Karol Kurantowicz ABEQ wyniki przekładnia planetarna
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Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Strona 1 z 8
Report of cylindrical gear calculation according to DIN 3990 , ISO 6336 Grzegorz Poniewaz Politechnika Lubelska Wydzial Mechaniczny; Katedra PKM ul. Nadbystrzycka 36 20-618 Lublin Tel: 815384206 Fax: 815384200 eMail: ---
08. November 2016 - 12:53 Version 3.04
Project: Default Filename: standard.pgt
Contents • Input values ◦ Geometry ◦ Allowances and quality ◦ Tool ◦ Load capacity ◦ Options • Results of calculation ◦ Geometry ◦ Test dimensions ◦ Tolerances ◦ Load capacity (general influence factors) ◦ Load capacity (flank) ◦ Load capacity (root) ◦ Load capacity (Scuffing) (ISO/TR 13989) ◦ References
Messages • Annulus: Max. diameter of the material data is less than the largest wheel diameter. • Planet - Annulus: Reduced mass will be calculated in addition to DIN 3990 Part 1 by using the moments of inertia. • Symmetric arrangement of the planets is possible.
Input values Geometry Planetary gear train Normal module (mn)
1.500 mm
Pressure angle (αn)
20.000 °
Helix angle (β)
0.000 °
Number of planets
3
Minimum distance between the planets
1.000 mm
Planet carrier
driven
Sun No. of teeth (z) Profile shift coefficient (x*) Face width (b)
Planet
Annulus
driving
driven
20
37
Gear box fixed -94
0.318
0.030
-0.377
17.000
17.000
17.000 mm
Addendum chamfer (hk)
0.000
0.000
0.000 mm
Chamfer
1.000
1.000
1.000 mm
Inner / Outer diameter
0.000
0.000
400.030 mm
Rim width (Pre-setting) (bS)
0.000
0.000
17.000 mm
Allowances and quality sun - planet Tolerance field
planet - annulus
js 8 (ISO 286)
js 8 (ISO 286)
Centre distance allowance max. value (Aae)
19.500
19.500
µm
Centre distance allowance min. value (Aai)
-19.500
-19.500
µm
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2016-11-08
Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Sun Quality
Planet
Strona 2 z 8
Annulus
6
6
Backlash allowance sequence
cd
cd
7 d
Tolerance sequence
25
25
26
Upper tooth thickness allowance (Asne)
-54.000
-70.000
-80.000 µm
Lower tooth thickness allowance (Asni)
-84.000
-110.000
-160.000 µm
Tool Sun Tool
Planet
Annulus
Hob
Basic rack profile
Hob
Gear shaper cutter
ISO 53 Profile C ISO 53 Profile C
ISO 53 Profile C
Tip form:
---
--- Radius with straight line
Tool tip radius (ρ*ao)
0.250
0.250
0.250
Addendum coefficient (h*aP)
1.250
1.250
1.250
Dedendum coefficient (h*fP)
1.000
1.000
1.000
Height of the buckling root flank (h*k0)
0.000
0.000
0.000
Angle of the buckling root flank
0.000
0.000
0.000 °
Protuberance (p*rpo)
0.000
0.000
0.000
Allowance (q)
0.000
0.000
0.000 mm
Angle of protuberance (αp)
0.000
0.000
0.000 °
No. of teeth (z0)
---
---
62
Profile shift coefficient (z 0)
---
---
0.377
Tip circle (z0)
---
---
97.882
Manufacturing centre distance (z 0)
---
---
-24.000
Manufacturing centre distance max. value (z 0)
---
---
-24.108
Manufacturing centre distance min. value (z0)
---
---
-24.213
Load capacity Min. safety for load capacity calculation Min. safety flank
1.100
Min. safety tooth root
1.300
Min. safety scuffing (integral) 2.000 Min. safety scuffing (flash)
3.000
Planetary gear train Calculation method ISO 6336 Method B Endurance
11000.000 h
Power
Sun Power (P)
Annulus -4
0 kW
26.711
-152.255
125.543 Nm
1430.000
250.877
Torque (T) Rotational speed (n)
Planet carrier 4
Factors for load capacity calculation sun - planet Face coefficient (KHβ)
planet - annulus
1.331
Calculation method of load distribution factor Bearing of the planet wheel
1.469 DIN 3990 T1 Method C securely fixed bolt
Pinion correction planetary gear train
without pinion correction
Bearing span (lp)
Application factor (KA) Mesh load factor (Kγ)
0.000 1/min
0.000 mm
1.350 1.000 No pitting permitted
Load stage in the FZG test
