Читать книгу A Catechism of the Steam Engine - C.E. John Bourne - Страница 13

63. Q.--In what way are the strengths of the different parts of a steam engine determined?

A.--By reference to the amount of the strain or pressure to which they are subjected, and to the cohesive strength of the iron or other material of which they are composed. The strains subsisting in engines are usually characterized as tensile, crushing, twisting, breaking, and shearing strains; but they may be all resolved into strains of extension and strains of compression; and by the power of the materials to resist these two strains, will their practical strength be measurable.

64. Q.--What are the ultimate strengths of the malleable and cast iron, brass, and other materials employed in the construction of engines?

A.--The tensile and crushing strengths of any given material are by no means the same. The tensile strength, or strength when extended, of good bar iron is about 60,000 lbs., or nearly 27 tons per square inch of section; and the tensile strength of cast iron is about 15,000 lbs., or say 6¾ to 7 tons per square inch of section. These are the weights which are required to break them. The crushing strain of cast iron, however, is about 100,000 lbs., or 44½ tons; whereas the crushing strength of malleable iron is not more than 27,000 lbs., or 12 tons, per square inch of section, and indeed it is generally less than this. The ultimate tensile strength, therefore, of malleable iron is four times greater than that of cast iron, but the crushing strength of cast iron is between three and four times greater than that of wrought iron. It may be stated, in round numbers, that the tensile strength of malleable iron is twice greater than its crushing strength; or, in other words, that it will take twice the strain to break a bar of malleable iron by drawing it asunder endways, than will cripple it by forcing it together endways like a pillar; whereas a bar of cast iron will be drawn asunder with one sixth of the force that will be required to break or cripple it when forced together endways like a pillar.

65. Q.--What is the cohesive strength of steel?

A.--The ultimate tensile strength of good cast or blistered steel is about twice as great as that of wrought iron, being about 130,000 lbs. per square inch of section. The tensile strength of gun metal, such as is used in engines, is about 36,000 lbs. per square inch of section; of wrought copper about 33,000 lbs.; and of cast copper about 19,000 lbs. per square Inch of section.

66. Q.--Is the crushing strength of steel greater or less than its tensile strength?

A.--It is about twice greater. A good steel punch will punch through a plate of wrought iron of a thickness equal to the diameter of the punch. A punch therefore of an inch diameter will pierce a plate an inch thick. Now it is well known, that the strain required to punch a piece of metal out of a plate, is just the same as that required to tear asunder a bar of iron of the same area of cross section as the area of the surface cut. The area of the surface cut in this case will be the circumference of the punch, 3.1416 inches, multiplied by the thickness of the plate, 1 inch, which makes the area of the cut surface 3.1416 square inches. The area of the point of the punch subjected to the pressure is .7854 square inches, so that the area cut to the area crushed is as four to one. In other words, it will require four times the strain to crush steel that is required to tear asunder malleable iron, or it will take about twice the strain to crush steel that it will require to break it by extension.

67. Q.--What strain may be applied to malleable iron in practice?

A.--A bar of wrought iron to which a tensile or compressing strain is applied, is elongated or contracted like a very stiff spiral spring, nearly in the proportion of the amount of strain applied up to the limit at which the strength begins to give way, and within this limit it will recover its original dimensions when the strain is removed. If, however, the strain be carried beyond this limit, the bar will not recover its original dimensions, but will be permanently pulled out or pushed in, just as would happen to a spring to which an undue strain had been applied. This limit is what is called the limit of elasticity; and whenever it is exceeded, the bar, though it may not break immediately, will undergo a progressive deterioration, and will break in the course of time. The limit of elasticity of malleable iron when extended, or, in other words, the tensile strain to which a bar of malleable iron an inch square may be subjected without permanently deranging its structure, is usually taken at 17,800 lbs., or from that to 10 tons, depending on the quality of the iron. It has also been found that malleable iron is extended about one ten-thousandth part of its length for every ton of direct strain applied to it.

68. Q.--What is the limit of elasticity of cast iron?

A.--It is commonly taken at 15,300 lbs. per square inch of section; but this is certainly much too high, as it exceeds the tensile strength of irons of medium quality. A bar of cast iron if compressed by weights will be contracted in length twice as much as a bar of malleable iron under similar circumstances; but malleable iron, when subjected to a greater strain than 12 tons per square inch of section, gradually crumples up by the mere continuance of the weight. A cast-iron bar one inch square and ten feet long, is shortened about one tenth of an inch by a compressing force of 10,000 lbs., whereas a malleable iron bar of the same dimensions would require to shorten it equally a compressing force of 20,000 lbs. As the load, however, approaches 12 tons, the compressions become nearly equal, and above that point the rate of the compression of the malleable iron rapidly increases. A bar of cast iron, when at its breaking point by the application of a tensile strain, is stretched about one six-hundredth part of its length; and an equal strain employed to compress it, would shorten it about one eight-hundredth part of its length.

