Machine Elements

the component parts of machines, each of which is a single piece and cannot be disassembled into simpler component elements without destruction. Machine elements also constitutes a scientific discipline, in which the theory, design, and construction of machines are studied.

The number of elements in complex machines reaches into the tens of thousands. The construction of machines from elements is dictated primarily by the necessity for the motion of the parts relative to one another. However, machine parts (links) that are fixed relative to the entire machine or relative to one another are also made of separate interconnecting elements. This makes it possible to use optimum materials and to restore the serviceability of worn-out machines by replacing only simple and inexpensive elements, simplifies the manufacture of machines, and facilitates their assembly.

Machine elements as a scientific discipline examines the following basic functional groups.

Body (housing) elements, which encase and support machine mechanisms and other units, include plates, which support machinery consisting of individual units; frames, which support the basic machine units; the frames of vehicles; the housings of rotary machines (turbines, pumps, and electric motors); cylinders and cylinder blocks; reduction-gear housings and gearboxes; and tables, carriages, supports, consoles, and brackets.

Transmissions are mechanisms that transmit mechanical energy over a distance, usually by the transformation of velocities and moments (torques), and sometimes by the transformation of the types and laws of motion. Transmissions of rotary motion are classified in turn according to their principle of operation as gear transmissions (toothed gears that operate without slippage), which include gear drives, worm gears, and chain drives, and friction drives (belt drives and rigid-link friction drives); and—depending on the presence or absence of an intermediate flexible link that allows considerable distances between shafts—as flexible gearing (belt and chain drives) or positive (direct) transmissions (gear drives, worm gears, and friction drives), respectively. According to the relative positioning of the shafts, a distinction is made among drives with parallel shaft axes (spur gear drives, chain drives, and belt drives), transverse shaft axes (bevel gear drives), and intersecting shaft axes (worm and hypoid gears). According to their basic kinematic characteristic, the gear ratio, a distinction is made between transmissions with a constant gear ratio (reducing drives and overdrives) and transmissions with a variable gear ratio, which in turn are subdivided into variable-speed transmissions (gearboxes) and infinitely variable transmissions (speed regulators). Transmissions that transform rotary motion into continuous translatory motion, or vice versa, are divided into screw drives (sliding and rolling), rack-and-pinion drives, worm-rack drives, and long half-nut-worm drives.

Shafts and axles serve as supports for rotating machine elements. A distinction is made between transmission shafts, which support the transmission elements (gears, sheaves, and sprockets), and main and special shafts, which support both the transmission elements and working members of motors or machinery equipment. For example, rotating and fixed axles are widely used to support nondriving wheels in vehicles. Rotating shafts and axles rest on bearings, but parts that move translationally (tables, rests, and so on) move along guides. Sliding bearings may operate with fluid, aerodynamic, or aerostatic friction or with mixed friction. Ball pivoted bearings are used for small and medium loads, and roller pivoted bearings are used for larger loads; needle pivoted bearings are used in cases of tight clearence. Antifriction (roller) bearings, which are manufactured in a wide range of outside diameters, from 1 mm to several meters, with weights ranging from fractions of a gram to several tons, are used most often in machines.

Couplings are used for shaft connections. This function may be combined with compensation for manufacturing and assembly errors, cushioning of dynamic actions, and regulation.

Elastic elements are designed for vibration elimination and damping of impact energy, to perform the functions of a mover (for example, watch springs), and for the creation of positive and negative allowances in machinery and mechanisms. Such elements include coil, spiral, and leaf springs and elastic rubber elements.

Connecting pieces, or adapters, constitute a separate functional group. A distinction is made between permanent connections, which do not permit separation without destruction of the elements, connecting pieces, or connecting layer (welded, soldered, riveted, adhesive, and rolled joints), and detachable connections, which permit separation and are formed by the relative alignment of the elements and frictional forces (most detachable connections) or only by relative alignment (such as prismatic key joints, or feather couplings). Depending on the form of the joining surfaces, distinction is made between plane joints (the majority) and joints of cylindrical or conical surfaces of revolution (shaft-hub). Welded joints are the most common type of connection used in machine building. The most commonly used detachable connections are threaded joints, which are made with screws, bolts, pins, and nuts.

