Mechanical Engineer''''s Reference Book 2011 Part 11 pptx

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

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

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 ( B l o ) 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 = pitch diameter of larger pulley (mm),

d = pitch diameter of smaller pulley (mm),

All prime movers fitted with centrifugal clutches, dry or fluid couplings or electronic 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

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

-

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 d s and therefore not recommended for cast iron pulleys

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

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):

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

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

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

10/24 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

Figure 10.59

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

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,

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

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

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

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

10/28 Power units and transmission

Table 10.7 General formulae for spur gears (without addendum modification)

(dimensions in mm)

Pitch circle diameter

(reference circle diameter) ( d )

Overall diameter (d,)

Diametral pitch (not used with metric gears) (p,)

Module (denotes tooth size) (m,)

0.25mn

Crest Addendum circle

Power transmissions 10/29

This can be seen from the illustration in Figure 10.66 of two meshing gears of differing diameters As an example we can give each gear a physical size:

Gears used in clocks have already been briefly mentioned and there is currently a growing interest in small mechanisms

For fine-pitch gears (m, < 1.0 mm) some manufacturers

tend to increase the tiphoot clearance by reducing the dia-

meter of the dedendum circle For machine-cut gears these

can be stated as follows

Standard dedendum = 1.4 X m , for fine-pitch gears with

modules below 1.00

Dedundum = 1.25 X rn, for fine-pitch gears with

modules 1.00 and above For general considerations the dedendum can be 1.25 x m,,

which is taken from the British Standard rack Variations in

these values for the tooth profile in the past gave rise to some

confusion The reason is that experience and method of

manufacture dictated to individual manufacturers the best

values for them to accept and, not unnaturally, different

manufacturers took different values

Obviously, when choosing gears of different overall dia-

meters ii is important that the tooth sizes are identical, and

this can be expressed by the module which is the reference

circle diameter jd) divided by the number of teeth ( z ) , i.e

m, = dlr

J

angle

Reference circle ( d )

such as may be used in instrumentation, etc These interests

have focused attention on the need for a standard tooth

configuration for small gears While these mechanisms cannot

be regarded as power transmissions, they may be of interest to

readers since the British Standards Institution have put

forward recommendations in BS 978 (imperial) and BS 4582

(metric module) which discuss the use of involute tooth

profiles together with a double-arc profile for very small

pinions with between six and 12 teeth The scope of these

British Standards relates to four accuracy grades for involute

spur, helical and crossed helical gears having modules of 1 or

finer (diametrical pitches finer than 20 in imperial units)

Examples are:

Class A Scientific instruments and control systems

Class B Navigational instruments and high-speed compo-

nents of control systems where quietness and

smooth running are essential and machine tool

speed control

Class C General-purpose instruments, counters, clockwork

mechanisms

10.2.2.3 Helical gears

Helical gears have several advantages over straight-cut spur

gears One is that shafts can be inclined at any angle from 0"

(parallel) to 90" (crossed axis helicals with small load capac-

ity), the helix being adjusted to suit One advantage of parallel

axis helicals is that, unlike the spur gear in which the load is

taken over the width of the next tooth instantaneously (unless

the tooth has tip relief), with the helical gear, the teeth mesh

gradually so that at no time is the full width of the tooth fully

engaged This eliminates some of the shock loading associated

with straight teeth and makes for much quieter running The

cost of producing helical gears is not the disadvantage that it

used to be Modern designs of gear-cutting machines can

handle helical gears with the same ease as spur gears

One drawback to the helical gear is the side thrust arising

from the helix angle This can be overcome by either using

thrust bearings or a double helical gear, often referred to as a

herringbone gear This may be cut from the solid or two

separate gears used, one with a left-hand helix and the other

with a right-hand helix Some authorities suggest that these

gears should be avoided, as spur gears are as good for

low-quality drives with the single helical being superior for

precision drives

For shafts lying parallel to each other one gear will have a

right-hand helix and the matching wheel a left-hand helix On

both gears the helix angle of generation will be the same With

shafts at 90" to each other both gears will have the same hand

(either left- or right-hand helix) Thrust reactions are shown in

Figures 10.70 and 10.71 With shafts arranged at less than 90"

to each other, if the sum of the helix angle of both gears equals

the shaft angle, the hand will be the same on both gears If,

however, the helix angle of one gear is greater than the angle

between the shafts, then each gear will be handed (see Figure

10.70)

10.2.2.4 Bevel gears

Bevel gears are used to connect shafts whose axes lie at an

angle to each other, although in most applications the shafts

are at right angles The tooth profile is basically the same as

used for spur gears except that the tooth gets progressively

smaller as it approaches the apex of the projected cone

Normally the teeth are straight cut and radiate from the apex

of the pitch cone, but it is possible to give them curved, skew

or spiroid form Generally, the shafts of conventional bevel

Figure 10.70 Thrust reactions using helical gears on parallel shafts

Figure 10.71 Thrust reactions using helical gears on shafts at right angles

gears intersect, although bevels can be designed to have the pinion offset When such a pinion has radial teeth, the crown wheel will also have straight teeth but offset in relation to the

axis A variation is the hypoid, where the teeth on both gears

are cut on the skew (Figure 10.73), in which situation they will act similarly to helical gears with consequent smoother runn- ing The spiroid gear has curved teeth and, in many cases, can

be likened to an offset worm drive These systems do, however, cause higher tooth pressures and, as a result, it is important that really efficient lubrication is provided

10.2.2.5 Worm drives

Worm drives have a number of advantages, one being that, given the helix angle is around 20" or less, the drive is considered to be unsatisfactory in reverse although not posit- ively irreversible Where the coefficient of friction, which can vary from 0.01 to 0.1 (with indifferent lubrication), equals the tangent of the helix angle, the gear is self-locking and cannot

be turned by the gearwheel However, the coefficient is not accurately predictable, as it can be affected by vibration, the

Helix angle (65") of

one shaft grea'ier than

other shaft angle (45")

: gears are handed

Sum o f helix angles equals shaft angle ' gears same hand

Figure 10.72 Handling of helix with shafts at an angle of less than

90"

'Radius

Figure 10.73 Hypoid gears allowing pinion offset

Chamfer /?$

finish of the tooth surface and, above all the degree and

efficiency of the lubrication For this reascn, if a truly irrever-

sible drive is required it is prudent to fit a brake in the system

Experiments have shown that the efficiency of a worm can be

quite high; the best figures being when the helix angle is about

45" although the rate of increase in efficiency is markedly

slower between 25" and 45" helix angle

Shafts normally lie at right angles with a worm drive but

other angles can be accommodated by adjusting the helix

angle on the worm While the worm can work in conjunction

with a spur gear, the contact area between the teeth is limited

and full ]power cannot be transmitted It is usual for the worm

wheel to' fit closely to the diameter of the worm itself, thus

providing the niaximum surface on which to transfer the load

(see Figure 10.74)

