Mechanical Engineers Reference Book 12 Part 11 ppsx

Power transmissions 10119 The pulley surfaces and especially the groove sidewalls should be machined such that the surface finish is a maximum of 3-2 pm when determined by the method described in BS 1134. Pulleys must be balanced either statically or dyna- mically, depending on the rim speed and ratio of face width to diameter. BS 3790 contains comprehensive balancing informa- tion. In general, for all pulleys operating below 10 m/s rim speed, and for pulleys with face widths half or less of the diameter operating below 20 m/s rim speed, static balancing is adequate. Pulleys employing split-taper bushings are most convenient for installation and removal in that they avoid the need for interference fits, keys, etc. A Taper-Lock pulley manufac- tured by J. H. Fenner & Co. Ltd is shown in Figure 10.55. pL _- OD Figure 10.53 Multi-groove pulley cross section. PL = pitch line, OD = outside diameter, h = groove depth from PL, b = distance between OD and PL, a’ = groove angle, e = centre-to-centre of grooves, f = edge of pulley to centre of first groove, g = top width of groove, dp = pulley pitch diameter, /p = pitch width of V-Belt Figure 10.54 Narrow V-Belts (better known as wedge belts) have a narrower profile than classical V-Belts, with a relative height of approximately 0.9. There is a more even distribution of the tension forces between the reinforcing cords and thereby a higher power rating compared to classical V-Belts of the same top width Figure 10.55 A Fenner Taper-Lock bushing for securing a large pulley to a shaft Table 10.2 ll Belt rp b h e f g (mm) (“1 dP (mm) section (mm) (mm) (mm) (mm) (mm) Y 5.3 1.6 4.7 8.0 7.0 32 463 6.2 36 >63 6.3 z-SPZ 8.5 2.5 9.0 12.0 8.0 34 480 10.0 38 >80 10.2 A-SPA 11.0 3.3 11.0 15.0 10.0 34 4118 13.1 38 >118 13.3 B-SPB 14.0 4.2 14.0 19.0 12.5 34 4190 16.6 38 >190 16.9 c-SPC 19.0 5.7 19.0 25.5 17.0 34 4315 22.5 38 >315 22.9 D 27.0 8.1 19.9 37.0 24.0 36 4500 32.3 38 >500 32.6 10/20 Power units and transmission Selection of belt drives BS 3790: 1981 contains all the infor- mation necessary to design a drive; power ratings, standard pulley diameters, service factors, correction factors for belt length, arc of contact and speed ratio. Similar details are usually given in the catalogues of manufacturers, some of whom operate a technical advisory service. The number of belts required for a particular drive can be obtained using the power table for the selected type and size of belt. The power rating given in the table for the particular pulley diameter and shaft speed is multiplied by the correction factors for belt length, arc of contact, etc., and then divided into the design power (actual power X service factor) of the drive. If the result of the division contains a fraction, the next whole number of belts is used. Power-correction factors for industrial service These are based on prime movers classified into two separate groups, with reference to Driven Machinery classified into four se- parate groups as detailed below. Table 10.3 gives the factors for periods of up to 10 hours, 10 to 16 hours and over 16 operational hours per day. The four separate groups of driving machines are defined as follows: Light duty - Agitators for liquids, blowers and exhausters. Centrifugal pumps and compressors. Fans up to 7.5 kW. Light-duty conveyors. Medium duty - Belt conveyors for sand, grain, etc. Dough mixers. Fans over 7.5 kW. Generators. Line shafts. Laundry machinery. Machine tools. Punches, presses and shears. Print- ing machinery. Positive-displacement rotary pumps. Revolv- ing and vibrating screens. Heavy duty - Brick machinery. Bucket elevators. Exciters. Piston compressors. Conveyors (drag-panscrew). Hammer mills. Papermill beaters. Piston pumps. Positive-displacement blowers. Pulverizers. Sawmill and wood-working machinery. Textile machinery. Extra heavy duty - Crushers (gyratory-jaw-roll). Mills (ball- rod-tube). Rubber calenders, extruders, mills. Table 10.3 Service factors for V-Belt drives For the above four groups (1) for speed-up and reversing drives multiply the factor given in Table 10.3 by 1.25, except where high torque is not present on starting. (2) If idler pulleys are used, add the following to the service factors: (a) idler pulley on