memoriu tehnic

1

MEMORIU TEHNIC

REDUCTOR TIP RI

RAD TUDOR DAN

2

1 Cuprins

1. Calcule Preliminare .....................................................................................................................................4

2. Transmisi prin curele ..................................................................................................................................6

2.1 Curele Trapezoidale ............................................................................................................................6

2.1.1 Formule de calcul .......................................................................................................................6

2.1.2 Calcule ........................................................................................................................................9

2.1.3 Raport ...................................................................................................................................... 13

2.2 Curele Dintate .................................................................................................................................. 15

2.2.1 Formule de calcul .................................................................................................................... 15

2.2.2 Calcule ..................................................................................................................................... 18

2.2.3 Raport ...................................................................................................................................... 21

3 Angrenaj Cilindric cu Dinti Inclinati ......................................................................................................... 23

3.1 Formule de calcul ............................................................................................................................ 23

3.2 Calcule ............................................................................................................................................. 37

3.3 Raport .............................................................................................................................................. 41

4 Transmisie cu Lant ................................................................................................................................... 45


4.2 Calcule ............................................................................................................................................. 52

4.3 Raport .............................................................................................................................................. 56

5 Arbori ....................................................................................................................................................... 59

5.1 Fortele rezultate din angrenare ....................................................................................................... 59

5.2 Dimensionarea constructiva a arborilor .......................................................................................... 60

5.3 Calculul reactiunilor din lagare folosind MathCad .......................................................................... 62

5.4 Formule de calcul in MechSoft ........................................................................................................ 64

5.5 Arborele 1 ........................................................................................................................................ 65

5.5.1 Rezultate calcul arbore 1 ......................................................................................................... 67

5.6 Arborele 2 ........................................................................................................................................ 72

5.6.1 Rezultate calcul arbore 2 ......................................................................................................... 74

6 Rulmenti .................................................................................................................................................. 79


6.2 Calcule rulment Arbore 1 ................................................................................................................ 81

6.3 Raport rulment arbore 1 ................................................................................................................. 83

6.4 Calcul rulment arbore 2 ................................................................................................................... 84

6.5 Raport rulment arbore 2 ................................................................................................................. 86

7 Pene ......................................................................................................................................................... 87

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7.2 Calcule ............................................................................................................................................. 88

7.2.1 Pana Capat Arbore 1 ................................................................................................................ 88

7.2.2 Raport pana capat arbore 1 ..................................................................................................... 88

7.2.3 Pana Roata Dintata Arbore 1 ................................................................................................... 89

7.2.4 Raport pana roata dintata arbore 1 ........................................................................................ 89

7.2.5 Pana Capat Arbore 2 ................................................................................................................ 90

7.2.6 Raport pana capat arbore 2 ..................................................................................................... 91

7.2.7 Pana Roata Dintata Arbore 2 ................................................................................................... 92

7.2.8 Raport pana roata dintata arbore 2 ........................................................................................ 92

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1. Calcule Preliminare

5

Toate calculele facute in MechSoft sunt facute pe gradul de expert.

6

2. Transmisi prin curele

2.1 Curele Trapezoidale

2.1.1 Formule de calcul Pentru calculul si dimensionarea a curelelor trapezoidale am folosit programul MechSoft care se

bazeaza pe urmatoarele formule:

7

It calculates forces, moments and speeds from the specified input power, speed and transmission

efficiency.

9

2.1.2 Calcule

In fereastra “Geometry” (fig. 2.1.1) s-a introdus puterea, turatia, diametrele rotilor de curea,

numarul de curele, numarul de roti, coeficientul de alunecare al curelei. Pentru calcul s-au ales

curele inguste de tip SPZ.

Figura 2.1.1 Fereastra “Geometry”

In fereastra “Strenght Calculation” (fig. 2.1.2) se alege factorul de serviciu in functie de tipul

masinariei, tipul motorului si numarul de ore de functionare pe zi. Tot aici se poate observa ca

valoarea sarcinii admisibile Pall este apropiata sarcinii calculate Pv.

Din calculul de dimensionare rezulta lungimea standardizata a curelei de 1250 mm, dimensiunea

rotilor de curea si distant axiala. In figura 2.1.3 si 2.1.4 sunt prezentate dimensiunile rotilor de

curea, se urmareste ca diametrul rotii 2 sa fie apropiat de cel al rotii 2 din angrenaj. In figura 2.1.5

este prezentata distanta axiala.

