in the rotor = 1113 W




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5.3 Heat generation in the bearing due to friction

The heat is generated in the angular contact ball bearing due to two types of friction power. The friction torque in the bearing due to lubrication viscosity,

The friction torque in the bearing due to load,

m

y

S

S L d F

C F

f M * * 1 β

=

r a F F F 1 . 0 cot 9 . 0 − = α β

a S r S S F Y F X F + =

L V M M M + =

F H Heat generation due to friction power

ω * M H F =

5.4 Heat generation in the bearing due to spin moment

The details of spin moment is shown in table 7.Heat generation of spindle part is also shown in table 8.

Heat generation due to spin moment ( S H )

8 3 ε i i

si a kQ M =

8 3 ε o o

so a kQ M =

5 . 1 i a i K Q δ =

5 . 1o a o K Q δ =

5 . 1

5 . 0

* B D K K a =

1 − + = D r

D r

B o i

i oi i i l l ∆ − = − δ

e oi e e l l ∆ − = − δ

σ ϖ ϖ * = roll

( ) 3 66 . 0 0 * * 45 . 0 m V d f M µω =




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D d m = σ

S roll S M H * ϖ =

Table 7: Details for finding spin moment

Table 8: Heat generation in spindle parts

Bearing set Rir(mm) Ror(mm) Ball diameter

Deflectio n (µm) Curvature K(*10^9)

I 4.95 5.15 9.52 10.4 0.049 9.04

II 4.495 4.605 8.731 10.1 0.0422 10.2

III 3.68 3.9 7.3 9.83 0.036 10.6

5.5 Convection

Convection Due To Rotation Of Ball With Lubricant In Bearing Convection due to rotation of ball with lubricant in angular contact ball bearing ( ) b h

5 . 0 4 . 0 * 33 . 0 * e r

O b R P k D h Nu = =

5 2

10 * 4 : * < = e e R D R µ

ω

217 7 . 0 : *

< < = r p

r P k

C P

η

Heat generation (W) due to Spindle parts Lubrication

friction Force friction

Spin Total heat generation(W)

Bearing I 0.122 155 26.1 181.22 Bearing II 0.081 170 22.42 191.66 Bearing III 0.080 105 18.9 123.8 Shaft 2226 2226 Rotor 1113 1113




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Convection due to rotation of rotor with air in motor

Convection due to rotation of rotor with air in motor ( ) r h

7 . 0 : 10

37 . 0 . 7 . 0 , 076 . 0 : * *

6 < <

− − − = =

r e

n e

m r

r r

P R

n m c R P c k D h

Nu

6.3 Convection due to coolant

Convection due to coolant ( c h )

C A v u &

& =

8 . 0 3 . 0 * 0225 . 0 *

e r c R P k b h

Nu = =

10000 : * > = e e R b u R

µ &

Convection of spindle part is shown in table 9. Table 9: Convection in spindle parts

The temperature distribution and thermal anlsyis in motorized spindle is shown in figure 713.

Figure 7: Temperature distributions in spindle parts

Spindle parts Convection(W/m2.K) Bearing I 163 Bearing II 178 Bearing III 200 Rotor 178.3 Coolant jacket 759




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Figure 8: Temperature distribution

Figure 9: steady state temperatures

Figure 10: Axial deflections in the spindle end position

Figure 11: Radial deflections in the spindle end position




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Figure 12: Axial deflection

Figure 13: Radial deflection

5.6 Results and discussion

5.6.1 Thermally induced preload on natural frequencies

The thermally induced preload has been estimated from the thermal analysis for 10000 rpm. The thermally induced preload and corresponding stiffness has also been calculated and tabulated. The natural frequencies including initial preload, thermally induced preload, centrifugal and gyroscopic effects have been extracted and tabulated. The critical speeds have also been calculated

These values is given in the table 6. The natural frequencies are extracted with and without these effects have been studied and found that the important of each effects .The critical speed is not uniform in any of the modes because the preload is varying depends on the time .So the time increases the natural frequencies increases. It seems to be good effect as increases the operating range. But the excess of thermally induced preload will cause the bearing failure. So the material should have more thermal stability to withstand temperature. If the material gets thermal deflection after a long time of operation, the thermally induced preload will be good to lift up the critical speed to have higher speed without bearing failure.

It is clear from table 7 that a good agreement exist between the numerical prediction and experimental natural frequencies of motorized high speed spindle




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Table 7: Modal analysis Comparison of spindle

5.6.2 The critical speed by including all the effects

The critical speed has been calculated from the Campbell diagram which is available in ANSYS .The results has been given are for 10000 rpm speed and 5000 seconds .