slack side, internal, 0; (b) idler pulley on slack side, external, 0.1. Power ratings Table 10.4 shows typical power ratings for each of the belt sections. The ratings are based on the range of motor pulley diameters normally associated with each section and the speeds are for the faster shaft. The values are only a guide and can vary considerably and it is prudent to consult the Standards or manufacturers' catalogues for a precise selection. Normally, pulleys should be chosen which will give a belt speed in the 15-20 m/s speed range and are of adequate diameter in relation to the motor bearings (see Table 10.4). Minimum motor pulley diameter Table 10.5 shows the mini- mum pulley diameter suitable for British metric electric mo- tors, to BS 5000: Part 10: 1978. The diameters were calculated to give a minimum bearing life (Blo) of 12 000 hours, and a tight to slack side tension ratio of 5 was assumed (180" arc of contact). All dimensions are in millimetres. Smaller diameters can be used but the drive end load should be calculated and referred to the motor manufacturer. Arc of contact correction factor The arc of contact x on the small pulley can be calculated from the following formula (see Table 10.6): (D - d) X 60 C x 180 - where x = angle of contact, D = pitch diameter of larger pulley (mm), d = pitch diameter of smaller pulley (mm), C = centre distance (mm), F = arc of contact factor. Driven machines group Electric motors A. C. - star delta start D.C. - shunt wound lnternal combustion engines with four or more cylinders. All prime movers fitted with centrifugal clutches, dry or fluid couplings or electronic soft-start devices Electric motors A. C. - direct-on-line start D. C. - series and compound wound Internal combustion engines with less than four cylinders Prime movers not fitted with soft- start devices 10 and Over 10 Over 16 and 10 and Over 10 Over 16 and under to 16 continuous under to 16 continuous incl. service incl. service Light duty 1.0 Medium duty 1.1 Heavy duty 1.2 Extra heavy 1.3 duty 1.1 1.2 1.1 1.2 1.3 1.2 1.3 1.2 1.3 1.4 1.3 1.4 1.4 1.5 1.6 1.4 1.5 1.5 1.6 1.8 Power transmissions 10/21 Table 10.4 Pulley Power (kW) at motor speeds Belt diameter section (mm) 2880 1440 960 SPZ SPA SPB SPC 67 140 100 200 160 315 224 560 2.11 7.72 5.03 16.93 14.35 18.70 - - 1.24 4.40 3.06 10.31 9.00 23.75 16.60 - 0.89 3.09 2.22 7.32 6.50 17.37 12.70 53.30 Y z A 20 50 50 90 75 I25 E 125 200 C 208 400 D 355 560 0.04 0.19 0.26 0.60 1.42 3.63 3.96 7.82 7.80 - 0.02 0.11 0.16 0.36 0.91 2.24 2.72 5.90 7.49 18.20 21.20 - 0.01 0.08 0.12 0.28 0.66 1.61 2.02 4.35 5.76 15.50 19.30 35.30 Note. The values are for 180" arc of contact on the small pulley. Interpolation can be used for speeds between those shown. The presence of a dash indicates that the pulley rim speed is above 40 ds and therefore not recommended for cast iron pulleys. Table 10.5 Nominal Motor power (kW) motor speed (rev/min) 3.0 4.0 5.5 7.5 11.0 15.0 18.5 22 30 37 45 2880 1440 960 Table 10.15 X0 F X0 F X0 F 180 177 174 1.000 0.99 0.99 0.98 0.97 0.97 0.96 160 0.95 157 0.94 154 0.93 151 0.93 148 0.92 145 0.91 142 0.90 139 0.89 136 0.88 133 0.87 130 0.86 127 0.85 123 0.83 120 0.82 Nore: Arcs of contact below 120" should not be used without confirmation of the drive details by the belt manufacturers 10122 Power units and transmission V-Belt formulae Let R = speed ratio C = centre distance (mm) L = pitch length of belt (mm) d = pitch diameter of small pulley (mm) D = pitch diameter of large pulley (mm) V = velocity or speed of belt (m/s) F = arc of contact correction factor K = service factor E = belt length factor N = number of belts required R = prime mover speed + driven machine speed V = d x revimin of small pulley + 19.100 C = A + .