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TERM PAPER

Topic: gyroscopic effects on milling machine

SUMMITTED TO: SUBMITTED BY:

MR.JASPREET SIR . HAZRAT BELAL

. ROLL NO:RB4912-A05.

REG NO:10901869

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ACKNOWLEDGEMENT

I HAVE GREAT SENSE OF HAPPINESS AND PRIDE IN WRITING THIS TERM PAPER. I HAVE WITNESSED THE UNTIRING EFFORTS MADE BY MY DYNAMATICS OF MATERIALS TEACHER MR. JASPREET SIR. I WOULD LIKE TO THANK MY TEACHERS IN GIVING ME IDEAS FOR MAKING THIS TERM PAPER. I WOULD LIKE TO THANK THE AUTHOR OF THE BOOKS WHICH I USED FOR REFERENCE. I WOULD LIKE TO THANK THE HOST AND CREATOR OF THE WEB SITES FROM WHICH I GOT THE INFORMATION ABOUT THE TERM PAPER

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S.No Contents Page no

1) Introduction 1-3

2) What is Gyroscope? 4

3) Discussion about Gyroscope 6

4) Gryscpic effect 7

5) Gyroscope Concepts 8

6) Equation of Gyroscopic effect 8

7) How Gyroscpe does work 9

8) Gyroscopic effect on milling 11

9) Power Density 12

10) Conclusion 14

11) References 14

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What is Gyroscope?

A gyroscope is a device for measuring or maintaining orientation, based on the principles of conservation of angular momentum

A mechanical gyroscope is essentially a spinning wheel or disk whose axle is free to take any orientation. This orientation changes much less in response to a given external torque than it would without the large angular momentum associated with the gyroscope's high rate of spin. Since external torque is minimized by mounting the device in gimbals, its orientation remains nearly fixed, regardless of any motion of the platform on which it is mounted.

Gyroscopes based on other operating principles also exist, such as the electronic, microchip-packaged MEMS gyroscope devices found in consumer electronic devices, solid state ring lasers, fibre optic gyroscopes and the extremely sensitive quantum gyroscope.

Description

A gyroscope flywheel will roll or resist about the output axis depending upon whether the output gimbals are of a free- or fixed- configuration. Examples of some free-output-gimbal devices would be the attitude reference gyroscopes used to sense or measure the pitch, roll and yaw attitude angles in a spacecraft or aircraft.

The centre of gravity of the rotor can be in a fixed position. The rotor

simultaneously spins about one axis and is capable of oscillating about the two other axes, and thus, except for its inherent resistance due to rotor spin, it is free to turn in any direction about the fixed point. Some gyroscopes have mechanical equivalents substituted for one or more of the elements, e.g., the spinning rotor may be suspended in a fluid, instead of being pivotally mounted in gimbals. A control moment gyroscope (CMG) is an example of a fixed-output-gimbal device that is used on spacecraft to hold or maintain a desired attitude angle or pointing direction using the gyroscopic resistance force.

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In some special cases, the outer gimbal (or its equivalent) may be omitted so that the rotor has only two degrees of freedom. In other cases, the centre of gravity of the rotor may be offset from the axis of oscillation and thus the centre of gravity of the rotor and the centre of suspension of the rotor may not coincide.

The gyroscopic effect

Wheels show the gyroscopic effect. First I'm going to demonstrate this with a bicycle wheel. A bicycle wheel is a commonplace object which has a gyroscopic effect when it spins. I would like you to examine this in some detail, and it's also one of the exercises. I want to show you how best to examine the gyroscopic effect.

One of the problems with a bicycle wheel is that if you try to hold it on the spindle you get your fingers stuck in the spokes. But if you go to a bike shop and get a stunt peg (preferably with little grooves) you can attach it to the bike wheel, giving you a handle, and making things much safer. Now spin the wheel. You'll feel really curious gyroscopic effects. It's rather hard to describe them, but I want to make it clear to you. So take a piece of string. If you get stunt pegs which have little grooves in them, the string can be attached very easily. Now spin the wheel, holding it up (vertically) on the piece of string. You should see clearly that something rather amazing is happening - the wheel spins round in the vertical plane. This is the gyroscopic effect, and it's called gyroscopic precession. In broad terms the reason why this is happening is because there is a spinning object, the wheel, and there is a couple or moment or torque being provided which is at right angles to the direction of spin, and I will explain this more in a minute.