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Figura 2.1.2 Fereastra “Strenght Calculation”

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Figura 2.1.3 Roata de curea 1


12

Figura 2.1.5 Distanta axiala

In continuare este prezentat raportul generat de MechSoft.

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2.1.3 Raport --------------------------------------------------------

12-05-2012 V-belts Component Wizard (Version 4.3.1040)

--------------------------------------------------------

--- Guide

Calculation Type - ISO

Length Calculation: Belt Length

Calculation Type: Strength Check

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

Belt Length: Standard

Belt Length: Pitch

--- Basic Parameters

Narrow V-belts,V-belts Component Wizard

Belt type SPZ

Belt Length Lp = 1250 mm

Number of Belts N = 2

Belt width w = 9.7 mm

Belt height h = 8 mm

--- Sheave Parameters

Sheave Width Bf = 28 mm

Calculated Belt Width Wp = 8.5 mm

Min. Groove Depth above Calculation Width bmin = 2 mm

Min. Groove Depth below Calculation Width hmin = 9 mm

Fillet Radius of Sheave Upper Edge r1 = 0.5 mm

Fillet Radius of Sheave Lower Edge r2 = 1 mm

Distance Between Groove Axes e = 12±0.3 mm

Distance Between Groove Axis and Sheave Face f = 8 +1 -1 mm

Groove surface texture Ra = 0.8 µm

Sliding Sheave = 2

--- Sheave 1

Pitch Diameter dp1 = 105 mm

Outer diameter Da1 = 109 mm

Groove Angle alpha1 = 38°

Speed n1 = 2250 rpm

Torque T1 = 23.4276 Nm

X Coordinate = 0 mm

Y Coordinate = 0 mm

Arc of Contact b1 = 157.54°

Arc of Contact Coefficient Ca1 = 0.94

--- Sheave 2

Pitch Diameter dp2 = 240.24 mm

Outer diameter Da2 = 244.24 mm

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Groove Angle alpha2 = 38°

Transmission Ratio i = 2.288

Speed n2 = 983.3916 rpm


X Coordinate = 347.266 mm

Y Coordinate = 0 mm

Center Distance = 347.266 mm

Arc of Contact b2 = 202.46°

Arc of Contact Coefficient Ca2 = 1.05

--------------------------------------------------

Strength Check

--------------------------------------------------

Power P = 5.52 kW

Efficiency h = 0.96

Belt Slip = 0 %

Service Factor Cp = 1.1

Belt Length Correction Coeff. Cl = 0.95

Number of Belts Coefficient Ck = 0.95

Tangential Force F = 446.24 N

Centrifugal Force Ff = 10.711 N

Force in Strained Belt Strand F1 = 554.295 N

Force in Loose Belt Strand F2 = 108.055 N

Min. Working Pre-tension Fu = 331.175 N

Radial Force in Bearings Fr = 655.457 N

Circumferential Velocity v = 12.37 m/s

Table Load Ptab = 3.983 kW

Allowable Load Pall = 6.789 kW

Calculated Load Pv = 6.072 kW

Strength Check - True

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2.2 Curele Dintate

2.2.1 Formule de calcul

Pentru calculul si dimensionarea a curelelor dintate am folosit programul MechSoft care se bazeaza

pe urmatoarele formule:

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2.2.2 Calcule

In fereastra “Geometry” (fig. 2.2.1) s-a introdus puterea, turatia, numarul de dinti ai rotilor de curea,

numarul de roti si randamentul. Pentru calcul s-au ales curele ISO 5296.

Figura 2.2.1 Fereastra “Geometry”

In fereastra “Strength” (fig. 2.2.3) se alege factorul de serviciu in functie de tipul masinariei, tipul

motorului si numarul de ore de functionare pe zi.

Din calculul de dimensionare rezulta numarul de dinti standardizat ai curelei 126, dimensiunea

rotilor de curea si distant axiala.


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Figura 2.2.3 Fereastra “Strength”

Dupa calculul de dimensionare se alege tipul de curea H 100 care o sarcina admisibila Fa de 620N

iar sarcina calculate Fc este de 607N.