12
Type of profile modification Relative structure factor (XW rel T)
1.000
Lubricant Kind of lubrication
Oil splash lubrication
http://abeg.gwj.de/tmp/journal1005791660125359651.html
2016-11-08
Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Describtion of lubricant
Strona 3 z 8
Standard ISO VG 220
Comment
Standard oil ISO viscosity class VG 220
Viscosity at 40°C
220.000 mm²/s
Viscosity at 100°C
17.770 mm²/s
Density
0.900 g/cm³
Temperature of lubricant
70.000 °C
Load stage in the FZG test
12
Material Source of data Sun
Datenbank Stahlwissen NaviMat 3.1, DIN EN 10084:1998-06, DIN 3990 Edition 12/87 Part 5
Material quality Sun Source of data Planet
MQ (according to DIN 3990 Part 5, edition 12/87) Datenbank Stahlwissen NaviMat 3.1, DIN EN 10084:1998-06, DIN 3990 Edition 12/87 Part 5
Material quality Planet
MQ (according to DIN 3990 Part 5, edition 12/87)
Source of data Annulus Datenbank Stahlwissen NaviMat 3.1, DIN EN 10084:1998-06, DIN 3990 Edition 12/87 Part 5 Material quality Annulus
MQ (according to DIN 3990 Part 5, edition 12/87)
Sun Material
Annulus
20MnCr5
20MnCr5
Case hardening steel
Case hardening steel
Case hardening steel
case hardened
case hardened
case hardened
618.000 HB
618.000 HB
618.000 HB
0.300
0.300
215000.000
215000.000
550.000
550.000
7.790
7.790
7.790 kg/dm³
1490.000
1490.000
1490.000 N/mm²
430.000
430.000
430.000 N/mm²
Type of material
Kind of treatment
Planet
20MnCr5
Hardness: Poisson's ratio (ν) E-Module Yield point (σB) Density (ρ) Fatigue strength of surface pressure (σHlim) Fatigue strength of nominal bending stress in the tooth root (σFlim) Roughness tooth flank (Rz)
0.300 215000.000 N/mm² 550.000
N/mm²
4.000
4.000
4.000 µm
16.000
16.000
16.000 µm
Hardening depth tooth root optimal
0.150
0.150
0.150
mm
Hardening depth tooth flank optimal
0.546
0.699
0.699
mm
Roughness tooth root (Rz)
Options Factor for minimal gear ring thickness 2.000
Results of calculation Geometry Planetary gear train Normal circular pitch (pn)
4.712 mm
Transverse pitch (pt)
4.712 mm
Circular pitch (pe)
4.428 mm
Transverse circular pitch (pet)
4.428 mm
Transverse pressure angle (αt) 20.000 ° Helix angle base diameter (βb)
0.000 °
Transverse module (mt)
1.500 mm
Ratio (i)
5.700
sun - planet Working transverse pressure angle (αwt)
planet - annulus
21.747
21.747
°
Helix Angle on the pitch circle diameter (βw)
0.000
0.000
°
Gear ratio (u)
1.850
-2.541
Working centre distance (a)
43.250
-43.250
mm
Standard centre distance (ad)
42.750
-42.750
mm
Sum of profile shift coefficients (x*)
0.347
-0.347
Transverse contact ratio (εα)
1.514
1.845
Face contact ratio (εβ)
0.000
0.000
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Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Strona 4 z 8
Total contact ratio (εγ)
1.514
1.845
Length of path of contact (gα)
6.702
8.170
mm
Beginning of path of contact (gf)
2.901
5.269
mm
End of path of contact (ga)
3.802
2.901
mm
Backlash pitch diameter min. value (jti)
109.805
135.805
µm
Backlash pitch diameter max. value (jte)
208.195
284.195
µm
Backlash normal plane min. value (jni )
103.183
127.615
µm
Backlash normal plane max. value (jne)
195.639
267.056
µm
Radial backlash min. value (jri)
137.636
170.225
µm
Radial backlash max. value (jre)
260.962
356.225
µm
Sun
Planet
Annulus
Generating shift coefficient min. value (x*E Min)
0.241
-0.071
-0.524
Generating shift coefficient max. value (x*E Max)
0.268
-0.034
-0.450
Addendum modification (k)
-0.021
-0.021
0.021 mm
Reference diameter (d)
30.000
55.500
-141.000 mm
Pitch circle diameter (dw)
30.351 56.149 / 56.149
-142.649 mm
Base diameter (db)
28.191
52.153
-132.497 mm
Diameter at V-Circle (dv)
30.953
55.589
-142.132 mm
Root diameter (df)
27.203
51.839
-145.882 mm
generated root diameter min. value (df Min)
26.973
51.537
-146.307 mm
generated root diameter max. value (df Max)
