DIN 3990 MDesign 2016 Esempio Spur Gear, Gear Rack

8/17/2019 DIN 3990 MDesign 2016 Esempio Spur Gear, Gear Rack

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Spur Gear, Gear Rack

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With the following program based on the standard calculations DIN 3960, the geometry of spur gears can be calculated.

This module has different operations and possibilities for calculation profile shift.These possibilities are the following: Automatic calculation and distribution of the total profile shift coefficient according to DIN 3992 (DIN 3993) Input of centre distance Input of total profile shift Input of profile shift

With the following program the strength examination (pitting load capacity, root load capacity, corrosion load capacity) of spur gears willbe calculated. Therefore the calculation base DIN 3990 and also the international ISO 6336 can chose by the user.

With this program standard gauges for spur gears will be calculated.

The application of the number of teeth thickness, spherical dim.-roll diameter DM, dev iations of center distance and dev iations of teeth

thickness are optional.

Groundwork calculations

Geometry of the spur gear pair and the gear

The standard calculations for this module are described by DIN 3960, edition March 1987.

The following DIN specifications will also be utilized: DIN 780 Module sequence for spur gears DIN 867 edition February 1986 (basic profile) DIN 3960 edition March 1987 (concept and dimension determination for spur gear pairs with involute gearing) DIN 3960 supplement 1, edition July 1980 DIN 3992 edition March 1964 (profile displacement for spur gears with outer gearing)

DIN 3993 edition August 1981, part 1 - 4 (geometric design of cy lindrical inner gear pairs).

Strength examination of spur gears

The standard calculations for this module are described by the following DIN specifications:

DIN 3990 Part 1 edition December 1987 (general influence factors) DIN 3990 Part 2 edition December 1987 (calculation of the pitting load capacity) DIN 3990 Part 3 edition December 1987 (calculation of the root load capacity) DIN 3990 Part 4 edition December 1987 (calculation of the corrosion load capacity) DIN 3990 Part 5 edition December 1987 (fatigue stress values and material qualities) DIN 3990 Part 6 edition December 1994 (operational stability) DIN 3990 Part 11 edition February 1989 (application standards for industrial gears) DIN 3961 edition August 1961 (ground tolerances) DIN 3962 Part 1 edition August 1978 (tolerances for deviation of individual determined dimensions)

DIN 3962 Part 2 edition August 1978 (tolerances for f lank line deviations) DIN 50 150, edition December 1976 1976 (conversion table for Vickers - Rockwell- Brinell hardness and ultimate strength) ISO 6336 Part 1 edition September 2006 (Basic principles, influence factors) ISO 6336 Part 2 edition September 2006 (Calculation of surface durability (pitting)) ISO 6336 Part 3 edition September 2006 (Calculation of tooth bending strength) ISO 6336 Part 6 edition September 2006 (Calculation of serv ice life under variable load) ISO 6336-1 Technical Corrigendum 1 ISO 6336-2 Technical Corrigendum 1 ISO 6336-3 Technical Corrigendum 1 ISO 1328 Part 1 edition August 2005 (Definitions and allowable values of deviations)

Gauge Design for Spur Gears

The standard calculations for this program are described by DIN 3960, edition March 1987.

The following DIN specifications will also be utilized: DIN 3961 edition August 1978 (tolerances for spur gearing) DIN 3962 supplement 1 edition August 1978 (tolerances for dev iation of individual determined dimensions) DIN 3964 edition November 1980 (axis position and Ax is position tolerances of housing for spur gears) DIN 3967 edition August 1978 (flank play, tooth thickness dimension, tooth thickness tolerances) DIN 3977 edition February 1981 (dimension diameter for the radial or diametric standard gauge of the tooth thickness of spur gears

(cylinder gears))


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Input data:


Calculation method Spur gear

Calculation variants All

Calculation standard DIN 3990

Type of toothing External toothing Spur gear geometry

Basic data

Normal modulus mn = 4,5 mm

Helical angle : 12 °

Centre distance a : 0 mm

Driving element Pinion

Input of geometry z1, z2

Number of teeth (pinion) z1 = 25

Number of teeth (wheel) z2 = 63

Translation ratio i = 2,52

Pinion Wheel

Tooth width b = 75 70 mm

Input method for tooth-tip height modification No input

Tip edge modification No

Addendum modification according to DIN 3992/3993

Input methode profile shift coefficients Input of x1 and x2

Profile shift coefficient (pinion) x1 = -0,257

Profile shift coefficient (wheel) x2 = -0,257

Basic gear rack Pinion Wheel

Tip clearance factor cP* = 0,25 0,25

Root fillet radius factor f P* : 0,45 0,45

Pressure angle p = 20 °

Tooth-tip thickness factor san* = 0,25

Pinion WheelTooth-tip height factor haP* = 1 1

Residual fillet undercut spr : 0 0 mm


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Cutter data Pinion Wheel

Number of cutter teeth z0 : 0 0

Basic gear rack profile shift coefficient x0 : 0 0

Spur Gear Calculation - Strength

Drive data

Load case Nominal load

Pinion Wheel

Number of meshed teeth nZE = 1 1

Application factor K A = 1

Dynamic factor K v : 0

Performance P = 15 kW

Rotation speed (pinion) n1 = 3000 1/min

Required lifetime Lh = 10000 h

Lubrication

Viscosity class for 40° oil = 32 cSt

Viscosity class for 100° oil = 1 cSt

Density for 15°C oil = 885 kg/m³

Oil temperature oil = 30 °C

Force level (according to FZG-test) 3

Type of oil distribution Splash lubrication

Material selection

Pinion - materials (strength values) according to MDESIGN database

International materials no

Material designation 16MnCr5

Material number 1.7131

Material group Casehardening steel

Heat treatment / State trial hardened

Standard dimension dNm = 16 mm

Standard dimension dNp = 16 mm

Ultimate strength for dNm R mN = 1000 N/mm²

Yield point for dNp R pN = 695 N/mm²

Tooth root strength Flim = 430 N/mm²

Surface durability (pitting) Hlim = 1500 N/mm²

Type of Material 4

Modulus of elasticity E = 210000 N/mm²

Poisson's ratio = 0,3

Hardness scale HBHardness = 0

Density = 7850 kg/m³

Linear expansion factor = 12 10^-6/K


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Temperature T = 20 °C

Wheel - materials (strength values) according to MDESIGN database

International materials no

Material designation 16MnCr5

Material number 1.7131

Material group Casehardening steel

Heat treatment / State trial hardened

Standard dimension dNm = 16 mm

Standard dimension dNp = 16 mm

Ultimate strength for dNm R mN = 1000 N/mm²

Yield point for dNp R pN = 695 N/mm²

Tooth root strength Flim = 430 N/mm²

Surface durability (pitting) Hlim = 1500 N/mm²

Type of Material 4

Modulus of elasticity E = 210000 N/mm²

Poisson's ratio = 0,3

Hardness scale HB

Hardness = 0Density = 7850 kg/m³

Linear expansion factor = 12 10^-6/K

Temperature T = 20 °C

Spur gear calculation material Pinion Wheel

Structure factor XW = 1 1

Thermal conduct ivity = 50 50 N/(s*K)

Heat capacity cM = 485 485 N*m/(kg

*K)

Root roughness R z = 1,6 1,6 µm

Tooth flank roughness R z = 1,6 1,6 µm

Data width load factor

Tooth modification No

Face load factor (root stress) K F : 0

Face load factor (contact stress) K H : 0

Face load factor (scuffing load) K B : 0

Bearing span l = 200 mm

Eccentricity (pinion) s : 0 mm

Shaft diameter at pinion dsh = 30 mm

Factor K' = 0.48

Type of helical toothing Simple


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Transverse load factors

Transverse load factor (root stress) K F : 0

Transverse load factor (contact stress) K H : 0

Transverse load factor (scuffing load) K B : 0

General input Pinion Wheel

Gearing quality 6 6

Design Disk Disk

Inner diameter of rim di : 0 0 mm

Tooth modification, base relief Ca : 0 0 µm

Loading type Pulsating Pulsating

Stress ratio = 0 0

Minimal root safety SFmin = 1

Minimal flank safety SHmin = 1

Minimal scuffing load safety SBmin = 1

Standard gauge spur gear

General data Pinion Wheel

Deviation of teeth thickness (DIN 3967) b b

Tolerances of teeth thickness (DIN 3967) 24 24

Number of teeth dimension k : 0 0

Spherical dimension- and roll diameter DM : 0 0 mm

Deviation of centre distances (DIN 3964) -

Free input deviations Pinion Wheel

Upper deviation of teeth thickness A sne : 0 0 µm

Lower deviation of teeth thickness A sni : 0 0 µm

Machining allowance q : 0 mm

Upper deviation of centre distances A ae : 0,01 µm

Lower deviation of centre distances A ai : 0 µm

Results:

General data

Effective number of teeth ratio u = 2,52

Effective translation ratio i = 2,52

Transverse pressure angle t = 20,41 °

Pressure angle at pitch cylinder wt = 18,455 °

Ground lead b = 11,267 °

Zero centre distance ad = 202,423 mm


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Centre distance a = 200,001 mm

Profile shift coefficient (pinion) x1 = -0,257

Profile shift coefficient (wheel) x2 = -0,257

Sum profile shift coefficient xs = -0,514

Length of path of contact g = 21,695 mm

Length of recess path ga = 7,844 mm

Length of approach path gf = 13,851 mm

Transverse cont act ratio = 1,602

Overlap ratio = 1,029

Total contact ratio

= 2,631

Number of teeth z = 25 63

Virtual number of teeth of helical gear zn = 26,573 66,963

Geometrical data

Reference diameter d = 115,013 289,834 mm

Base diameter db = 107,793 271,638 mm

Pitch diameter dw = 113,637 286,365 mm

Root diameter df = 101,45 276,271 mm

V-circle diameter dv = 112,7 287,521 mm

Tip diameter da = 121,482 296,302 mmTheoretical t ip diameter da th = 121,7 296,521 mm

Tip utility diameter dNa = 119,534 296,302 mm

Root form circle diameter dFf = 108,156 280,469 mm

Root form diameter dNf = 108,11 280,664 mm

Interference utility cF = -0,023 0,097 mm

Specific sliding at point A A = -4,677 0,824

Specific sliding at point E E = 0,424 -0,737

Tooth thickness on the t ip cylinder san = 3,651 3,774 mm

Tooth depth h = 10,016 10,016 mm Addendum ha = 3,234 3,234 mm

Dedendum hf = 6,782 6,782 mm

Root fillet radius factor f P* = 0,45 0,45

Root fillet radius F = 2,025 2,025 mm

Theoretical bottom clearance c = 1,125 1,125 mm

Actual topland play ctat = 1,125 1,125 mm

Tooth – tip height modification k = -0,1092 -0,1092 mm

Normal base pitch pen = 13,285 mm

Transverse base pitch pet = 13,546 mm

Normal pitch on base cylinder pbn = 13,285 mm

T ransverse pit ch on base cylinder pbt = 13,546 mm

Note:


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Condition for running without interference(cF1 > 0) is not met

Cutter data of gear rack

Cutter data pinion type cutter

Number of teeth z0 = 0 0

Profile shift coefficient x0 = 0 0

Topland height factor haP0* = 1,25 1,25

Root height factor hfP0* = 1 1

Reference diameter d0 = 0 0 mm

Base diameter db0 = 0 0 mm

Tip diameter da0

= 11,25 11,25 mm

Deddendum diameter (generat ion) dfE = 101,45 276,271 mm

Centre distance a0 = 56,241 143,724 mm

Zere centre distance ad0 = 57,507 144,917 mm

Pressure angle at pitch cylinder wt0 = 16,602 19,091 °

Results of calculation strength

Forces, moment, speed

Transverse tangential load

at reference cylinder

Ft = 830,277 N

Transverse tangential load

at pitch cylinder

Ftw = 840,333 N

Radial load at pitch cylinder Frw = 280,446 N

Axial load at pitch cylinder Faw = 176,481 N

Tooth load at pitch cylinder Fw = 903,302 N

Moment (pinion) T1 = 47,746 N*m

Moment (wheel) T2 = 120,321 N*m

Line load = 11,861 N/mm

Peripheral speed at reference cylinder v = 18,066 m/s

Peripheral speed at pitch cylinder vw = 17,85 m/s

Rotation speed (pinion) n1 = 3000 1/min

Rotation speed (wheel) n2 = 1190,476 1/min

Number of loading cycle (pinion) NL1 = 1800000000

Number of loading cycle (wheel) NL2 = 714285714

Note:

The lineload is < 100 N/mm so the risk of bad load distribution and vibrations is available !

