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SHAFTS、COUPLINGS、MATERIAL SELECTION AND TRANSMISSION METHOD June, 1992 by Keith Briere Shafts and couplings Virtually all machines contain shafts. The most common shape for shafts is circular and the cross section can be either solid or hollow (hollow shafts can result in weight savings). Rectangular shafts are sometimes used ,as in screw driver blades, socket wreches and control knob stems. A shaft must have adequate torsional strength to transmit torque and not be over stressed . It must also be torsionally stiff enough so that one mounted component does not deviat excessively from its original angular position relative to a second component mounted on the same shaft . Generally speaking , the angle of twist should ont exceed one degree in a shaft length equal to 20 diameters. Shafts are mounted in bearings and transmit power through such devices as gears , pulleys , cams and clutches .These devices introduce forces which attempt to bend the shaft ; bence , the bending deflection of a shaft should ont exceed 0.01 in per ft of length between bearing supports . In addition , the shaft must be able to sustain a combination of bending and torsional loads . Thus an equivalent load must be considered which takes into account both torsion and bending . Also , the allowable stress must contain a factor of safety which includes fatigue , since torsional and bending stress reversaks occur . For diameters less than 3 in. , the usual shaft material is cold-rolled steel containing about 0.4 percent xarbon . Shafts are either cold-rolled or forged in size . Plastic shafts are widely used for light load applications . One advantage of using plastic is safely in electrical applications , since plastic is a poor conductor of electricity . Components such as gears and pulleys are mounted on shafts by means of key . The design of the key and the corresponding keyway in the shaft must be properly evaluated . For example ,stress concentrations occur in shafts due to keyways , and the material removed to form the keyway further weakens theshaft . If shafts are run at critical speeds , severe vibrations can occur which can seriously damage a machine . It is important to know the magnitude of these critical speeds so that they can be avoided . As a general rule of thumb , the diference between the oprating speed and the critical speed should be at least 20 percent . Many shafts are supported by three or more bearings , which means that the problem is statically indeterminate . Texts on strength of materials give methods of solving such problems . The design effort should be in keeping with the economics of a given situation . For example , if one line shaft supported by three or more bearings is needed , it probably would be cheaper to make conservative assumptions as to moments and design it as though it were determinate . The extra cost of an oversize shaft may be less than the extra cost of an elaborate design analysis . Another important aspect of shaft design is the method of directly connecting one shaft to another . This is accomplished by devices such as rigid and flexible couplings. A coupling is a device for connecting the ends of adjacent shafts . In machine construction , couplings are used to effect a semipermanent connection between adjacent rotating shafts . The connection is permanent in the sense that it is not meant to be broken during the useful life of the machine , but it can be broken and restored in an emergency or when worn parts are replaced . There are several types of shaft couplings , their characteristics depend on the purpose for which they are used . If an exceptionally long shaft is required in a manufacturing plant or a propeller shaft on a ship , it is made in sections that are coupled together with rigid couplings . A common type of rigid coupling consists of two mating radial flanges (disk) that are attached by key driven hubs to the ends of adjacent shaft sections and bolted together through the flanges to form a rigid connection .Alignment of the connected shafts is usually effected by means of a rabbet joint on the face of the flanges . In connecting shafts belonging to separate devices (such as electric motor and a gearbox ) , precise aligning of the shafts is difficult and a flrxible coupling is used . This coupling connects the shafts in such a way as to minimize the harmful effects of shaft misalignment . Flexible couplings also permit the shafts to deflect under their separate systems of loads and to move freely (float) in the axial direction without interfering with one another . Flexible coupling can also serve to reduce the intensity of shock loads and vibrations transmitted from one shaft to another . Rolling Contact Bearing The concern of a machine designer with ball and rolling bearings is fivefold as follows:(a) life in relation to load; (b) stiffness, i.e. deflections under load;(c) friction; (d) wear; (e) noise. For moderate loads and speeds the correct selection of a standard bearing on the basis of load rating will usually secure satisfactory performance. the deflection of the bearing elements will become important where load are high, although this is usually of less magnitude than that of the shafts or other components associated with the bearing. Where speeds are high special cooling arrangements become necessary which may increase frictional drag. Wearing is primarily associated with the introduction of contaminants, and sealing arrangements must be chosen with regard to the hostility of the environment. Because the high quality and low price of the ball and roller bearings depends on quantity production, the task of the machine designer becomes one of selection rather than design. Rolling-contact bearings are generally made with steel which is through-hardened to about 900 HV, although in many mechanisms special races are not provided and the interacting surfaces are hardened to about 600 HV. It is not surprising that , owing to the high stresses involved, a predominant form of failure should be metal fatigue, and a good deal of work is currently in progress intended to improve the reliability of this type of bearing. Design can be based on accepted values of life and it is general practice in