27.055
51.647
-146.098 mm
Form diameter of dedendum (dFf)
28.419
53.059
-145.280 mm
Form diameter of dedendum min. value (dFf min)
28.341
52.903
-145.774 mm
Form diameter of dedendum max. value (dFf max)
28.367
52.958
-145.534 mm
Diameter of active flank root (dNf)
28.712 53.798 / 53.154
-144.899 mm
Diameter of active flank root min. value (dNf min)
28.678 53.761 / 53.104
-144.971 mm
Diameter of active flank root max. value (dNf max)
28.746 53.835 / 53.205
-144.826 mm
Tip diameter allowance max. value (Adae)
75.000
75.000
75.000 µm
Tip diameter allowance min. value (Adai)
-75.000
-75.000
-75.000 µm
Tip diameter (da)
33.911
58.547
-139.090 mm
Tip diameter min. value (da Min)
33.836
58.472
-139.165 mm
Tip diameter max. value (da Max)
33.986
58.622
-139.015 mm
Form diameter of addendum (dFa)
33.911
58.547
-139.090 mm
Diameter of active flank tip (dNa)
33.911 58.547 / 58.547
-139.090 mm
Tip clearance (c)
0.375
0.375 / 0.417
0.375 mm
Tip clearance min. value (cmin)
0.414
0.392 / 0.468
0.414 mm
Tip clearance max. value (cmax)
0.583
0.547 / 0.687
Sliding factor at tooth root (Kgf)
-0.294
-0.386 / -0.114
0.583 mm -0.063
Sliding factor at tooth point (Kga)
0.386
0.294 / 0.063
0.114
Specific sliding at tooth root (ζf)
-1.642
-1.642 / -0.622
-0.152
0.621
0.621 / 0.132
0.384
Specific sliding at tooth point (ζa)
Test dimensions Sun No. of the teeth for span measurement (k)
Planet
Annulus
3
5
Measurement diameter (span measurement) (dM)
30.567
56.124
-142.810 mm
Span measurement nominal value (Wk)
11.817
20.735
-53.286 mm
Span measurement min. value (Wk min)
11.738
20.631
-53.436 mm
Span measurement max. value (Wk max)
11.766
20.669
-53.361 mm
3.000
2.750
2.750 mm
Measurement diameter (measurement over balls) (dM)
31.189
55.959
-141.501 mm
Measurement over balls nominal value (MdK)
35.586
59.712
-137.809 mm
Measurement over balls min. value (MdK min)
35.428
59.456
-138.260 mm
Measurement over balls max. value (MdK max)
35.484
59.549
-138.035 mm
Measurement over pins nominal value (MdR)
35.586
59.712
-137.809 mm
Measurement over pins min. value (MdR min)
35.428
59.456
-138.260 mm
Measurement over pins max. value (MdR max)
35.484
59.549
-138.035 mm
Transverse tooth thickness (st)
2.703
2.389
1.944 mm
Transverse tooth thickness min. value (st min)
2.619
2.279
1.784 mm
Transverse tooth thickness max. value (st max)
2.649
2.319
1.864 mm
Transverse tooth thickness at V-Circle (svt)
2.392
2.360
2.387 mm
Transverse tooth thickness at V-Circle min. value (svt min)
2.306
2.250
2.226 mm
Transverse tooth thickness at V-Circle max. value (svt max)
2.336
2.290
2.307 mm
Chordal tooth thickness at V-Circle nominal value (svn)
2.390
2.359
2.387 mm
Chordal tooth thickness at V-Circle min. value (svn min)
2.306
2.250
2.225 mm
Chordal tooth thickness at V-Circle max. value (svn max)
2.336
2.290
2.306 mm
Diameter of ball or pin (DM)
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Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Strona 5 z 8
Chordal height (hv)
1.525
1.504
1.511 mm
Circular normal space width at V-Circle (evt)
2.470
2.360
2.363 mm
Normal chordal tooth thickness at standard pitch diameter nominal value (s n)
2.700
2.388
1.944 mm
Normal chordal tooth thickness at standard pitch diameter min. value (sn min)
2.616
2.279
1.782 mm
Normal chordal tooth thickness at standard pitch diameter max. value (sn max)
2.646
2.319
1.863 mm
Normal chordal tooth thickness at tip diameter nominal value (san)
0.873
1.143
1.269 mm
Normal chordal tooth thickness at tip diameter min. value (san min)
0.730
0.990
1.087 mm
Normal chordal tooth thickness at tip diameter max. value (san max)
0.860
1.106
1.215 mm
Chordal height at standard pitch diameter (ha)
2.017
1.549
0.948 mm
Circular normal space width at reference diameter (et)
2.009
2.324
2.768 mm
