Alegerea variantei constructive - cutia de viteze

Alegerea variantei constructive - cutia de viteze

Autoturismul pentru care se proiecteaza aceasta cutie de viteza este Opel Corsa 1,7 DI produs intre anii 2000-2003. Codul cutiei de viteze este F13/5 WR, fiind o cutie cu cinci trepte de mers inainte sincronizate si o treapa de mers inapoi nesincronizata. Construcia cutiei este cu doi arbori longitudinali ea fiind montata transversal pe caroseria autovehiculului. Acest gen de cutie de viteze este montata pe autoturismele cu solutia totul fata. Sincronizarea treptelor de viteza se face cu sincronizatoare conice cu inertie, cu inele de blocare si dispozitiv de fizare cu bile.

S-a ales aceasta varianta constructiva deoarece motorul are o capacitate cilindrica medie-mica, o putere medie si un cuplu motor mediu de la turatii scazute, fiind o cutie de viteze foarte performanta. Totodata faptul ca este cu doi arbori ofera avantajul gabaritului redus.

In general pe autoturismele din clasa mica-medie se monteaza astfel de cutii deoarece sunt simple, au pret de cost redus fata de alte tipuri constructive, asigra confortul schimbarii treptelor de viteza fara socuri si au o durabiliate buna. Aceasta alegere este confirmata si de alti producatori de masini cum ar fi: Volskwagen, Ford, Toyota, care pe modelele lor de la aceasta clasa au montat acelasi gen de cutii de viteze.

Cutia de viteze F13/5 WR are rapoartele de transmitere dupa cum urmeaza:

treapta 1-a: 3,73;

treapta 2-a: 1,96;

treapta 3-a: 1,31;

treapta 4-a: 0,95;

treapta 5-a: 0,76;

mers inapoi: 3,31;

raportul transmisiei centrale: 3,55;

Pentru confectionarea rotilor dintate si a arborlor s-a ales materialul OLC45. Acesta are rezitenta la tractiune Rm minim 610 N/mm², iar dupa tratament termic se ajunge la o valoare cuprinsa intre 700 si 840 N/mm². O roata dintata trebuie sa aiba miezul tenace pentru a face fata oboselii si flancul dinteliu trebuie sa fie dur, pentru a face fata uzurii de contac. Astfel pe flancurile dintilor s-a aplicat o calire cu CIF (curenti de inalta frecventa) iar duritatea lor a ajuns la 55 HRC pentru pinion si 50-51 HRC pentru roata condusa. Rezistenta la presiune de contact fiind σ_Hlim=1140 N/mm², iar la incovoierea dintelui σ_Flim=605 N/mm².

Fisa tehnica Opel Corsa 1,7 DI

Calculul angrenajelor

Dimensionarea s-a facut cu ajutorul programului Mechsoft, care face verificarile conform DIN 3990:1987.

Treapta a 1-a

--- Guide

External Gearing - DIN

Calculation of geometry: Calculates the number of teeth according to the center distance and module

Reaching the center distance: Teeth correction

Distribution of Correction: With Comp. of Slips

Load calculation: Calculates the torque according to the power and speed

Strength calculation: Strength check calculation

--- Basic Parameters

Desired Gear Ratio = 3.63

Pressure Angle alpha = 20°

Addendum a* = 1 (= 3 mm)

Clearance c* = 0.25 (= 0.75 mm)

Root Fillet = 0.38 (= 1.14 mm)

Addendum of Basic Rack = 1.25 (= 3.75 mm)

Helix Angle beta = 15°

Module m = 3 mm

Tangential Module mt = 3.1058 mm

Center Distance aw = 100 mm

Product Center Distance a = 99.387 mm

Total Unit Correction = 0.2089

Operating Pressure Angle alphaw = 20.9749°

Tangential Pressure Angle alphat = 20.6469°

Tan.Operating Pressure Angle alphatw = 21.5606°

Base Helix Angle betab = 14.0761°

Circular Pitch p = 9.425 mm

Tan. Circular Pitch pt = 9.757 mm

Base Circular Pitch ptb = 9.131 mm

Contact Ratio = 2.2345 (1.4107 + 0.8238)

Precision Specification 6e26

Limit Deviation of Helix Angle Fb = 0.01 mm

Limit Deviation of Axis Parallelity fx = 0.01 mm

Limit Deviation of Axis Parallelity fy = 0.005 mm

--- Gear 1

Number of Teeth = 14

Helix Direction = Right

Unit Correction = 0.4269 (= 1.281 mm)

Pitch Diameter d = 43.482 mm

Base Circle Diameter db = 40.689 mm

Outside Diameter do = 52.017 mm

Root Diameter df = 38.543 mm

Work Pitch Diameter dw = 43.75 mm

Tooth Thickness s = 5.645 mm

Outside Tooth Thickness = 0.4189 (= 1.257 mm)

Facewidth = 30 mm

Facewidth Ratio = 0.6899

Chordal Thickness T = 4.984 mm -0.03

-0.08

Chordal Thickness Height ht = 3.36 mm

Chordal Dimension M = 23.666 mm / 3 -0.028

-0.075

Dimension Over (Between) Wires M = 50.36 mm -0.07

-0.16

Wire Diameter dw = 4.5 mm

Comparative Number of Teeth zv = 15.4051

Limit Circumferential Run-out Fr = 0.016 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Gear 2

