TORSIVE STRENGTH.] 



APPLIED MECHANICS. 



815 



while the engines and paddles are moving at full speed, 

 a wave strikes one paddle and suddenly immerses it to a 

 great depth in water, so as at once to retard its rotation. 

 The shock thus communicated to the engine, through 

 the shaft which drives the paddle, is enormous, and oc- 

 casionally more than 100 times the average force passing 

 through the shaft. It is, therefore, essential to make 

 all shafts intended to communicate power, of much 

 greater strength than what is due to the mere average 

 strain passing through them. The power that is com- 

 municated through any shaft is generally reckoned in 

 horse-power ; and as power consists of two elements 

 pressure or weight moved, and the velocity or speed 

 with which it is moved it is necessary to ascertain not 

 only the assumed power passing through a shaft, but also 

 the speed with which that shaft rotates, or the number 

 of revolutions it makes in a given time, such as a minute, 

 before we can compute the strain to which it is subjected, 

 and the dimensions of which it should be made. The 

 more quickly a shaft rotates in communicating a certain 

 power, the less is the torsive strain to which it is sub- 

 jected, for power is pressure or strain multiplied by 

 velocity ; and if, to produce a certain power, the velocity 

 be increased, the strain must be proportionally dimi- 

 nished. The shafts of engines, and machinery connected 

 with them, are generally made of wrought or cast-iron. 

 As wrought-iron is more flexible and tenacious than 

 cast- iron, it is less subject to fracture by sudden vari- 

 ation* of strain, and is therefore preferable to cast-iron 

 for shafts, and may be made considerably lighter. 

 Again, the shafts which communicate the first effort of 

 the power from the steam-pressure to the fly-wheel, are 

 subjected to much greater variations of strain, than those 

 which communicate the power afterwards from the fly- 

 wheel shaft to other machinery. It is, therefore, ad- 

 visable to give the first shafts, or prime movers as they 

 are called, greater strength than is necessary for second 

 movers. Practical men generally make the prime 

 movers about twice as strong as the second movers ; 

 and the following rules embody the modes of computing 

 dimensions of shafts for conveying given power at given 

 velocities. 



I. For wrought-iron prime movers, given the horse- 

 power, and the number of revolutions per minute, to 

 ascertain the diameter. 



Suit. Divide the power by the velocity, extract the 

 cube root of the quotient, and multiply by 7, for the 

 diameter in inches. 



Example 1. Required the diameter of a wrought-iron 

 prime-moving shaft for 100 horse-power, making 20 re- 

 volutions per minute. 



20=5, cube root 17 inches, and 7 X 1'7 =11 '9, nearly 



12 inches. 



II. For cast-iron prime movers. 



Rule. Divide the power by the velocity, and take 7J 

 times the cube root of the quotient. 



Example 2. Required the diameter of a cast-iron 

 prime-moving shaft for 50 horse-power at 25 revolutions 

 per minute. 



H==2, cube root 1-26 X 7J=9'45 or 9J inches. 



III. For wrought-iron second movers. 



Rule. Divide the power by the velocity, and take 5J 

 times the cube root of the quotient. 



Example 3. Required the diameter of a wrought-iron 

 second mover for 40 horse-power at 15 revolutions per 

 minute. 



40 



jg = 2'6, cube root 1'4 X 5| = 7'7 or 7J inches. 



IV. For cast-iron second movers. 



Rule. Divide power by velocity, and take 6 times the 

 cube root of the quotient. 



Example 4. Required the diameter of a cast-iron 

 second mover for 22 horse-power at 36 revolutions per 

 minute. 



22 



30=0-6, cube root 0-87 X 6= 



5 -2 2 or 5J inches. 



For shaft? under very regular strain, and distantly 

 connected with the prime mover, the multipliers may be 

 for wrought-iron 5, and for cast-iron 5J. 



The dimensions computed by the above rules are those 

 of the weakest part of the shafts. When shafts are of 

 great length, or have great weights, such as fly-wheels, 

 and the like, fixed upon them, they are subject to the 

 deflection due to transverse strain. This deflection in a 

 revolving shaft is an important element of weakness, for 

 it continually changes in direction as the one side or 

 other of the shaft is uppermost, and thus subjects the 

 material to all the degradation of alternate strains in 

 opposite directions. In breaking a piece of wire, it is 

 not unusual to bend it backwards and forwards until its 

 tenacity is quite destroyed. The same kind of action 

 occurs in a shaft too light for its length, or for the weight 

 it bears, and gradually lessens its tenacity, and deprives 

 the fibres of their continuous texture. The very best 

 material employed in shafting undergoes a peculiar 

 change in its molecular constitution, after having been 

 long kept in revolution. The iron becomes quite short 

 and crystalline, although at first fibrous and tenacious, 

 and will often break otf as short as cast-iron in a shaft 

 which has been working for some years. This result is 

 very common in railway axles, which are exposed to 

 great vibration ; and extreme cold has a similar tendency. 

 For such cases the strengths should be made considerably 

 in excess of what they are computed to be. In this, as 

 in numerous other instances, experience must be the 

 guide of the practical mechanic in the absence of set 

 rules. 



5. CLIPPING OR SHEARING STRAIN. The 

 strain which a body undergoes when it is divided across 

 by means of shears, or any instrument consisting of two 

 blades that pass one another like those of a scissors or 

 shears, is of a kind very distinct from any of the other 

 strains which we have discussed. Under tensive strain, 

 the fibres are torn asunder by a force in the direction of 

 their length ; under compressive strain they are forced 

 out of their place, and have their lateral cohesion de- 

 stroyed ; under transverse strain they are subjected 

 partly to compression and partly to extension ; under 

 tyrrive strain they are extended in a screw or spiral di- 

 rection ; but under the clipping strain the particles are 

 forced across each other, as we have described in endea- 

 vouring to investigate torsive strain on the principle of 

 shearing. 



Besides actual clipping by instruments for the purpose, 

 there are various 

 circumstances un- 

 der which materi- 

 als may be exposed 

 to a strain of a si- 

 milar character. In 

 punching holes in a 

 plate of metal, a 

 similar action takes 

 place. The- punch 

 (Fig. 95) is a piece 

 of steel, the end of 

 which is made of 

 the size and shape 

 of the hole to be 

 punched, the edges 

 being keen and not 

 rounded off ; the 

 matrix is a block of 

 steel, or iron faced 



with steel, having a hole such as is to be punched, with 

 edges also keen. The punch and the matrix are so ad- 

 justed that the former shall pass exactly into the latter ; 

 and a plate of metal being placed on the matrix while 

 the punch is up, has a hole pierced in it by its descent 

 the piece of metal being punched or pressed down into 

 the hole of the matrix. When the edges of the punch 

 and matrix are keen, and they accurately fit each other, 



Fig. 95. 



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