Tooth depth (h)
3.354
3.354
3.396 mm
Tolerances Sun
Planet
Annulus
Profile form deviation (ff)
6
6
Profile slope deviation (fHα)
5
5
7 µm
Total profile deviation (Ff)
8
8
12 µm
Adjacent pitch deviation (fp)
7
7
11 µm
Tooth to tooth pitch deviation (fu)
8
9
14 µm
18
25
40 µm
8
10
16 µm
14
16
25 µm
Total tooth alignment deviation (Fβ)
9
9
12 µm
Tooth alignment slope deviation (fHβ)
8
8
11 µm
Tooth alignment form deviation (fβf)
4
4
5 µm
18
20
32 µm
Total deviation of circular pitch (Fp) Variation of tooth thickness (Rs) Runout (Fr)
Double flank pitch deviation (F´´i) Double flank pitch step (f´´i)
9 µm
6
8
14 µm
Single flank pitch deviation (F´ i)
22
28
45 µm
Single flank pitch step (f´i)
10
11
16 µm
Load capacity (general influence factors) sun - planet Carried width (tooth root) (b*)
planet - annulus
0.000
0.000
593.585
593.585
N
0.000
0.000
N
Radial force on the reference diameter (Fr)
216.047
216.047
N
Normal tooth force on the reference diameter (Fn)
631.680
631.680
N
Circumferential force on the pitch circle diameter (Ftw)
586.723
586.723
N
0.000
0.000
N
Radial force on the pitch circle diameter (Frw)
234.043
234.043
N
Normal tooth force on the pitch circle diameter (Fnw)
631.680
631.680
N
Circumferential speed (v)
1.852
1.852
m/s
Running-in allowance (yα)
0.525
0.825
µm
Running-in allowance (yf)
0.450
0.675
µm
Running-in allowance (yp)
0.525
0.825
µm
Layout value of the profile correction (Cay)
2.030
2.030
µm
Correction coefficient (CM)
0.800
0.800
Gear body coefficient (CR)
1.000
1.000
Basic rack profile coefficient (CBS)
0.975
0.975
Single spring stiffness (c´)
7.448
8.341
N/(mm µm)
Meshing spring stiffness (cγα)
10.317
13.626
N/(mm µm)
Meshing spring stiffness (cγβ)
8.769
11.582
N/(mm µm)
Reduced mass (mred)
0.001
0.010
Reference speed (N)
0.024
0.068
Sub-critical range
Sub-critical range
48246.176
9325.313
1.018
1.081
Nominal circumferential force at pitch cylinder (Ft) Axial force on the reference diameter (Fa)
Axial force on the pitch circle diameter (Faw)
Resonance speed (nE1) Dynamic coefficient (Kv)
kg/mm
1/min
Bearing of the planet Relative speed planet (nrel)
-637.364 1/min
Tangential force planet carrier (FtS) 1187.170 N Centrifugal force planet (Fz)
9.458 N
Sun
Planet
Annulus
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Load capacity (flank) sun - planet
Sun
planet - annulus
Planet
Annulus
Load capacity (root) sun - planet
planet - annulus
Sun
Load capacity (Scuffing) (ISO/TR 13989)
Planet
Annulus
sun planet
planet annulus
ϑ ϑ
Integral temperature method ϑ
ϑ ϑ ϑ ϑ
Flash temperature method ϑ
ϑ
ϑ ϑ
Contact temperature sun - planet A
B
C
-0,1
0
D
E
83,5 83 82,5 82 81,5 81 80,5 80 79,5 79 78,5 78 77,5 77 76,5 76
-0,6
-0,5
-0,4
-0,3
-0,2
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Contact temperature planet - annulus A
B
D
C
E
75,25 75 74,75 74,5 74,25 74 73,75 73,5 73,25 73 72,75 72,5
References
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
Strona 1 z 8
Report of cylindrical gear calculation according to DIN 3990 , ISO 6336 Grzegorz Poniewaz Politechnika Lubelska Wydzial Mechaniczny; Katedra PKM ul. Nadbystrzycka 36 20-618 Lublin Tel: 815384206 Fax: 815384200 eMail: ---
08. November 2016 - 12:53 Version 3.04
Project: Default Filename: standard.pgt
Contents • Input values ◦ Geometry ◦ Allowances and quality ◦ Tool ◦ Load capacity ◦ Options • Results of calculation ◦ Geometry ◦ Test dimensions ◦ Tolerances ◦ Load capacity (general influence factors) ◦ Load capacity (flank) ◦ Load capacity (root) ◦ Load capacity (Scuffing) (ISO/TR 13989) ◦ References
Messages • Annulus: Max. diameter of the material data is less than the largest wheel diameter. • Planet - Annulus: Reduced mass will be calculated in addition to DIN 3990 Part 1 by using the moments of inertia. • Symmetric arrangement of the planets is possible.
