Mechanical Design Data Book

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Gyles Elliott
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1 Mechanical Design Data Book

2 Contents:- Design Data Hand Book Friction Clutches Single late clutches 05 Multi late clutches 05 Cone clutches 06 Centrifugal clutches 06 Brakes External Contracting Brakes 08 Internal Exanding Brake 09 Band Brakes 0 Thermal Considerations 3 Belt Drives Geometrical Relationshis Analysis of Belt Tensions 3 Condition for Maximum Power 3 Selection of Flat Belts from the Manufacture s Catalogue 3 Selection of V-Belts 5 4 Chain Drives Roller Chains 0 Geometrical Relationshis 0 Power Rating of Roller Chains Srocket Wheels 4 5 Rolling Contact Bearings Stribeck s Equation 5 Equivalent Bearing Load 6

3 Load Life Relationshi 6 Selection of Bearing from the Manufacture s Catalogue 7 Selection of Taer Roller Bearings 3 Design for Cyclic Load and Seed 38 Bearing With a Probability of Survival Other Than 90 Percent 38 6 Sliding Contact Bearings Effect of Temerature on Viscosity 39 Hydrostatic Ste Bearing 40 Energy Losses in Hydrostatic Bearing 40 Reynold s Equation 4 Raimondi and Boyd Method 4 Temerature Rise 43 Bearing Design Selection of Parameters 44 7 Sur Gears Standard System of Gear Tooth 45 Force Analysis 50 Beam Strength of Gear Tooth 47 Effective Load on Gear Tooth 48 Estimation of Module Based on Beam Strength 50 Wear Strength of Gear Tooth 50 Estimation of Module Based on Wear Strength 5 Gear Design for Maximum Power Transmitting Caacity 5 8 Helical Gears Virtual Number of Tooth 5 Tooth Proortions 53 Beam Strength of Helical Gears 54 Effective Load on Gear Tooth 54 Wear Strength of Helical Gears 55 9 Bevel Gears Force Analysis 57

4 3 Beam Strength of Bevel Gears 58 Wear Strength of Bevel Gears 59 Effective Load on Gear Tooth 60 0 Worm Gears Proortions of Worm Gears 6 Force Analysis 64 Friction in Worm Gears 64 Strength Rating of Worm Gears 65 Wear rating of worm gears 67

5 4 Notations:- FRICTION CLUTCHES D outer diameter of friction disk. d inner diameter of friction disk. intensity of ressure. P total oerating force. ( t f M torque transmitted by friction. z number of airs of contacting surfaces, for single late clutch zone. (z number of lates. µ coefficient of friction. a intensity of ressure at the inner edge. α semi cone angle. r d radius of the drum. r g radius of the centre of gravity of the shoe in engaged osition. m mass of each shoe. P cf centrifugal force. P s Sring force ω running seed. (Rad/sec ω seed at which engagement starts. (Rad/sec

6 5 Single Plate & Multi Plate Clutches Uniform ressure theory P π ( D 4 ( M t f Pz μ 3 ( D ( D d 3 d d 3 Uniform wear theory a d P π ( D d Pz M t f μ ( D + d 4 (

7 6 Cone Clutches Uniform ressure theory P π ( D d μpz ( D d ( M t f 3sinα ( D d Uniform wear theory a d P π ( D d μpz M f ( D 4 sin ( d t + α Centrifugal Clutches mω rg Ps 000 μmr M ( t f g r d z( ω ω 000 Note: - here z number of shoes.

8 7 Notations:- Brakes E total energy absorbed by the brake. K.E kinetic energy absorbed by the brake. P.E otential energy absorbed by the brake. m mass of the system. I mass moment of inertia of the rotating body. k radius of gyration. v,v Initial and final velocities of the system ω,ω Initial and final angular velocities of the body M t braking torque. θ angle through which the brake drum rotates during the braking eriod. K. E m( v v K. E I( ω ω K. E mk ( ω ω P. E mgh E M t θ

9 8 External Contracting Brakes Block brake with short shoe M t μnr Where M t Braking Torque R Radius of the Brake Drum μ Coefficient of Friction N Normal reaction N lw Where Permissible ressure between the block and the brake drum l length of the block w width of the block R R X Y μn ( N P ( a μc P b N Pivoted block brake with long shoe P h P max cosφ 4R sinθ θ + sin θ

10 9 M t R X R Y μr wmax sinθ Rwmax (θ + sin θ μ Rwmax (θ + sin θ Internal exanding brake μmaxrw[ 4R( cosθ cosθ h( cos θ cosθ ] M f 4sinφmax Rwh[ ( θ θ ( sin θ sin θ ] M t M n μr max max sinφ max w(cosθ cosθ 4sinφ M M f P (Clock wise rotation of the brake drum C M n M f P + (Anti clock wise rotation of the brake drum C 0 0 φ 90 when θ > n max 90 0 max θ θ < 90 φ when max Where max maximum intensity of ressure. μ coefficient of friction.