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Figura 2.2.4 Distanta axiala

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2.2.3 Raport -----------------------------------------------------------------

12-05-2012 Synchronous Belt Component Wizard (Version 4.3.1031)

-----------------------------------------------------------------

--- Guide

Calculation type: Select belt type - ISO

Length Calculation: Belt length

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

Belt length: Standard

--- Base Parameters

Synchronous Belts,Synchronous Belt ISO 5296 Component Wizard

Standard Belt No. H 100

Number of Belt Teeth Lz = 126

Tooth pitch p = 12.7 mm

Belt Width b = 25.4 mm

Fillet radius inside belt rr = 1.02 mm

Fillet radius outside belt ra = 1.02 mm

Belt tooth height ht = 2.29 mm

Belt height hs = 4.3 mm

Tooth width s = 6.12 mm

--- Pulley Parameters

Number of Pulleys K = 2

Sliding Pulley = 2

Max. fillet radius of root r1 = 1.6 mm

Fillet radius of top r2 = 1.6 mm

Pulley tooth head width bg = 4.19 mm

Pulley tooth height hc = 3.05 mm

Tooth angle alpha = 40°

Unflanged Pulley Width Bf = 31.2 mm

--- Pulley 1

Number of Teeth N 1 = 33

Speed n1 = 2250 rpm


Pitch diameter dw = 133.4 mm

Outside diameter da = 132.028 mm

X Coordinate = 0 mm

Y Coordinate = 0 mm

--- Pulley 2


Transmission Ratio i = 2.2727

Speed n2 = 990 rpm


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Pitch diameter dw = 303.19 mm

Outside diameter da = 301.818 mm


Y Coordinate = 0 mm

Center Distance = 449.18 mm

--------------------------------------------------

Strength Check

--------------------------------------------------

Power P = 5.52 kW

Efficiency h = 0.96

Service Factor Cp = 1.6

Ratio Factor Ki = 0

Length Correction Factor Cl = 1

Teeth in Mesh Factor Kz = 1

Pulley Tractive Force F = 351.229 N

Pulley Centrifugal Force Ff = 44.954 N

Total Tensile Force Ft = 396.183 N


Table Load Ftab = 620 N

Allowable Load Fa = 620 N

Calculated Load Fc = 606.92 N


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3 Angrenaj Cilindric cu Dinti Inclinati

3.1 Formule de calcul

Pentru calculul si dimensionarea angrenajului cilindric am folosit programul MechSoft care se

bazeaza pe urmatoarele formule:

29

The strength calculation is also based on the fixed-end beam calculation and it contains many

factors for including the majority of effects.

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3.2 Calcule

Pentru calculul angrenajului incepem prin selectarea modului de calcul (fig. 3.1) si introducerea

clasei de tolerante din fereastra “Tolerances”. (fig. 3.2)

Figura 3.1 Fereastra “Guide”

Figura 3.2 Distanta axiala

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Puterea randamentul si turatia sunt introduse in fereastra “Load” (fig. 3.3)

Figura 3.3 Fereastra “Load”

In fereastra “Strength” (fig. 3.6) alegem materialul pentru rotile dintate, factorul de aplicatia KA si

durabilitatea angrenajului.

Materialul pentru pinion este de o durabilitate mai mica ca si materialul pentru roata condusa

deoarece dinti de pe pinion sunt solicitati mai frecvent.

Factorul de aplicatie este ales in functie de modul de transmisie a puterii.

Figura 3.4 Factorul de Aplicatie si Durabilitatea

Figura 3.5 Proprietatile materialelor alese pentru angrenaj

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Figura 3.6 Fereastra “Strength”

Figura 3.7 Fereastra “Geometry”

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In fereastra “Geometry” (fig. 3.7) s-a introdus: numarul de dinti ai rotilor, unghiul de inclinare a

dintilor, modulul, latimea rotilor si factorul de corectie a danturi. Dantura pinionului este inclinata

pe dreapta iar modulul si distant axiala sunt standardizate.

Dupa dimensionarea angrenajului in fereastra “Dimensions” (fig. 3.8) sunt afisate dimensiunile

rotilor dintate.

Figura 3.8 Fereastra “Dimensions”

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3.3 Raport -------------------------------------------------------------

12-06-2012 Spur Gearing Component Wizard (Version 4.3.1037)

-------------------------------------------------------------

--- Guide

External Gearing - ISO

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

correction and helix direction

Distribution of Correction: With Comp. of Slips


Strength calculation: Strength check calculation


Desired Gear Ratio = 5.0385

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 = 11°

Module m = 2.5 mm

Tangential Module mt = 2.5468 mm

Center Distance aw = 200.001 mm

Product Center Distance a = 199.923 mm

Total Unit Correction = 0.031

Operating Pressure Angle alphaw = 20.062°

Tangential Pressure Angle alphat = 20.3439°

Tan.Operating Pressure Angle alphatw = 20.4036°

Base Helix Angle betab = 10.3291°

Circular Pitch p = 7.854 mm

Tan. Circular Pitch pt = 8.001 mm

Base Circular Pitch ptb = 7.502 mm

Contact Ratio = 2.9946 (1.6341 + 1.3605)

