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1、Gears,Lesson One,Chapter One Mechanics Components,Spur and helical gears.,A gear having tooth elements that are straight and parallel to its axis is known as a spur gear. A spur pair can be used to connect parallel shafts only. Parallel shafts, however, can also be connected by gears of another type

2、, and a spur gear can be mated with a gear of a different type (Fig. 1-1).,Fig 1-1 Spur gears,Addendum circle 齿顶圆 Dedendum circle 齿根圆 Pitch circle 节圆 Base circle 基圆 Root circle Flank 齿侧 Chordal pitch 弦间距,split gear,To prevent jamming as a result of thermal expansion, to aid lubrication, and to compe

3、nsate for unavoidable inaccuracies in manufacture, all power-transmitting gears must have backlash. This means that on the pitch circles of a mating pair, the space width on the pinion must be slightly greater than the tooth thickness on the gear, and vice versa . On instrument gears, backlash can b

4、e eliminated by using a gear split down its middle, one half being rotatable relative to the other. A spring forces the split gear teeth to occupy the full width of the pinion space.,Helical gears have certain advantages; for example, when connecting parallel shafts they have a higher load carrying

5、capacity than spur gears with the same tooth numbers and cut with the same cutter. Because of the overlapping action of the teeth, they are smoother in action and can operate at higher pitch-line velocities than spur gears. The pitch-line velocity is the velocity of the pitch circle. Since the teeth

6、 are inclined to the axis of rotation, helical gears create an axial thrust. If used singly, this thrust must be absorbed in the shaft bearings.,The thrust problem can be overcome by cutting two sets of opposed helical teeth on the same blank. Depending on the method of manufacture, the gear may be

7、of the continuous-tooth herringbone variety or a double-helical gear with a space between the two halves to permit the cutting tool to run out. Double-helical gears are well suited for the efficient transmission of power at high speeds. Helical gears can also be used to connect nonparallel, non-inte

8、rsecting shafts at any angle to one another. Ninety degrees is the commonest angle at which such gears are used.,In order to achieve line contact and improve the load-carrying capacity of the crossed-axis helical gears, the gear can be made to curve partially around the pinion, in somewhat the same

9、way that a nut envelops a screw. The result would be a cylindrical worm and gear. Worm gears provide the simplest means of obtaining large ratios in a single pair. They are usually less efficient than parallel-shaft gears, however, because of an additional sliding movement along the teeth. Because o

10、f their similarity, the efficiency of a worm and gear depends on the same factors as the efficiency of a screw.,Worm and bevel gears.,Single-thread worms of large diameter have small lead angles and low efficiencies. Multiple-thread worms have larger lead angles and higher efficiencies (Fig.1-2).,Fi

11、g 1-2 worm gear set,The profiles of the teeth on bevel gears are not involutes; they are of such a shape that the tools for cutting the teeth are easier to make and maintain than involutes cutting tools. Since bevel gears come in pairs, as long as they are conjugate to one another they need not be c

12、onjugate to other gears with different tooth numbers.,For transmitting rotary motion and torque around corners, bevel gears are commonly used. The connected shafts, whose axes would intersect if extended, are usually but not necessarily at right angles to one another. When adapted for shafts that do

13、 not intersect, spiral bevel gears are called hypoid gears. The pitch surfaces of these gears are not rolling cones, and the ratio of their mean diameters is not equal to the speed ratio. Consequently, the pinion may have few teeth and be made as large as necessary to carry the load.,Words and Expre

14、ssions,Exercises,Gear trains The maximum gear ratio obtainable with a single of gears varies with the type of gear and the application. The following are approximate maxima for the various types for average load conditions: spur, 8; parallel-shaft helical, 10; straight bevel, 6; spiral bevel, 8; hyp

15、oid, 12; and worm, 80. For lightly loaded, instrument, and positioning gears, these ratios can be exceeded. Ratios as high as 400 or higher can be obtained with gears that resemble tapered worms meshing with hypoid gears. For heavily loaded gears, the given ratios may be so high that a reasonable ge

16、ar size precludes a satisfactory pinion.,Since the ratio in a single pair of gears is the quotient(商) of the tooth numbers, and since there usually are limitations on both the minimum anti maximum numbers of teeth on the available gears, it follows that the number of ratios obtainable in a single pa

17、ir is limited. To enlarge the coverage it is necessary to use multiple pairs, or trains The overall speed ratio in a train is the product(乘积) of the ratios in each pair. In certain cases an exact ratio cannot be obtained with gears, but by using two or more pairs, the desired ratio can be approximat

18、ed to any degree of precision.,Rolling Guides and Bearings,Lesson two,chapter One Mechanics Components,Rolling linear guides and guideways are widely used in practice,alongside plain linear guides. The following advantages are obtained when compared with plain guides:light running forces due to roll

19、ing friction,no stick-slip,trouble-free installation and immediate availability due to standardization of the rolling elements. The main disadvantage of this type of guide when compared with hydrostatic and hydrodynamic guides lies in the low damping effects in the direction normal to the movement.,