11 0 M f moment due to friction. M n moment due to normal force. M t elemental torque due to frictional force. R radius of the brake lining. w face width of frictional lining. Band Brakes P tension on the tight side of the band. P tension on the loose side of the band. θ angle of wra (rad. M t torque caacity of the brake. R radius of the brake drum. M t ( P P R P Rw P max Rw intensity of ressure. w width of the frictional lining. Differential band brake. P a b e ( μθ l

12 Thermal Considerations Δ t E mc Where ( C 0 Δ t temerature rise of the brake drum assembly E total energy absorbed by the brake m mass of the brake drum assembly c secific heat of the brake drum material

13 Belt Drives GEOMETRICAL RELATIONSHIPS Oen belt drive ( sin 80 C d D s α ( sin 80 C d D b + α C d D d D C L 4 ( ( π Cross belt drive ( sin 80 C d D b s + + α α C d D d D C L 4 ( ( π

14 3 Analysis of belt tension P P mv mv e fα (For flat belts P P mv mv e fα sin( θ (For V-belts Power transmitted ( P P v Condition for maximum ower transmission v 3 P i m SELECTION OF FLAT BELT FROM THE MANUFACTURES CATALOGUE ( kw max F ( kw a Where (kw max ower transmitted by the belt for the design urose

15 4 (kw actual ower transmitted by the belt F a load correction factor Tye of load F a (i Normal load.0 (ii Steady load, e.g. centrifugal ums-fans-light machine tools-conveyors. (iii Intermittent load, e.g. heavy duty fansblowers-comressors- recirocating ums-line.3 shafts-heavy duty machines (iv Shock load, e.g. vacuum ums-rolling millshammers-grinders.5 Arc of contact factor α s (degrees F d HI-SPEED FORT 0.08 kw er mm width er ly kw er mm width er ly

16 5 Standard widths of the belt are as follows 3-Ply Ply Ply Ply ( kw ( kw For HI-SPEED belt, For FORT belt, corrected max F d Corrected kw rating Corrected kw rating 0.08v ( v (5.08 SELECTION OF V-BELTS Dimensions of standard cross-sections Belt Section Width W(mm Thickness T(mm Minimum itch diameter of ulley(mm A B 7 00 C D E

17 6 Conversion of inside length to itch length of the belt Belt section A B C D E Difference between itch length and inside length (mm Preferred values for itch diameters (mm

18 7 Number _ of _ belts ( transmitted _ ower _ in _ kw F kw _ rating _ of _ belt F F d l a Where F a correction factor for industrial service F correction factor for arc of contact d F correction factor for belt length l

19 8

20 9 L i Belt section A B C D E F d α s (Degrees

21 0 Chain Drives Roller Chains Dimensions and breaking loads of roller chains ISO chain number Pitch (mm Roller diameter d (mm Width b (mm Transverse itch t (mm Breaking load for single strand chain (kn 06 B B B B B B B B B B Geometric Relationshis n z Velocity ratio, i n z zn Average velocity, v Length of the chain, L Ln Number of links in the a z + z z z chain, L n + + π a Where a centre distance between the axis of the driving and driven srockets.

22 a z + z + + z z z z Ln Ln 8 4 π POWER RATING OF ROLLER CHAINS P kw v 000 Where P allowable tension in the chain (N v average velocity of chain

23 ( kw _ to _ be _ transmitted kw rating of chain K K K s Where K s service factor Multile strand factors ( K Number of strands K

24 3 Tooth correction factor ( K Number of teeth on the driving srocket K

25 4 SPROCKET WHEELS

26 5 Rolling Contact Bearing Stribeck s Equation C 0 P + P cos β + P3 cos β + δ cos β δ δ δ P P C0 P M 3 ( Where, 5 5 M [ + ( cos β + ( cos β ] C 0 Static load δ,... δ radial deflections at the resective balls. β 360 z Where z is number of balls z M is ractically constant and Stribeck suggested a value of z M 5 for C 0 zp 5