the bearing industry to define to define the load capacity of the bearing as that value below which 90 per cent of a batch will exceed a life of one million revolutions. Notwithstanding the fact that responsibility for the basic design of ball and roller bearings rests with the bearing manufacturer, the machine designer must form a correct appreciation of the duty to be performed by the bearing and be concerned not only with bearing selection but with the conditions for correct installation. The fit of the bearing races onto the shaft or onto the housings is of critical importance because of their combined effect on the internal clearance of the bearing as well as preserving the desired degree of interference fit. Inadequate interference can induce serious trouble from fretting corrosion. The inner race is frequently located axially by abutting against a shoulder. A radius at this point is essential for the avoidance of stress concentration and ball races are provided with a radius or chamfer to allow space for this. Where life is not the determining factor in design, it is usual to determine maximum loading by the amount to which a bearing will deflect under load. Thus the concept of” static load-carrying capacity” is understood to mean the load that can be applied to a bearing which is either stationary or subject to slight swiveling motions, without impairing its running qualities for subsequent rotational motion. This has been determined by practical experience as the load which when applied to a bearing result in a total deformation of the rolling element and raceway at any point of contact not exceeding 0.01 per cent of the rolling-element diameter. This would correspond to a permanent deformation of 0.0025 mm for a ball 25 mm in diameter. The successful functioning of many bearings depends upon providing them with adequate protection against their environment, and in some circumstances the environment must be protected from lubricants or products of deterioration of the bearing surfaces. Achievement of the correct functioning of seals is an essential part of bearing design. Moreover, seals which are applied to moving parts for any purpose are of interest to tribologists because they are components of bearing systems and can only be designed satisfactorily on the basis of the appropriate bearing theory. Notwithstanding their importance, the amount of research effort that has been devoted to the understanding of the behavior of seals has been small when compared with that devoted to other aspects of bearing technology. Gears The transmission of rotary motion from one shaft to another occurs in nearly every machine one can imagine. Gears constitute one of the best of the various means available for transmitting this motion. A gear is virtually a wheel with very accurately shaped teeth. These teeth mesh with teeth of another gear, thus providing as positive-motion drive. The speed ratio between shafts carrying a pair of gears depends upon the numbers of teeth in the gear. For example, a 20tooth gear drives a gear of 50 teeth, the smaller gear will have to turn 2.5 times to cause the larger one to make 1 turn. Various types of gearing have been developed for different purposes. If the shafts are parallel, any of these types may be used, spur, bevel, or herring-bone. Spur gears are the simplest and least expensive type. They are generally used on drives requiring moderate speeds. Bevel gears serve to transmit power between tow intersecting shafts. Rack-and-pinion drives are used where it is desirable to transform the rotary motion of one part into linear motion for the other part or vice versa. Spur gears are used to transmit rotary motion between parallel shafts; they are usually cylindrical, and the teeth are straight and parallel to the axis of rotation. The following are definitions for some common terms used in study of gears. (1) The pitch circle is a right section of an imaginary cylinder (pitch cylinder), that the toothed gear may be considered for replacement. The diameter of the circle is called pitch diameter. (2) The addendum circle is a circle which passes through all the tooth ends, and the addendum is the radial distance between the pitch circle and addendum circle. (3) The dedendum or root circle bounds the spaces between the teeth, and the distance between the pitch circle and the dedendum circle is termed as dedendumm. (4) The tolerate between the dedendum of one gear and addendum of the mating gear is the clearance. (5) The top and bottom surfaces of a tooth are known as top land and bottom land respectively. (6) The face of the tooth is the part of the tooth between the pitch cylinder and addendum cylinder, and its width along the tooth element is known as face width. (7) The flank of the tooth is the part of the tooth lying between pitch cylinder and addendum cylinder。 (8) The tooth thickness is the thickness of the tooth measured along the arc of the pitch circle. (9) The tooth space is the circular distance between two successive teeth measured along the pitch circle. (10) Back ash is the difference between the tooth space of one gear and tooth thickness of the mating gear. (11) The circular pitch, Pc is the sum of tooth thickness and tooth space, measured along the pitch circle. If D is the pitch diameter, and T is the number of the teeth of a gear, the circular pitch Pc is given by Eqs (3-1) Pc=3.14D/T (3-1) (12) The diametral pitch, Pd is the number of the teeth of a gear per unit pitch diameter.Hence by Eqs Pd=T/D (3-2) The inverse of diametric pitch Pd is called module m of the gear. From Eqs (3-1) and (3-2), the relation between circular and diametric pitches can be obtained as (3-3) Pc Pd =3.1415926 (3-3) (13) The pinion is the smaller gear of a mating gear pair. (14) The pitch point is the point of tangency of the pitch circles ora pair of mating gear wheels, and the common tangent is a tangent to the pitch circles at the pitch point. (15) The line of action is a line normal to both the mating profiles at the contact point. (16) The path of contact is the path traced by the contact point. (17) The pressure angle between the common tangent and line of action. Material Selection During recent years the selection of engineering materials has assumed great