Spur Gear Des Mach Elem Mech. Eng. Department Chulalongkorn University

Size: px

Start display at page:

Download "Spur Gear Des Mach Elem Mech. Eng. Department Chulalongkorn University"

Norman Jefferson
5 years ago
Views:

1 Spur Gear Des Mach Elem Mech. Eng. Department Chulalongkorn University

2 Introduction Gear Transmit power, rotation Change torque, rotational speed Change direction of rotation Friction Gear + + Slip Less slip Small gear Pinion (usually driving) Large gear Gear

3 Gear tooth nomenclature (1) Center distance Center distance + + Same transmission + + Pitch circle Pitch surface Depend on the types of gears Pitch cylinder + The pitch circle is a theoretical circle upon which all calculations are usually based; its diameter is the pitch diameter.

4 Gear tooth nomenclature () Circular pitch (CP) Diametral pitch (DP) Module (m) = π D/z = z/d (inch.) = D/z (mm) D = pitch dia. z = number of teeth m = 5.4/DP CP DP = p

Module and tooth size Module For metric Diametral Pitch For inch Size gears Pressure angle Size gears 14.

5 Module and tooth size Module For metric Diametral Pitch For inch Size gears Pressure angle Size gears Module sizes shown are converted inch sizes Standard module โมด ลเล อก 1โมด ลน ยม st choice 1โมด ลน ยม st choice อ นด บสอง โมด ลเล อก nd choice nd choice อ นด บสอง

6 Gear tooth nomenclature (3) Pressure angle (deg.) 14.5 (FD) 0 (FD) 0 (Stub) Addendum a m m 0.8m Dedendum b 1.157m 1.5m m FD: Full depth Stub: Tooth is shorter than FD Tooth height a+b Working depth a 1 +a Top diameter (Addendum dia.) Root diameter (Dedendum dia.) Clearance D o = D+a D r = D-b b-a

Base cylinder is the circle used to construct an involute curve (not a dedendum

7 Involute Curve Gear profile is designed to be involute curve. With this design the velocity ratio of a gear pair is constant all the time. Base cylinder is the circle used to construct an involute curve (not a dedendum circle and cannot be located with the naked eye Construction of an involute curve Involute curve Involute curve Base cylinder

8 Pressure angle (1) φ Line of action (Pressure line) is perpendicular to Contact surface at contact point Line of action (pressure line) line that tangent with the base circles and pass the pitch point During meshing, transmitted force acts along the line of action φ φ Line tangent with the pitch circle r b = r p cosφ Pitch circle φ = Pressure angle (14.5, 0, 5 )

9 Pressure angle () φ Line of action (Pressure line) is perpendicular to Contact surface at contact point Base circle Driven φ φ Line tangent with the pitch circle Pitch circle Driving

10 Velocity ratio ω 1 (rad/s) n 1 (rpm) D 1 z 1 ω (rad/s) n (rpm) D z n D 1 1 m ω = = = n D1 = ω ω z z 1

11 Gear ratio & Center distance (1) Example Center distance 40 mm module 3 mm Velocity ratio 5:1 Pressure angle 0 R=40 + = ω ω = n = D 1 1 m ω = n D1 5 D m ω = = = 1 D1 z z 1 z z 1 Gear dia : Pinion dia 5: Divide the center distance into 5+1 = 6 parts R=00 Each part = 40/6 = 40 mm R pinion = 40, Dia. = 80

12 Gear ratio & Center distance () No. of pinion teeth z = D/m = 80/3 = 6.6 No. of gear teeth z gear = 5 z pinion = 5 7 = 135 choose 7 teeth pinion gear Dia. Pitch D = m z Center distance = (D pinion +D gear )/ 43 (40) Dia. Addendum = D+a = D+m Dia. Base = D cos(pa) = D cos(0 ) Addendum = m 3 Dedendum = 1.5m 3.75 Tooth depth = a+b 6.75 Tooth thickness = πd/z = πm/ 4.71

13 Gear ratio & Center distance (3) No. of pinion teeth No. of gear teeth z = D/m = 80/3 = Velocity ratio = 134/6 = 5.15 choose 6 teeth pinion gear Dia. Pitch D = m z Center distance = (D pinion +D gear )/ 40 Dia. Addendum = D+a = D+m Dia. Base = D cos(pa) = D cos(0 ) Addendum = m 3 Dedendum = 1.5m 3.75 Tooth depth = a+b 6.75 Tooth thickness = πd/z = πm/ 4.71