Input values Geometry Planetary gear train Normal module (mn)
1.500 mm
Pressure angle (αn)
20.000 °
Helix angle (β)
0.000 °
Number of planets
3
Minimum distance between the planets
1.000 mm
Planet carrier
driven
Sun No. of teeth (z) Profile shift coefficient (x*) Face width (b)
Planet
Annulus
driving
driven
20
37
Gear box fixed -94
0.318
0.030
-0.377
17.000
17.000
17.000 mm
Addendum chamfer (hk)
0.000
0.000
0.000 mm
Chamfer
1.000
1.000
1.000 mm
Inner / Outer diameter
0.000
0.000
400.030 mm
Rim width (Pre-setting) (bS)
0.000
0.000
17.000 mm
Allowances and quality sun - planet Tolerance field
planet - annulus
js 8 (ISO 286)
js 8 (ISO 286)
Centre distance allowance max. value (Aae)
19.500
19.500
µm
Centre distance allowance min. value (Aai)
-19.500
-19.500
µm
http://abeg.gwj.de/tmp/journal1005791660125359651.html
2016-11-08
Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Sun Quality
Planet
Strona 2 z 8
Annulus
6
6
Backlash allowance sequence
cd
cd
7 d
Tolerance sequence
25
25
26
Upper tooth thickness allowance (Asne)
-54.000
-70.000
-80.000 µm
Lower tooth thickness allowance (Asni)
-84.000
-110.000
-160.000 µm
Tool Sun Tool
Planet
Annulus
Hob
Basic rack profile
Hob
Gear shaper cutter
ISO 53 Profile C ISO 53 Profile C
ISO 53 Profile C
Tip form:
---
--- Radius with straight line
Tool tip radius (ρ*ao)
0.250
0.250
0.250
Addendum coefficient (h*aP)
1.250
1.250
1.250
Dedendum coefficient (h*fP)
1.000
1.000
1.000
Height of the buckling root flank (h*k0)
0.000
0.000
0.000
Angle of the buckling root flank
0.000
0.000
0.000 °
Protuberance (p*rpo)
0.000
0.000
0.000
Allowance (q)
0.000
0.000
0.000 mm
Angle of protuberance (αp)
0.000
0.000
0.000 °
No. of teeth (z0)
---
---
62
Profile shift coefficient (z 0)
---
---
0.377
Tip circle (z0)
---
---
97.882
Manufacturing centre distance (z 0)
---
---
-24.000
Manufacturing centre distance max. value (z 0)
---
---
-24.108
Manufacturing centre distance min. value (z0)
---
---
-24.213
Load capacity Min. safety for load capacity calculation Min. safety flank
1.100
Min. safety tooth root
1.300
Min. safety scuffing (integral) 2.000 Min. safety scuffing (flash)
3.000
Planetary gear train Calculation method ISO 6336 Method B Endurance
11000.000 h
Power
Sun Power (P)
Annulus -4
0 kW
26.711
-152.255
125.543 Nm
1430.000
250.877
Torque (T) Rotational speed (n)
Planet carrier 4
Factors for load capacity calculation sun - planet Face coefficient (KHβ)
planet - annulus
1.331
Calculation method of load distribution factor Bearing of the planet wheel
1.469 DIN 3990 T1 Method C securely fixed bolt
Pinion correction planetary gear train
without pinion correction
Bearing span (lp)
Application factor (KA) Mesh load factor (Kγ)
0.000 1/min
0.000 mm
1.350 1.000 No pitting permitted
Load stage in the FZG test
12
Type of profile modification Relative structure factor (XW rel T)
1.000
Lubricant Kind of lubrication
Oil splash lubrication
http://abeg.gwj.de/tmp/journal1005791660125359651.html
2016-11-08
Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Describtion of lubricant
Strona 3 z 8
Standard ISO VG 220
Comment
Standard oil ISO viscosity class VG 220
Viscosity at 40°C
220.000 mm²/s
Viscosity at 100°C
17.770 mm²/s
Density
0.900 g/cm³
Temperature of lubricant
70.000 °C
Load stage in the FZG test
12
Material Source of data Sun
Datenbank Stahlwissen NaviMat 3.1, DIN EN 10084:1998-06, DIN 3990 Edition 12/87 Part 5