Figure 10.74 Typical worm wheel rim section

Worms can be single-start or multi-start With a single-start worm the velocity ratio between worm and wheel is equal to the number of teeth on the wheel With multi-start worms the velocity ratio can be expressed thus:

Number of teeth on wheel Velocity ratio =

Number of teeth on worm The worm should be kept as small as possible consistent with stiffness needed to avoid deflection, as this will keep down surface speeds and friction BSI recommendations for the design of worms and worm wheels are given in BS 721

10/32 Power units and transmission

10.2.2.6 Gear trains

Internal gears are used in a variety of designs such as reduction

gears and epicyclic units In general, such units use standard

pinions or bevels and have the involute tooth form Figure

10.75 shows a typical epicyclic gear train and Figure 10.76 a

differential unit as used in an automobile for drive to the

wheels

10.2.2.7 Gear materials

Materials are normally selected according to the duties in-

tended for the gears For power transmissions, the physical

properties are critical and selection becomes more a question

of choosing the right steel rather than any other particular

material The exception would be if environmental conditions

dominated the specification For example, in a corrosive

atmosphere, stainless steel or reinforced plastics may be

considered Slow-moving gears at low stress levels will find

cast iron a suitable material while worm wheels are generally

made from phosphor-bronze Plastics gears are widely used

Figure 10.75 Epicyclic gear train

12 teeth

/ -To driving wheel

I ’

Shaft to gearbox

Figure 10.76 Differential gear as used in automobiles

for various mechanisms, but for reliable power transmissions they could be more expensive than a suitable steel They do, however, have the advantage that they are quieter running and have the ability to take up small deformation in tooth profile without causing damage

When choosing a suitable material for gears the questions of first cost, ease of machining, its response to heat treatment

and its behaviour in service must be considered A point to bear in mind is that case-hardened gears should not be used with softer metals such as mild steel

For heat-treatable steels, the addition of nickel tends to increase the hardness and strength with little sacrifice in

ductility Its use as an alloying element produces less distor-

tion due to lower quenching temperature In the case- hardening group, carburization takes place more slowly but grain growth is restricted Chromium increases the hardness and strength over that obtained by the addition of nickel but loss of ductility is greater It refines the grain and imparts a greater depth of hardness Manganese gives greater strength than nickel and a higher degree of toughness than chromium

Vanadium has a similar effect to manganese but the loss of ductility is greater: hardness penetration is also greater but machining is difficult Molybdenum has the property of increasing the strength without affecting ductility For the same hardness, steels containing molybdenum are more duc- tile than any other alloy steel and, having nearly the same strength, are tougher without increasing the difficulty of machining

For spur gears it is common practice for the pinion to be made from a harder material than the mating gear Carbon steel to BS 970 is in wide use in gear units and is of low cost

and offers reasonable wear resistance A Ni/Cr/Mo alloy steel

to BS 970 gives good hardenability and, when through- hardened and tempered, is widely used for pinions and

wheels A slightly less expensive alloy containing CrlMo offers good wear resistance A nitriding steel gives a very hard case but this is not deep enough to sustain continual shock loads A

carburizing case-hardening steel offers a deep hard case but subsequent tooth grinding will be needed, as distortion often

occurs during quenching A direct air-hardening steel is often

used for worms and for volume-production speed reducers When considering case-hardened steel the aim should be to have a core hardness of between 30 and 40 Rc A general run

of hardness for the surface layer after suitable tempering should be in the 55-65 Rc region with general-purpose gears at the lower end and maximum capacity highly loaded precision gears at the high end

10.2.2.8 Securing gear wheels to shafts

Securing the gear wheel to the shaft can be done in a variety of ways The criterion should be that the gear remains square with the shaft that the means of securing can meet the imposed loading without loosening and that it does not unduly weaken the shaft or gear Figure 10.77 shows a number of different ways of securing the gear in small or lightly loaded drives but in many cases the arrangement for securing may be part of an assembly and therefore a special integral arrange-

ment may be devised Friction holds such as a set screw (A in

Figure 10.77) must be carefully considered It would be inexcusable to use this method in, say, an automobile gearbox and for positive engineering applications, keyways and splined shafts are to be preferred

A standard square key (B in Figure 10.77) is ideal for a positive drive in one direction only For very large gears undergoing shock loads, two square keys - a tangential key (Figure 10.78) or a Kennedy key (Figure 10.77) -can be used

Figure 10.77 Methods of securing gear wheel to shaft (B and F are

the preferred engineering soluticns)

I

Type A

3

Taper 1 in 100 (parallel)

Figure 10.79 Kennedy keys

For smaller high-speed gears, splined or serrated shafts, though more expensive to produce, provide a positive drive and can allow, where necessary, some axial movement (see Figures 10.80 and 10.81) There are also a number of propriet- ary devices on the market in the form of a bushing which can

be expanded to grip both gear wheel and shaft

10.2.2.9 Gear units

During the last decade there has been a marked increase in the ranges of standard gearboxes employing spur, helical, bevel and worm gears suitable for a wide range of powers and with

an extensive selection of fixed ratios in single- and multiple- reduction types, with a choice of parallel shafts, right-angled output shafts, co-axial shafts and offset parallel axis shafts A

high degree of standardization has been achieved and inter- changeable components have been developed by many manu- facturers There are now British Standards for many external dimensions, particularly in respect to methods of mounting the units

It is usual to consider the use of motorized units so that a complete package of motor/reduction unit is available requir- ing only the choice of coupling to the driven machine This gives a single form of transmission and provides an economical and efficient package

10134 Power units and transmission

Figure 10.80 Square spline

Figure 10.81 Serrated shaft

10.2.2.10 Lubrication

An essential factor in the lubrication of gearing is the main-

tenance of a fluid film between the surfaces of the gear teeth

By separating the surfaces in this way, there is a reduction in

the degree of contact between the asperities on the mating

parts Inadequate separation leads to scuffing and possibly the

localized welding together of the mating surfaces In practice,

gearing will most often be operating under combined condi-

tions of boundary and hydrodynamic lubrication, which means

that some of the loading will be taken directly by the opposing

asperities and some by the fluid film Choosing a lubricant for

a given duty thus becomes a matter of ensuring that an

adequate film thickness is always present at the mating

surfaces This film thickness should be in excess of the

combined heights of the asperities, and will depend on the

relative velocity of those surfaces, their dimensions and the

viscosity of the oil The major oil companies have considerable

documentation which they will generally make available to

engineers concerned with the selection of the correct lubri-

cant

Surface finish is dependent, within limits, on the method of

manufacture and the material used Lightly loaded gears

hobbed from steel banks will probably have a surface finish of

1.0-2.5 pm (cla) and require no further finish Those intended

for heavier duties will possibly be hardened and tempered,

and the teeth may then need grinding or shaving, which will

produce a surface finish of around 0.13-1.0 pm (cla)