14 Gear train P out P in Increase gear ratio Change direction of rotation No. of teeth of gear G dose not affect to the ratio ω i z 1 z z 3 z 4 m ω = ω i /ω o m ω = (z /z 1 ) (z 4 /z 3 ) (z 6 /z 5 ) z 5 z 6 ω o

center point Sun gear Planet carrier Ring gear Each part can

15 Planetary gear train Epicyclic gear train, Planetary gear train Sun gear Planet carrier All parts rotate around the center point Sun gear Planet carrier Ring gear Each part can be set to be input, output or fixed Various gear ratio can be obtained

16 Planetary gear train Epicyclic gear train, Planetary gear train Z p = 0 Fixed member Input (rpm) Planet (rpm) Output (rpm) Ratio (ω i /ω o ) Ring fix Carrier 9 36 Sun Sun fix Carrier 9 36 Ring Carrier fix sun 9 7 Ring Z R = 100 Z s = 60

Planetary gear train http://www.diseno-art.

17 Planetary gear train

Gear manufacture Methods of machining Form milling : used mostly for large gears.

Shaping : frequently used for internal gears.

Hobbing : similar process to milling except that both the workpiece and the cutter

18 Gear manufacture Methods of machining Form milling : used mostly for large gears. A milling cutter that has the shape of the tooth space is used. Shaping : frequently used for internal gears. Cutter used reciprocates on a vertical spindle. Hobbing : similar process to milling except that both the workpiece and the cutter rotate in a coordinated manner. Casting : used most often to make blanks for gears which will have cut teeth. Possible to use to make toothed gears with little or no machining Milling cutter Hobbing Shaping VDO

19 Gear quality (1) Quality in gearing is the precision of the individual gear teeth and the precision with which two gears rotate in relation to one another. Runout Tooth-to-tooth spacing Profile Schematic diagram of a typical gear rolling fixture Chart of gear-tooth errors of a typical gear when run with a specific gear in a rolling fixture.

20 Gear quality () Gear quality is specified by AGMA as quality numbers. Quality numbers range from 5 to 15 with increasing precision (AGMA) Besides AGMA standard, there are also other standards (JIS, DIN, ISO-similar to DIN) Selected values for total composite tolerance Table of Gear Precision Grade

21 Gear quality (3) Recommended AGMA quality numbers Pitch line speed: Velocity at the pitch circle v pitch circle

22 Materials Steel: medium-carbon steel is usually used Due to low surface endurance capacity, heat treatment (Flame hardening, Induction hardening, Carburizing, Nitriding) is required Surface finishing (grinding) is probably done after heat treatment to obtain high precision gear Cast iron: Cheap, ASTM grade 0, 30, 40, 50, 60 are normally used surface fatigue strength is higher than bending fatigue strength Quieter than steel due to the damping property of cast iron Ductile or nodular cast-iron is probably used to increase strength of gear

23 Gear force analysis (1) Gear FBD Gear F b φ Pressure line Pressure line φ F F r F r F Base circle Pitch circle Pressure line φ F b Pinion Pinion Neglect sliding friction in FBD

24 Gear force analysis () From FBD F b = F cosφ F r = F sinφ FBD Gear Transmitted torque can be calculated from T = F r b = F b r F b φ Pressure line Transmitted power can be calculated from ( F r ) ω = ( F ) ω P = Tω = r b b F F r F r F r b = base radius r = pitch radius Pressure line φ F b Pinion

25 Gear tooth strength Max. stress position Contact point Tooth root Failure Pitting Crack Photoelasic pattern of stresses in a spur gear tooth Design principle Contact stress Hertzian stress Bending stress Lewis equation

26 Gear tooth bending stress (1) Lewis equation Assumptions 1. Gear tooth is considered as a cantilever beam. All transmitted force acts at the tooth tip of a tooth pair 3. F r is neglected 4. Sliding friction is neglected b F b σ = Mc I = F L( t / ) ( bt /1) b = 3 6Fb L bt L σbt F b = 6L t

27 Gear tooth bending stress () Hence σby F b = P F b = σbym σbt F b = 6L F b σ = σ = For constant bending stress b L = σ 6Fb t = (const.) t The relation between L and t is parabola. Tooth tip area has more material than parabola, hence the failure will occur at the tooth root (BED) From triangle relation x = σ b p = σbyp 3p F b P by F b bym x t / = t / L t L = 4 x p : circular pitch y : Lewis form factor Y : Lewis form factor P : Diametral pitch m : module