Precision Specification 7

Limit Deviation of Helix Angle Fb = 0.02 mm

Limit Deviation of Axis Parallelity fx = 0.02 mm

Limit Deviation of Axis Parallelity fy = 0.01 mm

--- Gear 1

Number of Teeth = 26

Helix Direction = Right

Unit Correction = 0.29983 (= 0.75 mm)

Pitch Diameter d = 66.217 mm

Base Circle Diameter db = 62.086 mm

Outside Diameter do = 72.716 mm

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Root Diameter df = 61.466 mm

Work Pitch Diameter dw = 66.242 mm

Tooth Thickness s = 4.473 mm

Outside Tooth Thickness = 0.6287 (= 1.572 mm)

Facewidth = 58 mm

Facewidth Ratio = 0.8457

Chordal Thickness T = 3.949 mm

Chordal Thickness Height ht = 2.531 mm

Chordal Dimension M = 27.304 mm / 4

Dimension Over (Between) Wires M = 70.617 mm

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 27.3664

Limit Circumferential Run-out Fr = 0.03 mm

Limit Deviation of Axial Pitch fpt = ±0.012 mm

Limit Deviation of Basic Pitch fpb = ±0.011 mm

--- Gear 2

Number of Teeth = 131

Helix Direction = Left

Unit Correction = -0.26883 (= -0.672 mm)

Pitch Diameter d = 333.63 mm

Base Circle Diameter db = 312.819 mm

Outside Diameter do = 337.285 mm

Root Diameter df = 326.036 mm

Work Pitch Diameter dw = 333.759 mm

Tooth Thickness s = 3.438 mm

Outside Tooth Thickness = 0.8307 (= 2.077 mm)

Facewidth = 56 mm

Facewidth Ratio = 0.1679

Chordal Thickness T = 3.036 mm

Chordal Thickness Height ht = 1.275 mm

Chordal Dimension M = 118.771 mm / 16

Dimension Over (Between) Wires M = 335.164 mm

Wire Diameter dw = 3.5 mm

Comparative Number of Teeth zv = 137.8848

Limit Circumferential Run-out Fr = 0.052 mm

Limit Deviation of Axial Pitch fpt = ±0.014 mm

Limit Deviation of Basic Pitch fpb = ±0.013 mm

--- Load (Gear 1; Gear 2)

Power P = 5.273; 5.1675 kW

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Efficiency = 0.98

Speed n = 983.378; 195.1743 rpm

Torque Mk = 51.2046; 252.8324 Nm

Tangential Force Ft = 1546.5782 N

Radial Force Fr = 575.2783 N

Axial Force Fa = 300.6243 N

Normal Force Fn = 1677.2998 N


Resonance Speed nE1 = 13739.41 rpm

----------------------------------------------------

Strength Check According to ISO 6336:1996

----------------------------------------------------

Durability Lh = 25000 hour

--- Material Values

&Material designation: 37Cr4; 37MnSi5

Tensile Strength = 883; 880 MPa

Yield Point in Tensile = 637; 635 MPa

Contact Fatigue Limit SigmaHlim = 690; 658 MPa

Bending Fatigue Limit SigmaFlim = 512; 493 MPa

Hardness in Tooth Core = 200; 200 HV

Hardness in Tooth Side = 600; 600 HV

Base Number of Load Cycles in Contact [10^6] = 50; 50

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

Wöhler Curve Exponent for Contact = 10; 10

Wöhler Curve Exponent for Bending = 6; 6

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

Poisson's Ratio = 0.3; 0.3

Type of Treatment = 0; 0

--- Factors for Contact

Application Factor KA = 1.25

Dynamic Factor KHv = 1.215

Face Load Factor KHb = 1.836

Transverse Load Factor KHa = 1.867

Total KH = 5.207

One-time Overloading Factor KAS = 1

Elasticity Factor Ze = 189.81

Zone Factor Zh = 2.453

Contact Ratio Factor Zeps = 0.782

Single Pair Tooth Contact Factor ZB = 1; 1

Life Factor Zn = 1; 1

Lubricant Factor Zl = 0.937

Roughness Factor Zr = 1

Velocity Factor Zv = 0.944

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Helix Angle Factor Zb = 0.991