While it may be seen that the higher the viscosity of the

lubricant, the better for providing an adequate film thickness,

a high viscosity also means oil drag or frictional loss in the

transmission system This in itself will raise the operating

temperature and thus reduce the viscosity until an equilibrium

is attained Thus the higher the loading between the teeth, the higher the viscosity of the oil that is needed while the higher the speed, the lower the viscosity needed

In practical terms, most gearing is of the straight-tooth spur

or helical types and can be lubricated with straight oils Helical gears with lower tooth stresses for the same power transmitted would be happy with a lighter, less viscous grade Additives would only become necessary if the gears were loaded beyond their designed capacity or other circumstances dictated a lighter oil Bevel gears, with either straight- or spiral-cut teeth, will have requirements similar to the spur and helical gear, although two additional factors may be relevant One is that the angle between the shafts needs to be accurately main- tained and second, the thrust, particularly with the spiral bevel, may adversely affect the bearings so that bearing lubrication may be the governing factor in a bevel unit Generically, the hypoid gear falls between the spiral bevel and a worm gear The offset pinion produces a high slide-to- roll ratio so that tooth stresses are high This combination of high loading and high rubbing velocity should be met with the use of a full EP (Extreme Pressure) oil Worm gears have the distinction that the relative motion between the worm and worm wheel is virtually all sliding, which generates consider- able heat The lubricant helps to dissipate this heat and, in most cases, the power transmitted by the worm is limited by this temperature rise Worm gear lubricants are mostly straight mineral oils designed to resist thermal breakdown and oxidation

The essence of gear lubrication is to keep apart the con- forming surfaces of mating gear teeth Since this objective is never achieved, gear teeth will always wear in service, and the best to be hoped for is a nominal rate of wear Accelerated wear may be due to abrasive wear conditions in which the surface of the teeth is removed and circulates in the oil, producing additional abrasion and scratching Thus some method of filtering the oil to remove any hard particles should

be considered, although the most obvious way is to ensure that the teeth have as smooth a surface as economically possible Further details are presented in Chapter 9

10.2.2 I 1 Transmission shafts

Shafts used in power transmissions will invariably be either solid or thick-walled tubes In gearboxes and similar assemblies, the shafts will be comparatively short and the design objective will be for these to be made as stiff as possible Torsional stresses are unlikely to be of major con- cern

In many applications a transmission shaft will be machined, will incorporate many different diameters along its length and may contain splines or serrations as well as through-diametric holes All these features add up to stress discontinuities, and therefore adequate attention must be given to avoiding a sudden change of section and to ensure adequate blending radii If the shaft is particularly complicated it is likely that the chief mode of failure will be one of fatigue

For relatively short straightforward shafts where torque is transferred from one end to the other, the stresses are limited

to torsion and bending Standard textbook formulae for solving the working stresses under these conditions exist For more complex shaft geometries, recourse to the computer and finite-element methods will give the best analysis

10.2.2.12 Bearing reactions

When a single-spur gear is mounted o n a shaft and the bearings are assumed to provide simple support, the bearing

With straight-cut bevels there will be an end thrust in both shafts tending to force the gears out of mesh The magnitude

of these thrusts will alter proportionally when curved teeth are used in the bevels

In a worm drive the major load is end thrust in the worm

shaft, its magnitude depending on its helix angle There is also

a side thrust on both worm and worm wheel arising from the frictional force between worm and worm wheel teeth

loads can be assessed by taking moments in terms of the

nominal tooth load This load in ail but the most detailed of

calculations can be taken as the resultant of the tangential load

at the PCD and what can be termed the separation load

tending to force the teeth out of mesh In the simple arrange-

ments in1 Figures 10.82 and 10.83 it can be seen that the major

bearing reaction will be to the tooth load; reaction to the

separation force, S , will be at right angles to the tooth load

With a lielical gear, part of the tooth load will be translated

into axial thrust

Separation force S Normal t o o t h

A disadvantage of the chain drive is that centre distance for sprockets has to be either adjustable or worked on the basis of standard chain pitches Alternatively, a jockey wheel or similar device can be used on the slack side of the chain, although this will generally preclude the drive being reversed Chains need to be adequately lubricated and must work in a clean environment Dust and dirt will quickly wear chains and

Bearing reaction

to load F

A Reaction t o separation

Reaction t o separation force S

Side thrust due t o and component of

friction helix angle

10136 Power units and transmission

Hardened steel bearing surfaces and clearances

n for lubricant

Link plates

n

Bush / Roller Bearing pin

Figure 10.84 Typical section through roller chain (with

acknowledgements to Tribology Handbook, Butterworths)

they will become noisy A section through a typical roller

chain is shown in Figure 10.84

In addition to the standard roller chains, attempts have been

made to design chains to operate even more quietly These are

based on a shaped link plate that rolls on a sprocket tooth

rather than impacting

For 15 000-hour chain life, the selection chart in Figure

10.85 is based on a steady load application with a 19-tooth

sprocket For different numbers of teeth, the relevant selec- tion factor should be included Where impulsive loads are encountered the selection factor should also be applied, irrespective of the sprocket size Tables 10.8 and 10.9 indicate the types of loading likely to be encountered

In general, the smallest pitch should be used, even if it means going to duplex or triplex chains The centre distance should normally be kept to within 30-80 times the chain pitch For large ratio drives the angle of lap on the sprocket should

be not less than 120" Manufacturers' literature usually con- tains the necessary data to establish which chain should be used for a specific task

10.2.4 Shaft couplings

An important element in power transmission systems is the coupling whereby two relating shafts can be joined together For large-diameter shafts revolving at low speeds, the simplest device is a solid flanged coupling but this does not allow for any misalignments in the shafts For smaller installations it would be prudent to introduce a coupling that could cater for small shaft offsets and deviations in parallelism A coupling becomes even more important if one of the shafts is the output from a prime mover where there are inherent vibrations Selecting the right coupling will avoid transmitting these vibrations into the second shaft and its assembly

