Article citation information:

Němček, M. Remarks and corrections to the standard ISO 6336. Scientific Journal of Silesian University of Technology. Series Transport. 2018, 99, 115-124. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2018.99.11.

 

 

Miloš NĚMČEK[1]

 

 

 

REMARKS AND CORRECTIONS TO THE STANDARD ISO 6336

 

Summary. The standard ISO 6336 for the calculation of load capacity of spur and helical gears was introduced in 2006. There were some later amendments, but several typographical and other errors. These can cause some misunderstandings during applications of the standard and are irritating for its users. This contribution seeks to highlight some aspects of the use of this standard, as well as drawing users’ attention to the errors it contains and, at the same time, properly worded content. To fully appreciate this article, the reader is advised to have a copy of the standard itself. Parts 3 and 6 of the standard are covered in the contribution.

Keywords: ISO 6336; Part 3; Part 6; typos; errors; recommendations

 

 

1. INTRODUCTION

 

ISO 6336 is a key standard for gear checking and loading capacity assessment. It also addresses service life. In any task related to the design and optimization of the drive of mechanical systems, its application is absolutely necessary. Therefore, the standard cannot be misinterpreted or misunderstood. As such, this article highlights some of the mistakes and misinterpretations it contains. Due to the scale of this standard, only the third and sixth parts are addressed, as the other parts are highly effective. The results of this work will be immediately applied to the software.

2. ISO 6336, PART 3

 

“Calculation of Tooth Bending Strength”, which is the third part of the standard ISO 6336 on the calculation of load capacity of spur and helical gears, was introduced in 2006. This part was amended in 2008 with Technical Corrigendum 1, which is still valid. This is a basic standard and instruction for highly important calculations of bending stress in the roots of gear teeth. This chapter deals with some aspects of the use of this part of the standard. It also draws users’ attention to the typographical and other errors it contains. At the same time, it highlights where the content is properly worded.

The latest edition of this part of the standard is considerably shorter (42 against 72 pages). It is interesting that the simplified calculation method C was fully removed from this part. In addition, some procedures for the calculations of some factors were changed. Of note is the revised procedure for calculating the form factor YF2 for internal gearing. The tooth root’s critical section (sFn2) starts from the root radius at a tangent point of the line inclined at 60° towards to the tooth axis; see Fig. 1 (it was 30° in the previous edition). Unfortunately, the new calculation of the tooth root’s critical section sFn2 shows a relatively large deviation from the exact value; see Tab. 1.

We can even say that the equations used, e.g., in the standard DIN 3990 for the calculation of the form factor YF2 for internal gearing, give more accurate (although not entirely accurate) results than ISO 6336. Several comparative calculations for setting up the form factor YF2 for internal gearing are given in Tab. 1, which compares the calculations from the latest version of ISO 6336 - 3 with the calculations made for exact geometric dimensions sFn2 a hFe2 (see Fig. 1).  This geometrical calculation is quite easy (simple numerical calculation).

 

 

Fig. 1. Tooth root’s critical section

 

There are examples for internal gear pairs in Tab. 1. These are concerned with manufacturing internal gearing with straight teeth, with a standard basic profile and the module mn=1 [mm]. A tool is the standard pinion-type shaper cutter with z0=25 teeth and a sharp addendum (ρa02=0). Its addendum modification coefficient is simply x0=0. The mating pinion has always 20 teeth.

The manufacturing pair z 0=25, z 2=-40 with shifting coefficients x 0=0, x 2=-0.968 comprises the so-called pole gears (the pitch point lies on the tip of the circle of the wheel). In this case, a tool (pinion-type shaper cutter) does not create a root radius; rather, it only makes its “imprint” on the gear blank during manufacturing. Hence a ”sharp” root is created: ρf2=0.

 

                                                                                                                                          Tab. 1.

Calculation of the form factor YF2 

z 2

x 2

ISO 6336 - 3

Exact geometric calculations

 

sFn2

hFe2

ρF2

YF2

sFn2

hFe2

ρF2

YF2

ΔYF2

[mm]

[mm]

[mm]

[ - ]

[mm]

[mm]

[mm]

[ - ]

[% ]

-40

0

2.488

1.161

0.297

1.123

2.851

1.159

0.081

0.8539

31.5

-40

-0.968

2.857

1.500

0.560

1.065

3.019

1.305

0

0.830

28.3

-80

0

2.379

1.175

0.247

1.245

2.729

1.179

0.128

0.949

31.2

-80

-0.8

2.508

1.267

0.340

1.186

2.826

1.198

0.069

0.883

34.3

 

 

2.1. ISO 6336, Part 3: typographical and other errors

 

Page 3, Paragraph 3 - replace ... YDT.   with … YDT.

 

Page 8, in the middle - replace … amount mn … with … amount xE · mn

 

Page 16, under the figure - replace … Y β > 25°… with … Y β for β > 25°

 

Page 18, Line 2, from the top down - replace … 2 ≤ εαn <2,5 … with … 2,05 ≤ εαn

 

Page 21, note b - replace … ZNT … with … YNT

 

Page 21, note b - remove text … , where pitting must be minimal

 

Page 22 - number (49) belongs to the previous equation

 

Page 23, note b - replace … σS0,2. with … σ0,2.

