Читать книгу Farm Machinery and Equipment - Harris Pearson Smith - Страница 15

A clear conception of the fundamental principles of mechanics, as well as of their practical application to machinery, is necessary to a comprehensive study of farm machinery.

Force. Mechanics is the science that treats of forces and their effect. Force is the action of one body upon another which tends to produce or destroy motion in the body acted upon. Force may vary in magnitude and in method of application. In general, force is associated with muscular exertion. This, however, does not completely cover the scope and action of force because flow of an electric current, freezing of a liquid, and ignition of explosives may exert a certain amount of force. In order to compare different forces, they must all be in terms of the same unit. One such unit is called the pound weight.

Work. Whenever a force is exerted to the extent that motion is produced, work is performed. Work is measured by the product of the force times the distance moved, and it can be expressed in several combinations of units of weight (force) and distance, as inch-pounds, foot-pounds, and foot-tons. A foot-pound of work is done when a body is moved 1 foot against a force of 1-pound weight. The amount of work required to place a 100-pound bag of grain on a wagon that has a box 4 feet from the ground can be determined by multiplying the weight, 100 pounds, by the height, 4 feet, which will equal 400 foot-pounds of work done to place the bag of grain upon the wagon, or

Work = force × distance

or

W = F × D

W = 100 × 4 = 400 ft.-lb. of work

If a force moves in a circular direction to give a twisting action, this rotating force is termed torque. For example, a belt which exerts a force to turn a pulley and thus transmits power through a shaft gives the shaft a twisting action or a torque force. The pull on the belt in pounds multiplied by the radius of the pulley equals the torque in foot-pounds or, rather, pound-feet.

A force which produces the same effect upon a body as two or more forces acting together is called their resultant. The separate forces which can be so combined are called components. The finding of the resultant of two or more forces is called the composition of forces. The finding of two or more components of a given force is called the resolution of the force.

The moment of a force with respect to a point is the product of the force multiplied by the perpendicular distance from the given point to the direction of the force. In Fig. 3–1, the moment of the force P with relation to the point A is P times AB. The perpendicular distance is called the lever arm of the force. The moment is a measure of the tendency of the force to produce rotation about the given point, which is termed the center of moments. If the force is measured in pounds and the distance in inches, the moment is expressed in pound-inches; if measured in pounds and feet, the expression would be pound-feet. If P is a force of 10 pounds and 20 inches from A, its moment about A is 200 pound-inches.

Power. Power is the rate of doing work. To determine the power used or transmitted by a machine, the force must be measured, also the distance through which the force acts, and the length of time required for the force to act through this distance. The units of power ordinarily used in America are the foot-pound per second, the foot-pound per minute, and the horsepower.

FIG. 3–1. The moment of forces.

If a body is moved 1 foot per second against a force of 1-pound weight, the rate of work is 1 foot-pound per second. If it moves 1 foot per minute against the same force the rate is 1 foot-pound per minute. If it moves so that 33,000 foot-pounds are done each minute, the rate is 1 horsepower. The horsepower is based on the rate at which a 1,500-pound horse can do work. If such a horse pulls 150 pounds, 10 per cent of its weight, and moves at the rate of 220 feet per minute, or 2 1/2 m.p.h., it would do 33,000 foot-pounds of work per minute, this being equal to 150 times 220, or 33,000 foot-pounds, or 1 horsepower.

Energy. Energy is defined as the capacity for doing work. When a 1-pound weight has been raised 1 foot, it is said to have 1 foot-pound of work greater potential energy than it had in its original position. The energy possessed by a body, such as a tractor, due to its motion, is termed kinetic energy. Inertia is the property of a body which causes it to tend to continue in its present state of rest or motion, unless acted upon by some force such as a brake.

Simple Machines. A machine is a device that gives a mechanical advantage which facilitates the doing of work. The term is usually associated with such tools as grain binders, threshing machines, mowing machines, and so forth. But really, such machines are made up of many simple machines. There are six simple machines, namely:

1. The lever

2. The wheel and axle

3. The pulley

4. The inclined plane

5. The screw

6. The wedge

Any simple machine is capable of transmitting work done upon it to some other body. The mechanical advantage of a machine is the ratio of the force delivered by the machine to the force applied. The force which operates the machine is called the applied force. The efficiency of the machine is the ratio of the work accomplished by the machine to the work applied to the machine. If the efficiency of a machine could be 100 per cent, perpetual motion would exist. Since there is always a loss due to friction, the efficiency of the machine falls below 100 per cent.

FIG. 3–2. The three classes of levers.