There are numerous designs of couplings to cater for almost every conceivable condition, and the task of the engineer is to choose the right sort of coupling at the lowest cost commen- surate with performance Torsion stiffness is another factor which should receive consideration The majority of couplings tend to fall into two groups - those that have some flexible

_ I ,

Pinion speeds (revlminl

Figure 10.85 Performance curves for roller chain drives to BS 228: 1984 (with acknowledgements to Tribology Handbook, Butterworths)

Power transmissions 10/37 Table 10.8 Selection factors

Table 10.9 Machinery characteristics

Conveyors and elevators - uniform feed Propeller drives Oilwell machinery

Wire drawing

medium interposed between two halves each of which is

carried by the shafts to be connected, and those that are

mechanically flexible, examples being the internal gear coup-

ling and Hooke joint Some of the many variations are given

below Most manufacturers carry a wide range of variations in

each half of the coupling to allow the use of different methods

by which these can be secured to the shafts (e.g using

standard keys or proprietary shaft locking bushes)

The optimum choice of a flexible coupling for any applica-

tion is the result of a compromise between many factors, and

while performance at minimum cost is important, subsequent

maintenance should also be considered Specifically, the fol-

lowing points should be investigated:

1 Decide if the coupling should be torsionally soft or rigid

2 Consider whether a small amount of backlash is acceptable

3 Calculate the required torque and add in any appropriate

Soft types are generally less expensive

Backlash-free couplings are usually more expensive

service factors For example:

Torque = 9550 x (WN) X k X S

where P = power transmitted (kw); N = rev/min,

k = starting frequency based on maximum number of

1.0 to 1.75 for light even loads

1.25 to 2.25 for irregular shock loading

1.5 to 2.5 for arduous drive conditions

10.2.4.1 Types of couplings

In addition to the standard types given below there are special couplings made to meet specific requirements and may incor- porate the features of one or more of the standard types: for example, telescopic couplings to allow considerable axial movements; quick-disconnect couplings; spacer-type coup- lings to take up any space between the ends of the two shafts; couplings with shear pins which free one half of the coupling when a severe overload is transmitted, etc

Pin couplings These couplings can cater for a wide range of

power ratings by the optimum use of pins ranging in numbers usually from three to 16 The pins are rigidly fixed to one half

of the coupling with the free end terminating in a flexible bush

of rubber or plastics material An example would be the Renold Pinflex (see Figure 10.86)

Flexible disk couplings This type uses steel pins fixed in the

metal half bodies of the coupling to transmit the torque through a flexible disk interposed between the two halves The disk can be of staggered layers of rubberized fabric or a suitable solid polymer such as polyurethane (see Figure 10.87)

Flexible spider coupling The flexible spider coupling trans-

mits the torque through an oil-resistant rubber spider assembled between two metal half bodies In some designs the spider is replaced by separate rubber blocks, manufacturers having their own particular designs to give a positive drive and

to take up angular and linear displacements as well as to absorb any shock loads (see Figure 10.88)

Tyre-type coupling This coupling consists of two half bodies

connected by an external polymer tyre and is available in a

range of shaft sizes to cater for torques from 65 to 1690 Nm,

Bush Flexible t y r e

- H u b m e m b e r H u b member

Clamping disks

Figure 10.86 Section through Pinflex coupling (with

acknowledgements to Renold Gears)

Laminated flexible disk

Figure 10.89 Section through a Renold Uratyre coupling (with acknowledgements to Renold Gears)

each size being able to handle 4" angular misalignment as well

as end-float and axial displacement A typical example is the

Renold Uratyre (see Figure 10.89)

Chain coupling A chain coupling comprises two chain sprockets encircled by a duplex chain and contained within a housing Disconnecting the chain provides a quick and easy means of disconnecting the shafts This type of coupling is not designed to cater for anything other than minimal mis- alignment (see Figure 10.90)

Internal gear coupling Two basic types of internal gear couplings are available, the operating principle using a pair of externally cut gear hubs engaging the teeth of an internally cut gear in the housing The teeth on the hubs are radiused so that the coupling can accommodate limited angular deflections (see Figure 10.91(a)) An alternative is to use one gear hub and to fit the engaging ring on the other shaft (see Figure 10.91 (b))

Figure 10.87 Section through disk flexible coupling (with

acknowledgements to Renold Gears)

Figure 10.88 Section through spider flexible coupling (with

acknowledgements to Renold Gears)

Duplex chain

Figure 10.90 Section through a chain type coupling (with acknowledgements to Renold Gears)

Figure 10.91 Sections through internal gear coupling (a) Renold

standard double-engagement type); (b) Renold single-engagement

type

Oldham coupling This coupling consists of two halves each

containing a diametric tenon placed at 90" to each other and

mating with a centre-floating disk with two mating grooves

This is historically one of the earliest designs of couplings and

will accommodate both angular and axial displacements A

typical example of the small size of the Huco Oldham coupling

is shown in Figure 10.92

Face tooth coupling Face tooth coupling rings may be used

wherever precise indexing or positioning of one shaft to

another is required A pair of rings constitute a coupling for

accurate location capable of transmitting high torque The

mating faces of each ring are machined to produce straight-

sided radial V-teeth which, when meshed together, form a

rigid angular and radial location The rings can be bolted

direct to a flanged member fitted to the ends of each shaft (see

Figure 10.93)

Hooke coupling or universal joint This form of coupling has

long been used in automobiles to accommodate the angular

movement of the carden shaft connecting the gearbox to the

rear axle; it is similarly used in front-wheel drive cars

Basically, the joint consists of two fork members attached to

the ends of each shaft, the fork ends being secured to a centre

Spring coupling These consist of two hubs connected by single or multiple torsion spring elements They can be wound different hands to cater for reversible drives Standard coup- lings can be used for torques up to 900 Nm and different hub fittings are widely available (see Figure 10.95)

Bellow coupling These are usually regarded as more suitable for low-power transmission with standard couplings from, for example, Simplatroll, available to take torque up to 1 Nm They are torsionally rigid, free from backlash and extremely light (see Figure 10.96)

All-metal dry flexible coupling The all-metal construction of this type of coupling avoids the need for any form of lubrica- tion or extensive maintenance High-torsion rigidity and good inherent balance makes the coupling ideal for high-speed

applications In essence, it is similar to the disk coupling

shown in Figure 10.87, except that the centre disk is usually made of layers of thin flexible metal disks