Number of Teeth = 50

Helix Direction = Left

Unit Correction = -0.218 (= -0.654 mm)

Pitch Diameter d = 155.291 mm

Base Circle Diameter db = 145.317 mm

Outside Diameter do = 159.957 mm

Root Diameter df = 146.483 mm

Work Pitch Diameter dw = 156.25 mm

Tooth Thickness s = 4.236 mm

Outside Tooth Thickness = 0.8113 (= 2.434 mm)

Facewidth = 30 mm

Facewidth Ratio = 0.1932

Chordal Thickness T = 3.741 mm -0.056

-0.136

Chordal Thickness Height ht = 1.652 mm

Chordal Dimension M = 59.438 mm / 7 -0.052

-0.127

Dimension Over (Between) Wires M = 158.664 mm -0.18

-0.38

Wire Diameter dw = 4.5 mm

Comparative Number of Teeth zv = 55.0182

Limit Circumferential Run-out Fr = 0.022 mm

Limit Deviation of Axial Pitch fpt = ±0.008 mm

Limit Deviation of Basic Pitch fpb = ±0.0075 mm

--- Load (Gear 1; Gear 2)

Power P = 48; 46.56 kW

Efficiency = 0.97

Speed n = 4400; 1232 rpm

Torque Mk = 104.1741; 360.889 Nm

Tangential Force Ft = 4791.6427 N

Radial Force Fr = 1893.3394 N

Axial Force Fa = 1283.9168 N

Normal Force Fn = 5312.7078 N

Circumferential Velocity v = 10.0174 m/s

Resonance Speed nE1 = 37264.29 rpm

Strength Check According to DIN 3990:1987

Durability Lh = 25000 hour

--- Material Values

Tensile Strength = 640; 640 MPa

Yield Point in Tensile = 390; 390 MPa

Contact Fatigue Limit SigmaHlim = 1140; 1140 MPa

Bending Fatigue Limit SigmaFlim = 605; 605 MPa

Hardness in Tooth Core = 200; 200 HV

Hardness in Tooth Side = 600; 600 HV

Base Number of Load Cycles in Contact [10^6] = 100; 100

Base Number of Load Cycles in Bending [10^6] = 3; 3

Wöhler Curve Exponent for Contact = 10; 10

Wöhler Curve Exponent for Bending = 9; 9

Modulus of Elasticity in Tension [10^3] = 206; 206 MPa

Poisson's Ratio = 0.3; 0.3

Type of Treatment = 4; 4

--- Factors for Contact

Application Factor KA = 1

Dynamic Factor KHv = 1.088

Face Load Factor KHb = 1.3

Transverse Load Factor KHa = 1.117

Total KH = 1.581

One-time Overloading Factor KAS = 1

Elasticity Factor Ze = 189.81

Zone Factor Zh = 2.368

Contact Ratio Factor Zeps = 0.858

Single Pair Tooth Contact Factor ZB = 1.009; 1

Life Factor Zn = 1; 1

Lubricant Factor Zl = 0.962

Roughness Factor Zr = 1

Velocity Factor Zv = 1

Helix Angle Factor Zb = 0.983

Size Factor Zx = 1; 1

Work Hardening Factor Zw = 1

--- Factors for Bending

Application Factor KA = 1

Dynamic Factor KFv = 1.088

Face Load Factor KFb = 1.212

Transverse Load Factor KFa = 1.117

Total KF = 1.474

One-time Overloading Factor KAS = 1

Form Factor YFa = 2.093; 2.191

Stress Correction Factor YSa = 3.226; 2.417

Teeth with Grinding Notches Factor YSag = 1; 1

Helix Angle Factor Yb = 0.897

Contact Ratio Factor Yeps = 0.75

Alternating Load Factor Ya = 1; 1

Production Technology Factor Yt = 1; 1

Life Factor Yn = 1; 1

Notch Sensitivity Factor Yd = 1.734; 1.414

Size Factor Yx = 1; 1

Tooth Root Surface Factor Yr = 1

--- Results

Factor of Safety from Pitting SH = 1.052; 1.061

Factor of Safety from Tooth Breakage SF = 2.942; 3.058

Static Safety in Contact SHst = 2.263; 2.283

Static Safety in Bending SFst = 4.242; 5.408

Strength Check - True

Treapta a 2-a

--- Guide

External Gearing - DIN

Calculation of geometry: Calculates the number of teeth according to the center distance and module

Reaching the center distance: Teeth correction

Distribution of Correction: With Comp. of Slips

Load calculation: Calculates the torque according to the power and speed

Strength calculation: Strength check calculation

--- Basic Parameters

Desired Gear Ratio = 1.96

Pressure Angle alpha = 20°

Addendum a* = 1 (= 2.5 mm)

Clearance c* = 0.25 (= 0.625 mm)

Root Fillet = 0.38 (= 0.95 mm)

Addendum of Basic Rack = 1.25 (= 3.125 mm)