Material quality Sun Source of data Planet
MQ (according to DIN 3990 Part 5, edition 12/87) Datenbank Stahlwissen NaviMat 3.1, DIN EN 10084:1998-06, DIN 3990 Edition 12/87 Part 5
Material quality Planet
MQ (according to DIN 3990 Part 5, edition 12/87)
Source of data Annulus Datenbank Stahlwissen NaviMat 3.1, DIN EN 10084:1998-06, DIN 3990 Edition 12/87 Part 5 Material quality Annulus
MQ (according to DIN 3990 Part 5, edition 12/87)
Sun Material
Annulus
20MnCr5
20MnCr5
Case hardening steel
Case hardening steel
Case hardening steel
case hardened
case hardened
case hardened
618.000 HB
618.000 HB
618.000 HB
0.300
0.300
215000.000
215000.000
550.000
550.000
7.790
7.790
7.790 kg/dm³
1490.000
1490.000
1490.000 N/mm²
430.000
430.000
430.000 N/mm²
Type of material
Kind of treatment
Planet
20MnCr5
Hardness: Poisson's ratio (ν) E-Module Yield point (σB) Density (ρ) Fatigue strength of surface pressure (σHlim) Fatigue strength of nominal bending stress in the tooth root (σFlim) Roughness tooth flank (Rz)
0.300 215000.000 N/mm² 550.000
N/mm²
4.000
4.000
4.000 µm
16.000
16.000
16.000 µm
Hardening depth tooth root optimal
0.150
0.150
0.150
mm
Hardening depth tooth flank optimal
0.546
0.699
0.699
mm
Roughness tooth root (Rz)
Options Factor for minimal gear ring thickness 2.000
Results of calculation Geometry Planetary gear train Normal circular pitch (pn)
4.712 mm
Transverse pitch (pt)
4.712 mm
Circular pitch (pe)
4.428 mm
Transverse circular pitch (pet)
4.428 mm
Transverse pressure angle (αt) 20.000 ° Helix angle base diameter (βb)
0.000 °
Transverse module (mt)
1.500 mm
Ratio (i)
5.700
sun - planet Working transverse pressure angle (αwt)
planet - annulus
21.747
21.747
°
Helix Angle on the pitch circle diameter (βw)
0.000
0.000
°
Gear ratio (u)
1.850
-2.541
Working centre distance (a)
43.250
-43.250
mm
Standard centre distance (ad)
42.750
-42.750
mm
Sum of profile shift coefficients (x*)
0.347
-0.347
Transverse contact ratio (εα)
1.514
1.845
Face contact ratio (εβ)
0.000
0.000
http://abeg.gwj.de/tmp/journal1005791660125359651.html
2016-11-08
Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Strona 4 z 8
Total contact ratio (εγ)
1.514
1.845
Length of path of contact (gα)
6.702
8.170
mm
Beginning of path of contact (gf)
2.901
5.269
mm
End of path of contact (ga)
3.802
2.901
mm
Backlash pitch diameter min. value (jti)
109.805
135.805
µm
Backlash pitch diameter max. value (jte)
208.195
284.195
µm
Backlash normal plane min. value (jni )
103.183
127.615
µm
Backlash normal plane max. value (jne)
195.639
267.056
µm
Radial backlash min. value (jri)
137.636
170.225
µm
Radial backlash max. value (jre)
260.962
356.225
µm
Sun
Planet
Annulus
Generating shift coefficient min. value (x*E Min)
0.241
-0.071
-0.524
Generating shift coefficient max. value (x*E Max)
0.268
-0.034
-0.450
Addendum modification (k)
-0.021
-0.021
0.021 mm
Reference diameter (d)
30.000
55.500
-141.000 mm
Pitch circle diameter (dw)
30.351 56.149 / 56.149
-142.649 mm
Base diameter (db)
28.191
52.153
-132.497 mm
Diameter at V-Circle (dv)
30.953
55.589
-142.132 mm
Root diameter (df)
27.203
51.839
-145.882 mm
generated root diameter min. value (df Min)
26.973
51.537
-146.307 mm
generated root diameter max. value (df Max)
27.055
51.647
-146.098 mm
Form diameter of dedendum (dFf)
28.419
53.059
-145.280 mm