\/(Az - B) where A = L/4 - 0.3925 (D + d) and L = 2C + (D - d)’/4C + 1.57 (D + d) B = (D - d)*/8 Actual power X K Basic power per belt X F X E N= Note: Although contemporary practice uses pitch dimensions for all calculations, in the past it was common to define classical belts by inside length. In the event of only the inside length of a belt being known, a conversion to pitch length can be made by adding the following constants (dimensions in millimetre units): A B C D 35 43 56 79 Example Determine the basic drive equipment for a piston pump running at 1150 rev/min and driven by a 1440 rev/min, 22 kW electric motor, star delta starting 12-hour day duty, approximate centre distance 730 mm. 1. Service factor = 1.3 2. Minimum motor pulley = 140 mm 3. Speed ratio = 1440 t 1150 = 1.25:l 4. Choose standard pulleys 160 and 200 mm 5. By observation it can be seen that a 160 SPB pulley running at 1440 rev/min transmits 9.00 kW 6. Belt length required = 2 X 730 + (200 - 160)’ t 4 x 730 + 1.57 (200 + 160) = 2026 mm (SPB 2020 will suffice) (200 - 160) X 60 7. Arc of contact = 180 - = 177” 730 :. Factor = 0.99 8. From BS 3790, belt length factor for SPB 2020 = 0.93 22 X 1.3 9.00 x 0.99 x 0.93 9. N= = 3.45 (say, 4 belts) Installation of V-Belts When fitting it is necessary to move the motor towards the driven pulley so that the belts may be placed in their grooves by hand. The use of a lever of any kind to force the belts onto the pulley can damage the load-bearing cords leading to premature failure. The accepted method of belt tensioning is by the application of a force normal to the belt spans, at the span centre, to achieve a stated deflection. This method is fully described in both BS 1440 and BS 3790, and also in manufacturers’ catalogues and installation instructions. The high performance of modern belts, especially wedge, can only be realized by proper tensioning and this is particularly important in the early life of the drive when bedding-in and initial stretch are taking place; nothing damages belts more rapidly than the heat generated by slip. Where an adjustable centre distance cannot be arranged it is necessary to use a jockey pulley tensioning device. With classical belts this may be either a flat-faced pulley running on the outside of the belts or a grooved pulley running on the inside. For wedge belts only the latter should be used. In either case, it should be positioned so as to preserve the arc of contact on the powered small pulley and any adjustment to the service and arc of contact factors, occasioned by its use, made to the design calculations. When multi-belt drives are installed, matched sets of belts, coded for length, must be used to ensure correct load sharing. When replacing belts always order a matched set and do not mix old and new belts. Finally, pulleys should be properly aligned by normal workshop methods and the drive fitted with a ventilated guard for safety and to allow heat dissipation and air calculation. Raw-edge V-Belts Recent years have seen the development of the raw-edge V-Belt. These are available with a smooth flat underside or a cogged underside and are manufactured by accurately cutting cured sleeves to the required section dimen- sions. Raw-edge V-Belts have no textile case, and this, together with a cogged underside, reduces resistance to bend- ing and allows them to operate on smaller pulley diameters than the conventional V-Belt. However, when cogged belts are used in larger pulleys the contact area and therefore the power-transmission capability are somewhat reduced. Raw-edge V-Belts are normally manufactured in the wedge belt sections but they are also available from some manufac- turers in the classical sections. They are commonly used as fan belts for cars but have become of growing importance in the industrial market. 10.2.1.3 Synchronous belt drives Both flat belts and V-Belts lose a very small amount of speed (less than 1%) due to belt ‘creep’ (a condition not to be confused with slip) which is due to the change in belt section and tension as it moves around the pulley. If absolute synchro- nization is required then some type of geared drive is called for. The idea of cogged, rubber driving belt for synchronous power transmission originated with the Singer Sewing Machine Company in America. The aim was to maintain register of the different moving parts of the machines without the possibility of oil contamination, The idea became a reality in 1940 and the use of synchronous belts spread to other small machines and instruments. This concept was developed and applied to other machinery and became more generally ac- cepted during the 1950s. As with chain, the tooth pitching became standardized and the early types were based on the inch system of units. There are five pitches generally available: XL, L, H, XH and XXH. XL is generally