The future for dry membrane couplings is excellent as industry looks more and more for increased machinery life between shutdowns and reduced maintenance services Another trend is towards gas turbine drives for non-generating equipment such as pumps and compressors Gas turbine makers have developed aero-derivatives for industrial applica- tions Here the needs of the couplings will be lighter weight, reduced overhung moments and higher speed and power capabilities Performance monitoring is another area that is developing as rotating equipment operators seek improved plant efficiencies, preventative maintenance programmes and

Two rings (one coupling)

shown disengaged

Rings engaged

I Two extraction holes

Figure 10.93 A TI Matrix Engineering face tooth coupling ring

torque measuring system as an integral part of their Meta- stream flexible couplings

The following (contributed by Flexibox Ltd) will give users and designers an appreciation of the capability and design of all-metal multiple membrane type power transmission coup- lings and, by the application of simple disciplines, obtain the practically infinite life for which the couplings are designed While reference is made extensively to Flexibox Metastream ranges of power transmission couplings, many of the principles and most of the practices can be applied to power transmission couplings in general Flexibox Metastream power transmission couplings have proved their effectiveness in transmitting torque under shaft misalignment in a wide variety of driver/ driven machinery combinations

10.2.4.2 All-metal mebrane couplings

The M, LS and T series couplings are all-metal non-lubricated membrane couplings which require no additional services, have no wearing parts and are easily installed without special tools These couplings accommodate shaft misalignment in deflection of thin metal membranes These are normally stainless steel, although non-ferrous membranes in Monel and Inconel are used for special applications where safety or

corrosion merit particular attention A number of these

membranes are assembled into a pack (membrane bank) according to torque rating of the coupling The membrane bank is (usually permanently) built into a membrane unit In the spacer type coupling a membrane unit is fitted to either end of a spacer piece to produce a spacer unit (transmission unit) The M series range includes a double-bank membrane

Power transmissions 10/41

Figure 10.96 Examples of bellow type shaft couplings (with acknowledgements to Simplatroll Ltd)

Figure 10.95 (a) Examples of torsion spring type couplings; (b) typical

application of torsion spring coupling (with acknowledgements to

Simplatroll Ltd)

unit (MODO) where two membranes banks are permanently

fixed to a central ring, which is effectively a short spacer The

transmission unit is fitted between the driving and driven

flanges of hubs or adaptors on the respective machines The

membrane units and transmission units include spacer-

retention features that prevent parts of the couplings being

thrown if the membranes shear

In the ring form LS and T series ranges a spacer-retention

feature is provided by bushes on the drive bolts These bushes

are shrouded by clearance holes in the coupling flanges and

retain the spacer assembly if the membranes are damaged

This shrouded bush arrangement also provides an emergency/

overload drive facility

they can be dynamically balanced to high qualities and, as there are no wearing parts, this quality will not deteriorate during the life of the coupling, provided a few basic disciplines are observed

Couplings are dynamically balanced to reduce the dynamic loads generated by mass eccentricity and rotation of non- symmetric masses

Concentricity between coupling components and machinery shafts is achieved by close control of spigothecess locations and is maintained by rigid assembly at the interfaces The influences of non-symmetrical masses are minimized by either removing material or adding counterbalance masses Dynamic balancing equipment is used to indicate the magni- tude and position of such corrections

Match-marking of corresponding flanges and match- weighing of replaceable fasteners enable duplication of the quality achieved on balancing machines to be ensured The high-quality manufacturing procedures used by Flexi- box produce couplings that are symmetrical and will rotate concentric with machine shafts The couplings have no wear- ing parts and are torsionally rigid so the balance quality will not change over the coupling life Standard membrane coup- lings are used on most low- and medium-speed applications without dynamic balancing

Coupling ranges such as MHS, TSK and the high- performance ranges for high-speed operation are dynamically balanced according to the needs of the equipment The ultimate speed limit of balanced couplings is dictated by the material strength under centrifugal forces A change of ma- terial (for example, to a high-grade steel such as EN24T or high-strength alloy) can increase the coupling speed capabil- ity

Speed and dynamic balance All-metal membrane couplings Dynamic balancing I S 0 1940, ‘Balancing quality of rotating are the ideal choice for high-speed rotating machinery because rigid bodies’, specifies permissible residual unbalance of rotat-

10142 Power units and transmission

ing components as a function of machinery type and speed of

operation The type of machinery is denoted by a Quality

Grade ‘G’

Thus, a component for a relatively heavy diesel engine

would be balanced to quality grade G16, whereas a compo-

nent for a comparatively lightly constructed gas turbine would

require a balance quality grade G2.5

Although the majority of applications where dynamic

balancing is necessary would be satisfied by quality grade

G6.3, Flexibox has standardized on the higher-quality grade

G2.5 for normal commercial balancing The acceptable resi-

dual unbalance and couple per unit of rotor mass in 8 mmikg

on centre of gravity displacement in micrometres is shown in

Figure 10.97

Normal commercial practice produces a coupling with only

the transmission unit dynamically balanced The hubs or

adaptors are balanced after fitting to their appropriate shafts

as part of the machine rotor assembly by the machine builder

For very high-speed applications and lightweight equip-

ment, Flexibox have supplied couplings balanced to a higher

quality as well as individually balanced hubs and adaptors

The high-performance range is balanced to higher specifica-

tions in line with the needs of high-speed lightweight turbine

drives

Torque and misalignment Power transmission coupling ele-

ments are subjected to various stresses which may initially be

considered separately as steady and cyclic stresses:

Maximum service speed of rotation (rev/min)

Figure 10.97 Unbalance versus speed (with acknowledgements to

Steady stress factors are accommodated in the basic coup- ling design, giving an adequate design margin over ultimate stress capabilities of the membrane material used Maximum torque capacity is usually expressed as a power-to-speed ratio, i.e the coupling rating:

Power Selection: Coupling rating = -

Speed This is usually expressed in kW per 1000 rev/min or HP per

100 rev/min

Maximum axial misalignment capacities of couplings are very generous and alignment within 10% of the coupling’s limit is easily achieved Allowance for the thermal growth of shafts can normally be made without exceeding the coupling’s capacity in the cold and hot dynamic states

Because cyclic stresses have a great effect on coupling life, these must be given more attention

Axial shuttle is not normally a problem on machines where the shaft positions are axially located within the bearing arrangements Moreover, stress levels caused by axial shuttle are low, and Flexibox membrane couplings have a non-linear axial stiffness characteristic which tends to damp out axial exciting vibrations