69. Q.--But to what strain may the iron used in the construction of engines be safely subjected?

A.--The most of the working parts of modern engines are made of malleable iron, and the utmost strain to which wrought iron should be subjected in machinery is 4000 lbs. per square inch of section. Cast iron should not be subjected to more than half of this. In locomotive boilers the strain of 4000 lbs. per square inch of section is sometimes exceeded by nearly one half; but such an excess of strain approaches the limits of danger.

70. Q.--Will you explain in what way the various strains subsisting in a steam engine may be resolved into tensile and crushing strains; also in what way the magnitude of those strains may be determined?

A.--To take the case of a beam subjected to a transverse strain, such as the great beam of an engine, it is clear, if we suppose the beam broken through the middle, that the amount of strain at the upper and lower edges of the beam, where the whole strain may be supposed to be collected, will, with any given pressure on the piston, depend upon the proportion of the length to the depth of the beam. One edge of the beam breaks by extension, and the other edge by compression; and the upper and lower edges may be regarded as pillars, one of which is extended by the strain, and the other is compressed. If, to make an extreme supposition, the depth of the beam is taken as equal to its length, then the pillars answering to the edges of the beam will be compressed, and extended by what is virtually a bellcrank lever with equal arms; the horizontal distance from the main centre to the end of the beam being one of the arms, and the vertical height from the main centre to the top edge of the beam being the other arm. The distance, therefore, passed through by the fractured edge of the beam during a stroke of the engine, will be equal to the length of the stroke; and the strain it will have to sustain will consequently be equal to the pressure on the piston. If its motion were only half that of the piston, as would be the case if its depth were made one half less, the strain the beam would have to bear would be twice as great; and it may be set down as an axiom, that the strain upon any part of a steam engine or other machine is inversely equal to the strain produced by the prime mover, multiplied by the comparative velocity with which the part in question moves. If any part of an engine moves with a less velocity than the piston, it will have a greater strain on it, if resisted, than is thrown upon the piston. If it moves with a greater velocity than the piston, it will have a less strain upon it, and the difference of strain will in every case be in the inverse proportion of the difference of the velocity.

71. Q.--Then, in computing the amount of metal necessary to give due strength to a beam, the first point is to determine the velocity with which the edge of the beam moves at that point were the strain is greatest?

A.--The web of a cast-iron beam or girder serves merely to connect the upper and lower edges or flanges rigidly together, so as to enable the extending and compressing strains to be counteracted in an effectual manner by the metal of those flanges. It is only necessary, therefore, to make the flanges of sufficient strength to resist effectually the crushing and tensile strains to which they are exposed, and to make the web of the beam of sufficient strength to prevent a distortion of its shape from taking place.

72. Q.--Is the strain greater from being movable or intermittent than if it was stationary?

A.--Yes it is nearly twice as great from being movable. Engineers are in the habit of making girders intended to sustain a stationary load, about three times stronger than the breaking weight; but if the load be a movable one, as is the case in the girders of railway bridges, they make the strength equal to six times the breaking weight.

73. Q.--Then the strain is increased by the suddenness with which it is applied?

A.--If a weight be placed on a long and slender beam propped up in the middle, and the prop be suddenly withdrawn, so as to allow deflection to take place, it is clear that the deflection must be greater than if the load had been gradually applied. The momentum of the weight and also of the beam itself falling through the space through which it has been deflected, has necessarily to be counteracted by the elasticity of the beam; and the beam will, therefore, be momentarily bent to a greater extent than what is due to the load, and after a few vibrations up and down it will finally settle at that point of deflection which the load properly occasions. It is obvious that a beam must be strong enough, not merely to sustain the pressure due to the load, but also that accession of pressure due to the counteracted momentum of the weight and of the beam itself. Although in steam engines the beam is not loaded by a weight, but by the pressure of the steam, yet the momentum of the beam itself must in every case be counteracted, and the momentum will be considerable in every case in which a large and rapid deflection takes place. A rapid deflection increases the amount of the deflection as well as the amount of the strain, as is seen in the cylinder cover of a Cornish pumping engine, into which the steam is suddenly admitted, and in which the momentum of the particles of the metal put into motion increases the deflection to an extent such as the mere pressure of the steam could not produce.

74. Q.--What will be the amount of increased strain consequent upon deflection?

A.--The momentum of any moving body being proportional to the square of its velocity, it follows that the strain will be proportional to the square of the amount of deflection produced in a specified time.