28 Lewis Form Factor Y, y Load near tip of teeth Total transmitted force acts at the tooth tip (actually at this point double teeth meshing occurs, hence the force acting on a tooth pair is reduced) Safer design Load near middle of teeth Total transmitted force acts at the position near the middle of teeth (single tooth meshing occurs) Close to the actual condition No Teeth Load Near Tip of Teeth Load at Near Middle of Teeth 14 1/ deg 0 deg FD 0 deg Stub 5 deg 14 1/ deg 0 deg FD Y y Y y Y y Y y Y y Y y 10 0,176 0,056 0,01 0,064 0,61 0,083 0,38 0, ,19 0,061 0,6 0,07 0,89 0,09 0,59 0,08 1 0,1 0,067 0,45 0,078 0,311 0,099 0,77 0,088 0,355 0,113 0,415 0, ,3 0,071 0,64 0,084 0,34 0,103 0,93 0,093 0,377 0,1 0,443 0, ,36 0,075 0,76 0,088 0,339 0,108 0,307 0,098 0,399 0,17 0,468 0, ,45 0,078 0,89 0,09 0,349 0,111 0,3 0,10 0,415 0,13 0,49 0, ,55 0,081 0,95 0,094 0,36 0,115 0,33 0,106 0,43 0,137 0,503 0, ,64 0,084 0,30 0,096 0,368 0,117 0,34 0,109 0,446 0,14 0,51 0, ,7 0,086 0,308 0,098 0,377 0,1 0,35 0,11 0,459 0,146 0,5 0, ,77 0,088 0,314 0,1 0,386 0,13 0,361 0,115 0,471 0,15 0,534 0,17 0 0,83 0,09 0,3 0,10 0,393 0,15 0,369 0,117 0,481 0,153 0,544 0, ,89 0,09 0,36 0,104 0,399 0,17 0,377 0,1 0,49 0,156 0,553 0,176 0,9 0,093 0,33 0,105 0,404 0,19 0,384 0,1 0,496 0,158 0,559 0, ,96 0,094 0,333 0,106 0,408 0,13 0,390 0,14 0,50 0,16 0,565 0,18 4 0,30 0,096 0,337 0,107 0,411 0,131 0,396 0,16 0,509 0,16 0,57 0,18 5 0,305 0,097 0,34 0,108 0,416 0,13 0,40 0,18 0,515 0,164 0,58 0, ,308 0,098 0,344 0,109 0,41 0,134 0,407 0,13 0,5 0,166 0,584 0, ,311 0,099 0,348 0,111 0,46 0,136 0,41 0,131 0,58 0,168 0,588 0, ,314 0,1 0,35 0,11 0,43 0,137 0,417 0,133 0,534 0,17 0,59 0, ,316 0,101 0,355 0,113 0,434 0,138 0,41 0,134 0,537 0,171 0,599 0, ,318 0,101 0,358 0,114 0,437 0,139 0,45 0,135 0,54 0,17 0,606 0, ,3 0,101 0,361 0,115 0,44 0,14 0,49 0,137 0,554 0,176 0,611 0, ,3 0,101 0,364 0,116 0,443 0,141 0,433 0,138 0,547 0,174 0,617 0, ,34 0,103 0,367 0,117 0,445 0,14 0,436 0,139 0,55 0,175 0,63 0, ,36 0,104 0,371 0,118 0,447 0,14 0,44 0,14 0,553 0,176 0,68 0, 35 0,37 0,104 0,373 0,119 0,449 0,143 0,443 0,141 0,556 0,177 0,633 0, ,39 0,105 0,377 0,1 0,451 0,144 0,446 0,14 0,559 0,178 0,639 0, ,33 0,105 0,38 0,11 0,454 0,145 0,449 0,143 0,563 0,179 0,645 0, ,333 0,106 0,384 0,1 0,455 0,145 0,45 0,144 0,565 0,18 0,65 0, ,335 0,107 0,386 0,13 0,457 0,145 0,454 0,145 0,568 0,181 0,655 0, ,336 0,107 0,389 0,14 0,459 0,146 0,457 0,145 0,57 0,181 0,659 0,1 43 0,339 0,108 0,397 0,16 0,467 0,149 0,464 0,148 0,574 0,183 0,668 0, ,34 0,108 0,399 0,17 0,468 0,149 0,468 0,149 0,579 0,184 0,678 0, ,346 0,11 0,408 0,13 0,474 0,151 0,477 0,15 0,588 0,187 0,694 0,1 55 0,35 0,11 0,415 0,13 0,48 0,153 0,484 0,154 0,596 0,19 0,704 0,4 60 0,355 0,113 0,41 0,134 0,484 0,154 0,491 0,156 0,603 0,19 0,713 0,7 65 0,358 0,114 0,45 0,135 0,488 0,155 0,496 0,158 0,607 0,193 0,71 0,3 70 0,36 0,115 0,49 0,137 0,493 0,157 0,501 0,159 0,61 0,194 0,78 0,3 75 0,361 0,115 0,433 0,138 0,496 0,158 0,506 0,161 0,613 0,195 0,735 0, ,363 0,116 0,436 0,139 0,499 0,159 0,509 0,16 0,615 0,196 0,739 0, ,366 0,117 0,44 0,141 0,503 0,16 0,516 0,164 0,619 0,197 0,747 0, ,368 0,117 0,446 0,14 0,506 0,161 0,51 0,166 0,6 0,198 0,755 0, ,375 0,119 0,458 0,146 0,518 0,165 0,537 0,171 0,635 0,0 0,778 0, ,378 0,1 0,463 0,147 0,54 0,167 0,545 0,173 0,64 0,04 0,787 0, ,38 0,1 0,471 0,15 0,534 0,17 0,554 0,176 0,65 0,07 0,801 0,55 Rack 0,39 0,14 0,484 0,154 0,55 0,175 0,566 0,18 0,66 0,1 0,83 0,6