restricted to small business machines such as electric typewriters and photocopiers and XXH tends to be uneconomical for the power capacity, leaving L, H and XH in general industrial use. The teeth have an involute shape the same as gears to ensure smooth, rolling contact as the belt enters and leaves the pulley. Tooth form and size are covered by BS 4548. Figures 10.56 and 10.57 show the tooth profile and dimensions for L and H pitch. Because stable length is essential for synchronous belts they were originally reinforced with steel. Today glass-fibre rein- forcement is common and aramid is used if maximum capacity is required. The load-carrying tension numbers are moulded into a very thin layer of neoprene (synthetic rubber). To this are moulded the uniformly spaced and pitched neoprene teeth. The facing material is a layer of nylon fabric, providing Power transmissions 10123 L pitch Figure 10.56 H oitch I Figure 10.57 a wear-resisting surface for the entire running surface of the belt and its teeth. Figure 10.58 illustrates the typical compo- nents of a timing belt. Depending on the application, timing belts have consider- able advantages over chains, gears, V-Belts and flat belts due to one or more of the following features: 1 Owing to the use of a fibre-glass cord the timing belt has no stretch whatsoever in service, and this in itself eliminates the necessity of expense on automatic take-up devices and/or periodic maintenance. It also permits installation in other- wise inaccessible locations. Fixed-centre drives become possible. Except gears, all other forms of indirect transmis- sion require periodic take-up. 2 The timing belt drive requires no lubrication and this allows for very substantial economies in initial drive design since oiltight housing and gear cases, seals, lubrication lines and accessories are all completely eliminated? while, at the same time, maintenance costs are also drastically reduced. In many industries such as food handling, strict process restric- tions do not permit the use of lubricants in close proximity to the products being processed. 3. The timing belt drive allows for positive synchronization and this feature is daily becoming of more importance with the greatly increased use of automation, computerization and the necessity for very accurate, synchronized industrial drives. 4. Because of the very thin cross section, timing beits are extremely flexible and will operate efficiently over smaller pulleys than those used with comparable V-Belt or flat belt drives. Since arc of contact is not as criticai a feature in timing belt drive design, larger ratios and shorter centre distances can be easily accommodated, ensuring consider- able saving in space and weight. While arc of contact is not a critical design feature, it is most important, in order to gain the full advantage of belt width, to note that the belt teeth in mesh with the pulley grooves must not be less than 6. When the belt teeth in mesh are 5 or less the shear strength of the tooth becomes the critical factor in design, and this invariably results in an increase in belt width. Synthetic neoprene compound (strong and flexible) opposite twist Figure 10.58 10/24 Power units and transmission 5. The very thin section ensures that the heat generation when the belt is flexing around the pulley is kept to an absolute minimum; furthermore, there is no creep or slip to gen- erate heat. The belt profile also allows for very high belt speeds of up to 60 m/s, although drives of above 30 m/s must be carefully considered because of pulley material. Timing pulleys Standard timing pulleys are normally pro- duced from steel and cast iron, and most manufacturers follow a similar coding system consisting of numbers and letters. The first numbers indicate the number of grooves in the pulley, the letter represents the pitch of the grooves and the final number the belt width that the pulley accepts. Therefore, the code symbol 24H200 represents a timing pulley with 24 grooves, ;-inch pitch and accepts a 2-inch wide belt. Pulleys are also recognizable by ‘type’, which refers to the particular design of pulley. All timing pulleys up to and including 48 grooves in L and H pitch are supplied with flanges. Even on perfectly aligned pulleys, a standard cons- truction