Form diameter of dedendum min. value (dFf min)
28.341
52.903
-145.774 mm
Form diameter of dedendum max. value (dFf max)
28.367
52.958
-145.534 mm
Diameter of active flank root (dNf)
28.712 53.798 / 53.154
-144.899 mm
Diameter of active flank root min. value (dNf min)
28.678 53.761 / 53.104
-144.971 mm
Diameter of active flank root max. value (dNf max)
28.746 53.835 / 53.205
-144.826 mm
Tip diameter allowance max. value (Adae)
75.000
75.000
75.000 µm
Tip diameter allowance min. value (Adai)
-75.000
-75.000
-75.000 µm
Tip diameter (da)
33.911
58.547
-139.090 mm
Tip diameter min. value (da Min)
33.836
58.472
-139.165 mm
Tip diameter max. value (da Max)
33.986
58.622
-139.015 mm
Form diameter of addendum (dFa)
33.911
58.547
-139.090 mm
Diameter of active flank tip (dNa)
33.911 58.547 / 58.547
-139.090 mm
Tip clearance (c)
0.375
0.375 / 0.417
0.375 mm
Tip clearance min. value (cmin)
0.414
0.392 / 0.468
0.414 mm
Tip clearance max. value (cmax)
0.583
0.547 / 0.687
Sliding factor at tooth root (Kgf)
-0.294
-0.386 / -0.114
0.583 mm -0.063
Sliding factor at tooth point (Kga)
0.386
0.294 / 0.063
0.114
Specific sliding at tooth root (ζf)
-1.642
-1.642 / -0.622
-0.152
0.621
0.621 / 0.132
0.384
Specific sliding at tooth point (ζa)
Test dimensions Sun No. of the teeth for span measurement (k)
Planet
Annulus
3
5
Measurement diameter (span measurement) (dM)
30.567
56.124
-142.810 mm
Span measurement nominal value (Wk)
11.817
20.735
-53.286 mm
Span measurement min. value (Wk min)
11.738
20.631
-53.436 mm
Span measurement max. value (Wk max)
11.766
20.669
-53.361 mm
3.000
2.750
2.750 mm
Measurement diameter (measurement over balls) (dM)
31.189
55.959
-141.501 mm
Measurement over balls nominal value (MdK)
35.586
59.712
-137.809 mm
Measurement over balls min. value (MdK min)
35.428
59.456
-138.260 mm
Measurement over balls max. value (MdK max)
35.484
59.549
-138.035 mm
Measurement over pins nominal value (MdR)
35.586
59.712
-137.809 mm
Measurement over pins min. value (MdR min)
35.428
59.456
-138.260 mm
Measurement over pins max. value (MdR max)
35.484
59.549
-138.035 mm
Transverse tooth thickness (st)
2.703
2.389
1.944 mm
Transverse tooth thickness min. value (st min)
2.619
2.279
1.784 mm
Transverse tooth thickness max. value (st max)
2.649
2.319
1.864 mm
Transverse tooth thickness at V-Circle (svt)
2.392
2.360
2.387 mm
Transverse tooth thickness at V-Circle min. value (svt min)
2.306
2.250
2.226 mm
Transverse tooth thickness at V-Circle max. value (svt max)
2.336
2.290
2.307 mm
Chordal tooth thickness at V-Circle nominal value (svn)
2.390
2.359
2.387 mm
Chordal tooth thickness at V-Circle min. value (svn min)
2.306
2.250
2.225 mm
Chordal tooth thickness at V-Circle max. value (svn max)
2.336
2.290
2.306 mm
Diameter of ball or pin (DM)
http://abeg.gwj.de/tmp/journal1005791660125359651.html
-12
2016-11-08
Report of cylindrical gear calculation according to DIN 3990 , ISO 6336
Strona 5 z 8
Chordal height (hv)
1.525
1.504
1.511 mm
Circular normal space width at V-Circle (evt)
2.470
2.360
2.363 mm
Normal chordal tooth thickness at standard pitch diameter nominal value (s n)
2.700
2.388
1.944 mm
Normal chordal tooth thickness at standard pitch diameter min. value (sn min)
2.616
2.279
1.782 mm
Normal chordal tooth thickness at standard pitch diameter max. value (sn max)
2.646
2.319
1.863 mm
Normal chordal tooth thickness at tip diameter nominal value (san)