Transient thermal analysis has been carried out to find temperature, axial and radial deflection to estimate thermally induced preload. The steady state condition is reached nearly at 6 hours and 39 minutes. It has been given in the figure 9. The axial and the radial deflections of end position of the spindle are calculated and given in the figure 10 to 13.

5.7 Conclusion

The natural frequencies are extracted by considering stiffness and mass of the body will not be sufficient to find critical speed for high speed spindle. Because the stiffness of the rotating body will be varying depends on the speed. So the speed effects like centrifugal and gyroscopic effects of the spindle bearing system have been considered. The centrifugal and the gyroscopic effects are damping the natural frequencies significantly.

The gyroscopic effects are damping the natural frequencies little than the centrifugal effects and these effects can be minimized by keeping same shaft crosssection and placing motor in the middle position to have mass balance.

The centrifugal effects can be reduced if the cross sections are reduced but the strength of the spindle depends on the cross section so these effects cannot be minimized effectively so the preload should be increased to balance the damping to have higher critical speed. The stiffness of the bearing based on preload which is given by locknut only will not be sufficient. The thermally induced preload should also be included to have more and appropriate preload because if you give only initial preload to compensate the centrifugal and gyroscopic damping, the thermally induced preload will be added due to thermal behavior and will cause bearing failure.

The preload which is given by both thermally induced and through locknut is shared to lift up the critical speed to have higher range of operating speed. The estimation of thermally induced preload and corresponding natural frequencies has been calculated and shown that critical speed has been lifted to have high range of operating speed for 10000 rpm for different time .

S.No Natural Frequencies(Hz) Experimental Numerical

ModeI Mode II ModeI Mode II

Motorized High Speed Spindle

112 220 122 224




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These analysis is helped to identify the highly heat distributed parts of the spindle bearing system .The thermo structural analysis is done to know the axial and radial deflection of the spindle end positions.

6. References

1. Mohammad R. Movaheedy and Peiman Mosaddegh, 2006, Prediction of chatter in high speed milling including gyroscopic effects, International journl of machine tools and manufacture, 46, pp 9961001.

2. C.Salomon, (1981),Verfahren zur Bearbeitung von Metallen oder Bei Bearbeitung durch schneidende Werkzeuge von sichah nlich Verhaltenden Werkstoffen, Deutsches Patent Nr.523594.

3. R.Komanduri, J.McGee, R.A.Thompson ,J.P.Covy, F.J.Truncale, V.A.Tipnis, R.M.Stach, R.I.King, (1985),On a methodology for establishing the machine tool system requirements for highspeed/highthrough put machining, Journal of Engineering for Industry,TransactionsoftheASME107316–324.

4. M.Kaufeld, (1990), Highspeed milling from a user’s and machine builder’s viewpoint, Werkstatt and Betrieb 123 (10), pp 797–801.

5. B.Bossmanns, J.F.Tu, (1999), Thermalmodel for high speed motorized spindles, International Journal of Machine Tools and Manufacture,39(9), pp13451366.

6. B.Bossmanns,J.F.Tu, (2001),A power flow model for high speed motorized spindles—heat generation characterization, ASME Journal of Manufacturing Science and Engineering 123(3), pp494–505.

7. Heisel M Gringel, (1996), Machine Tool Design Requirements for High Speed Machining, in CIRP AnnalsManufacturing Technology, 45(1), pp 389392.

8. Bernd Bossmanns, Jay F. Tu, (2001), “A Power Flow Model for High Speed Motorized SpindlesHeat Generation Characterization”. Transactions of the ASME Vol123.

9. Mohammad R. Movahhedy, Peiman Mosaddegh , (2006) , Prediction of chatter in high speed milling including gyroscopic effects, International Journal of Machine Tools & Manufacture 46 , pp 996–1001.

10. Jung Do Suh and Dai Gil Lee, (2008), Design and manufacture of hybrid polymer concrete bed for highspeed CNC milling machine, International journal of Mechanical Material Design, volume 4, pp 113121.

11. Ju Ho Kim, Jae Eung Lee, and Seung Hwan Chang, (2008), Robust design of microfactory elements with high stiffness and high damping characteristics using foamcomposites and sandwich structures”, in Composite Structures, volume 86, pp 220226.




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12. Dai Gil Lee , Jung Do Suh, Hak Sung Kim, and Jong Min Kim, (2004), Design and manufacture of composite high speed machine tool structures, in Composites Science and Technology”, volume64, pp15231530.

13. Michael R Hatch, (2000), Vibration Simulation using ANSYS and Matlab, Chapman and Hall, 1 st edition.

REVIEW ARTICLE ISSN - Integrated Publishing Association ...Two lock nuts are used to give preload....

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