timing belt will ‘track’, and it is for this reason that one pulley (generally, the smaller of the two) is flanged to prevent the timing belt ‘walking off‘ the drive. Figure 10.59 shows a typical flanged pulley. Unlike any other type of drive, the pitch diameter of the timing pulleys is so arranged that it is actually in the centre of the flexing part of the timing belt where the load-carrying cords are situated. As mentioned previously, because of this, the pitch diameter of the timing pulley is always greater than its 0.d. Figure 10.60 shows the basic dimensional details. HTD drives Recent modifications of traditional trapezoidal tooth profiles to more circular forms offer a more uniform load distribution, increased capacity and smoother, quieter action. These newer synchronous belts with rounded curvili- near tooth design are known as HTD, which stands for High Torque Drive. Figure 10.61 shows a comparison between the standard involute belt and the newer HTD curvilinear design and illustrates the different stress patterns. The HTD belt was developed to handle the higher torque capabilities normally associated with chain. The new design allowed, for the first time, metric pitched drives, and the standard pitch dimensions are 3 mm, 5 mm, 8 mm and 14 mm. Figure 10.62 shows dimensional details of 5,8 and 14 mm pitch belts. Both the belts and pulleys are manufactured in similar materials to the standard timing belt range. As the belt is fully metric the designation is straightforward. For example, in 1610-14M-85 mm, the first figure indicates the pitch length in Flared steel flange / - \. /! Pullev Ditch circle Figure 10.60 vv / J/ belt pitch line // Figure 10.61 (a) Standard involute belt tooth profile showing loading concentrated at the point of contact: (b) HTD curvilinear design showing improved contact and substantial root stress distribution Figure 10.59 Power transmissions 10125 Pitch rcle 5 rnm HTD I 2.06mm 5 mm. 3.8 mm I 8 rnm pi-tch 14 mm pitch II Figure 10.62 millimetres, followed by the metric pitch and lastly the belt width. The belt pitch length is the total length (circumference in millimetres as measured along the pitch line). The theore- tical pitch line of a HTD belt lies within the tensile member (see Figure 10.63). The belts are available in a range of standard lengths up to 4500 mm pitch length and a range of widths from 9 mm to 125 mm. 10.2.1.4 Miscellaneous belt drives In addition to the flat belts and V-Belts described above, there are also V-link belts made up from a number of separate links fastened together to form an endless belt. With these, access to pulley areas necessitated by the use of endless belts does not apply. Second. since belt length can be adjusted by increasing Figure 10.63 or decreasing the number of links, fixed pulley centres can be used. In general, V-link belts are more expensive than the endless belt but some economic advantages may be gained by holding a stock of links rather than a variety of endless belts. When flexing round a pulley, V-link belting does not suffer distortion as does the solid V-Belt; adjacent links slide over one another and there is little or no internal stress generated and in consequence, lower heat. Thus smaller-diameter pulleys can be used. While most of these belts are made from various polymers in combination with fibre reinforcements, there are also all-metal belts. These are made from thin metal strips ranging from carbon steel through beryllium copper to stainless steel, titanium and, in the case of high temperatures, Inconel. The belt is perforated with holes and the pulleys can have teeth of various shapes, ranging from round or rectangular pegs to formed teeth. These belts are not in common use but offer potential in new projects. 