Monday, February 7, 2011
Hot Rolling Mill
Sunday, February 6, 2011
Machines make work easier for us
It is good to start with clear definitions, so that we know what we are talking about. Let us say that a machine is a collection of resistant bodies arranged to change the magnitude, direction or point of application of moving forces. Motion is an essential part of a machine; without it, at least in principle, we have no machine, but a structure. The restriction to resistant bodies sets hydraulic and other fluid machines aside; these deserve special treatment. Some authors classify the hydraulic press as a machine. In a sense it is, of course, and depends on statics, but we will leave it aside. An ideal machine is one in which the parts are considered to be weightless, frictionless and rigid. Real machines are not ideal, but ideal machines aid thought and analysis, and in many cases are adequate approximations, so they are quite useful. A simple machine is a machine from which no part can be removed without destroying it as a machine. A mechanism is a machine considered solely from the point of view of its motions, kinematically, without consideration of loads. Some authors say a mechanism is a machine with "that does no useful work," but this is not a helpful distinction. A steam engine valve gear is essentially a mechanism to obtain a particular motion, but it also does useful work on the valve. A structure transmits force without motion.
It may be useful to define an engine as a machine in which the input is not in the form of mechanical energy, but which is converted into forces and torques by the machine. For example, the input could be electrical, or provided by a heat engine. It could also include machines worked by men or animals considered as part of the machine and not as users of it. A prime mover is an engine whose power is derived from some nonmechanical source, such as a heat engine. A prime mover is capable of motion, or being moved, without connection to any other system. However, windmills, water wheels and turbines are considered to be prime movers, as clearly are men and animals. Fundamentally, engine and machine are actually two words for the same thing, derived from Latin and Greek, respectively.
There are many ways of transmitting forces in machines, such as fluids pressing on a piston in a cylinder, or exerting their weight in buckets, flexible agents such as ropes, belts, cables and chains, springs, and weights themselves. These means are not part of the machine itself. Weight is the force of gravity on massive bodies, and form a very common load on a machine. A link is a member that transmits an axial force of compression or tension, and is connected by pins or sliders at its ends. A link is not a machine by itself (it does not transform its input), but is a typical part of a mechanism, and may transmit forces between simple machines. A slotted link with a sliding block may permit a variable amount of motion to be transmitted.
Every machine has an input and an output, and the output is a modification of the input, not a simple replication of it. A machine is a processor or transformer in some sense. The motion of the output is fully constrained by the motion of the input, by their kinematic connection. The force at the input is called the effort, and the force at the output, a load. The mechanical advantage, which we shall call simply the advantage, is the ratio of the load to the effort. The velocity ratio is the ratio of the movement of the load to the movement of the effort, in linear displacement or rotation. In an ideal machine the product of the advantage and the velocity ratio is unity, as we shall see. There is a trade-off between force and speed. In a real machine the product is less than unity. As a consequence, an ideal machine in equilibrium (when the effort and the load balance) can be moved by the least impetus, as well in one direction as in the other, so the machine is reversible. A real machine, however, requires a certain effort to move it in either direction; it is irreversible, and there is an unavoidable loss of energy whenever it moves.
It is reasonable to exclude from our definition those devices that depend essentially on inertial forces. The pendulum is one such device, as is the whole family of fluid turbines, and perhaps sails and airfoils as well. Simple machines can, however, form a part of such devices. These devices all deserve special consideration, and involve matters not essential to the machines that will be discussed here. Therefore, our machines depend only on the principles of statics and kinematics, not dynamics. Dynamics may have to be considered in connection with the design of machine elements, however.
The inputs and outputs of a machine may be either forces or torques, and a machine may convert one into the other. A torque or moment tends to cause rotation, while a force causes linear motion. The work done is either torque times angle of rotation, or force times distance. The dimensions of torque are force times distance, and this should be carefully distinguished from work, which has the same dimensions. Sometimes, torque is stated in, for example, pound-foot while work is in foot-pound to make this clear. A fundamental property of machines is that the input and output work are the same, except for frictional losses that make the output work smaller. This principle of the conservation of energy is a very important generalization, and will be considered in more detail later.
To understand the magnitudes of the forces in a machine, the methods of statics are used. If you already know statics, then the application to machines will be easy. If you do not, machines are an excellent and graphic way to learn about statics, and will help you to understand it. Briefly, we note that forces add according to the parallelogram rule, and can be resolved trigonometrically into components in many ways, the most useful being the rectangular components. The moment of a force about an axis is the product of the force and the shortest distance between its line of action and the axis. A body is in equilibrium if the sum of the forces acting upon it is zero, and the moment of these forces about any axis is zero. This gives up to six equations that may be used to find the magnitude and direction of unknown forces. In applying these principles, it is best to draw the body in question isolated from all others, and show the forces acting on it, and only those forces.