0.873
1.143
1.269 mm
Normal chordal tooth thickness at tip diameter min. value (san min)
0.730
0.990
1.087 mm
Normal chordal tooth thickness at tip diameter max. value (san max)
0.860
1.106
1.215 mm
Chordal height at standard pitch diameter (ha)
2.017
1.549
0.948 mm
Circular normal space width at reference diameter (et)
2.009
2.324
2.768 mm
Tooth depth (h)
3.354
3.354
3.396 mm
Tolerances Sun
Planet
Annulus
Profile form deviation (ff)
6
6
Profile slope deviation (fHα)
5
5
7 µm
Total profile deviation (Ff)
8
8
12 µm
Adjacent pitch deviation (fp)
7
7
11 µm
Tooth to tooth pitch deviation (fu)
8
9
14 µm
18
25
40 µm
8
10
16 µm
14
16
25 µm
Total tooth alignment deviation (Fβ)
9
9
12 µm
Tooth alignment slope deviation (fHβ)
8
8
11 µm
Tooth alignment form deviation (fβf)
4
4
5 µm
18
20
32 µm
Total deviation of circular pitch (Fp) Variation of tooth thickness (Rs) Runout (Fr)
Double flank pitch deviation (F´´i) Double flank pitch step (f´´i)
9 µm
6
8
14 µm
Single flank pitch deviation (F´ i)
22
28
45 µm
Single flank pitch step (f´i)
10
11
16 µm
Load capacity (general influence factors) sun - planet Carried width (tooth root) (b*)
planet - annulus
0.000
0.000
593.585
593.585
N
0.000
0.000
N
Radial force on the reference diameter (Fr)
216.047
216.047
N
Normal tooth force on the reference diameter (Fn)
631.680
631.680
N
Circumferential force on the pitch circle diameter (Ftw)
586.723
586.723
N
0.000
0.000
N
Radial force on the pitch circle diameter (Frw)
234.043
234.043
N
Normal tooth force on the pitch circle diameter (Fnw)
631.680
631.680
N
Circumferential speed (v)
1.852
1.852
m/s
Running-in allowance (yα)
0.525
0.825
µm
Running-in allowance (yf)
0.450
0.675
µm
Running-in allowance (yp)
0.525
0.825
µm
Layout value of the profile correction (Cay)
2.030
2.030
µm
Correction coefficient (CM)
0.800
0.800
Gear body coefficient (CR)
1.000
1.000
Basic rack profile coefficient (CBS)
0.975
0.975
Single spring stiffness (c´)
7.448
8.341
N/(mm µm)
Meshing spring stiffness (cγα)
10.317
13.626
N/(mm µm)
Meshing spring stiffness (cγβ)
8.769
11.582
N/(mm µm)
Reduced mass (mred)
0.001
0.010
Reference speed (N)
0.024
0.068
Sub-critical range
Sub-critical range
48246.176
9325.313
1.018
1.081
Nominal circumferential force at pitch cylinder (Ft) Axial force on the reference diameter (Fa)
Axial force on the pitch circle diameter (Faw)
Resonance speed (nE1) Dynamic coefficient (Kv)
kg/mm
1/min
Bearing of the planet Relative speed planet (nrel)
-637.364 1/min
Tangential force planet carrier (FtS) 1187.170 N Centrifugal force planet (Fz)
9.458 N
Sun
Planet
Annulus
http://abeg.gwj.de/tmp/journal1005791660125359651.html
2016-11-08
Load capacity (flank) sun - planet
Sun
planet - annulus
Planet
Annulus
Load capacity (root) sun - planet
planet - annulus
Sun
Load capacity (Scuffing) (ISO/TR 13989)
Planet
Annulus
sun planet
planet annulus
ϑ ϑ
Integral temperature method ϑ
ϑ ϑ ϑ ϑ
Flash temperature method ϑ
ϑ
ϑ ϑ
Contact temperature sun - planet A
B
C
-0,1
0
D
E
83,5 83 82,5 82 81,5 81 80,5 80 79,5 79 78,5 78 77,5 77 76,5 76
-0,6
-0,5
-0,4
-0,3
-0,2
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Contact temperature planet - annulus A
B
D
C
E
75,25 75 74,75 74,5 74,25 74 73,75 73,5 73,25 73 72,75 72,5
References
-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
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