10.2.1.5 Manufacturers Graton and Knight Ltd, Warwick Road, Boreham- wood, Herts WD6 1LX J. H. Fenner & Co Ltd, Marfleet, Hull HU9 5RA BTL Ltd, Hudson Road, Leeds LS9 7DF Pirelli Transmissions (UK) Ltd, Arthur Drive, Moor-Farm Industrial Estate, Kidderminster, Worcs The Gates Rubber Co. Ltd, Heathhall, Dumfries, Scotland DG1 1QA Extruded polyester V-belting Nycor flat belting Round section polyurethane belting (&;in dia.) V-belting Wedge belting Synchronous belts Link belts and special section belts Timing belts Synchronous belts 10126 Power units and transmission 10.2.2 Gears and gearing Gearing is an essential part of most power transmission systems and, wherever possible, the use of ready-prepared units is recommended. Gear design and manufacture is a highly specialized venture, and success can only be bought at the price of experience. Noise, vibration and short life are some of the penalties to be paid for gears imperfectly designed and manufactured. An ambitious research programme involving a further in- vestment of E8 million has been approved by the government without which it is believed that much of the UK gear industry would decline significantly. The programme is the result of several years of planning by the BGA (British Gear Associa- tion) Gear Research Council which has determined and prioritized the industry's research needs and established where the research might be carried out. The programme relates to four main technological themes: gear materials, gear design, gear lubrication and gear manufacturing and metrology. It is expected that it will develop to include projects in other areas of mechanical power transmission technology such as clutches and flexible couplings. The programme will be flexible to cater for the changing needs of the industry and as such, indicates the prudency of buying-in ready-made gears. This programme is timely, as a deal of confusion exists in the mind of many engineers regarding gear design and selec- tion. It appears to be centred first, on the change from imperial to metric working and second, the introduction of new geometry considerations. It must also be recognized that the majority of manufacturers' literature and technical data is still given in imperial dimensions. This is primarily to cater for spares and replacements, although most companies cover metric gears which are not direct replacements for imperial- dimensioned gears. As part of the engineering commitments of the BGA, new teaching modules are being developed in conjunction with the University of Sheffield. In the following, formulae have been given using descriptive terms together with the new symbols from the teaching modules (where these are known) in parentheses. It is, of course, recognized that the use of standard gear units may not always be possible but the guiding principle is that, wherever possible, use standard bought-out manufac- tured gears of gear units. The cost of cutting, grinding and finishing is likely to be expensive with any new in-house operation. However, it is important that basic aspects of gear design are understood so that the limitations are recognized. Other matters of significance include methods of securing gears to their shafts, their lubrication, their size in relation to their duties and the selection of appropriate materials. 10.2.2.1 Tooth profile The profile of a gear tooth must be chosen bearing in mind the following: 1. All the gears must mate and mesh with a smooth uniform action. 2. The tooth must have a section sufficiently strong for the applied loads. 3. The tooth must be free from weakening undercuts. 4. The tooth will mesh at the correct shaft centre distance. 5. The profile of the teeth offers no manufacturing difficul- ties. 6. The geometry provides an adequate tooth overlap. The involute curve provides the most widely used profile for gear teeth although there are other profiles such as the cycloid and a variety of profiles found in horological designs. There has also been a revival of the basic Russian Novokov gear, which never found favour in the West until Westland Heli- copters Ltd recently redeveloped the profile under the name of conformal gears. In industry, the involute profile has been the subject of intensive design and manufacturing studies and had enabled manufacturers to provide silent, accurate and long-lasting gears while the use of vacuum-melted steels has removed the dangers of inclusions, and peening and honing have improved surfaces. Westland adopted the conformal tooth form in a parallel shaft gear configuration because:* 1. They are more tolerant than involutes to the large out-of- plane shaft misalignments experienced in high power-to- weight ratio aircraft transmissions. This is explained by the differences in contact geometry (see Figure 10.64) misa- lignment resulting in localized concentration of the narrow line contact of the involute form compared with an inconse- quential axial movement of the elliptical conformal con- tact. Contact stresses would thus be increased in involute teeth but unaffected in conformals. 