Since ancient times, simple machines have been classified as lever, wedge, wheel and axle, pulley and screw. Sometimes the wedge and screw are considered special cases of the inclined plane, so there are either four or six simple machines. This is no more than an arbitrary and incomplete taxonomy. Since classifications should be useful, you should try to make your own classification that reminds you of the principal similarities and differences. I prefer to divide simple machines into three families, those of the lever, the inclined plane and the pulley, and will treat machines in that order in this paper. Each family has various tribes, and some tribes are descendants of two families. There is also a miscellaneous family in which mechanisms are put that fit nowhere else. In complex machines, the families are mixed and connected in glorious variety.
There are ingeneous devices that, while not machines in themselves, are very important parts of machines. These include bearings, couplings, clutches, cams, springs and gears.
It may be useful to define an engine as a machine in which the input is not in the form of mechanical energy, but which is converted into forces and torques by the machine. For example, the input could be electrical, or provided by a heat engine. It could also include machines worked by men or animals considered as part of the machine and not as users of it. A prime mover is an engine whose power is derived from some nonmechanical source, such as a heat engine. A prime mover is capable of motion, or being moved, without connection to any other system. However, windmills, water wheels and turbines are considered to be prime movers, as clearly are men and animals. Fundamentally, engine and machine are actually two words for the same thing, derived from Latin and Greek, respectively.
There are many ways of transmitting forces in machines, such as fluids pressing on a piston in a cylinder, or exerting their weight in buckets, flexible agents such as ropes, belts, cables and chains, springs, and weights themselves. These means are not part of the machine itself. Weight is the force of gravity on massive bodies, and form a very common load on a machine. A link is a member that transmits an axial force of compression or tension, and is connected by pins or sliders at its ends. A link is not a machine by itself (it does not transform its input), but is a typical part of a mechanism, and may transmit forces between simple machines. A slotted link with a sliding block may permit a variable amount of motion to be transmitted.
Every machine has an input and an output, and the output is a modification of the input, not a simple replication of it. A machine is a processor or transformer in some sense. The motion of the output is fully constrained by the motion of the input, by their kinematic connection. The force at the input is called the effort, and the force at the output, a load. The mechanical advantage, which we shall call simply the advantage, is the ratio of the load to the effort. The velocity ratio is the ratio of the movement of the load to the movement of the effort, in linear displacement or rotation. In an ideal machine the product of the advantage and the velocity ratio is unity, as we shall see. There is a trade-off between force and speed. In a real machine the product is less than unity. As a consequence, an ideal machine in equilibrium (when the effort and the load balance) can be moved by the least impetus, as well in one direction as in the other, so the machine is reversible. A real machine, however, requires a certain effort to move it in either direction; it is irreversible, and there is an unavoidable loss of energy whenever it moves.
It is reasonable to exclude from our definition those devices that depend essentially on inertial forces. The pendulum is one such device, as is the whole family of fluid turbines, and perhaps sails and airfoils as well. Simple machines can, however, form a part of such devices. These devices all deserve special consideration, and involve matters not essential to the machines that will be discussed here. Therefore, our machines depend only on the principles of statics and kinematics, not dynamics. Dynamics may have to be considered in connection with the design of machine elements, however.
The inputs and outputs of a machine may be either forces or torques, and a machine may convert one into the other. A torque or moment tends to cause rotation, while a force causes linear motion. The work done is either torque times angle of rotation, or force times distance. The dimensions of torque are force times distance, and this should be carefully distinguished from work, which has the same dimensions. Sometimes, torque is stated in, for example, pound-foot while work is in foot-pound to make this clear. A fundamental property of machines is that the input and output work are the same, except for frictional losses that make the output work smaller. This principle of the conservation of energy is a very important generalization, and will be considered in more detail later.
To understand the magnitudes of the forces in a machine, the methods of statics are used. If you already know statics, then the application to machines will be easy. If you do not, machines are an excellent and graphic way to learn about statics, and will help you to understand it. Briefly, we note that forces add according to the parallelogram rule, and can be resolved trigonometrically into components in many ways, the most useful being the rectangular components. The moment of a force about an axis is the product of the force and the shortest distance between its line of action and the axis. A body is in equilibrium if the sum of the forces acting upon it is zero, and the moment of these forces about any axis is zero. This gives up to six equations that may be used to find the magnitude and direction of unknown forces. In applying these principles, it is best to draw the body in question isolated from all others, and show the forces acting on it, and only those forces.
Since ancient times, simple machines have been classified as lever, wedge, wheel and axle, pulley and screw. Sometimes the wedge and screw are considered special cases of the inclined plane, so there are either four or six simple machines. This is no more than an arbitrary and incomplete taxonomy. Since classifications should be useful, you should try to make your own classification that reminds you of the principal similarities and differences. I prefer to divide simple machines into three families, those of the lever, the inclined plane and the pulley, and will treat machines in that order in this paper. Each family has various tribes, and some tribes are descendants of two families. There is also a miscellaneous family in which mechanisms are put that fit nowhere else. In complex machines, the families are mixed and connected in glorious variety.
There are ingeneous devices that, while not machines in themselves, are very important parts of machines. These include bearings, couplings, clutches, cams, springs and gears.
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