Lever. The lever is a rigid bar, straight or curved, which rotates about a fixed point called the fulcrum. It has an applied force and a resisting force that are well defined by their names. The lever arms for a straight bar are the parts or ends on each side of the fulcrum, if the forces act perpendicular to the bar. The mechanical advantage of the lever is the ratio of the length of the lever arm of the applied force to the length of the arm of the resistance force, or

Weight × weight arm = applied force × force arm

Levers are of three classes (Fig. 3–2). In the lever of the first class, the applied force is at one end and the resisting force, or force exerted by the object to be moved, at the other. The fulcrum, or fixed point, is placed between the applied and the resisting forces. Such a lever may have a mechanical advantage of any value, depending directly upon the length of the lever arm between the fulcrum and the point of applied force as compared with the length of the lever arm between the fulcrum and the point of resisting force. The majority of levers found on farm machinery will fall in this class.

Levers of the second class have the applied force at one end, the fulcrum at the other, and the resisting force between them. This class of levers will have a mechanical advantage that will always be greater than unity. As in the case of the lever of the first class, a lever of the second class sacrifices speed and distance for a gain in pull or force.

A lever of the third class has the resisting force at one end, the fulcrum at the other, and the applied force between them. The mechanical advantage of this kind of lever is always less than unity, and, unlike the two previous classes, work is sacrificed for a gain in speed and distance. An ordinary crane is a lever of this kind.

Wheel and Axle. This is a modification of the lever and acts on the same principle, only the forces operate constantly (Fig. 3–3). The center of the axle corresponds to the fulcrum, the radius of the axle to the short arm, and the radius of the wheel to the long arm. The mechanical advantage is expressed by the equation

F × R = W × r

where W = weight

F = force applied

R = radius of wheel

r = radius of axle

FIG. 3–3. Wheel and axle.

Pulley. A pulley consists of a grooved wheel turning freely in a frame called a block; it is a lever of the first or second class. There are several different applications of pulleys, depending on their arrangement. A single fixed pulley affords no mechanical advantage except to change the direction of motion. When one or more fixed pulleys and one or more movable pulleys (Fig. 3–4) are used in combination, they form the block and tackle. The mechanical advantage varies directly as the number of ropes that support the movable pulley and the weight,

w × h = F × 3h

or

where w = weight

h = distance weight moves

F = force applied

3 = number of ropes supporting w

The differential pulley (Fig. 3–5) is a modification of a block and tackle but differs in that the two pulleys D and C are of different radii and rotate as one piece about a fixed axis B. The endless chain passes under and supports the movable pulley G and any weight attached to it. To raise a load, force is applied downward to chain F, which will rotate pulleys C, D, and G, causing the chain to wind up on the larger fixed pulley D and unwind on the smaller fixed pulley C, thus raising movable pulley G. In operation consider that point D of the section of chain DH moves up through an arc whose length is equal to BD. At the same time the point C of the section of chain CA will move downward an arc, a distance equal to BC. The length of the chain loop DHAC will be shortened to BD — BC, which will cause pulley G to be raised half this amount. P, the pulley force, is then applied to the section of chain EF, and the weight W is lifted at G. The mechanical advantage will be

FIG. 3–4. Block and tackle.

FIG. 3–5. Differential hoist.

FIG. 3–6. Geared differential hoists: A, worm-geared hoist; B, planetary-geared hoist.

P × BD = W × 1/2((BD — BC)

Figure 3–6 shows a geared differential hoist.

Inclined Plane. The inclined plane, shown in Fig. 3–7, is an even surface sloping at any angle between the horizontal and the vertical. The law or principle which governs the inclined plane in mechanics is that the force applied is increased as many times as the length of the inclined plane is greater than the elevation H. Briefly, it is equal to the length over the height, varying with the direction in which the force is applied. Instead of lifting the entire weight of the object vertically, part is supported on the plane and part by the force. Referring to Fig. 3–7, if the force F causes the weight W to move from A to C and parallel to the plane, the work done is F times AC, while the work done against gravity is the weight W times CE, if friction is disregarded, or briefly,

FIG. 3–7. The inclined plane.

FIG. 3–8. Screw.

F × AC = W × CE

If the force is parallel to the base AE, the advantage would be

F × AE = W × CE

Screw. The screw (Fig. 3–8) is the application or modification of the inclined plane combined with the lever. The threads winding around a cylinder bear the same relation to the inclined plane that a winding staircase bears to a straight one. When the screw is turned on its axis with the aid of a lever or gear, its sloping thread causes the load to move slowly in the direction of its vertical axis. The vertical distance between threads is called the pitch of the screw. The mechanical advantage is figured upon the condition that the applied force moves through a distance equal to the circumference of a circle whose radius is the length of the jackscrew bar or the radius of the driving gear, while the weight is being moved through a distance equal to the pitch of the screw.

Wedge. The wedge is a modification of the inclined plane. Actually it consists of two inclined planes placed base to base (Fig. 3–9). The force pushing on the wedge into any material, such as a log, will cause forces to act perpendicular to each of the two faces of the wedge.

FIG. 3–9. Wedge.