Helix Angle beta = 15°

Module m = 2.5 mm

Tangential Module mt = 2.5882 mm

Center Distance aw = 100 mm

Product Center Distance a = 99.645 mm

Total Unit Correction = 0.1436

Operating Pressure Angle alphaw = 20.5693°

Tangential Pressure Angle alphat = 20.6469°

Tan.Operating Pressure Angle alphatw = 21.1795°

Base Helix Angle betab = 14.0761°

Circular Pitch p = 7.854 mm

Tan. Circular Pitch pt = 8.131 mm

Base Circular Pitch ptb = 7.609 mm

Contact Ratio = 2.3859 (1.562 + 0.8238)

Precision Specification 6e26

Limit Deviation of Helix Angle Fb = 0.01 mm

Limit Deviation of Axis Parallelity fx = 0.01 mm

Limit Deviation of Axis Parallelity fy = 0.005 mm

--- Gear 1

Number of Teeth = 26

Helix Direction = Right

Unit Correction = 0.2201 (= 0.55 mm)

Pitch Diameter d = 67.293 mm

Base Circle Diameter db = 62.971 mm

Outside Diameter do = 73.385 mm

Root Diameter df = 62.144 mm

Work Pitch Diameter dw = 67.532 mm

Tooth Thickness s = 4.328 mm

Outside Tooth Thickness = 0.6614 (= 1.654 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.3715

Chordal Thickness T = 3.821 mm -0.04

-0.1

Chordal Thickness Height ht = 2.351 mm

Chordal Dimension M = 27.213 mm / 4 -0.038

-0.094

Dimension Over (Between) Wires M = 71.323 mm -0.12

-0.25

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 28.6095

Limit Circumferential Run-out Fr = 0.02 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Gear 2

Number of Teeth = 51

Helix Direction = Left

Unit Correction = -0.0765 (= -0.191 mm)

Pitch Diameter d = 131.998 mm

Base Circle Diameter db = 123.52 mm

Outside Diameter do = 136.606 mm

Root Diameter df = 125.365 mm

Work Pitch Diameter dw = 132.468 mm

Tooth Thickness s = 3.788 mm

Outside Tooth Thickness = 0.7915 (= 1.979 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.1894

Chordal Thickness T = 3.345 mm -0.056

-0.136

Chordal Thickness Height ht = 1.696 mm

Chordal Dimension M = 49.813 mm / 7 -0.052

-0.127

Dimension Over (Between) Wires M = 134.471 mm -0.18

-0.38

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 56.1186

Limit Circumferential Run-out Fr = 0.022 mm

Limit Deviation of Axial Pitch fpt = ±0.008 mm

Limit Deviation of Basic Pitch fpb = ±0.0075 mm

--- Load (Gear 1; Gear 2)

Power P = 48; 46.56 kW

Efficiency = 0.97

Speed n = 4400; 2243.1373 rpm

Torque Mk = 104.1741; 198.2113 Nm

Tangential Force Ft = 3096.1384 N

Radial Force Fr = 1199.6407 N

Axial Force Fa = 829.6078 N

Normal Force Fn = 3423.6218 N

Circumferential Velocity v = 15.5032 m/s

Resonance Speed nE1 = 14609.53 rpm

Strength Check According to DIN 3990:1987

Durability Lh = 25000 hour

--- Material Values

Tensile Strength = 640; 640 MPa

Yield Point in Tensile = 390; 390 MPa

Contact Fatigue Limit SigmaHlim = 1140; 1140 MPa

Bending Fatigue Limit SigmaFlim = 605; 605 MPa

Hardness in Tooth Core = 200; 200 HV

Hardness in Tooth Side = 600; 600 HV

Base Number of Load Cycles in Contact [10^6] = 100; 100

Base Number of Load Cycles in Bending [10^6] = 3; 3

Wöhler Curve Exponent for Contact = 10; 10

Wöhler Curve Exponent for Bending = 9; 9

Modulus of Elasticity in Tension [10^3] = 206; 206 MPa

Poisson's Ratio = 0.3; 0.3

Type of Treatment = 4; 4

--- Factors for Contact

Application Factor KA = 1.25

Dynamic Factor KHv = 1.24

Face Load Factor KHb = 1.229

Transverse Load Factor KHa = 1.144

Total KH = 2.179

One-time Overloading Factor KAS = 1

Elasticity Factor Ze = 189.81

Zone Factor Zh = 2.417

Contact Ratio Factor Zeps = 0.81

Single Pair Tooth Contact Factor ZB = 1.003; 1

Life Factor Zn = 1; 1

Lubricant Factor Zl = 0.962

Roughness Factor Zr = 1

Velocity Factor Zv = 1.015

Helix Angle Factor Zb = 0.981

Size Factor Zx = 1; 1

Work Hardening Factor Zw = 1

--- Factors for Bending

Application Factor KA = 1.25

Dynamic Factor KFv = 1.24

Face Load Factor KFb = 1.173

Transverse Load Factor KFa = 1.144

Total KF = 2.08

One-time Overloading Factor KAS = 1

Form Factor YFa = 2.132; 2.163

Stress Correction Factor YSa = 2.8; 2.495

Teeth with Grinding Notches Factor YSag = 1; 1

Helix Angle Factor Yb = 0.887

Contact Ratio Factor Yeps = 0.694

Alternating Load Factor Ya = 1; 1

Production Technology Factor Yt = 1; 1

Life Factor Yn = 1; 1

Notch Sensitivity Factor Yd = 1.595; 1.478

Size Factor Yx = 1; 1

Tooth Root Surface Factor Yr = 1

--- Results

Factor of Safety from Pitting SH = 1.237; 1.241

Factor of Safety from Tooth Breakage SF = 2.549; 2.612

Static Safety in Contact SHst = 2.617; 2.625

Static Safety in Bending SFst = 3.995; 4.419

Strength Check - True

Treapta a 3-a

--- Guide

External Gearing - DIN

Calculation of geometry: Calculates the number of teeth according to the center distance and module