Size Factor Zx = 1; 1

Work Hardening Factor Zw = 1

--- Factors for Bending

Application Factor KA = 1.25

Dynamic Factor KFv = 1.215

Face Load Factor KFb = 1.712

Transverse Load Factor KFa = 1.867

Total KF = 4.856

One-time Overloading Factor KAS = 1

Form Factor YFa = 2.267; 2.218

Stress Correction Factor YSa = 1.622; 1.654

Teeth with Grinding Notches Factor YSag = 1; 1

Helix Angle Factor Yb = 0.908

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 = 1.092; 1.09

Size Factor Yx = 1; 1

Tooth Root Surface Factor Yr = 1

--- Results

Factor of Safety from Pitting SH = 1.049; 1

Factor of Safety from Tooth Breakage SF = 4.656; 4.331

Static Safety in Contact SHst = 3.036; 3.026

Static Safety in Bending SFst = 10.657; 9.934

Strength Check – True

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4 Transmisie cu Lant


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4.2 Calcule

In fereastra “Geometry” (fig. 4.1) introducem puterea, randamentul, numarul de scripeti, numarul

de lanturi, numarul de dinti ai rotilor de lant si turatia. Pentru calcul s-a ales lanturi standardizate

ISO. Numarul de zale s-a ales par deoarece acest tip de lant este mai rezistent.

Figura 4.1 Fereastra “Geometry”

Figura 4.2 Fereastra “Strength”

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In fereastra “Strength” (fig. 4.2) este introdus factorul de utilizare, factorul de lubrefiere si

durabilitatea lantului.

Figura 4.3 Factor utilizare Y

Figura 4.4 Factor lubrefiere

In fereastra “Resonance” (fig 4.5) sunt prezentate turatiile limita pentru care lantul intra in

rezonanta, observam ca lantul sadisface conditiile de siguranta.

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Figura 4.5 Fereastra “Resonance”

Figura 4.6 Fereastra “Dimensions”

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Dupa dimensionarea transmisiei in fereastra “Dimensions” sunt ilustrate dimensiunile rotilor de lant

si in figura 4.7 este prezentata distant axiala.

Figura 4.6.1 Fereastra “Dimensions 2”


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4.3 Raport -------------------------------------------------------------

12-06-2012 Roller Chain Component Wizard (Version 4.3.1036)

-------------------------------------------------------------

--- Guide

Calculation type: Strength Check - ISO

Length Calculation: Number of chain links


Number of chain links: Only even


Chains,Roller Chain Component Wizard

Standard Chain No. 24 B

Number of Chain Strands r = 2

Number of Chain Links X = 46

--- Sprockets Parameters

Number of Sprockets K = 2

Sliding Sprocket = 2

Chain Pitch p = 38.1 mm

Sprocket tooth width bf1 = 23.622 mm

Sprocket rim width bfx = 71.982 mm

Transverse pitch pt = 48.36 mm

Fillet radius of tooth rx = 38.1 mm

Width of Chamfer ba = 4.953 mm

Tooth roughness Ra = 6.3 µm

--- Sprocket 1


Speed n1 = 195.174 rpm

Torque T 1 = 250.311 Nm

Shaft Moment of Inertia I1 = 10 kgm2

Pitch diameter of sprocket d = 159.204 mm

Addendum diameter of sprocket da = 167.215 ÷ 181.429 mm

Max. diameter of sprocket rim dgmax = 105.864 mm

Dedendum diameter of sprocket df = 133.804 mm

Caliper Diameter Dc = 132.643 mm

X Coordinate = 0 mm

Y Coordinate = 0 mm

Minimum form:

Radius of tooth space bottom ri = 12.827 mm

Radius of sprocket tooth side re = 45.72 mm

Sprocket angle alpha = 133°

Maximum form:



57


--- Sprocket 2


Gear Ratio i = 2.2308

Speed n2 = 87.4918 rpm

Torque T 2 = 541.635 Nm

Shaft Moment of Inertia I2 = 10 kgm2

Pitch diameter of sprocket d = 352.389 mm

Addendum diameter of sprocket da = 362.987 ÷ 374.614 mm

Max. diameter of sprocket rim dgmax = 299.049 mm

Dedendum diameter of sprocket df = 326.989 mm

Caliper Diameter Dc = 326.473 mm


Y Coordinate = 0 mm

Minimum form:




Maximum form:




--------------------------------------------------

Strength Check

--------------------------------------------------

Power P = 5.116 kW

Efficiency h = 0.97

Stroke Factor Y = 1.4

Lubrication Factor m = 0.3

Required Chain Life Lh = 25000 hour

Maximum Chain Elongation dL = 3 %

Diagram Power Pd = 49.678 kW

Sprocket Tractive Force F = 3175.349 N

Sprocket Centrifugal Force Ff = 36.861 N

Total Tensile Force Ft = 3212.21 N


Static Safety Coeff. ks = 87.167 > 7

Dynamic Safety Coeff. kd = 62.262 > 6.7

Calculated Joint Pressure pc = 2.899 MPa

Allowable Joint Pressure pa = 4.035 MPa

Calculated Chain Life th = 102938 hour

Pins and Plates Life thl = 1.003E+12 hour

Rollers and Bushings Life thr = 168568 hour


58

--- Resonance Speed

for Transversal Vibration nt1 = 90.813 rpm

for Longitudinal Vibration nt2 = 4380.687 rpm

from Polygonal Effect nt3 = 216.942 rpm

from Circumferential Run-out nt4 = 2820.245 rpm

from Non-precise Pitch nt5 = 108.471 rpm

59

5 Arbori

5.1 Fortele rezultate din angrenare

Pentru dimensionarea arborilor este necesar cunoasterea sensului si directiei fortelor ce actioneaza

in angrenaj. In figura 5.1 sunt prezentate fortele ce actioneaza intr-un angrenaj cilindric cu dinti

inclinati, dantura pinionului fiind inclinata pe dreapta si acesta se roteste in sens orar.

Valoarea fortelor este preluata din MechSoft, prezentate in figura 3.3.


Pornind de la aceasta figura am prezentat fortele ce actioneaza asupra arborilor in figura 5.2.

Figura 5.2 Incarcarea arborilor

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5.2 Dimensionarea constructiva a arborilor Arborii sunt dimensionati constructive pornind de la capatul acestora si momentul de torsiune care

este transmis.

Pentru primul arbore s-a ales un diametru de 28mm iar pentru al doilea arbore unul de 42mm.

Momentul de torsiune in functie de care s-a facut selectia este corespunzator coloanei b. Momentul

pentru arborele 1 este de 51.2 Nm iar pentru arborele 2 este de 250 Nm, aceste moment sunt

calculate la pagina 4.

Figura 5.3 Selectarea capetelor de arbore

In functie de diametrul capatului de arbore se alege lungimea acestuia de serie scurta.

Figura 5.4 Selectarea lungimea capetelor de arbore

Dimensionarea constructive a arborilor este prezentata in figura 5.5.

61

Figura 5.5 Schita Arborilor

62

5.3 Calculul reactiunilor din lagare folosind MathCad

Pornind de la aceasta schita am calculate reactiunile in lagare folosind Mathcad.

64

5.4 Formule de calcul in MechSoft

Arbori sunt verificati folosind MechSoft care efectueaza calculele dupa urmatoarele formule.

This is the calculation of a beam with variable sections lying on M supports with N loaded places.

The number of supports is limited to 10 and number of loaded places to 20.

65

5.5 Arborele 1

In MechSoft arborele este construit pornind de la schita prezentata in figura 5.5.

Figura 5.6 Arborele 1

In urmatorul pas sunt introduse punctele de reazam si fortele ce actioneaza asupra arborelui.

Figura 5.7 Coordonatele reazamului 1

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Figura 5.9 Fortele ce solicita arborele 1

In stanga sunt introduse fortele ce actioneaza la capatul arborelui iar in dreapta fortele ce actioneaza

din angrenaj conform schitei din figura 5.2.

Figura 5.10 Reactiunile din lagare conform MechSoft

Se observa ca suma reactiunilor din reazeme sunt identice cu cele din MathCad calculate la pagina

62.

67

5.5.1 Rezultate calcul arbore 1

Figura 5.11 Forte taietoare

Figura 5.12 Momente de incovoiere

68

Figura 5.13 Unghi de rotatie

Figura 5.14 Sageata

69

Figura 5.15 Eforturi de incovoiere

Figura 5.16 Eforturi de forfecare

70

Figura 5.17 Eforturi de torsiune

Figura 5.18 Eforturi axiale

71

Figura 5.19 Suma eforturilor

Figura 5.20 Dimensiuni recomandate

72

5.6 Arborele 2

In MechSoft arborele este construit pornind de la schita prezentata mai sus.

Figura 5.21 Arborele 2

In urmatorul pas sunt introduse punctele de reazam si fortele ce actioneaza asupra arborelui.


73


Figura 5.24 Fortele ce solicita arborele 2

In stanga sunt introduse fortele ce actioneaza la capatul arborelui iar in dreapta fortele ce actioneaza

din angrenaj conform schitei din figura 5.2.