This is nothing special - bike wheels aren't the only things that do this. I have my 2 year-old daughter's spinning top with me. I can attach a piece of string to the bottom, then put the string in my mouth so I have both hands free, then hold the top in one hand and spin it with the other. If you try this, then hold the string

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and watch the top, you will see it precess around the string. Even a 2 year-old's top shows these amazing gyroscopic effects! The question is, why?

concepts. The first is the concept of the couple (also known as moment or torque). In the diagram you can see a couple defined as an angular force. Note the two pink forces marked f applied in opposite directions to a bar, this is called a couple - because there are two forces. I can use the right hand rule to

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define the direction of the couple. If my fingers curl in the actual turning direction, then my thumb will point upwards in the direction of the couple.

I can also demonstrate a couple if I sit on a rotating stool, and someone pushes my shoulders round, so I go round and round. What happens is that if one of my shoulders is pulled and the other pushed, I go round, because there are two forces in opposite directions moving me.

The next concept we have to understand is that of moment of inertia. Moment of inertia is the angular equivalent of mass. On the left of the picture to the left, I have a dumbbell shaped object which has two masses relatively close together on it, on the right of the slide there is the same dumbbell shaped object but the masses are further apart. The one on the right has a higher angular mass than the one on the left, as we shall see shortly. The angular mass we call moment of inertia.

The other thing we can talk about is called angular momentum. Angular momentum is the product of the moment of inertia and the angular velocity, 1#1 where J is moment of inertia, and 1#1 is angular velocity. This is just the same as defining linear momentum as the product of mass and linear velocity. A heavy car has more linear momentum when going at a certain speed than a light car travelling at the same speed - it takes more effort to stop it. Similarly a

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heavy pair of dumbbells has more angular momentum than a light pair of dumbbells, and it takes more effort to stop it rotating.

What is interesting about this, is that I can change the moment of inertia of the dumbbells by moving the weights in and out. I can demonstrate the concept of moment of inertia by holding two heavy weights (5kg) close to my chest. It is quite easy for someone to apply a couple to my shoulders and spin me around. If I hold the weights at arm's length, it is much harder for someone to apply a couple to my shoulders and spin me round. The reason is that I have a higher moment of inertia. It's like having a higher mass. A heavier car is harder to push than a lighter one. An object with high moment of inertia is harder to spin than one with a low moment of inertia.

Gyroscope concepts

A gyroscope has three axes. First, a spin axis, which defines the gyroscope strength or moment. Let us call the other two the primary axis and the secondary axis. These three axis are orthogonal to each other.

The spin axis rotates around the vertical line. The primary axis rotates the whole gyroscope in the plane of the page, and the secondary axis rotates the gyroscope up-and-over into the page.

The spin axis is the source of the gyroscopic effect. The primary axis is conceptually the input or driving axis, and the secondary the output. Then if the gyroscope is spun on its spin axis, and a torque is applied to the primary axis,

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the secondary axis will precess. The primary axis appears infinitely stiff to the applied torque and does not give under it. This is the generally recognised characteristic of gyroscopic behaviour.

It is important not to confuse the concepts of angular momentum and gyroscopic moment. When a mass ‘m’ moves in a straight line at velocity ‘v’ it exhibits linear momentum (m.v ). It is trivial to predict that if it is constrained to travel in a radius ‘r’ it will produce an angular momentum (m.v.r). However with the angular momentum an effect that could not have been predicted turns up - gyroscopic behaviour. The fact that in the larger world the two effects occur together and in simple proportion to each other does not mean that this is always the case - gyroscopic behaviour occurs without angular momentum in electron behaviour, even though the terms ‘spin’ and ‘spin angular momentum’ are still used for historical reasons, even though there is no direct evidence that the electron’s mass or charge spins on its own axis. It may simply be that rotating an object exposes the gyroscopic moments of the elementary particles that make it up, possibly through the asymmetric relativistic effects created by the centripetal acceleration; some major experimental work is required in this area.