Occasionally, however (for example, on sleeve bearing motor applications), it may be necessary to move the operat- ing position up the stiffness curve by deliberately adding an axial displacement, thereby inducing a resisting force against the axial excitation Cyclic stresses due to torsional fluctua- tions are usually accommodated by the use of a service factor

in the coupling selection procedure These service factors have been derived from a wealth of experience and knowledge of the torque characteristics of driving and driven machinery:

Power Coupling rating Speed Service factor Max torque = - -

Therefore:

Power x service factor Speed Required rating =

While the service factor effectively reduces the coupling rating by increasing the design margin, the axial and lateral misalignment capacities are unaffected However, because higher speeds mean higher cyclic frequencies, it becomes necessary at very high speeds to reduce the angular (and, consequently, lateral) misalignment limit of flexible couplings according to design and speed

Lateral (or angular) misalignment leads to many more coupling failures than all other causes combined Lateral misalignment is accommodated in an angular deflection of each of the membrane banks in a spacer coupling configura- tion The effects of angular and lateral shaft misalignment are therefore additive in producing cyclic stresses in the coupling

To reduce these stresses within the membrane material capacity, therefore, accurate shaft alignment is crucial A relatively small improvement in angularllateral alignment greatly reduces cyclic stress levels and consequently extends coupling life expectancy Coupling misalignment capacities and ratings given in suppliers’ technical literature should allow for the anticipated stresses due to misalignment and torque simultaneously

10.2.4.3 Flexible coupling ranges

Metastream Flexible couplings are designed to accommodate the inevitable displacement which occurs between the centre lines of two rotating shafts Flexible elements are in the form

Power transmissions 10143

Condition-monitoring couplings Torsionally stiff membrane

couplings have no wearing parts; they need no lubrication or adjustment; they have a predictable high torsional stiffness that does not alter over a period of time and they have accessible low-stressed spacer tubes These features make such couplings ideal for both the train-gauge and phase- displacement torque-measuring systems The coupling is supplied with a factory-assembled transmission unit ensuring dynamic balance integrity and measuring system accuracy throughout the virtually unlimited life of the coupling

Axially split couplings The TSEW coupling is a precision

built, six-link, non-spacer T series coupling with two membrane units connected by an axially split spacer The coupling is designed to allow maintenance of the membrane assemblies without moving either of the rotating machines Shaft separations of only 3 mm can be achieved while allowing

a practical misalignment capacity

Optional features Membrane couplings can be supplied in

spark-resistant designs for hazardous areas Normal atmos- pheric corrosion protection is provided by stainless steel membranes and a phosphated finish on other steel parts For more severe environments, other materials such as titanium aluminium alloys and other types of finishes can be specified For applications that need continuity of drive under overload

or after membrane failure, modifications are available to meet these requirements There are also torque-limiting devices and

overload shear devices as well as an in-situ line-balancing

correction

of membrane banks, usually made of stainless steel or other

corrosion-resistant materials As all flexing occurs within the

membranes, there are no wearing parts and therefore no

necessity for lubrication, adjustment or any other form of

maintenance All Flexibox M, LS and T series membrane

couplings incorporate spacer-retention anti-fly devices

M series ‘spoke form’ membrane couplings The flexible

element of the M series is a bank of spoked membranes

secured rigidly at their inner and outer diameters Designed

for iow-, medium- and high-speed operation, the M series

design meets the AP1 610 specification and is particularly

suitable for process pump applications The axial stiffness of

the M series membrane unit is strongly non-linear, making it

inherently self-damping and therefore ideal for unlocated

rotor motor applications without recourse to end stops

In the event of a seizure or mal-operation of the driven or

driving machinery, the coupling will spin freely after

membrane failure and can therefore be used to protect major

equipment The MHSO Single bank non-spacer coupling

accommmodates axial and angular misalignment only Its use is

limited to such applications as three-bearing systems and

cardan shaft configurations, using one coupling at each end of

long spacer shaft or tube The MHSS single-bank spacer

coupling accommodates axial, angular and lateral misalign-

ments Lateral misalignment capacity is increased by longer

DBSEs (distance between shaft ends) The coupling is used in

most prsocess and industrial machinery, particularly where

there is a need for a shaft gap when changing machine

bearings, seals, etc., without disturbing either machine

The MODO non-spacer double-bank coupling accepts

axial, anguiar and limited lateral misalignment and is used on

close coupled machinery, where some lateral shaft misalign-

ment ha:i to be anticipated

R i n g - f o m tangential wansmission link designs Metastream

‘ T series flexible couplings employ ring-form banks of stain-

less steel membranes to combine a high power transmission/

weight ratio with maximum flexibility and high torsional

stiffness The membranes are arranged to transmit the driving

torque as a pure tensile load The ‘waisted’ form ensures that

the bending and fatigue stresses arising from misalignment are

at a minimum in the critical areas around the driving bolts

This form permits high torque ratings with relatively small

diameters so that the coupling can be used at high speeds

without (exceeding acceptable levels of stress

The T series is sub-divided into the several ranges of

couplings which, between them, offer a wide variety of

capabilities and features required by rotating equipment de-

signers The LS spacer coupling design is an inexpensive

simple arrangement for general industrial applications at low

and medium speeds, with ratings from 2 up to 24 000 kW per

1000 revlmin

High-performance couplings The high-performance range of

Metastream couplings has been specifically designed to meet

the requirements of manufacturers and users of high-

performance rotating equipment and comply with API stan-

dard 671 High-performance coupling speeds can be as high as

30 000 I-evimin Coupling sub-assemblies are dynamically

balanced to a limit of G1.25 I S 0 1940, and assemblies check

balanced to G6.3 The designs are specified for unspaced

turbine and compressor applications at ratings up to 38 MW

per 1000 revimin The inverted hub design allows the coupling

effective centre of gravity to be moved close to the bearing for

reduced overhung moment and minimized bearing loads (see

Table 10.10)

10.2.5 Clutches, freewheels and brakes

Clutches, freewheels and brake units are important compo- nents in transmission systems and can be included as separate items or integrated with other transmission units In the following the various types of clutches and brakes will be described as separate items

In most machinery, the clutch or brake is remote from the operator and consequently they are provided with the means

of remote control These may be electric, pneumatic or hydraulic, and most manufacturers have a range of compo- nents catering for all these alternative means of control For example, a typical air-operated ciutch from Wichita is shown

in Figure 10.98

10.2.5.1 Dog clutches

These are positive-drive components and are normally oper- ated only when they are stationary Various tooth forms are used (see Figure 10.99); (1) straight-cut square teeth, (2) sawtooth formation and (3) gear type radial teeth Because these components are more often regarded as couplings mention has been made of ring-face tooth coupiings in Section 10.2.4 An example of an electromagnetically operated tooth clutch is shown in Figure 10.100