Figura 5.25 Reactiunile din lagare conform MechSoft

Se observa ca suma reactiunilor din reazeme sunt identice cu cele din MathCad calculate la pagina

62.

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5.6.1 Rezultate calcul arbore 2

Figura 5.26 Forte taietoare

Figura 5.27 Momente de incovoiere

75

Figura 5.28 Unghi de rotatie

Figura 5.29 Sageata

76

5.30 Eforturi de incovoiere

Figura 5.31 Eforturi de forfecare

77

5.32 Eforturi de torsiune

Figura 5.33 Eforturi axiale

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5.34 Suma eforturilor

Figura 5.35 Dimensiuni recomandate

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6 Rulmenti

Pentru calculul rulmentilor s-a folosit MechSoft si deoarece cei doi rulmenti de pe arbore sunt

identici s-a dimensionat doar acela care este supus la sarcini mai mari. In cazul reversarii sensului

de rotatie se schimba doar sensul fortei tangential si axiale ceea ce nu influenteaza suma reactiunilor

din lagare.


Rulmenti sunt calculati in MechSoft cu urmatoarele formule:

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6.2 Calcule rulment Arbore 1

Figura 6.1 Dimensionare rulment arbore 1

Pentru arborele unu am ales rulmenti cu role conice. Ca si sarcini am introdus ce-a mai mare forta

din reazem si forta axiala ce rezulta din angrenare. Temperatura de functionare este de 70 °C si

durabilitatea necesara este de 25000 ore de functionare. Coeficientul fd este ales din figura 6.2.

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Figura 6.2 Factor de utilizare

Figura 6.3 Rezultate rulment arbore 1

Conform rezultatelor rulmentul ce indeplineste conditiile de durabilitate este de tip 33208

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6.3 Raport rulment arbore 1 ----------------------------------------------------------------

12-18-2012 Rolling Bearing Component Wizard (Version 4.3.1010)

----------------------------------------------------------------

--- Guide

Strength Calculation Type: Check Calculation

--- Input

Required Life Lh = 22000 hour

Coeffic. of Add'l Forces fd = 1.5

Working Temperature ft = 70 °C

Required Reliability a1 = 90 %

Lubrication Type - Oil

--- Load Conditions

Number of Different Load Conditions Ni = 1

Radial Load Fr1 = 1808 N

Axial Load Fa1 = 300.6 N

Bearing Speed n1 = 983.378 rpm

Work Time t1 = 100 %

--- Bearing type

SKF (B),Tapered roller single row bearings SKF

Bearing designation: 33208

Inside Bearing Diameter d = 40 mm

Outside Bearing Diameter D = 80 mm

Bearing Width B = 32 mm

Radius of Bearing Fillet or Chamfer r = 1.5 mm

Min. Diameter of Shaft Shoulder damin = 47 mm

Max. Diameter of Hub Shoulder Damax = 73 mm

Max. Fillet Radius of Shoulder ramax = 1 mm

Bearing Mass m = 0.77 kg

Dynamic loading capacity of bearing = 23605 N

Static loading capacity of bearing = 29674.77 N

Limiting speed for lubrication by grease [rpm] = 4300

Limiting speed for lubrication by oil [rpm] = 5600

--- Results

Equivalent Dynamic Load P = 2712 N

Equivalent Static Load P0 = 1808 N

Static Safety Coefficcient s0 = 16.41

Power Loss by Friction Pz = 10.05 W

Necessary Minimum Load Fmin = 472.1 N

Calculated Bearing Life Lh = 22988.2 hour

Coeffic. of Over-revolving kn = 5.69

84

6.4 Calcul rulment arbore 2

Figura 6.4 Dimensionare rulment arbore 2

Pentru arborele doi am ales rulmenti cu role conice. Ca si sarcini am introdus ce-a mai mare forta

din reazem si forta axiala ce rezulta din angrenare. Temperatura de functionare este de 70 °C si

durabilitatea necesara este de 25000 ore de functionare. Coeficientul fd este ales din figura 6.2

identic cu cel folosit la dimensionarea rulmentului de pe arborele unu.