29 Gear tooth bending stress (3) The effect of Fr 1. Compressive stress at B side increase, but tensile stress at D side decrease.. Most material can withstand compressive force more than tensile force. Fatigue will occur at tensile side. 3. The presence of Fr will increase strength of gear tooth, since it help to reduce the stress in tensile side σ = σ = F b P by F b bym Lewis form factor, Y or y 1. Y and y increase when no. of teeth is increased. More Y or y, gear tooth can withstand more Fb 3. Pinion has lower no. of gear teeth than gear. Pinion can withstand low load than gear. 4. Calculation is done at pinion

30 AGMA Stress Equation (bending) American Gear Manufacturers Association (AGMA) proposed the method to design gear based on the Lewis equation (bending stress consideration) Lewis Equation σ = F b bym s = t AGMA Equation (bending) W FY t J m O s m B v σ F b b Y s t W t F YJ Y J : Geometry factor is Y that include the effect of root fillet stress-concentration factor O : Overload factor s : Size factor m : Load-distribution factor B : Rim thickness factor v : Dynamic factor >= 1.0 (Always)

31 Geometry factor (Y J ) s = t Wt FY m J O s m B v Bending strength geometry factor YJ for full depth teeth spur gears 0 pressure angle 5 pressure angle

32 Overload factor ( O ) s = t Wt FY m J O s m B v Suggested overload factors, O Driven Machine Power source Uniform Light shock Moderate shock Heavy shock Uniform Light shock Moderate shock Power sources Uniform: Electric motor, Constantspeed gas turbine Light shock: Water turbine, variablespeed drive Moderate shock: Multicylinder engine Driven machine Uniform: Continuous-duty generator Light shock: Fans and low speed centrifugal pump, variable-duty generators, uniform loaded conveyors Moderate shock: High-speed centrifugal pumps, reciprocating pumps and compressors, heavy duty conveyors, machine tool drives Heavy shock: Rock crushers, punch press drivers

33 Size factor ( s ) s = t Wt FY m J O s m B v Suggested size factors, s Diametral pitch, Pd Metric module, m Size factor, s >=5 <=

34 Load dist. factor ( m ) s = t Wt FY m J O s m B v Used to reflect nonuniform distribution of load across the line of contact. If load is uniformly distributed m = 1.0 Causes of nonuniform distribution 1. Gear tooth error. Misalignment, Eccentricity 3. Deformation of gear, shaft, bearing, housing 4. Clearance between shaft, gear, bearing, housing 5. Deformation from the temperature 6. Gear tooth modification (crowning, end relief) The method to reduce m (min = 1.0) 1. Use high quality gear (high quality number). Narrow face widths 3. Locate gear at the center between two bearings 4. Short shaft spans between bearing 5. Large shaft diameters (high stiffness) 6. Rigid stiff housings 7. High precision, small clearance on all drive components

= 1. 0 + C + pf C mc = lead correction factor pm C mc = 1 for uncrowned teeth C mc = 0.