20、Rolling guides,Figure 1-3 shows in its upper section a rolling guide using a roller chain. Generally rolling elements travel half the distance moved by the slide. When roller chains are employed,their length must at least equal the sum of half the slide travel plus its own length. Hence,for long mov

21、ements rolling guideways in general employ recirculating roller elements,as shown in the lower half of Fig1-3. In this case the rollers run in an endless track,so that the movement is limited only by the length of the running surface.,For accurate operation of the complete rolling guideway,considera

22、tion must not only be given to the quality of both guiding surfaces but also to the dimensional and geometric accuracy of the rolling elements and their control in the cage When cylindrical rollers are used,inaccurate cages as well as non-parallel guideway surfaces can lead to angular motion and sid

23、e thrust of the rollers on the cage,which in turn will result in damage to the guiding surfaces and the cage itself, due to the friction generated. This problem is not encountered when balls are used as rolling elements,but such guides have the disadvantage of even lower stiffness and load-carrying

24、capacity when compared with roller linear guides (point contact instead of line contact).,Rolling-contact bearings. Ball bearings Figure 1-4(top)Shows two views of one quarter of the most widely used type of modern ball bearing It consists of four parts:an inner race b, an outer race c the balls d a

25、nd a separator or retainer which is also called a cage,Figure 1-4 types of bearings,The races in which the balls roll have grooves with radii of curvature slightly greater than the radius of a ball. Some bearings are assembled by moving the inner race radially,inserting the balls,centering the inner

26、 race,spacing the balls uniformly,and applying the retainer that holds the balls loosely in all equally spaced position. Other bearings have a notch in one of the races that permits more balls to be inserted. With more balls,the bearing can carry more radial load R (Figure 1-4 top) but less thrust l

27、oad T on account of the notch.,Although the bearing in Figure 1-4 (top) is classified as a radial ball bearing,it has considerable thrust or axial load capacity. The thrust capacity T can be increased by extending the races to sections ff so that the groove in the outer race is deeper on the left si

28、de and the groove in the inner race is deeper on the right side;some angular-contact bearings are made like this. If all of the load on a bearing is axial,an axial-thrust bearing can be used. This is simply two grooved washers with balls between them.,Roller bearings These bearings have rollers inst

29、ead of balls between the races. The rollers may be cylindrical,tapered,or spherical. Cylindrical roller bearings have rollers with a length to diameter ratio of about one and run in cylindrical racesOne of which may have retaining shoulders;they cannot carry a thrust load. Needle bearings have long,

30、small-diameter rollers and may be installed with or without retainers and with or without races Needle bearings cannot carry thrust loads,but they have the highest radial load,Tapered roller bearings (Figure 1-4)have a high load capacity and when used in opposed pairs can carry thrust loads in eithe

31、r direction. Spherical roller bearings have either convex or concave rollers in both single and double rows. All these bearings have a self aligning ability obtained by grinding either the outer or inner race spherical. The most commonly used type of spherical roller bearing is the double-row bearin

32、g with convex rollers.,Words and Expressions,Exercises,Serf-Aligning Ball Bearings Self-aligning ball beatings normally have two rows of balls that roll in a common spherical race in the outer ring, as shown in Figure. Because of this design, the inner ring, with the ball complement, can align itsel

33、f freely around the axis of the shaft. When the shaft bends under load, the bearing-will follow the deflection of the shaft without resistance. Self-alignment also contributes to smooth running by neutralizing the effect of the balls wobbling in the grooves. This bearing is therefore particularly us

34、eful in applications in which it is difficult to obtain exact parallelism between the shaft and housing bores.,Thrust Ball Bearings The simplest form of thrust ball bearings is shown in Figure. In this type of bearing, a single row of balls set in a separator runs in two similar grooves formed in th

35、e stationary and revolving rings. The revolving ring is fixed to a shaft. These grooves are usually shallower than the groove in a deep-groove radial ball bearing. Thrust ball bearings are designed to carry pure thrust load and if any radial load is present, separate radial bearings must be used. Fr

36、om the viewpoint of both economics and simplicity of design, it is wise to seek the use of an angular-contact bearing where both radial and thrust loads are present,Clutches,Lesson three,Words and Expressions,A clutch is a device for quickly and easily connecting or disconnecting a rotatable shaft a

37、nd a rotating coaxial shaft . Friction clutches Friction clutches have pairs of mating conical,disk,or ring-shaped surfaces and means for pressing the surfaces together The pressure may be created by a spring or by a series of levers locked in position by the wedging action of a conical spool.,On a

38、spring-loaded clutch the operator,by controlling the rate at which the spring pressure is applied to the clutch,can regulate the speed of clutch engagement and the torque applied to the driven shaft. There is always some slippage,however,and the efficiency of a friction clutch can never exceed 50 pe

39、rcent;i.e., during a clutching operation at least one-half of the input energy is lost by friction in the clutch and produces heat.,The friction surfaces on clutches should have a high coefficient of friction and be able to conduct the heat away rapidly. These properties are difficult to obtain in a

40、 single material and for this reason,one of each pair of mating surfaces is usually metallic,while the other is either leather, cork,or an asbestos-based facing riveted to a metal plate. Some friction clutches are run dry,while others operate in oil . Dry clutches have a higher coefficient of fricti