10.2.5.2 Freewheel clutches

These are more often referred to as freewheel, or over- running, clutches or even jamming roller clutches There are two types The first uses either balls or rollers spaced in inclined wedge-shaped spaces around the periphery of the hub (see Figure 10.101) If the speed of the driven shaft overtakes that of the driver, the balls or rollers tend to roll back out of contact with the driven member and a positive drive is

disconnected If the speed of the driver increases beyond the

driven member, the balls or rollers are dragged into contact

10144 Power units and transmission

Table 10.10 Gear coupling versus dry membrane coupling

Up to full replacement and regular oil seals New coupling Frequent new oil seals Dismantle coupling

Lube oils can be tailored to suit specific application for best service, but ‘compromised’

by economic expedient Must be clean and cool Oil must be chemically compatible The oil seal can limit misalignment capacities High

Limited by oil and oil seals (100°C typical) Comparable

High Very efficient use of materials Ideal

Lube oil contamination Progressive Rate is sensitive to the efficiency

of the lube system ‘Wear band’ can reduce misalignment capability unless designed with

‘full tooth engagement’

Plating and oil seals must resist environmental and internal (oil) attack Teeth are exposed to oil

Change with wear

Changes with wear, lube oil path, centrifuging Excessive overload will do permanent damage

By nature Chemical and metallurgical analyses can give clear indication of causes

Some, initially increasing with wear Needs end stop

Needs modification Negligible in ideal conditions But ‘torque lock’ is common and imposes high loads on bearings gears, seals, etc

Manufacturing accuracy is crucial to evenly stressed teeth and shared torque load sharing

Staggeringly complex design calculations lead

to arbitrary and empirical formulae Disintegration and loss of drive function

Competitive Negligible Membrane assemblies Low, even if re-aligning and balancing Membranes are visible

None

Very high Not usually a problem up to 200°C Comparable

Adequate even with thermal growth Very efficient use of materials Standard modification Generally no problem None

Stainless St membrane and phosphated steel parts Paintingispecial materials available for hostile areas

Accurately predictable and consistent High qualities achievable

Consistent over coupling life

Taken by collars to protect against permanent damage

By guard ring designs Membrane fracture pattern point to possible causes

Virtually zero Non-linear axial stiffness gives inherent damping No end stop needed Usually no modification Very low generally, but excessive axial displacement produces high thrust reaction forces

Relatively easy to get right

M series - drive disconnected

LS & T series - drive maintained

with the outer member and the positive drive is established

Balls are only used in very light power applications as they

have only a point contact; rollers, on the other hand, have a

line contact and can be used for substantial torque loadings

Generally, the larger the angle of the wedge, the greater the

roller diameter and hence torque capacity while a small angle

provides a more positive engagement Response is virtually

instantaneous since the rollers are always in contact with the

inner and outer races Thus, taking up the drive is a matter of

breaking the intervening oil film and the natural deformation

of the material under load Rollers are normally energized by

spring and plunger assemblies acting on them in the direction

of the trapping angle In a phased roller clutch, the rollers are precisely located and guided by a cage which is spring ener- gized so that all rollers engage in unison Compared with the individual roller clutch, it can offer more uniform loading of the rollers and a greater torque capacity for a given size

A variation of this type of clutch or freewheel is the sprag clutch in which the space between an inner and outer revolving race is filled with a series of cams or sprags whose major diameter is slightly greater than the radial space between the races (see Figure 10.102) Rotation of one race in the driving direction causes the sprags to tilt, thus transmitting the torque

in full from one race to the other Conversely, rotation of the

Figure 10.98 Typical air-operated clutch (with acknowledgements to

Wichita Co Ltd)

race in the other direction frees the sprags and permits

over-running between the races A tilting force keeps the

sprags in light contact with both inner and outer races and this

can be done using various spring arrangements There is thus

no loss of motion, the driving torque being instantaneously

transmitted between race In general, sprag clutches are able

to transmit greater torques for a given overall size than other

types of freewheel devices

10.2.5.3 Cone friction clutch

The cone clutch (see Figure 10.103) embodies the mechanical

advantage of the wedge which reduces the axial force required

to transmit a given torque In general engineering its use is

restricted to the more rugged applications such as contractors’

plant In a smaller form it is often used in machine tools

10.2.5.4 Plate friction clutch

This can be of single-plate type (see Figure 10.104) or multi-

plate construction (Figure 10.105) Basically, the clutch cons-

ists of friction lining(s) sandwiched between driving and driven

plate(s) Springs usually provide the clamping pressures With

I

inner race

Figure 10.101 The wedging of rollers between inner and outer races

to provide power transmission

teeth

Figure 10.99 Various forms of teeth in a dog clutch

10146 Power units and transmission

Outer race

Inner race Dimension AA

is greater t h a n

dimension BB

Band spring exerting radial force to keep sprags in light contact with inner and outer races

Figure 10.102 Elements in a sprag clutch

Figure 10.104 Section through a typical single-plate friction clutch

Pressure Operating Friction

Driving sleeve Figure 10.105 Section through a typical multi-plate friction clutch

multi-plate clutches the diameter can generally be reduced for

a given torque as against a single-plate clutch Many multi- plate clutches run in oil which helps to conduct away the generated heat

10.2.5.5 Expanding ring friction clutch

This will transmit high torque at low speed and centrifugal force increases the gripping power but adequate clutch with- drawal force must be provided for disengagement (see Figure 10.106)

10.2.5.6 Centrifugal friction clutch

Automatic in operation, the torque, without spring control, increases as the square of the speed Motors with low starting torque can commence engagement without shock A spring control can be added (see Figure 10.107) so that engagement does not take place until the motor has reached a predefined speed (often 75% of full speed)

Power transmissions 10147 Release spring bringing Switch closed for Magnetic field

Wedge in driven member wedge t o dotted line engagement of

/

Two-diameter operating shaft

(moved axially to operate the clutch)

Figure 10.106 Expanding ring type of friction clutch

Retaining Shoe with friction

material

,""k

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

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

and are suited to repetitive starts and stops or controlled

accelerations The same principle can be applied to braking

Figure 10.108 Typical single-plate electromagnetic clutch

Outer field ring

Non-magnetic material

\

Stationary coil and housing

Figure 10.109 Typical multi-plate electromagnetic clutch

For example the Magne range of magnetic particle clutches and brakes from R A Rodriguez consist of only two parts, the inner race called the rotor and the outer race or drive cylinder The space between the members is fi!led with a fine magnetic powder, and when 2 magnetic field is created through a stationary d.c coil the powder forms a link between the two members and torque is thus transmitted With the Magneclutch, both members are rotating to provide trans- mitted torque; with the Magnebrake, the outer member is held stationary, resulting in braking torque Transmitted torque 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