General factors

Hekix slope deviation f H = 10 10 µm

Transverse pitch deviation f pe = 9 10 µm

Profile form deviation f f = 10 10 µm

Effect ive meshing slope deviat ion f pe eff = 9,287 µm

Effective profile form deviation f f eff = 9,25 µm

Flank line deviation f x = 10,271 µm

Manufacturing - flank line deviat ion f ma = 10 µm

Flank line deviation through pinion def. f sh = 0,204 µm


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Reduced mass / tooth width mred = 0,035 kg/mm

Individual spring rigidity c' = 1,469 N/(mm*µm)

Meshing spring rigidity c = 2,132 N/(mm*µm)

Resonance velocity (pinion) nE1 = 2965,243 1/min

Resonance velocity (gear) nE2 = 1176,684 1/min

Basic velocity NR = 1,012

Dynamic factor K v = 2,016

Face load factor (root stress) K F = 1,326

Face load factor (contact stress) K H = 1,389

Face load factor (scuffing load) K B = 1,389

Transverse load factor ( root st ress) K F = 1,165Transverse load factor (contact stress) K H = 1,165

Transverse load factor (scuffing load) K B = 1,165

Helix angle factor K B = 1,245

Pitting load capacity

Zone factor ZH = 2,587

Elasticity factor ZE = 191,646

Contact ratio factor Z = 0,79

Helix angle factor Z = 0,989

Work hardening factor ZW = 1

Lubricant factor ZL = 0,922 -

Ve locity factor Zv = 1,017 -

Roughness factor ZR = 1,071 -

Life factor for contact stress ZNT = 1 1,019

Size factor ZX = 1 1

Single pair tooth contact factor ZB = 1 ZD = 1,000

Pitting stress limit HG = 1507,76 1536,617 N/mm²

Allowable flank pressure HP = 1507,76 1536,617 N/mm²

Contact stress H = 265,68 265,68 N/mm²

Safety factor for pitting SH

= 5,675 5,784

At tainable lifet ime Lh = fat. strength fat. strength

Root load capacity

Overlapping factor (root stress) Y = 0,7

Helix angle factor Y = 0,9

Deep tooth factor Y DT = -

Rim thickness factor Y B = - -

Tooth form factor Y F = 1,494 1,362

Stress correction factor Y S = 1,71 1,874

Relativ notch sensitivity factor Y relT = 0,946 0,966

Relativ survace factor Y RrelT = 1,024 1,024Size factor Y X = 1 1

Life factor for tooth root stress Y NT = 1 1

Mean stress influence factor Y M = 1 1


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Tooth root stress limit FG = 833,799 850,981 N/mm²

Allowable root stress FP = 833,799 850,981 N/mm²

Toot h root stress F = 17,629 17,624 N/mm²

Safety factor for tooth breakage SF = 47,297 48,284

At tainable lifet ime Lh = fat. strength fat. strength

Scuffing load capacity

Angle factor X = 0,95

Lubricant factor XS = 1

Flash temperature calculation way

Load distribution factor X = 0,333

Flash factor XM = 50,235

Geometry factor XB = 0,264

Tangential line force at weigth wBt = 48,194 N/mm

Scuffing temperature = 99,42 °C

Corrosion safety factor SB = 25,759

Integral calculation way

Flash factor XM = 50,235

Geometry factor (pinion tip) XBE = 0,264

Pitch factor XQ = 1Tip relief factor XCa = 1

Contact ratio factor X = 0,337

Mass temperature M = 31,535 °C

Integral temperature int = 34,823 °C

Scuffing integral temperature intS = 99,42 °C

Corrosion safety factor SintS = 2,855

Scuffing load safety factor SSL = 14,394

Ultimate strengt h for pinion R m = 684,7 N/mm² (for deff = 107,79 mm )

Ultimate strength for gear R m = 545,7 N/mm² (for deff = 271,64 mm )

Yielding point for pinion R e = 475,9 N/mm² (for deff = 107,79 mm )

Yielding point for gear R e = 379,3 N/mm² (for deff = 271,64 mm )

Results check gauge

Case centre distance a = 200,001 mm

Maximum case centre distance amax = 200,001 mm

Minimum case centre distance amin = 200,001 mm

Theoretical backlash jt = 0,396 mm

Maximum theoretical backlash jt max = 0,429 mm

Minimum theoretical backlash jt min = 0,363 mm

Upper deviat ion of t eeth t hickness A sne = -125 -230 µm

Lower deviat ion of t eeth t hickness A sni = -150 -270 µm

Tolerance of teeth thickness Tsn = 25 40 µm

Fluctuation of teeth thickness R s = 14 18 µm


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Nominal teeth thickness (theoretical) snth = 6,227 6,227 mm

