Gearbox Design by Chitale

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CHAPTER

17

Design of Machine Tool Gear Box

17.1

INTRODUCTION: MACHINE TOOL SYSTEM

The various elements of a machine tool are assembled together so as to provide maximum rigidity to the system; however. this assembly has revolving. sliding and fixed or stationary components. Generally the drives of a machine tool are covered and hidden. but operated by controls which are accessible to the operator. Variouselements of a machine tool are made integral or fabricated and assembled together to make a system quite homogeneous in appearance and operation. 17.1.1

DrIves and Regulatlon of MotIon on Metal-cuttIng MachInes

Metal-cutting machines receive working motions (speed and feed) from electric motors. which usually have constant revolutions per minute. In order to fulfil different operations. it is necessary to find out various numbers of spindle revolutions as wel! as different values of feed. For these purposes. speed and feed boxes

which work by either stepped or unstepped principle of regulation are used. 17.1.2

VarIous Motions of Machine Tool System

To drive the various components of the machine tool system, we can have four methods: (i) Mechanical (iii) Hydraulic

(ii) Electrical (iv) Pneumatic.

The choice of a particular method of drive will depend upon many factors such as cost. operating speeds and feeds. power to weight ratio. rigidity. reliability. maintenance costs. intended use. sophistication. and control. 316

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TEXTBOOK Of PRODUCllON ENGINEERING

Generally, today the user of machine tools demands beuer quality, improved performance, and higher operating speeds, and this has led to a design system quite complex in nature-consisting of anyone of the drive methods stated above-s-of the machine tool system. The field of machine dynamics, particularly that of the load bearing components of a system such as base, bed, table, saddle, columns and spindle support, are important for technological gains, as these components are made up of iron castings, but their design as steel weldments offers functional and economic advantages. The functional advantage is the possibility of using higber speeds and feeds, and the economic advantage is the low power to weight ratio and thus lower cost and ease of handling. There are two types of motion in a machine tool systems: (i) the main motions, viz. cutting speed and feed, and (ii) the subsidiary motions such as fixing of workpiece, tool seuing, machine control, ere, Sometimes the primary motion is only in one axis as in the case of a broaching macbine, but more often such motions are required in two or more than two planes. Insuch situations, we prefer to have an individual drive rather than a common drive. The line shaft drive is most obsolete. as there is not much control of speed in such a system of speed regulation. The hydraulic or pneumatic speed regulation devices are used where an infinite number of speeds. within a range of maximum and minimum speed, are required; however, stepless regulation can also be achieved by a DC motor with a resistance control or mechanical drives using pressure variations, but for a very limited range. Hydraulic speed regulation is good for straight line motions, e.g. broaching, grinding, milling and shaping machines. 17.2

FUNDAMENTALS OF MECHANICAL REGULATION

The ideal regulation of speed is stepless drive; but it has ccnain limitations. due to which it cannot be incorporated in all types of machine tools. Some idea regarding this fact has already been given in previous sections. The cost of a gear box increases as the number of speeds increases, and this limitation hampers many users; therefore such machine tools are not commercially prospective. Inview of the above fact, it is customary to design (for a set of speeds) a gear box which has a optimum numbers of speeds, with minimum speed loss. Alternative approaches to this problem have posed various solutions, out of which we have to pickup the best one. Ifstepless regulation is not available, then the increment of speeds from a minimum level can be arranged in an AP. GP or HP series; it has been 'proved that tbe GP (Geometric Progression) gives minimum speed loss, and the GP series has other advantages too. As we know that Va

nn 1000

-=--=k=tan¢

do

which reveals that to get v/np a constant for the same diameter, we need to change n such that "o,tnt is equal to trd,tlOOO. lf we have a GP series such as

then this can be written as II, n¢,

nf ... nI/f'-', ... , n¢!'

If you multiply this series by ¢, you will bave II¢.IIf. nif •... , nl/l'. n¢!,+1

'

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-

...'"'iiI<

."".

C~'~ ...

','

,

""

Thus we get another orientation of the speeds, just shifting the first speed to the next higher one and so on, without affecting the structural change in case of a geometric series with a common rates 4J whicb is not possible for AP or HP series. Preferred numbers can be used in this series, which is not possible in other cases. At present, we shall consider only rotary motions and other types of motions later on. Let the RPM of the lathe spindle be "l; "l; "1; ... ; "4--1; "k; "«I; ... What is the law governing these numbers? For this purpose, let us examine tberadial diagram. Let us tum a sbaft which has a diameter d•. According to the theory of metal cutting, we know that the cutting speed is given as under. Ird"" rnImm . V = -1000 0111

V =

or

A

1r11

1000

d A

If n is constant, then this relationship will be a straight line which passes through the origin (see Fig. 17.1). K = tan

I/!

In our example. it is necessary to have the speed corresponding to the point A. But we must work either with the speed VA' or with the speed VB (see Fig. 17.1). It is necessary to work with the speed VB because it is near the speed VN

f

t

n= constant

II------r Therefore. from the above formula prepresenting a straight line equation. it is possible to draw line diagrams which are called ray diagrams. These are sbown in Fig. 17.4. Let us draw the ray diagram of the gear box having 6 speeds, i.e. 6 = 3 x 2. Shaft nos. 1st III

II Main group

Gearing group

n.

II Gearing group

n.

n.

n.

n,

n,

n,

n,

n,

n.



n, (a) Crossed type speed layoul Flg.17.4

III Main group

Symmetric

n, (b) Open type speed layout ray diagrams.

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The ray diagram represents the method of gear arrangement, and also provides the values of motor speed and its power for various kinematic pairs as well as arrangements of groups. The ray diagram does not provide the values of transmission ratios, and this diagram is drawn symmetrically. Motor

II

III

Motor

II

III

n,. "'"

9c

are suitable for the main group. For the first gearing group, R e/"3 1/1'; the maximum value of ¢ is as follows:

=

for the main motion, ¢ = ~

=

= 1.67;

for the cbain of feed motion, ¢ = ~ = 1.94; for the second gearing group, R = .-/e) = rf/'; and therefore the maximum value of ¢ is as follows: for the chain of feed motion, ¢ = ~ = 1.41; for the chain of feed motion, t/> = ~ = 1.93. It appears that displacement of gearing group will change nothing. Hence, the value of t/> is limited and depends on the number of shans and on the number of steps of revolution are obtained here. 17.4

RAY DIAGRAM FOR OVERLAPPING SPEEDS

Overlapping speeds are obtained by reducing the power by one or more degrees in one of the gearing groups. Let us take up a mechanism of 12 = 2·3·2speeds. the main group of which is the travel block of gears.

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The 'open structure' ray diagram is shown in Fig. 17.7. II

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