27 6 P kd Where d is, the ball diameter and factor k deends uon radii of curvature at the oint of contact and on the modulii of elasticity of the materials. Stribeck s Equation kd z C 0 5 Equivalent Bearing Load P XF r + YF a Where, P equivalent dynamic load F r radial load F a axial or thrust load X and Y are radial and thrust factors resectively and there values are given in the manufactures catalogue. Load Life Relationshi C L P Where L bearing life (in million revolutions C dynamic load caacity (N 3 (for ball bearing 0/3 (for roller bearing

28 7 Relationshi between life in million revolutions and and life in working hours is given by 60nLh L 6 0 Where L h bearing life (hours n seed of rotation (rm Selection of bearing from manufacture s catalogue X and Y factors for single-row dee groove ball bearings F a C F F a r e F F a > X Y X Y r e e P XF r + YF a

29 Dimensions and static and dynamic load caabilities of single row dee groove ball bearings. Princial dimensions (mm Basic load ratings(n Designation d D B C C

32 3 Dynamic load caacity L C P

33 3 Selection of Taer Roller Bearings F a 0.5Fr Y Where Y is the thrust factor Equivalent dynamic load for single row taer roller bearings is given by P P Fr when a 0.4F + YF r ( F F a r e when ( F F > e a r Dimensions, Dynamic caabilities and calculation factors for single row taer roller bearing d D B C Designation e Y X X B X B

34 X B B X TEE X T7FC TED B X

35 TED T7FC B X T5ED TEE T7FC B X TED T7FC T4FE

36 B X TED B X TED T4CB X TEE X X

37 X X

38 37

39 38 Design for Cyclic Load and Seeds 3 3 Σ Σ N BP P e Bearing With a Probability of Survival Other Than 90 Percent b e e R R L L log log Where b.7

40 39 Sliding Contact Bearing Effect of Temerature on Viscosity

41 40 Hydrostatic Ste Bearing The following notations are used in the analysis, W Trust load R 0 outer radius of the shaft R i inner radius of the shaft P i suly of inlet ressure P o outlet or atmosheric ressure h 0 fluid film thickness Q flow of the lubricant μ viscosity of the lubricant Q W πp h 6μ log i π P i e 3 0 R R 0 i R log 0 e R R R i 0 i Energy Losses in Hydrostatic Thrust Bearing ( kw Q( P P i 0 (0 6 ( kw ower loss in uming 4 4 μn ( R0 Ri ( kw f h0 ( kw ower loss due to friction f

42 4 ( kw ( kw + ( kw t ( kw t total ower loss Reynold s Equation h x 3 + h x z 3 f h 6μU z x Raimondi and Boyd Method l d Dimensionless erformance arameters for full journal bearings with side flow ε h 0 φ c S r f c Q rcn s l Q s Q max π 0 _ _ π 0 _

43 _ ½ π 0 _ _.0 0 ¼ π 0 _ _.0 0 c R-r Where c radial clearance (mm R radius of bearing r radius of journal e ε c Where e eccentricity ratio, ε eccentricity ratio ε h 0 c Where h 0 film thickness

44 43 h 0 c is called the minimum film thickness variable The Sommerfed number is given by S r c μn Where n s journal seed unit bearing ressure The Coefficient of Friction Variable (CFV is given by r ( CFV f c Where f is the coefficient of friction ( kw Frictional ower f 6 0 The Flow Variable (FV is given by Q ( FV rcnsl Where l length of the bearing Q flow of the lubricant s πn Temerature Rise 8.3( CFV Δt ( FV Δt Tav Ti + s fwr

45 44 Bearing Design Selection of Parameters

46 45 Sur Gears The itch circle diameter is given by d mz Centre to centre distance, mn ( z + zg a z g Here transmission ratio i z n n g Standard System of Gear Tooth Choice.00 (referred 5.00 Choice Addendum ( h a (m Dedendum ( h f.5m Clearance(c 0.5m Tooth thickness.5708m Fillet radius 0.4m

47 46 M t ( kw πn t m d t P r P t tanα Pt P N cosα Number of Teeth Force Analysis z min sin α Pressure angle ( α z min (Theoretical z min (Practical Face Width (3m<b< (m In reliminary stages of gear design, the face width assumed as ten times of module.