2. Power losses in conformal teeth are lower than in equiva- lent involute gears (particularly a planetary set) due to the lower sliding velocities and increased surface separation. 3. Lubricant film generation benefits from the greater en- training speeds - an order of magnitude higher than involutes because conformal contact traverses a large pro- portion of tooth length during rotation of one tooth pitch. 4. Conformal gears have proved to be more tolerant to tooth imperfections than involutes, whether these be surface damage or variations in long-wave surface finish character- istics within manufacturing tolerances. 10.2.2.2 Involute profile An involute curve can be constructed by tracing the end of a cord unwound from the periphery of a circular disk (see Figure 10.65). The contour of the involute curve is governed only by the diameter of the disk from which it is developed. As there is no limit to the length of an involute curve, in practice, the best portion to meet working conditions has to be chosen. Under working conditions, the contact between two teeth at the pitch point is pure rolling contact. Either side of that point, the contact is sliding and the rate of sliding constantly varies. Standard gear tooth forms are obtained using cutters of standard geometry and corresponding to a basic rack as defined in BS 436: Parts 1 and 2. Gear teeth are sometimes crowned (see Figure 10.67(b)), which is a progressive reduction of the tooth thickness from the middle part towards each end face, in order to ensure the transmittance of the stresses of a flank to its mating flank under the best conditions. The choice of a suitable pressure angle for the basic rack (see BS 436: Part 2) is important, for it governs the thickness of the tooth at the root, the length of contact made by teeth on the flanks of the mating gear and the number of teeth in a small-diameter pinion before tip interference commences. Although pressure angles used in the past varied from le to 20", experience has shown that the generally accepted pressure angle is the British Standard value of 20". As the number of teeth in a gear diminishes, a point is reached where good ~~ *According to a paper presented by Cox and Rees of Westland Helicopters Ltd at a Seminar on 'Transmission technology for propfan and geared fan engines', IMechE Aerospace Division, 1985. Power transmissions 60127 Contac? length 20.7 rnm contact width Involute form Max. 1677 Figure 10.64 Comparison of contact areas and stresses for involute and conformal gears of similar pitch circle diameters and tangential load erence zone whict lead to undesirab cutting I Figure 10.65 Developing an involute curve Figure 10.66 Tooth interference contact between the mating gears cannot be maintained. For a full-depth involute tooth form, the minimum number of teeth is given Iby the expression: 2 -where a is the pressure angle (2Oq Sin2 a :. Minirnum number of teeth = 2/Sin2 20 = 2/0.342* = 17.09 In practice this would mean. say, 17 teeth. but with adequate radius at the tip of the tooth the minimum could be reduced to 14 without undercutting the roots of the teeth (see Figure 10.66). Table 10.7, used in conjunction with Figures 10.47 and 10.68, indicates some of the general terms and formulae used in connection with the design of gears and gearing. For efficient running it is important that correct meshing of teeth is ensured, and with bought-out gears this comes down primariiy to establishing the correct centre distances for the shafts. Tolerances will depend on size and duty, and values are given in BS 436: Parts 1 and 2. The addendum modification consists of shifting the profile of the gear teeth to compensate for deflection under load and for manufacturing errors, and this involves certain limiting values which are summarized in British Standards PD 6457. [...]... from the British Gear Association, St James’s House, Frederick Road, Edgbaston, Birmingham B15 1JJ Fuels and combustion Eric M Goodger 11. 2 General fuel types 111 3 11. 3 Major property overview 11. 