Angular momentum has the form “kilogram-meters2 per second”. Gyroscopic moment has the form “Newton-meters per Hertz”, or torque required to produce a precession rate of one Hertz. For those familiar with dimensional analysis, both have the dimensions ‘L2M/T’, which means only that they are related by a simple scalar number. However (as far as the author has been able to determine) the actual value has never been researched; it may be unity, it may not. Whatever the case, from here on I will ignore angular momentum and consider only the gyroscopic moment, regardless of how it is generated.

Basic gyroscope equations

The strength of a gyroscopic effect is termed the gyroscopic moment. I use the symbol ‘G’, in units “Newton-meters/Hertz”. A higher moment requires more torque to precess at the same frequency, or for the same torque precesses at a lower rate

Where a gyroscope receives torque on the primary axis and precession on the secondary, no work is being done. The torque ‘TP’ on the primary axis has no

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precession associated with it, while the precession rate ‘vS’ on the secondary axis is...

vS = TP / G

...and has no torque associated with it. Since the rate of doing work on each axis is the torque times the precession on that axis, it follows that in this simple case no energy is involved.

Gyroscopes do not differentiate between primary and secondary axes - this is a purely artificial definition of my own.  A torque on the secondary axis creates precession on the primary axis. Simultaneous torque on both axis will result in simultaneous precession. In this case each axes will have both torque (creating precession on the other axis) and precession (created by torque on the other axis). Then the rate of doing work ‘PP’ on the primary axis is...

PP = TP.vP / G

...and on the secondary...

PS = TS.vS / G

Now by applying the conservation of energy...

PP = - PS

i.e. the work done on one axis must appear on the other.

So far I have dealt purely with behaviour, but to go further we need to look at why it behaves this way - what mechanism is at work?  Let us go through the basic operation where torque on one axis creates precession on the other (those familiar with electric motor theory will be familiar with the following ideas).

First apply a forcing torque to the primary axis; at this stage in the argument imagine that the primary axis presents no stiffness against the forcing torque. The secondary axis would precess at an infinite frequency, but for a limiting mechanism that comes into play; just as torque creates precession, so precession creates torque. So as the secondary axis precesses it creates a reverse torque TPF

on the primary axis...

TPF =  -vS.G

The precession rate always runs at that point where TPF is exactly equal and opposite to TP. At this point...

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TPF = -vS.G= - ( TP / G ).G

= - TP

The reverse torque generated by the precession exactly opposes the applied torque so that the net torque is zero. If it was more the work would be done by the gyroscope. If it was less the primary axis would give way under the applied torque and work would be done with no outlet for it. Both conditions violate conservation of energy principles.

To sum up, the gyroscope precesses the right rate on the secondary axis to exactly oppose the applied torque on the primary axis. This leads directly to an aspect of gyroscopic behaviour that is seldom experienced in conventional gyroscopes, but is important in the behaviour of electrons:- If the secondary axis is locked against rotation and the primary axis is driven, no opposing torque will appear on the primary axis - it is free to rotate without hindrance. No work is transferred through the gyroscope - there is motion without torque on the primary axis. The secondary axis has no motion - it is locked - but instead experiences a torque TSF...

TSF = vP.G

This is the identical situation to basic gyroscope operation, but viewed from the other side. Instead of saying that torque on the primary axis leads to precession the secondary we say that precession on the secondary axis leads to torque on the primary axis. It is exactly the same thing.

How Gyroscopes Work

Gyroscopes can be very perplexing objects because they move in peculiar ways and even seem to defy gravity. These special properties make gyroscopes extremely important in everything from your bicycle to the advanced navigation system on the space shuttle. A typical airplane uses about a dozen gyroscopes in everything from its compass to its autopilot. The Russian Mir space station used 11 gyroscopes to keep its orientation to the sun, and the Hubble Space Telescope has a batch of navigational gyros as well. Gyroscopic effects are also central to things like yo-yos and Frisbees!

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In this edition of HowStuffWorks, we will look at gyroscopes to understand why they are so useful in so many different places. You will also come to see the reason behind their very odd behavior!

gyroscopic effects on milling machine

Gyroscopic Bearing

To reduce viscosity losses further, spindle maker Ibag says it designed its water bearing spindle to use only one bearing. A self-stabilizing gyroscopic effect lets this bearing act alone to support the spindle shaft.