Prototypes of many machine elements have been known since ancient times; the earliest were the lever and wedge. More than 25,000 years ago, man began to use the spring principle in bows for shooting arrows. The first flexible gearing was used in the bow drill for making fire. Rollers, which worked on the principle of rolling friction, were known more than 4,000 years ago. The wheel, axle, and bearing used in carriages and carts are regarded as the first machine elements that were similar in operation to modern elements. Winches and pulleys were also used in ancient times for the construction of temples and pyramids. Metal pivots, gears, cranks, rollers, and block and tackle were mentioned in the writings of Plato and Aristotle (fourth century B.C.). Archimedes used the screw, which apparently was known even earlier, in a water-lifting machine. Helical gears, gears with rotating spindles, antifriction bearings, and articulated link chains are described in the notes of Leonardo da Vinci. Information on belt and rope drives, load screws, and couplings is found in the literature of the Renaissance. Improvements were made in the design and construction of machine elements, and new modifications appeared. At the turn of the 19th century, riveted joints were widely used in boilers, railroad bridges, and similar structures. In the 20th century, riveted joints were gradually replaced by welded joints. The fastening-screw thread system developed in England in 1841 by J. Whitworth was the first attempt to establish standardization in the machine-building industry. The use of flexible (belt and rope) gearing was brought about by the necessity of distributing the energy from a steam engine to the floors of a factory with transmission drives. With the development of the individual electric drive, rope transmissions and belt drives came to be used for the transmission of energy from electric motors and prime engines to the drives of light-duty and medium-duty machines. V-belt drives were widely used in the 1920’s. Multiwedge V-belts and cogged belts were a subsequent development of flexible gearing. Gear drives were continually improved: the lantern-wheel (mangle) gear and the rounded-profile rectilinear-face gear were replaced by the cycloidal gear and, later, by the involute tooth system. Another important development was the appearance of M. L. Novikov’s circular helical gear. Antifriction bearings were first used on a large scale in the 1870’s. Considerable use was also made of hydrostatic bearings and guides and air-lubricated bearings.

The materials used for machine elements determine to a large extent the quality of the machines and account for a considerable portion of their cost (for example, 65-70 percent for motor vehicles). Steel, cast iron, and nonferrous alloys are the main materials for machine elements. Plastics are used as electric-insulation, friction, antifriction, corrosion-resistant, heat-insulation, and high-strength materials (fiberglass-reinforced plastics) and as materials with good processing properties. Rubber is used as a material with high elasticity and wear resistance. Critical machine elements (gears, highly stressed shafts, and so on) are made of chilled or refined steel. Materials such as nonchilled steel and cast iron, which make possible the manufacture of perfectly shaped elements, are used for machine elements whose size is determined by conditions of rigidity. Machine elements that operate at high temperatures are made of refractory or heat-resistant alloys. Since the surfaces of machine elements are subjected to extreme nominal bending and twisting stresses, local and contact stresses, and wear, the machine elements are case-hardened by chemical-thermal, thermal, mechanical, and thermomechanical treatment.

Machine elements must, with a given probability, be in operating condition over their specified service life, at the minimum cost required for their manufacture and operation. Therefore, they must satisfy the operating efficiency criteria of strength, rigidity, wear resistance, and heat resistance. The structural strength of machine elements that are subjected to variable loads may be calculated according to nominal stresses and safety factors, with allowance made for stress concentration and the scale factor or for variability of operating conditions. A design based on a given probability of trouble-free operation is considered to be the most valid. The rigidity of machine elements is usually calculated from the satisfactory operating condition of mated members (absence of increased edge pressures) and the conditions of serviceability of the machines, such as the production of precision products on a lathe. To provide wear resistance, an attempt is made to create conditions for fluid friction, in which the thickness of the oil layer must exceed the sum of the heights of the microscopic irregularities and other deviations from the proper geometric form of the surfaces. When the creation of fluid friction is not possible, the pressure and speeds are limited to values established in practice, or the wear of the elements is calculated on the basis of similar operational data for units and machines of the same type.

The design of machine elements is developing in the following directions: the optimization of structural design, the expansion of calculations on electronic computers, the introduction of time factors into the calculations, the introduction of probability methods, the standardization of design calculations, and the use of tabular design calculations for machine elements of centralized manufacture.

The principles of machine element design theory were established by research works in gear theory (L. Euler and Kh. I. Gokhman), the theory of thread friction on drums (L. Euler and others), and the theory of lubricant hydrodynamics (N. P. Petrov, O. Reynolds, and N. E. Zhukovskii). In the USSR machine element research is conducted at the Institute of Machine Science, the Scientific Research Institute of Machine-building Technology, and the Bauman Moscow Technical College. The main periodical is Vestnik mashinostroeniia (Journal of Machine Building), which publishes materials on the design, construction, and use of machine elements.

Developments are being made in the following areas of machine element construction: the improvement of the parameters of machine elements and development of high-parameter elements, the use of the optimum potentials of mechanical devices with solid component elements, hydraulic, electric, electronic, and other devices, the design of machine elements for the period of obsolescence of the machines, the increase of reliability, the optimization of forms in connection with new technological possibilities, the improvement of friction methods (liquid, gas, and rolling friction), hermetic sealing of mated machine elements, the manufacture of machine elements that operate in an abrasive medium from materials whose hardness exceeds that of the abrasive, standardization, and the organization of centralized production.

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