35 Load dist. factor ( m ) s = t Wt FY m J O s m B v Load distribution factor ( m ) can be calculated by m mc ( C C C C ) = C + pf C mc = lead correction factor pm C mc = 1 for uncrowned teeth C mc = 0.8 for crowned teeth ma e C pf = pinion proportion factor = F C 10d 0.05 pf F C pf = F 10d d, d p = pinion diameter F 1in 1< F 17 in C pm = pinion proportion modifier C pm = 1 S1/S < C pm = 1.1 S1/S 0.175

Load dist. factor ( m ) s = t Wt FY m J O s m B v Load distribution factor ( m ) can be calculated by m mc ( C C C C ) = 1. 0 + C + pf pm ma e C e = mesh alignment correction factor C e = 0.

36 Load dist. factor ( m ) s = t Wt FY m J O s m B v Load distribution factor ( m ) can be calculated by m mc ( C C C C ) = C + pf pm ma e C e = mesh alignment correction factor C e = 0.8 for gearing adjusted at assembly, compatibility is improved by lapping C e = 1 for all other conditions C ma = mesh alignment factor C ma = A + BF + CF Condition A B C Open gearing (10-4 ) Commercial, enclosed units (10-4 ) Precision, enclosed units (10-4 ) Extraprecision enclosed gear units * Face width F in Inches (10-4 )

37 Rim thickness factor ( B ) s = t Wt FY m J O s m B v Used when the rim thickness is not sufficient to provide full support for the tooth root. b.4 =1.6ln m B =1 m B 1. b t m B = h R t m B < 1.

Dynamic factor ( v ) s = v t Wt FY m To compensate the effect of vibration, dynamic unbalance that will increase load that the gear tooth must withstand especially at high velocity.

38 Dynamic factor ( v ) s = v t Wt FY m To compensate the effect of vibration, dynamic unbalance that will increase load that the gear tooth must withstand especially at high velocity. J O s m B v = A + C A v t B A = (1.0 B) B = 0.5(1 Qv ) C = 1 for v t in ft/min C = 00 for v t in m/s Q v = Gear quality number v t = Pitch line velocity Maximum recommended pitch line velocity: v t,max [ A + ( Q = C v 3)]

39 Selection of material (bending stress) AGMA Equation (bending) (Load that the gear must withstand) s = t Wt FY m J O s m B v < Adjusted Allowable Bending Stress Numbers (Depend on the material property) s at = s at YN SF s at : Allowable bending stress Y N : Bending strength stress cycle number R : Reliability factor SF : factor of safety (design decision) R R : Reliability factor Reliability R 0.90, one failure in , one failure in , one failure in , one failure in SF : factor of safety (design decision) To compensate any uncertainty in analysis, material property, or error in manufacturing Most of factors are included in AGMA equation, hence the recommended SF is around

40 Allowable bending stress, S at Allowable bending stress number for through-hardened steels Allowable bending stress number for nitriding steel gears

41 Bending strength stress cycle number, Y n N 60Lnq = N : expected number of cycles of loading L : design life in hours n : rotational speed of the gear (rpm) q : number of load applications per revolution

42 Bending strength stress cycle number, Y n Application Design life (h) Domestic appliances 1,000-,000 Aircraft engines 1,000-4,000 Automotive 1,500-5,000 Agricultural equipment 3,000-6,000 Elevators, industrial fan, multipurpose gearing 8,000-15,000 Motors, industrial blowers, general industrial machines 0,000-30,000 Pumps and compressors 40,000-60,000 Critical equipment in continuous 4-h operation 100,000-00,000

43 Gear tooth contact stress (1) Driving Driven W W r 1 + r 1 r 1 + r r + + F Base circle W r W The contact of gear teeth can be modeled as the contact of two cylinders r is radius of involute curve at the contact point (not the radius of pitch cylinder) Radius r is changed along the meshing position W is force in the direction of pressure line and = W rb = Wt r W cosφ = Wt Stress at contact point can be calculated by Hertzian stress equation T

44 Gear tooth contact stress (1) r p r G + + F W W Hertzian stress can be calculated from σ = σ = C W (1/ r1 Fπ[(1 ν ) E p / r ) + (1 ν ) W t 1 cos sin F φ φ d P E 1 + d G ] 1/ 1/ Define Cp (Elastic coefficient) C p r = r = = π [(1 ν ( d P sin ) ( sin ) 1 φ d G φ W = W t cosφ 1 1 ) E1 + (1 ν ) E] 1/ σ = C p Fd P W 1 t mg + cos sin φ φ mg 1/ Define I (Geometry factor) cosφ sinφ mg I = m + 1 m = Z Z = d G G P G G d P σ = C p W Fd t P I 1/ Basic equation related closely with AGMA for contact stress