41、on than wet clutches,but the oil helps to carry off the heat.,Figure l-5 shows a half-section of a multiple-plate disk clutch in which input member 2 is keyed to the driving shaft 1 and output member 3 is keyed to the driven shaft 4.,The friction plates b have external gear teeth or splines that mat

42、e with teeth on the inside of member 2,while friction plates c have internal teeth that mate with external teeth on member 3. Plates b can slide axially in 2,while plates c can slide axially on 3. The clutch is engaged by moving the spool to the left,which,by a wedging action, rotates the lever abou

43、t the pivot p and creates a force that squeezes the plates together,Fig. 1-5 Multiple-plate disk clutch,Magnetic clutches Magnetic-particle clutches have an annular (ring-shaped) gap between the driving and driven members that is filled with powdered iron and graphite. When a magnetic field is induc

44、ed across the gap by a direct-current control coil,the iron particles form chains across the gap and transmit a torque that depends on the strength of the field. Controlled by varying the current, the load can be engaged smoothly and there is no slippage when the clutch is transmitting the torque fo

45、r which it was designed.,Exercises,Automatic clutches:Automatic, smooth engagement is obtained with a centrifugal clutch. The friction shoes are segments of rings that are pivoted to or carried around by the driving member. As the drivers speed increases the shoes gradually make firmer and firmer co

46、ntact with the internaI cylindricaI surface of the driven member. Centrifugal clutches allow the driving motor to reach operating speed,before being loaded. They are particularly useful on internal-combustion engines driving chain saws,and on helicopter rotor drives. They eliminate the need for a ma

47、nually operated clutch,and the engine cannot stall when overloaded,since the clutch will slip when the speed drops below that necessary to create the torque required by the load.,An overruning clutch transmits torque in one direction only and permits the driven shaft of a machine to “freewheel”, or

48、keep on rotating when the driver is stopped. Modern designs utilize the wedging action of rolls or sprags (struts) with rolls , a series of wedge-shaped pockets,with a roll in each,is formed between the periphery of one member and the inside of a ring on the other member. Rotation of either member i

49、n one direction causes the rolls to roll up the incline in the pocket and lock the members together. In sprag clutches a number of especially shaped rocking wedges are located in the annular space between concentric circular races, and are kept in contact with both races at all times by means of a s

50、pring,Ball screw and nuts,Lesson Four,chapter One Mechanics Components,Words and Expressions,Precision ball screw assembly are mainly used in various kinds of precision NC. Machine-tools,machining center,autodrafting machines,measuring devices and precision instruments where exactly positioning and

51、continuous controls are required.,Conventional ball screw assembly are utilized extensively in save labour and sensitive gearing,such as adjustments for hospital doors,beds and chairs,starters,lifting jacks,opening and closing of valves, metallurgical machinery,civil-architectural machining,atomic r

52、eactors, submarines,satellite,trackers and steering gears for automobiles and tractors,etc.,The development of NC machine tools (see Volume 3) demanded among other things the provision of feed and guiding systems free from stick slip and backlash. This required the availability of low-friction drivi

53、ng and guiding elements. Rolling guideways and recirculating-ball screw systems are the outcome of efforts in that direction. A recirculating-ball screw system may be regarded as a rolling guide on a shaft like all other screw nut systems,it serves to transform rotary motion into linear motion,or vi

54、ce versa. The main areas of application are for feed mechanisms and in measuring machines,The principal positive features of a recirculating ball screw are: (a) very high mechanical efficiency due to rolling friction (up to 95) (b) no stick-slip; (c) when correctly designed almost no wear and hence

55、a very long life; (d) able to be pre-loaded; (e) adequate stiffness The only disadvantage which must be mentioned is their low damping property.,As the balls rotate in the guiding grooves of the screw and nut,they are subjected to a tangential or circumferential movement. Hence it is necessary to pr

56、ovide for the return of the balls into the system. Figure 1-6 shows in the upper diagram screw with a ball-return track at the end of each thread pitch. The advantage of this design lies in its small physical size. The unfavorable angles of the ball inlet and exit bring about the disadvantage of une

57、ven rolling effects.,In the lower part of the diagram a ball screw is shown on which the ball return is effected over the full length of the nut by means of a return tube. By suitably shaping the tube,the balls leave and return to the load-bearing part of the nut tangentially,resulting in an even an

58、d shock-free running condition and permitting high rotational speeds to be used. An important disadvantage of this design is the ease with which the return tube may be damaged;this would binder the ball motion and thus lead to further damage of the screw-nut assembly.,Ball screw and nut with return

59、channel at end of a pitch,Ball spindle with return tube at end of nut,Fig. 1-6 Recirculating ball screw and nut systems,If a high degree of stiffness andor freedom from backlash is required, then the ball screw and nut system must be pre-loaded. To this end the nut must be in two parts (double nut). Figure 1-7 shows such a system. In the upper part a double nut with an external thread is shown. The pre-load is applied by turning one half of the nut:subsequent keying then prevents it turning in the opposite direction. In the lower half of the diagram calibrat

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