A magnetic bearing is capable of a similar self-stabilizing effect. Comparison with a magnetic bearing is natural here because the company also offers a magnetic spindle. However, in a fluid bearing, the gyroscopic effect is less complex, says North American company president Bill Popoli. Stabilizing a magnetic bearing requires sensors to adjust the intensity of the magnetic field. The fluid bearing achieves the same effect through fluid mechanics alone.

The resulting freedom to use just one bearing brings viscosity losses down to the range of 10 to 15 percent, where some hydrostatic spindle designs have losses of 40 to 50 percent, Mr. Popoli says.

Ibag's fluid bearing spindle will initially be available in two different continuous power and top speed combinations: 32 kW/32,000 rpm and 40 kW/40,000 rpm. The cost will fall between that of mechanical and magnetic bearing spindles. A magnetic spindle represents a 50 to 100 percent premium over a roughly comparable ball bearing spindle, he says. By comparison, the premium for the hydrostatic spindle will be about 25 to 30 percent.

In the company's further development of this technology, one fluid bearing advantage being given careful attention is the bearing's applicability across a wide range of speeds, Mr. Popoli says. High fluid pressure can make a fluid bearing very stiff, but using the same high pressure at high speeds would make viscosity losses excessive.

"But what about a spindle that varies fluid pressure in proportion to the speed?" he says. "We are evaluating designs that do exactly that—increase pressure as

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speed goes down." If feasible, the result would be a spindle that is just as capable in slow, heavy cutting as it is in high speed machining.

Power Density

The design efforts of another spindle maker, Fischer, have resulted in a spindle that concentrates high power in a small volume. This company's soon-to-be-released "Hydro F" water bearing spindle delivers 80 kW continuous power and 40,000 rpm. By contrast, the company's high-end mechanical bearing spindle delivers 40 kW/40,000 rpm. At double the power, the hydrostatic spindle fits in the same size housing as its mechanical predecessor.

Testing of this spindle has involved high-metal-removal-rate aerospace milling. Test applications include high speed machining of aluminum at high depth and chip load using a 3/4-inch tool.

However, Fischer USA president Martin Rüegsegger says high speed and high power machining is only an introductory step. His company foresees fluid bearings applied not just in this application, but in every application where the company's spindles are used.

"We're not focused on any application in particular," he says. "We are evaluating fluid bearings as a potential replacement for mechanical bearings throughout our product line."

If fluid bearing spindles gain acceptance, he says, there is every reason to believe the price of manufacturing them will come down. They may become less expensive than the mechanical bearing variety. Certainly the after-market costs will be considerably less.

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"With our fluid bearing spindle design, we eliminate one-third to one-half of the moving parts," he says. This simplifies service. For example, part of the difficulty of servicing a mechanical bearing is the lubrication system that forms a critical and complex connection between stationary and rotating parts. In a fluid bearing design, this connection goes away, making the rotating parts far more accessible.

Conclution:-

It’s a predict feels highghly oblisised that I am try to complete my term paper about the topic GYROSCOPIC EFFECT ON MILLING,its my glad to do this term paper with the help of internet and some books and somes pdf files.i hope that I have done my best hard work to do this work hard to hardest to achieve my goal.And thanx to my sir that he has given to me this work to better myself

Refferences

Links-

1. http://cat.inist.fr/?aModele=afficheN&cpsidt=9569622. http://www.informaworld.com/smpp/section?

content=a782815665&fulltext=7132409283. en.wikipedia.org/wiki/Gyroscope4. http://www.manufacturingit.net/Sections/Formulea/Equations/

Dynamics/Gyroscopic%20Effects.htm

Books and others

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1. Schmitz, T., and Duncan, G.S., 2005, Three-Component Receptance Coupling Substructure Analysis for Tool Point Dynamics Prediction,Journal of Manufacturing Science and Engineering, 127/4: 781-790.

2. Nelson, H.D., 1980, A Finite Rotating Shaft Element Using Timoshenko Beam Theory, Journal of Mechanical Design, 102: 793-803