48 47 S b Beam Strength of Gear Tooth mbσ Y b Values of the Lewis form factor Y for 0 0 full deth involute system z Y z Y z Y Rack 0.484

49 48 Effective Load on Gear Tooth (For ordinary and commercially cut gears made with form cutters with v<0m/s 3 C v 3 + v ( For actually hobbled and generated gears with v<0m/s, 6 C v 6 + v (3 For recision gears with shaving, grinding and laing oerations and with v>0m/s, 5. 6 C v v The itch line velocity is given by πd' n v The effective load between two meshing teeth is given by Cs Pt P eff C v n the final stages of gear design, when the gear dimensions are known, the errors secified and the quality of gears determined, the dynamic load is calculated by the equations derived by Prof. Sotts. The effective load is given by P eff ( Cs Pt + Pd where Pd is the dynamic load Deending uon the materials of the inion and the gear, there are three equations for the dynamic load. ( Steel Pinion with steel gear: en z br r Pd 530 r + r (

50 49 ( C.I Pinion with C.I gear: enz br r Pd 3785 r + r ( (3 Steel Pinion with C.I Gear enz br r Pd 360 r + 0.9r ( e sum of errors between two meshing teeth (mm e e + e g where e error for inion e error for gear g Tye of driven machines Electric motor Source of ower Turbine/Multi cylinder engine Single-cylinder engine Generators-feeding mechanisms-belt conveyorsblowers-comressors-agitators and mixers Machine tools-hoist and cranes-rotary drives-iston ums-distribution ums Blanking and shearing resses -rolling mills-centrifuges-steel work machinery

51 50 Estimation of Module Based on Beam Strength 60 0 m π 6 znc ( kw C ( fs v s b S m 3 ut Y Wear Strength of Gear Tooth 3 K σ ( E E sinα cosα.4 c +

52 5 S w bqd z g Q z z g K Exression for the load stress factor K can be simlified when all the gears are made of steel with a 0 0 ressure angle. in this secial case, E α 0 E N mm 0 σ c 0.7(9.8( BHN N mm where BHNBrinell Hardness Number. Therefore, BHN K Estimation of Module Based on Wear Strength 60 0 m π 6 z ( kw C ( fs 3 s b n Cv QK m Gear Design for Maximum Power Transmitting Caacity S w P d P P t d S w

53 5 P n m n P cosψ mcosψ m n normal module m transverse module a tanψ cosψ d tanα zm n cosψ n tanα mn ( z + z a cosψ ω z g i ω z g Helical gears Where iseed ratio for helical gear Suffixes and g refer to the inion and gear resectively a is the centre to centre distance between two helical gears having z and z as the number of teeth. The normal ressure angle is usually 0 0. z z 3 cos ψ Virtual number of teeth

54 53 Tooth roortions In helical gears, the normal module m n should be selected from standards. The first reference values of the normal module are m n (mm,.5,.5,,.5,3,4,5,6,8 and0. The standard roortions of the addendum and dedendum are, Addendum ( h a mn Dedendum ( h f. 5mn Clearance ( c 0. 5mn Addendum circle diameter d a is given by z d a m n + cos ψ Dedendum circle diameter d f is given by d f z mn. 5 cosψ π m n b sin ψ This is the minimum face width. Force Analysis t r Tangential comonent Radial comonent a Axial or thrust comonent t cosα n cosψ a t tanψ

55 54 r t tanα n cosψ mt t d Beam strength of helical gears S b m σ Y n b Effective load on gear tooth M t ( kw πn P t M d P eff t Cs Pt C v C s service factor (from table C v velocity factor The velocity factor, 5. 6 C v Dynamic load is given by v

56 55 P d en z br r 530 r + r P ( C P + P cos cosψ eff s t d α n S b P eff ( fs Wear strength of helical gears S Q w bqd K cos ψ zg z + z g zg Q z + z g for internal helical gear Q z z g g z K σ c sinα n cosα n E.4 + E

57 56 α Normal ressure angle (0 0 n K BHN S w P eff ( fs

58 57 Bevel Gears D r b cosγ z z cosγ tan γ tan Γ z z z z π γ + Γ g g The cone distance A0 is given by A 0 D D + g Force Analysis r m D bsin γ Where r m radius of the inion at the mid oint along the face width b face width of the tooth

59 58 P t M r m t P s P t tanα Where P t tangential or useful comonent which is erendicular to the lane of the aer. P s the searating force between the two meshing teeth Pr Pt tanα cosγ P P tanα sinγ a t Beam Strength of Bevel Gears S b Where teeth mbσ by b A 0 Sb beam strength of the tooth m module at the large end of the tooth b face width σ ermissible bending stress ( S 3 b Y Lewis form factor based on formative number of A 0 cone distance M t Pt D face width of the bevel gear is generally taken as (0 m or whichever is smaller ( A 0 3 ut