Reaching the center distance: Teeth correction

Distribution of Correction: With Comp. of Slips

Load calculation: Calculates the torque according to the power and speed

Strength calculation: Strength check calculation

--- Basic Parameters

Desired Gear Ratio = 1.31

Pressure Angle alpha = 20°

Addendum a* = 1 (= 2.25 mm)

Clearance c* = 0.25 (= 0.562 mm)

Root Fillet = 0.38 (= 0.855 mm)

Addendum of Basic Rack = 1.25 (= 2.812 mm)

Helix Angle beta = 15°

Module m = 2.25 mm

Tangential Module mt = 2.3294 mm

Center Distance aw = 100 mm

Product Center Distance a = 98.998 mm

Total Unit Correction = 0.4606

Operating Pressure Angle alphaw = 21.5678°

Tangential Pressure Angle alphat = 20.6469°

Tan.Operating Pressure Angle alphatw = 22.1201°

Base Helix Angle betab = 14.0761°

Circular Pitch p = 7.069 mm

Tan. Circular Pitch pt = 7.318 mm

Base Circular Pitch ptb = 6.848 mm

Contact Ratio = 2.4631 (1.5477 + 0.9154)

Precision Specification 6e26

Limit Deviation of Helix Angle Fb = 0.01 mm

Limit Deviation of Axis Parallelity fx = 0.01 mm

Limit Deviation of Axis Parallelity fy = 0.005 mm

--- Gear 1

Number of Teeth = 37

Helix Direction = Right

Unit Correction = 0.2548 (= 0.573 mm)

Pitch Diameter d = 86.187 mm

Base Circle Diameter db = 80.651 mm

Outside Diameter do = 91.764 mm

Root Diameter df = 81.708 mm

Work Pitch Diameter dw = 87.059 mm

Tooth Thickness s = 3.952 mm

Outside Tooth Thickness = 0.7143 (= 1.607 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.2901

Chordal Thickness T = 3.489 mm -0.04

-0.1

Chordal Thickness Height ht = 2.154 mm

Chordal Dimension M = 31.57 mm / 5 -0.038

-0.094

Dimension Over (Between) Wires M = 91.182 mm -0.11

-0.23

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 40.7135

Limit Circumferential Run-out Fr = 0.02 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Gear 2

Number of Teeth = 48

Helix Direction = Left

Unit Correction = 0.2058 (= 0.463 mm)

Pitch Diameter d = 111.81 mm

Base Circle Diameter db = 104.628 mm

Outside Diameter do = 117.167 mm

Root Diameter df = 107.111 mm

Work Pitch Diameter dw = 112.941 mm

Tooth Thickness s = 3.871 mm

Outside Tooth Thickness = 0.7527 (= 1.694 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.2236

Chordal Thickness T = 3.418 mm -0.04

-0.1

Chordal Thickness Height ht = 2.056 mm

Chordal Dimension M = 45.161 mm / 7 -0.038

-0.094

Dimension Over (Between) Wires M = 116.7 mm -0.115

-0.24

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 52.8175

Limit Circumferential Run-out Fr = 0.02 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Load (Gear 1; Gear 2)