75. Q.--But will not the inertia of a beam resist deflection, as well as the momentum increase deflection?

A.--No doubt that will be so; but whether in practical cases increase of mass without reference to strength or load will, upon the whole, increase or diminish deflection, will depend very much upon the magnitude of the mass relatively with the magnitude of the deflecting pressure, and the rapidity with which that pressure is applied and removed. Thus if a force or weight be very suddenly applied to the middle of a ponderous beam, and be as suddenly withdrawn, the inertia of the beam will, as in the case of the collision of bodies, tend to resist the force, and thus obviate deflection to a considerable extent; but if the pressure be so long continued as to produce the amount of deflection due to the pressure, the effect of the inertia in that case will be to increase the deflection.

76. Q.--Will the pressure given to the beam of an engine in different directions facilitate its fracture?

A.--Iron beams bent alternately in opposite directions, or alternately deflected and released, will be broken in the course of time with a much less strain than is necessary to produce immediate fracture. It has been found, experimentally, that a cast-iron bar, deflected by a revolving cam to only half the extent due to its breaking weight, will in no case withstand 900 successive deflections; but, if bent by the cam to only one third of its ultimate deflection, it will withstand 100,000 deflections without visible injury. Looking, however, to the jolts and vibrations to which engines are subject, and the sudden strains sometimes thrown upon them, either from water getting into the cylinder or otherwise, it does not appear that a strength answering to six times the breaking weight will give sufficient margin for safety in the case of cast-iron beams.

77. Q.--Does the same law hold in the case of the deflection of malleable iron bars?

A.--In the case of malleable iron bars it has been found that no very perceptible damage was caused by 10,000 deflections, each deflection being such as was due to half the load that produced a large permanent deflection.

78. Q.--The power of a rod or pillar to resist compression becomes very little when the diameter is small and the length great?

A.--The power of a rod or pillar to resist compression, varies nearly as the fourth power of the diameter divided by the square of the length. In the case of hollow cylindrical columns of cast iron, it has been found, experimentally, that the 3.55th power of the internal diameter, subtracted from the 3.55th power of the external diameter, and divided by the 1.7th power of the length, will represent the strength very nearly. In the case of hollow cylindrical columns of malleable iron, experiment shows that the 3.59th power of the internal diameter, subtracted from the 3.59th power of the external diameter, and divided by the square of the length, gives a proper expression for the strength; but this rule only holds where the strain does not exceed 8 or 9 tons on the square inch of section. Beyond 12 or 13 tons per square inch of section, the metal cannot be depended upon to withstand the strain, though hollow pillars will sometimes bear 15 or 16 tons per square inch of section.

79. Q.--Does not the thickness of the metal of the pillars or tubes affect the question?

A.--It manifestly does; for a tube of very thin metal, such as gold leaf or tin foil, would not stand on end at all, being crushed down by its own weight. It is found, experimentally, that in malleable iron tubes of the respective thicknesses of .525, .272, and .124 inches, the resistances per square inch of section are 19.17, 14.47, and 7.47 tons respectively. The power of plates to resist compression varies nearly as the cube, or more nearly as the 2.878th power of their thickness; but this law only holds so long as the pressure applied does not exceed from 9 to 12 tons per square inch of section. When the pressure is greater than this the metal is crushed, and a new law supervenes, according to which it is necessary to employ plates of twice or three times the thickness, to obtain twice the resisting power.

80. Q.--In a riveted tube, will the riveting be much, damaged by heavy strains?

A.--It will be most affected by percussion. Long-continued impact on the side of a tube, producing a deflection of only one fifth of that which would be required to injure it by pressure, is found to be destructive of the riveting; but in large riveted structures, such as a ship or a railway bridge, the inertia of the mass will, by resisting the effect of impact, prevent any injurious action from this cause from taking place.

81. Q.--Will the power of iron to resist shocks be in all cases proportional to its power to resist strains?

A.--By no means. Some cast iron is very hard and brittle; and although it will in this state resist compression very strongly, it, will be easily broken by a blow. Iron which has been remelted many times generally falls into this category, as it will also do if run into very small castings. It has been found, by experiment, that iron of which the crushing weight per square inch is about 42 tons, will, if remelted twelve times, bear a crushing weight of 70 tons, and if remelted eighteen times it will bear a crushing weight of 83 tons; but taking its power to resist impact in its first state at 706, this power will be raised at the twelfth remelting to 1153, and will be sunk at the eighteenth remelting to 149.

82. Q.--From all this it appears that a combination of cast iron and malleable iron is the best for the beams of engines?

A.--Yes, and for all beams. Engine beams should be made deeper at the middle than they are now made; the web should be lightened by holes pierced in it, and round the edge of the beam there should be a malleable iron hoop or strap securely attached to the flanges by riveting or otherwise. The flanges at the edges of engine beams are invariably made too small. It is in them that the strength of the beam chiefly resides.