60 59 b (0 m or ( 3 A (Whichever is smaller 0 WEAR STRENGTH OF BEVEL GEARS Buckingham s equation S w bqd K Where S w wear strength b face width of gears Q ratio factors d itch circle diameter of the formative inion K material constant d r b S Q w z 0.75bQD K g z + z cosγ g tanγ (Buckingham s equation σ c sinα cosα + E Eg K.4 When inion as well as the gear is made of steel with ressure angle, the value of K is given by BHN K

61 60 M t EFFECTIVE LOAD ON GEAR TOOTH ( kw πn P t P eff M D t C s C P v t C s service factor (from table Tye of driven machines Electric motor Source of ower Turbine/Multi cylinder engine Single-cylinder engine Generators-feeding mechanisms-belt conveyorsblowers-comressors-agitators and mixers Machine tools-hoist and cranes-rotary drives-iston ums-distribution ums Blanking and shearing resses -rolling mills-centrifuges-steel work machinery C v velocity factor The velocity factor for cut teeth is given by

62 6 6 C v 6 + v For general teeth, 5. 6 C v Dynamic load is given by en z b r r Pd 530 r + r r,r Radii of the inion and gear resectively b Axial width of the gear blank r r D D eff g bsinγ bcosγ P + ( Cs Pt Pd Stress in gear tooth due to bending S P ( fs b eff Stress in gear tooth due to itting Sw Peff ( fs v

6 Worm Gears Notations:- z number of starts on the worm z number of teeth on the worm wheel q diametral quotient m module d itch circle diameter of the worm d a outer diameter of the worm d a outer

63 6 Worm Gears Notations:- z number of starts on the worm z number of teeth on the worm wheel q diametral quotient m module d itch circle diameter of the worm d a outer diameter of the worm d a outer diameter of the worm wheel d itch circle diameter of the worm wheel l lead of the worm x axial itch of the worm a the centre distance i the seed ratio. F the effective face width l the length of the root of the worm gear teeth. r Proortions of Worm Gears

64 63 d q m l x z d mz x π m l πmz a m( q + z

65 64 i z z F m ( q + l r ( d a + csin d a F + c Force Analysis ( P t tangential comonent on the worm ( P a axial comonent on the worm ( P r radial comonent on the worm ( P t M d ( P a ( P t ( P r ( P t t ( cosα cosγ μ sinγ ( cosα sinγ + μ cosγ sinα (cosα sinγ + μ cosγ Friction in worm gears v s rubbing velocity v itch line velocity of the worm v itch line velocity of the worm wheel v π d ( 60 ( πd n v s (60000 cosγ ( cosα μ tanγ η ( cas α + μ cotγ n 000

torque on the worm wheel X b, X b seed factors for the strength

66 65 ( M ( M Strength Rating Of Worm Gears t t ( t 7.65X 7.65X b b S b S b ml r ml d r d cosγ cosγ M, ( M t ermissible torque on the worm wheel X b, X b seed factors for the strength of worm and worm wheel S b, S b bending stress factors for worm and worm wheel

67 66 m module l the length of the root of the worm gear teeth. r d itch circle diameter of the worm wheel γ lead angle of the worm Power transmitting caacity of the worm gear based on the beam strength is given by Where ( t kw πnm t 60 0 M is the lower value between M and 6 ( t ( M t.

67 Wear Rating of Worm Gears ( M t 3 8.64X c S c Y Z ( d.8 m.8 ( M t 4 8.

68 67 Wear Rating of Worm Gears ( M t X c S c Y Z ( d.8 m.8 ( M t X cscyz ( d m ( M t 3, ( M t 4 ermissible torque on the worm wheel X c, X c seed factors for the strength of worm and worm wheel S c, S c surface stress factors of the worm and worm wheel Y zone factor z Thermal Considerations H g 000( ηkw Where H g rate heat generation

69 68 η efficiency of the of the worm gear (fraction kw ower transmitted by the gears H d k t t A ( 0 Where H d rate of heat dissiation k overall heat transfer coefficient of housing 0 walls ( W m C t temerature of the lubrication oil. ( 0 C t 0 temerature of the surrounding air ( 0 C A effective surface area of housing k( t t0 A kw 000( η 000( η kw t t0 + ka

+ + = integer (13-15) πm. z 2 z 2 θ 1. Fig Constrained Gear System Fig Constrained Gear System Containing a Rack

+ + = integer (13-15) πm. z 2 z 2 θ 1. Fig Constrained Gear System Fig Constrained Gear System Containing a Rack Figure 13-8 shows a constrained gear system in which a rack is meshed. The heavy line in Figure 13-8 corresponds to the belt in Figure 13-7. If the length of the belt cannot be evenly divided by circular