Power P = 48; 46.56 kW

Efficiency = 0.97

Speed n = 4400; 3391.6667 rpm

Torque Mk = 104.1741; 131.0905 Nm

Tangential Force Ft = 2417.4053 N

Radial Force Fr = 982.5935 N

Axial Force Fa = 647.7418 N

Normal Force Fn = 2691.1048 N

Circumferential Velocity v = 19.856 m/s

Resonance Speed nE1 = 8982.39 rpm

Strength Check According to DIN 3990:1987

Durability Lh = 25000 hour

--- Material Values

Tensile Strength = 640; 640 MPa

Yield Point in Tensile = 390; 390 MPa

Contact Fatigue Limit SigmaHlim = 1140; 1140 MPa

Bending Fatigue Limit SigmaFlim = 605; 605 MPa

Hardness in Tooth Core = 200; 200 HV

Hardness in Tooth Side = 600; 600 HV

Base Number of Load Cycles in Contact [10^6] = 100; 100

Base Number of Load Cycles in Bending [10^6] = 3; 3

Wöhler Curve Exponent for Contact = 10; 10

Wöhler Curve Exponent for Bending = 9; 9

Modulus of Elasticity in Tension [10^3] = 206; 206 MPa

Poisson's Ratio = 0.3; 0.3

Type of Treatment = 4; 4

--- Factors for Contact

Application Factor KA = 1.25

Dynamic Factor KHv = 1.24

Face Load Factor KHb = 1.229

Transverse Load Factor KHa = 1.144

Total KH = 2.179

One-time Overloading Factor KAS = 1

Elasticity Factor Ze = 189.81

Zone Factor Zh = 2.417

Contact Ratio Factor Zeps = 0.81

Single Pair Tooth Contact Factor ZB = 1.003; 1

Life Factor Zn = 1; 1

Lubricant Factor Zl = 0.962

Roughness Factor Zr = 1

Velocity Factor Zv = 1.015

Helix Angle Factor Zb = 0.981

Size Factor Zx = 1; 1

Work Hardening Factor Zw = 1

--- Factors for Bending

Application Factor KA = 1.25

Dynamic Factor KFv = 1.24

Face Load Factor KFb = 1.173

Transverse Load Factor KFa = 1.144

Total KF = 2.08

One-time Overloading Factor KAS = 1

Form Factor YFa = 2.132; 2.163

Stress Correction Factor YSa = 2.8; 2.495

Teeth with Grinding Notches Factor YSag = 1; 1

Helix Angle Factor Yb = 0.887

Contact Ratio Factor Yeps = 0.694

Alternating Load Factor Ya = 1; 1

Production Technology Factor Yt = 1; 1

Life Factor Yn = 1; 1

Notch Sensitivity Factor Yd = 1.595; 1.478

Size Factor Yx = 1; 1

Tooth Root Surface Factor Yr = 1

--- Results

Factor of Safety from Pitting SH = 1.463; 1.467

Factor of Safety from Tooth Breakage SF = 2.938; 3.011

Static Safety in Contact SHst = 3.095; 3.104

Static Safety in Bending SFst = 4.605; 5.093

Strength Check - True

Treapta a 4-a

--- Guide

External Gearing - DIN

Calculation of geometry: Calculates the number of teeth according to the center distance and module

Reaching the center distance: Teeth correction

Distribution of Correction: With Comp. of Slips

Load calculation: Calculates the torque according to the power and speed

Strength calculation: Strength check calculation

--- Basic Parameters

Desired Gear Ratio = 0.95

Pressure Angle alpha = 20°

Addendum a* = 1 (= 2.25 mm)

Clearance c* = 0.25 (= 0.562 mm)

Root Fillet = 0.38 (= 0.855 mm)

Addendum of Basic Rack = 1.25 (= 2.812 mm)

Helix Angle beta = 15°

Module m = 2.25 mm

Tangential Module mt = 2.3294 mm

Center Distance aw = 100 mm

Product Center Distance a = 98.998 mm

Total Unit Correction = 0.4606

Operating Pressure Angle alphaw = 21.5678°

Tangential Pressure Angle alphat = 20.6469°

Tan.Operating Pressure Angle alphatw = 22.1201°

Base Helix Angle betab = 14.0761°

Circular Pitch p = 7.069 mm

Tan. Circular Pitch pt = 7.318 mm

Base Circular Pitch ptb = 6.848 mm

Contact Ratio = 2.4668 (1.5514 + 0.9154)

Precision Specification 6e26

Limit Deviation of Helix Angle Fb = 0.01 mm

Limit Deviation of Axis Parallelity fx = 0.01 mm

Limit Deviation of Axis Parallelity fy = 0.005 mm

--- Gear 1

Number of Teeth = 43

Helix Direction = Right

Unit Correction = 0.2281 (= 0.513 mm)

Pitch Diameter d = 100.163 mm

Base Circle Diameter db = 93.73 mm

Outside Diameter do = 105.62 mm

Root Diameter df = 95.565 mm

Work Pitch Diameter dw = 101.176 mm

Tooth Thickness s = 3.908 mm

Outside Tooth Thickness = 0.7374 (= 1.659 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.2496

Chordal Thickness T = 3.451 mm -0.04

-0.1

Chordal Thickness Height ht = 2.101 mm

Chordal Dimension M = 38.38 mm / 6 -0.038

-0.094

Dimension Over (Between) Wires M = 105.072 mm -0.115

-0.24

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 47.3157

Limit Circumferential Run-out Fr = 0.02 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Gear 2

Number of Teeth = 42

Helix Direction = Left

Unit Correction = 0.2325 (= 0.523 mm)

Pitch Diameter d = 97.834 mm

Base Circle Diameter db = 91.55 mm

Outside Diameter do = 103.31 mm

Root Diameter df = 93.255 mm

Work Pitch Diameter dw = 98.824 mm

Tooth Thickness s = 3.915 mm

Outside Tooth Thickness = 0.734 (= 1.652 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.2555

Chordal Thickness T = 3.457 mm -0.04

-0.1

Chordal Thickness Height ht = 2.109 mm

Chordal Dimension M = 38.351 mm / 6 -0.038

-0.094

Dimension Over (Between) Wires M = 102.826 mm -0.115

-0.24

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 46.2153

Limit Circumferential Run-out Fr = 0.02 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Load (Gear 1; Gear 2)