5 Combustion 11/ 14 11. 5.1 Fundamentals 11/ 14 11. 5.2 Applications 11/ 16 111 3 ... double circular arc type gears Part 3 Gears for instruments and clockwork mechanisms: bevel gears Part 4 Gears for instruments and clockwork mechanisms: worm gears Part 5 Fine pitch gears: hobs and cutters BS 2519: 1976 Glossary of gears Part 1 Geometrical definitions Part 2 Notation BS 4582 Fine pitch gears (metric module) Part 1: 1984 Involute spur and helical gears Part 2: 1978 Hobs and cutters BS... Figure 10 .111 ) With V-belt pulley Output via flexible coupling Figure 10. 112 Examples o using a fluid coupling in conjunction with f other transmission elements Power transmissions 10149 10.2.5.1I Brakes Many of the principles used in friction clutches can be applied to brakes Large brake units of the type used in contractors’ equipment can be band, caliper disk or drum types (Figures 10 .113 -10 .115 ) Smaller... (with acknowledgements to Stieber Ltd) I I I Figure 10 .115 Example of a caliper disk brake (with acknowledgements to Stieber Ltd) Power transmissions 10151 BS 545: 1982 Bevel gears (machine cut) BS 721: Specification for worm gearing Part 1: 1984 Imperial units Part 2: 1983 Metric units BS 978: 1968 Part 1 Fine pitch gears: involute spur and helical Part 2 Gears for instruments and clockwork mechanisms:... disconnected A fluid coupling can be used in conjunction with other transmission elements as shown diagrammatically in Figure 10. 112 Basic coupling With brake disk Figure 10 .110 (a) Application o Magne particle clutch (with f acknowledgementsto R A Rodriguez);(b) typical magnetic particle clutches (with acknowledgements to Huco Engineering Industries Ltd) 10.2.5.10 Fluid coupling Input and output flange... master gears Part 1: 1984 Spur and helical gears (metric module) BS 4185 Machine tool components Figure 10 .116 Surestop electromagneticallyreleased caliper brake system (with acknowledgementsto TI Matrix Engineering) BS 5265: Part 1: 1979 Mechanical balancing of rotating bodies API 671 Special purpose couplings for refinery services (American Petroleum Institute) Mott, R L., Machine Elements in Mechanical. .. Figure l (11. 113Examples of band brakes Dudley, D W., Handbook of Practical Gear Design, McGraw-Hill, New York Dyson, Evans and Snidle, ‘Wildhaber-Novokov circular arc gears: Some properties of relevance to their design’, Proc Royal Society (1989) Gear Lubrication, BGA Technical Memorandum No 11 Merritt, H E., Gear Engineering, Wiley, Chichester 10150 Power units and transmission Figure 10 .114 Example... is proportional to the strength of the magnetic field A typical application is shown in Figure 10 .110 10.2.5.9 Wrap spring clutch 10.2.5.8 Particle clutches These consist of inner and outer races with the annular space between being filled with magnetic particles When a suitable current is applied the particles lock together with the races and form a drive They can be used when constant slip is required... clutch Figure i (11. 107 Typical machanism of a centrifugal clutch with spring control 10.2.5.7 Magnetic friction clutches These are compact units and operated by a direct magnet pull with no end thrust on the shafts (see Figures 10.108 and 10.109) It i s ideal for remote control For example the Magne range of magnetic particle clutches and brakes from R A Rodriguez consist of only two parts, the inner... Pitch circle diameter (reference circle diameter) ( d ) z Overall diameter (d,) ( z + 2) x m, Diametral pitch (not used with metric gears) (p,) llm, or zld (reciprocal of m,) X m, Module (denotes tooth size) (m,) (number of teeth) ( z ) p,,h or dlz (reciprocal of p n ) dlm, or ( d , x p,) - 2 or d x p n Circular pitch on reference circle (p,) T X Addendum (ha) 1 X m, Tooth thickness pn12 or d 2 p , or 1 . >63 6.3 z-SPZ 8.5 2.5 9.0 12. 0 8.0 34 480 10.0 38 >80 10.2 A-SPA 11. 0 3.3 11. 0 15.0 10.0 34 4118 13.1 38 > ;118 13.3 B-SPB 14.0 4.2 14.0 19.0 12. 5 34 4190 16.6 38 >190 16.9. 0.87 130 0.86 127 0.85 123 0.83 120 0.82 Nore: Arcs of contact below 120 " should not be used without confirmation of the drive details by the belt manufacturers 1 0122 Power units. 560 2 .11 7.72 5.03 16.93 14.35 18.70 - - 1.24 4.40 3.06 10.31 9.00 23.75 16.60 - 0.89 3.09 2.22 7.32 6.50 17.37 12. 70 53.30 Y z A 20 50 50 90 75 I25 E 125 200