45 AGMA Stress Equation (contact) Hertzian stress AGMA Equation (Contact) σ = C p W Fd t P I 1/ s c C W Fd t = p O s m v PI 1/ โดย C p = π[(1 ν cosφ sinφ mg I = m ) E1 + (1 ν ) E] G 1 d P : Pitch diameter (pinion) F : Face width 1/ O : Overload factor s : Size factor m : Load-distribution factor v : Dynamic factor Can be found as same as the bending stress cal.

46 Elastic coefficient, C W s C p t c = p O s m v PI Fd 1/ C p = π[(1 ν 1 1 ) E1 + (1 ν ) E] 1/ Subscript: 1 - Pinion - Gear

47 Geometry factor, I 1/ = v m s O P t p c I Fd W C s 1 sin cos + = G G m m I φ φ P G P G G d d Z Z m = =

48 Selection of material (Contact stress) s c AGMA Equation (contact) (Load that the gear must withstand) C W Fd R : Reliability factor Reliability t = p O s m v PI R 0.90, one failure in , one failure in , one failure in , one failure in / As same as bending case < Adjusted Allowable Contact Stress Numbers (Depend on the material property) s ac = s ac Z NCH SF R s ac : Allowable contact stress Z N : Pitting resistance stress cycle number factor C H : Hardness ratio factor R : Reliability factor SF : factor of safety (design decision) SF : factor of safety (design decision) To compensate any uncertainty in analysis, material property, or error in manufacturing Most of factors are included in AGMA equation, hence the recommended SF is around

49 Allowable contact stress, S ac Contact-fatigue strength Sc at 10 7 cycles and 0.99 reliability for through-hardened steel gears. ANSI/AGMA 001-D04 and 101-D04. Repeatedly Applied Contact Strength Sc at 10 7 Cycles and 0.99 Reliability for Steel Gears ANSI/AGMA 001-D04.

50 Pitting resistance stress cycle number factor, Z N N = 60Lnq N : expected number of cycles of loading L : design life in hours n : rotational speed of the gear (rpm) q : number of load applications per revolution As same as bending case

Hardness ratio factor, C H Pinion is smaller and rotate faster than gear If the surface of pinion is harder than gear, the capacity of pitting resistance is increase H BP :

51 Hardness ratio factor, C H Pinion is smaller and rotate faster than gear If the surface of pinion is harder than gear, the capacity of pitting resistance is increase H BP : Brinell hardness of pinion H BG : Brinell hardness of gear C H is used for gear only (does not use for pinion calculation) If the hardness of pinion and gear are equal, C H = 1

52 Design Guidelines 1. Gear ratio should be less than 1:6 (Too much gear ratio will bring about interference problem and large gear will cause the weight and size problem).. If gear ratio more than 1:6 is required, multi-stages gear reduction should be used. 3. Recommended face width is around 8m < F < 16m (commonly use 1m). 4. Very large face width will bring about the alignment and load distribution problem. 5. At the same center distance, the gear pair with small teeth + more no. of teeth is quieter than the gear pair with large teeth + less no. of teeth. 6. Small no. of teeth make the compact gear pair, but the interference must be checked.

53 Design Guidelines Data for all curves: m G = 4, N P = 4 O = 1.0, Class 1 service 0 full-depth teeth

54 Example A gear pair is to be designed to transmit 15 kw of power to a large meat grinder in a commercial meat processing plant. The pinion is attached to the shaft of an electric motor rotating at 575 rpm. The gear must operate at rpm. The gear unit will be enclosed and of commercial quality. Commercially hobbed (quality number 5), 0, full depth, involute gears are to be used in the metric module system. The maximum center distance is to be 00 mm. Specify the design of the gears. [Ex.9-6 Machine Elements in Mechanical Design. Robert L. Mott]

12/25/ :27 PM. Chapter 14. Spur and Helical Gears. Mohammad Suliman Abuhaiba, Ph.D., PE

12/25/ :27 PM. Chapter 14. Spur and Helical Gears. Mohammad Suliman Abuhaiba, Ph.D., PE Chapter 14 Spur and Helical Gears 1 2 The Lewis Bending Equation Equation to estimate bending stress in gear teeth in which tooth form entered into the formulation: 3 The Lewis Bending Equation Assume