Power P = 48; 46.56 kW

Efficiency = 0.97

Speed n = 4400; 4504.7619 rpm

Torque Mk = 104.1741; 98.6989 Nm

Tangential Force Ft = 2080.093 N

Radial Force Fr = 845.4875 N

Axial Force Fa = 557.3592 N

Normal Force Fn = 2315.6018 N

Circumferential Velocity v = 23.0759 m/s

Resonance Speed nE1 = 7545.77 rpm

Strength Check According to DIN 3990:1987

Durability Lh = 25000 hour

--- Material Values

Tensile Strength = 640; 640 MPa

Yield Point in Tensile = 390; 390 MPa

Contact Fatigue Limit SigmaHlim = 1140; 1140 MPa

Bending Fatigue Limit SigmaFlim = 605; 605 MPa

Hardness in Tooth Core = 200; 200 HV

Hardness in Tooth Side = 600; 600 HV

Base Number of Load Cycles in Contact [10^6] = 100; 100

Base Number of Load Cycles in Bending [10^6] = 3; 3

Wöhler Curve Exponent for Contact = 10; 10

Wöhler Curve Exponent for Bending = 9; 9

Modulus of Elasticity in Tension [10^3] = 206; 206 MPa

Poisson's Ratio = 0.3; 0.3

Type of Treatment = 4; 4

--- Factors for Contact

Application Factor KA = 1.25

Dynamic Factor KHv = 1.24

Face Load Factor KHb = 1.229

Transverse Load Factor KHa = 1.144

Total KH = 2.179

One-time Overloading Factor KAS = 1

Elasticity Factor Ze = 189.81

Zone Factor Zh = 2.417

Contact Ratio Factor Zeps = 0.81

Single Pair Tooth Contact Factor ZB = 1.003; 1

Life Factor Zn = 1; 1

Lubricant Factor Zl = 0.962

Roughness Factor Zr = 1

Velocity Factor Zv = 1.015

Helix Angle Factor Zb = 0.981

Size Factor Zx = 1; 1

Work Hardening Factor Zw = 1

--- Factors for Bending

Application Factor KA = 1.25

Dynamic Factor KFv = 1.24

Face Load Factor KFb = 1.173

Transverse Load Factor KFa = 1.144

Total KF = 2.08

One-time Overloading Factor KAS = 1

Form Factor YFa = 2.132; 2.163

Stress Correction Factor YSa = 2.8; 2.495

Teeth with Grinding Notches Factor YSag = 1; 1

Helix Angle Factor Yb = 0.887

Contact Ratio Factor Yeps = 0.694

Alternating Load Factor Ya = 1; 1

Production Technology Factor Yt = 1; 1

Life Factor Yn = 1; 1

Notch Sensitivity Factor Yd = 1.595; 1.478

Size Factor Yx = 1; 1

Tooth Root Surface Factor Yr = 1

--- Results

Factor of Safety from Pitting SH = 1.609; 1.614

Factor of Safety from Tooth Breakage SF = 3.414; 3.499

Static Safety in Contact SHst = 3.404; 3.414

Static Safety in Bending SFst = 5.351; 5.919

Strength Check - True

Treapta a 5-a

--- Guide

External Gearing - DIN

Calculation of geometry: Calculates the number of teeth according to the center distance and module

Reaching the center distance: Teeth correction

Distribution of Correction: With Comp. of Slips

Load calculation: Calculates the torque according to the power and speed

Strength calculation: Strength check calculation

--- Basic Parameters

Desired Gear Ratio = 0.76

Pressure Angle alpha = 20°

Addendum a* = 1 (= 2.25 mm)

Clearance c* = 0.25 (= 0.562 mm)

Root Fillet = 0.38 (= 0.855 mm)

Addendum of Basic Rack = 1.25 (= 2.812 mm)

Helix Angle beta = 15°

Module m = 2.25 mm

Tangential Module mt = 2.3294 mm

Center Distance aw = 100 mm

Product Center Distance a = 98.998 mm

Total Unit Correction = 0.4606

Operating Pressure Angle alphaw = 21.5678°

Tangential Pressure Angle alphat = 20.6469°

Tan.Operating Pressure Angle alphatw = 22.1201°

Base Helix Angle betab = 14.0761°

Circular Pitch p = 7.069 mm

Tan. Circular Pitch pt = 7.318 mm

Base Circular Pitch ptb = 6.848 mm

Contact Ratio = 2.4631 (1.5477 + 0.9154)

Precision Specification 6e26

Limit Deviation of Helix Angle Fb = 0.01 mm

Limit Deviation of Axis Parallelity fx = 0.01 mm

Limit Deviation of Axis Parallelity fy = 0.005 mm

--- Gear 1

Number of Teeth = 48

Helix Direction = Right

Unit Correction = 0.2058 (= 0.463 mm)

Pitch Diameter d = 111.81 mm

Base Circle Diameter db = 104.628 mm

Outside Diameter do = 117.167 mm

Root Diameter df = 107.111 mm

Work Pitch Diameter dw = 112.941 mm

Tooth Thickness s = 3.871 mm

Outside Tooth Thickness = 0.7527 (= 1.694 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.2236

Chordal Thickness T = 3.418 mm -0.04

-0.1

Chordal Thickness Height ht = 2.056 mm

Chordal Dimension M = 45.161 mm / 7 -0.038

-0.094

Dimension Over (Between) Wires M = 116.7 mm -0.115

-0.24

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 52.8175

Limit Circumferential Run-out Fr = 0.02 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Gear 2

Number of Teeth = 37

Helix Direction = Left

Unit Correction = 0.2548 (= 0.573 mm)

Pitch Diameter d = 86.187 mm

Base Circle Diameter db = 80.651 mm

Outside Diameter do = 91.764 mm

Root Diameter df = 81.708 mm

Work Pitch Diameter dw = 87.059 mm

Tooth Thickness s = 3.952 mm

Outside Tooth Thickness = 0.7143 (= 1.607 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.2901