These are generally used for low-torque applications and low speeds They consist of a helical spring arranged to wrap against a drum surface As the grip of the spring increases in proportion to the transmitted torque the helical spring locks the driving and driven drum together When the sleeve is released, the clutch is engaged; holding the sleeve unwinds the spring and this engages the clutch

10148 Power units and transmission

Dynamometer

Magne clutch/brake controller

/

Test motor (a)

Figure 10.111 The principle of fluid coupling (with acknowledgements

to Hansen Transmissions Ltd)

Figure 10.110 (a) Application of Magne particle clutch (with

acknowledgements to R A Rodriguez); (b) typical magnetic particle

clutches (with acknowledgements to Huco Engineering Industries Ltd)

10.2.5.10 Fluid coupling

A very important type of coupling or clutch is that employing a

fluid drive These couplings give the engineer an efficient,

simple and reliably mechanical means of controlling the speed

of the driven machinery at the same time, allowing the use of

comparatively low-cost constant-speed squirrel-cage motors

In addition, they offer the advantage of a no-load start,

smooth and progressive acceleration and protection from

shock loadings

The fluid drive is situated in the drive line between the

motor and driven machine As in all fluid couplings operating

on the hydrodynamic principle, there are only two basic

elements - the impeller and the runner (see Figure 10.111)

The power is transmitted from input to output by the flow of oil between the two elements There is no mechanical connec- tion between them The speed of the output shaft can be varied steplessly between maximum and minimum speeds by adjusting the quantity of oil in the working circuit between impeller and runner To stop the machine, the oil is emptied

from the working circuit and the drive is thus disconnected A

fluid coupling can be used in conjunction with other transmis- sion elements as shown diagrammatically in Figure 10.112

disk

Input and output

Output via flexible coupling

With V-belt pulley

Figure 10.112 Examples of using a fluid coupling in conjunction with other transmission elements

Power transmissions 10149

Couplings

10.2.5.1 I 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 versions than those used in contrac-

tors’ mai:hinery are available and an example of a caliper

brake is shown in Figure 10.116 It can be used for dynamic

braking I;O bring equipment to rest or as a holding brake to

prevent motion

10.2.5.12 Suppliers of couplings, clutches and brakes

Alanco-Alamatic Ltd, Wilton Disk brakes

Street, Denton, Manchester

Figure l(11.113 Examples of band brakes

Flexibox Ltd, Nash Road, Trafford Park, Manchester M17 1SS

Fluidrive Engineering Co Ltd, Broad Lane, Bracknell, Berks RG12 3BH

Hansen Transmissions, Beeston Royds Industrial Estate, Geldern Road, Leeds LS12 6EY

Huco Engineering Industries Ltd, Peerglow Centre, Marsh Lane, Ware, Herts SG12 9QL Renold Gears, PO Box 224, Wentloog Corporate Park, Wentloog Road, Cardiff CF3 SYT

R A Rodriguez (UK) Ltd, Icknield House Eastcheap

Letchworth, Herts SG6 3DF Simplatroll Ltd, Caxton Road, Bedford MK41 OHT

Stieber Ltd, Stieber House, Works Road, Letchworth, Herts SG6 1PF

TI Matrix Engineering Ltd, Brechin, Angus, Scotland DD9 7EP

Twiflex Ltd, The Green

Twickenham, Middlesex TW2 5AQ

Voith Engineering Ltd,

6 Beddington Farm Road, Croydon, Surrey CRO 4XB Warner Electric Ltd, St Helen Auckland, Bishops Auckland,

Co Durham DL14 9AA Wellman Bibby Co Ltd, Cannon Way, Mill Street West, Dewsbury, West Yorkshire WF13 1EH

Wichita Co Ltd Ampthill Road, Bedford MK42 9RD

Fluid couplings

Fluid couplings, gear units, disk and drum brakes, flexible couplings Couplings

Flexible couplings

Electromagnetic particle brakes and clutches Torque limiters, electromagnetic clutches and brakes

Disk caliper brakes, drum brakes, freewheels, couplings

Clutches, brakes, couplings, caliper disk brakes

Disk brakes, flexible couplings, clutches, fluid couplings

Fluid couplings, mechanical couplings, hydrodynamic caliper and drum brakes

Electromagnetic couplings and brakes, wrap spring brakes, freewheels Flexible couplings, torque limiters brakes, clutches

Air-operated clutches and brakes, flexible couplings

Acknowledgements

Sections 10.2.1.2 (V-Belts) and 10.2.1.3 (Synchronous belt drives) were provided by J M Woodcock, Group Product Manager, Indirect Drives at Fenner Power Transmissions, and Section 10.2.4.2 on the Metastream ranges of power transmission couplings was supplied by Flexibox Ltd These contributions are gratefully acknowledged

Further reading

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

Figure 10.114 Example of industrial drum brake (with acknowledgements to Stieber Ltd)

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:

cycloid type gears plus Addendum No 1 (1959) on

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

Figure 10.1 16 Surestop electromagnetically released caliper brake

system (with acknowledgements to TI Matrix Engineering)

Mott, R L., Machine Elements in Mechanical Design, Merrill,

New York

Neale, M J., Tribo/ogy Handbook, Butterworths, London

Watson, H J., Modern Gear Production, Pergamon, Oxford

BS 228: 1984 ( I S 0 60-1982) Gears for electric traction (in-

cludes guidance for tooth profile modification)

BS 436: 1986: Parts 1, 2 and 3 Spur and helical gears

BS 4582 Fine pitch gears (metric module)

Part 1: 1984 Involute spur and helical gears

Part 2: 1978 Hobs and cutters

BS 3027: 1968 Dimensions of worm gear units

BS 3696 Specification for master gears

Part 1: 1984 Spur and helical gears (metric module)

BS 4185 Machine tool components

BS 5265: Part 1: 1979 Mechanical balancing of rotating

bodies API 671 Special purpose couplings for refinery services

(American Petroleum Institute)

PD 3376 (1984) Addendum 1 to BS 978: Part 2 Double

circular arc type gears

PD 6457 (1984) Guide to the application of addendum modi-

fication to involute spur and helical gears Further information may be obtained from the British Gear Association, St James’s House, Frederick Road, Edgbaston, Birmingham B15 1JJ