Nominal teeth thickness sn = 6,227 6,227 mm

Maximum nominal teeth thickness sn max = 6,102 5,997 mm

Minimum nominal teeth thickness sn min = 6,077 5,957 mm

Base tangent lengt h (theoretical) Wkth = 34,099 89,788 mm

Base tangent length Wk = 34,099 89,788 mm

Maximum base tangent length Wk max = 33,981 89,572 mm

Minimum base tangent length Wk min = 33,958 89,534 mm

Number of teeth dimension k = 3 7

Measure roller diameter DM = 7,5 7,5 mm

Radial gauge spheres/roller Mrk = 61,165 148,419 mmMaximum radial gauge spheres/roller Mrke = 61,182 148,447 mm

Minimum radial gauge spheres/roller Mrk i = 61,147 148,391 mm

Diametral gauge spheres Mdk = 122,103 296,748 mm

Diametral gauge roller MdR = 122,329 296,838 mm

max. Diametral gauge spheres Mdke = 122,137 296,804 mm

min. Diametral gauge spheres Mdk i = 122,068 296,693 mm

max. Diametral gauge roller MdRe = 122,364 296,894 mm

min. Diametral gauge roller MdRi = 122,294 296,783 mm

Factor of deviation of base tangent lengthA w = 0,94 0,94

Factor of deviation radial spheres/roller A mr = 1,39 1,391

Factor of deviat ion diamet ral rolle r A md = 2,78 2,782

Factor of deviation diametral spheres A md = 2,774 2,781

Specific sliding accord. to DIN 3960

External toothing

x1 = -0,257

x2 = -0,257

xs = -0,514

ga = 7,844

gf = 13,851

g = 21,695

Kga1 = 0,246

Kga2 = 0,341

Kgf1 = 0,341

Kgf2 = 0,246

spec. sliding: pinion

A = -4,677

E = 0,424

spec. sliding: gear

A = 0,824

E = -0,737

Meshing Line

[mm]

Kg

1,3

-1,3

2,6

-2,6

3,9

-3,9

5,2

-5,2

0

0 6,331 18,994 31,657 44,320 56,983

12

C

A E

Kg1

Kg2

0,442

-0,442

1,114

-1,114

0,2460,341

-0,246-0,341


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Tooth profile (evolvent) pinion

df1

d1

dw1

da1

Tooth profile (evolvent) gear

df2

d2

dw2

da2


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Gap of tooth (envelope curve, evolvent) pinion

df1

d1dw1

da1

Gap of tooth (envelope curve, evolvent) gear

df2

d2

dw2

da2


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Side view pinion

d f1 d1 da1

Side view gear

d f2 d2 da2


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Front view pinion

df1 d1da1

Front view gear

df2 d2da2


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Gear wheel (evolvent) pinion

Gear wheel (evolvent) gear


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Pinion, Pitting Bearing Capacity Diagram

material : 16MnCr5

load cycle

HG

[N/mm²]

0

600

1200

1800

2400

3000

210 310 410 510 610 710 810 910 1010

load cycle [-] lifetime [h]

1010 55555,56

910 5555,56

810 555,56

710 55,56

610 5,56

510 0,56

410 0,06

310 0,01

210 0,00

static

time strength

fatigue strength

Gear, Pitting Bearing Capacity Diagram

material : 16MnCr5

load cycle

HG

[N/mm²]

0

600

1200

1800

2400

3000

210 310 410 510 610 710 810 910 1010


1010 140000,00

910 14000,00

810 1400,00

710 140,00

610 14,00

510 1,40

410 0,14

310 0,01

210 0,00

static

time strength

fatigue strength


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Pinion, Root Bearing Capacity Diagram

material : 16MnCr5

load cycle

FG

[N/mm²]

0

600

1200

1800

2400

3000

210 310 410 510 610 710 810 910 1010


1010 55555,56

910 5555,56

810 555,56

710 55,56

610 5,56

510 0,56

410 0,06

310 0,01

210 0,00

static

time strength

fatigue strength

Gear, Root Bearing Capacity Diagram

material : 16MnCr5

load cycle

FG

[N/mm²]

0

600

1200

1800

2400

3000

210 310 410 510 610 710 810 910 1010


1010 140000,00

910 14000,00

810 1400,00

710 140,00

610 14,00

510 1,40

410 0,14

310 0,01

210 0,00

static

time strength

fatigue strength

DIN 3990 MDesign 2016 Esempio Spur Gear, Gear Rack

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Transcript of DIN 3990 MDesign 2016 Esempio Spur Gear, Gear Rack