Chordal Thickness T = 3.489 mm -0.04

-0.1

Chordal Thickness Height ht = 2.154 mm

Chordal Dimension M = 31.57 mm / 5 -0.038

-0.094

Dimension Over (Between) Wires M = 91.182 mm -0.11

-0.23

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 40.7135

Limit Circumferential Run-out Fr = 0.02 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Load (Gear 1; Gear 2)

Power P = 48; 46.56 kW

Efficiency = 0.97

Speed n = 4400; 5708.1081 rpm

Torque Mk = 104.1741; 77.8919 Nm

Tangential Force Ft = 1863.4166 N

Radial Force Fr = 757.4159 N

Axial Force Fa = 499.301 N

Normal Force Fn = 2074.3933 N

Circumferential Velocity v = 25.7591 m/s

Resonance Speed nE1 = 6923.92 rpm

Strength Check According to DIN 3990:1987

Durability Lh = 25000 hour

--- Material Values

Tensile Strength = 640; 640 MPa

Yield Point in Tensile = 390; 390 MPa

Contact Fatigue Limit SigmaHlim = 1140; 1140 MPa

Bending Fatigue Limit SigmaFlim = 605; 605 MPa

Hardness in Tooth Core = 200; 200 HV

Hardness in Tooth Side = 600; 600 HV

Base Number of Load Cycles in Contact [10^6] = 100; 100

Base Number of Load Cycles in Bending [10^6] = 3; 3

Wöhler Curve Exponent for Contact = 10; 10

Wöhler Curve Exponent for Bending = 9; 9

Modulus of Elasticity in Tension [10^3] = 206; 206 MPa

Poisson's Ratio = 0.3; 0.3

Type of Treatment = 4; 4

--- Factors for Contact

Application Factor KA = 1.25

Dynamic Factor KHv = 1.24

Face Load Factor KHb = 1.229

Transverse Load Factor KHa = 1.144

Total KH = 2.179

One-time Overloading Factor KAS = 1

Elasticity Factor Ze = 189.81

Zone Factor Zh = 2.417

Contact Ratio Factor Zeps = 0.81

Single Pair Tooth Contact Factor ZB = 1.003; 1

Life Factor Zn = 1; 1

Lubricant Factor Zl = 0.962

Roughness Factor Zr = 1

Velocity Factor Zv = 1.015

Helix Angle Factor Zb = 0.981

Size Factor Zx = 1; 1

Work Hardening Factor Zw = 1

--- Factors for Bending

Application Factor KA = 1.25

Dynamic Factor KFv = 1.24

Face Load Factor KFb = 1.173

Transverse Load Factor KFa = 1.144

Total KF = 2.08

One-time Overloading Factor KAS = 1

Form Factor YFa = 2.132; 2.163

Stress Correction Factor YSa = 2.8; 2.495

Teeth with Grinding Notches Factor YSag = 1; 1

Helix Angle Factor Yb = 0.887

Contact Ratio Factor Yeps = 0.694

Alternating Load Factor Ya = 1; 1

Production Technology Factor Yt = 1; 1

Life Factor Yn = 1; 1

Notch Sensitivity Factor Yd = 1.595; 1.478

Size Factor Yx = 1; 1

Tooth Root Surface Factor Yr = 1

--- Results

Factor of Safety from Pitting SH = 1.898; 1.904

Factor of Safety from Tooth Breakage SF = 3.811; 3.906

Static Safety in Contact SHst = 4.015; 4.027

Static Safety in Bending SFst = 5.973; 6.608

Strength Check - True

Treapta de mers inapoi

--- Guide

External Gearing - DIN

Calculation of geometry: Calculates the number of teeth according to the center distance and module

Reaching the center distance: Teeth correction

Distribution of Correction: With Comp. of Slips

Load calculation: Calculates the torque according to the power and speed

Strength calculation: Strength check calculation

--- Basic Parameters

Desired Gear Ratio = 3.31

Pressure Angle alpha = 20°

Addendum a* = 1 (= 3 mm)

Clearance c* = 0.25 (= 0.75 mm)

Root Fillet = 0.38 (= 1.14 mm)

Addendum of Basic Rack = 1.25 (= 3.75 mm)

Helix Angle beta = 15°

Module m = 3 mm

Tangential Module mt = 3.1058 mm

Center Distance aw = 100 mm

Product Center Distance a = 99.387 mm

Total Unit Correction = 0.2089

Operating Pressure Angle alphaw = 20.9749°

Tangential Pressure Angle alphat = 20.6469°

Tan.Operating Pressure Angle alphatw = 21.5606°

Base Helix Angle betab = 14.0761°

Circular Pitch p = 9.425 mm

Tan. Circular Pitch pt = 9.757 mm

Base Circular Pitch ptb = 9.131 mm

Contact Ratio = 2.115 (1.4285 + 0.6865)

Precision Specification 6e26

Limit Deviation of Helix Angle Fb = 0.01 mm

Limit Deviation of Axis Parallelity fx = 0.01 mm

Limit Deviation of Axis Parallelity fy = 0.005 mm

--- Gear 1

Number of Teeth = 15

Helix Direction = Right

Unit Correction = 0.4018 (= 1.205 mm)