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Figura 6.5 Rezultate rulment arbore 2

Conform rezultatelor rulmentul ce indeplineste conditiile de durabilitate este de tip 32312

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6.5 Raport rulment arbore 2 ----------------------------------------------------------------

12-18-2012 Rolling Bearing Component Wizard (Version 4.3.1010)

----------------------------------------------------------------

--- Guide

Strength Calculation Type: Check Calculation

--- Input

Required Life Lh = 25000 hour

Coeffic. of Add'l Forces fd = 1.5

Working Temperature ft = 70 °C

Required Reliability a1 = 90 %

Lubrication Type - Oil

--- Load Conditions

Number of Different Load Conditions Ni = 1

Radial Load Fr1 = 5647 N

Axial Load Fa1 = 300.6 N

Bearing Speed n1 = 195.174 rpm

Work Time t1 = 100 %

--- Bearing type

SKF (B),Tapered roller single row bearings SKF

Bearing designation: 32312

Inside Bearing Diameter d = 60 mm

Outside Bearing Diameter D = 130 mm

Bearing Width B = 46 mm

Radius of Bearing Fillet or Chamfer r = 3 mm

Min. Diameter of Shaft Shoulder damin = 74 mm

Max. Diameter of Hub Shoulder Damax = 118 mm

Max. Fillet Radius of Shoulder ramax = 2 mm

Bearing Mass m = 2.85 kg

Dynamic loading capacity of bearing = 51481 N

Static loading capacity of bearing = 65194.58 N

Limiting speed for lubrication by grease [rpm] = 2600

Limiting speed for lubrication by oil [rpm] = 3600

--- Results

Equivalent Dynamic Load P = 8470.5 N

Equivalent Static Load P0 = 5647 N

Static Safety Coefficcient s0 = 11.54

Power Loss by Friction Pz = 9.35 W

Necessary Minimum Load Fmin = 1029.62 N

Calculated Bearing Life Lh = 34985.89 hour

Coeffic. of Over-revolving kn = 18.45

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7 Pene


Penele sunt dimensionate in MechSoft folosind urmatoarele formule.

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7.2 Calcule

7.2.1 Pana Capat Arbore 1

Figura 7.1 Dimensionare pana capat arbore 1

Ca date de intrare sunt introduse: puterea, turatia arborelui, diametrul tronsonului pe care se afla

canalul de pana si lungimea acestuia. Materialul ales pentru toate tipurile de pene este otel de o

rezistenta de rupere la tractiune minima de 590 MPa conform STAS.

7.2.2 Raport pana capat arbore 1

--------------------------------------------------------

12-13-2012 Key Component Wizard : 1 (Version 4.3.1120)

--------------------------------------------------------

Loads:

Power P = 5.273 kW

Speed n = 983.378 rpm

Torque T = 51.205 Nm

Dimensions:

Shaft Diameter d = 28.00 mm

Key 8x7

Key Length L = 32 mm

Active Key Length Lf = 24 mm

Keyway Length = 32 mm

Joint Properties:

Material = Steel

Allowable Pressure = 150 MPa

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Tensile Strength = 600 MPa

Reduced Allowable Pressure = 150 MPa

Keys [No.] = 1

Reduction Coefficients of Joint Capacity Due to :

- Product. Inaccur. on More Key Joints = 1

- Mounting Type and Character of Load = 1

Calculation Results:

Min. Active Key Length = 6.967 mm

Calculated pressure = 43.542 MPa


7.2.3 Pana Roata Dintata Arbore 1

Figura 7.2 Dimensionare pana roata dintata arbore 1

Observam ca diametrul arborelui si dimensiunea penei sunt afisate cu rosu, asta se intampla

deoarece pana de dimensiuni mici nu este recomandata pentru un diametru asa de mare al

tronsonului. Aceasta nu este o problema deoarece pana rezista la solicitare.

7.2.4 Raport pana roata dintata arbore 1

--------------------------------------------------------


--------------------------------------------------------

Loads:

Power P = 5.273 kW



Dimensions:

90


Key 8x7




Joint Properties:

Material = Steel




Keys [No.] = 1








7.2.5 Pana Capat Arbore 2

Figura 7.3 Dimensionare pana capat arbore 2

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7.2.6 Raport pana capat arbore 2

--------------------------------------------------------


--------------------------------------------------------

Loads:

Power P = 5.116 kW



Dimensions:


Key 12x8




Joint Properties:

Material = Steel




Keys [No.] = 1








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7.2.7 Pana Roata Dintata Arbore 2

Figura 7.4 Dimensionare pana roata dintata arbore 2

Aici problema este similara cu ce-a de la arborele 1.

7.2.8 Raport pana roata dintata arbore 2

--------------------------------------------------------


--------------------------------------------------------

Loads:

Power P = 5.116 kW



Dimensions:


Key 12x8




Joint Properties:

Material = Steel




Keys [No.] = 1


93







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