importance . Moreover , the process should be one of continual reevaluation . New materials often become available and there may be a decreasing availability of others . Concerns regarding environmental pollution , recycling and worker health and safety often impose new constraints .The desire for weight reduction or energy savings may dictate the use of different materials . Pressures from domestic and foreign competition , increased serviceability requirements , and customer feedback may all promote materials reevaluation . The extent of product liability actions , often the result of improper material use , has had a marked impact .In addition , the interdependence between materials and their processing has become better recognized . The development of new processes often forces reevaluation of the materials being processed . Therefore , it is imperative that design and manufacturing engineers exercise considerable care in selecting , specifying ,and utilizing materials if they are to achieve satisfactory results at reasonable cost and still assure quality . The first step in the manufacture of any product is design , which usually takes place in several distinct stages : (a) conceptual ;(b) functional ;(c) production . During the conceptual-design stage , the designer is concerned primarily with the functions the product is to fulfill .Usually several concepts are visualized and considered ,and a decision is made either that the idea is not practical or that the idea is sound and one or more of the conceptual designs should be developed further . Here ,the only concern for materials is that materials exist that can provide the desired properties . If no such materials are available ,consideration is given as to whether there is a reasonable prospect that new one could be developed within cost and time limitations . At the functional or engineering-design stage , a practical ,workable design is developed .Fairly complete drawings are made , and materials are selected and specified for the various components . Often a prototype or working model is made that can be tested to permit evaluation of the product as to function ,reliability , appearance , serviceability , and so on . Although it is expected that such testing might show that some changes may have to be made in materials before the product is advanced to the product is advanced to the production-design stage ,this should not be taken as an excuse for not doing a thorough job of material selection . Appearance , cost ,and reliability factors should be considered in detail , together with the functional factors . There is much merit to the practice of one very successful company which requires that all prototypes be built with the same materials that will be used in production and ,insofar as possible , with the same manufacturing techniques . It is of little value to have a perfectly functioning prototype that cannot be manufactured economically in the expected sales volume , or one that is substantially different from what the production units will be in regard to quality and reliability . Also , it is much better for design engineers to do a complete job of material analysis , selection , and specification at the development stage of design rather than to leave it to the production-design stage , where changes may be made by others , possibly less knowledgeable about all of the functional aspects of the product . At the production-design stage , the primary concern relative to materials should be that they are specified fully , that they are compatible with , and can be processed economically by , existing equipment , and that they are readily available in the needed quantities . As manufacturing progresses , it is inevitable that situations will arise that may require modifications of the materials being used . Experience may reveal that substitution of cheaper materials can be made . In most cases , however , changes are much more costly to make after manufacturing is in progress than before it starts . Good selection during the production-design phase will eliminate the necessity for this type of change . The more common type of change that occurs after manufacturing starts is the result of the availability of new materials .these , of course , present possibilities for cost reduction and improved peformance . However , new materials must be evaluated very carefully to make sure that all their characteristics are well established . One should always remember that it is indeed rare that as much is known about the properties and reliability of a new material as about those of an existing one . A large proportion of product failure and product liability cases have resulted from new materials being substituted before their long-term properties were really known . Product liability actions have made it imperative that designers and companies employ the very best procedures in selecting materials . The five most common faults in material selection have been : (a) failure to know and use the latest and best information available about the materials utilized ; (b) failure to foresee , and take into account the reasonable uses for the product (where possible , the designer is further advised to foresee and account for misuse of the product , as there have been many product liability cases in recent years where the claimant , injured during misuse of the product , has sued the manufacturer and won ) ;(c) the use of materials about which there was insufficient or uncertain data , particularly as to its long-term properties ; (d) inadequate , and unverified , quality control procedures ; and (e) material selection made by people who are completely unqualified to do so . An examination of the faults above will lead one to conclude that there is no good reason why they should exist . Consideration of them provides guidance as to how they can be eliminated . While following the very best methods in material selection nay not eliminate all product-liability claims , the use of proper procedures by designers and industries can greatly reduce their numbers . From the previous discussion , it is apparent that those who select materials should have a broad , basic understanding of the nature and properties of materials and their processing . 54