Pitch Diameter d = 46.587 mm

Base Circle Diameter db = 43.595 mm

Outside Diameter do = 54.972 mm

Root Diameter df = 41.498 mm

Work Pitch Diameter dw = 46.875 mm

Tooth Thickness s = 5.59 mm

Outside Tooth Thickness = 0.4574 (= 1.372 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.5366

Chordal Thickness T = 4.936 mm -0.03

-0.08

Chordal Thickness Height ht = 3.294 mm

Chordal Dimension M = 23.661 mm / 3 -0.028

-0.075

Dimension Over (Between) Wires M = 53.099 mm -0.075

-0.165

Wire Diameter dw = 4.5 mm

Comparative Number of Teeth zv = 16.5055

Limit Circumferential Run-out Fr = 0.016 mm

Limit Deviation of Axial Pitch fpt = ±0.007 mm

Limit Deviation of Basic Pitch fpb = ±0.0066 mm

--- Gear 2

Number of Teeth = 49

Helix Direction = Left

Unit Correction = -0.1929 (= -0.579 mm)

Pitch Diameter d = 152.186 mm

Base Circle Diameter db = 142.411 mm

Outside Diameter do = 157.002 mm

Root Diameter df = 143.528 mm

Work Pitch Diameter dw = 153.125 mm

Tooth Thickness s = 4.291 mm

Outside Tooth Thickness = 0.8076 (= 2.423 mm)

Facewidth = 25 mm

Facewidth Ratio = 0.1643

Chordal Thickness T = 3.789 mm -0.056

-0.136

Chordal Thickness Height ht = 1.719 mm

Chordal Dimension M = 59.444 mm / 7 -0.052

-0.127

Dimension Over (Between) Wires M = 155.638 mm -0.175

-0.375

Wire Diameter dw = 4.5 mm

Comparative Number of Teeth zv = 53.9178

Limit Circumferential Run-out Fr = 0.022 mm

Limit Deviation of Axial Pitch fpt = ±0.008 mm

Limit Deviation of Basic Pitch fpb = ±0.0075 mm

--- Load (Gear 1; Gear 2)

Power P = 48; 46.56 kW

Efficiency = 0.97

Speed n = 4400; 1346.9388 rpm

Torque Mk = 104.1741; 330.0931 Nm

Tangential Force Ft = 4472.1999 N

Radial Force Fr = 1767.1168 N

Axial Force Fa = 1198.3223 N

Normal Force Fn = 4958.5273 N

Circumferential Velocity v = 10.733 m/s

Resonance Speed nE1 = 32857.59 rpm

Strength Check According to DIN 3990:1987

Durability Lh = 25000 hour

--- Material Values

Tensile Strength = 640; 640 MPa

Yield Point in Tensile = 390; 390 MPa

Contact Fatigue Limit SigmaHlim = 1140; 1140 MPa

Bending Fatigue Limit SigmaFlim = 605; 605 MPa

Hardness in Tooth Core = 200; 200 HV

Hardness in Tooth Side = 600; 600 HV

Base Number of Load Cycles in Contact [10^6] = 100; 100

Base Number of Load Cycles in Bending [10^6] = 3; 3

Wöhler Curve Exponent for Contact = 10; 10

Wöhler Curve Exponent for Bending = 9; 9

Modulus of Elasticity in Tension [10^3] = 206; 206 MPa

Poisson's Ratio = 0.3; 0.3

Type of Treatment = 4; 4

--- Factors for Contact

Application Factor KA = 1

Dynamic Factor KHv = 1.24

Face Load Factor KHb = 1.229

Transverse Load Factor KHa = 1.144

Total KH = 1.743

One-time Overloading Factor KAS = 1

Elasticity Factor Ze = 189.81

Zone Factor Zh = 2.417

Contact Ratio Factor Zeps = 0.81

Single Pair Tooth Contact Factor ZB = 1.003; 1

Life Factor Zn = 1; 1

Lubricant Factor Zl = 0.962

Roughness Factor Zr = 1

Velocity Factor Zv = 1.015

Helix Angle Factor Zb = 0.981

Size Factor Zx = 1; 1

Work Hardening Factor Zw = 1

--- Factors for Bending

Application Factor KA = 1

Dynamic Factor KFv = 1.24

Face Load Factor KFb = 1.173

Transverse Load Factor KFa = 1.144

Total KF = 1.664

One-time Overloading Factor KAS = 1

Form Factor YFa = 2.132; 2.163

Stress Correction Factor YSa = 2.8; 2.495

Teeth with Grinding Notches Factor YSag = 1; 1

Helix Angle Factor Yb = 0.887

Contact Ratio Factor Yeps = 0.694

Alternating Load Factor Ya = 1; 1

Production Technology Factor Yt = 1; 1

Life Factor Yn = 1; 1

Notch Sensitivity Factor Yd = 1.595; 1.478

Size Factor Yx = 1; 1

Tooth Root Surface Factor Yr = 1

--- Results

Factor of Safety from Pitting SH = 1.03; 1.033

Factor of Safety from Tooth Breakage SF = 2.647; 2.713

Static Safety in Contact SHst = 2.178; 2.184

Static Safety in Bending SFst = 4.148; 4.589

Strength Check - True