 

Page 24, Fig. 10 - one of the arrows at GG, GGG(ferr) belongs to the line above

 

Page 25, Fig. 12 - the curve for the material GTS is missing

 

Page 29, in the text and in Fig. 14 - data for the material GTS are missing

 

Page 29, Line 3, from the top down - replace … (55) to (61). with … (56) to (62).

 

Page 29 - what is Rz > 40 valid for?

 

Page 34, Line 7, from the bottom up - replace … σ k lime … with … σ p lim

 

Page 36, Line 4, from the bottom up - replace … of YSa or qs and the material, all relevant to the gear   with … of qs, and the material of the gear

 

Subclauses A.6.3.2.2, A.6.4.2.2, A.7.2.2.2 and Fig. A1 - data for the material GTS are missing

 

Page 37, Eq. (A.15) - replace … Yδk = … with … Yδ = …

 

Page 38, Eq. (A.17) - replace … YRk = … with … YR rel k = …

 

Page 39, Line 6, from the top down - replace … 1 μm < Rs < 40 μm with … 1 μm ≤ Rs ≤ 40 μm

 

Page 40, line 9, from the top down - replace … 1 > R > 0. with … -1.2 < R <0.

 

Page 41, Line 2, from the top down - replace … with R = 1 … with … with R = -1

 

 

Fig. 2. Current Fig. 10

 

Fig. 3. Corrected Fig. 10

 

 

2.2. ISO 6336, Part 3: conclusion

 

The latest edition of the third part of the standard ISO 6336 improves on the previous edition. Firstly, it is shorter and more readable. However, the simplified calculation method C was apparently omitted. There is no need to simplify a calculation for bending stress. But it is a pity that not all errors were caught by Technical Corrigendum 1. That said, we can say that this part of the standard is still of great benefit to users, although it is advisable to consider modifying the calculation of the form factor YF2 for internal gearing.

 

 

3. ISO 6336, PART 6

 

“Calculation of Service Life Under Variable Load”, which is the sixth part of the standard ISO 6336 for the calculation of load capacity of spur and helical gears, was introduced in 2004.  This part was updated in 2006 and is still valid. This is a fairly effective tool, which defines the procedure for processing a gear pair loading spectrum using stress levels method. On this basis, we can numerically calculate service life or safety factors for the required service life. This chapter also seeks to highlight some aspects of the use of this standard, as well as draw users’ attention to the typographical and other errors. At the same time, we point out where the wording is properly worded.

The standard firstly describes the so-called the Palmgren-Miner’s rule, which states that the order in which each stress cycle is applied is not considered significant and the damage accumulation takes place linearly. Failure should be expected when the sum equals 1. The standard further mentions that, when stress is calculated, for each level, all factors K (for contact and bending) should be separately determined. The rotational speed for the concerned level is the mean one. For the determination of the resulting safety factors for the required service life, the standard provides a graphic algorithm for the necessary numerical calculation (Fig. 4 in the standard).

Of interest is Annex A, which contains a technique to determine the application factor KA without knowledge of an endurance limit. For the calculation of KA from a loading spectrum, it is enough to know the values of the slope of the Wöhler damage line p and the endurance limit cycles Nlim.

There is also presented a classical calculation for an equivalent torque Teq  in the form of  an equation (Eq. A2 in the standard). Standard ISO 6336 rightly points out that this principle is incorrect. The limit cycles Nlim are achieved in the same way as described earlier; see Figs. 3 and A2 in the standard. In other words, using Eq. A2 leads to the application of a greater number of cycles in the calculation (this technique is not correct). For potential applications, precise values of an equivalent torque for loading spectra, according to Tab. A2, are as follows:

 

According to Eq. A2, ... Teq = 1138,4      KA = 1,198

 

According to the Fig. A2, ... Teq =1124,9      KA = 1,184

 

This means that the gear design according to Eq. A2 would give a greater gear pair.

 

 

3.1. ISO 6336, Part 6: typographical and other errors

 

Tab. 3 - replace N38 with n38; replace N39 with n39

Under Fig. 3 -  replace de damage with damage

Eq. (5) - replace KFαii with KFαi

Fig. 4 - fourth box from above, replace ... to 5.1 to 5.3 with ... to 5.1 to 5.4

Page 10 - fourth line from below, replace ... in A.2.2 shall ...  with ... in A.3.2 shall  

Under Fig. A.2 -  replace (T2e, N2e) with (T2, N2e)

Page 12 - second line from below - replace ... cycles NL ...  with ... cycles NLref

Tab. A.2 - heading for the fourth column - replace  with 

Tab. B3 - replace calendars with calenders; should sleve be slave?

Tab. B4 - change Moderate to Light; change Medium to Moderate

Tab. C1 - see Tabs. 2 and 3 in all columns


                                                           Tab. 2.                                                                  Tab. 3. 

Item

Pinion

Wheel

Unit

 No. of teeth, z

17

80

-

 Gear ratio, u

3,529 41

-

 Normal module, m n

8,467

mm

 Normal pressure angle, α n

25

°

 Helix angle, β

15,5

°

 Centre distance, a

339,738

mm

 Face width, b

152,4

mm

 Tip diameter, d a

169,192

544,127

mm

 Profile shift coefficient, x

0,172 0

0,001 5

-

                      C1 (incorrect)                                                               C1 (correct)                      

 

Item

Pinion

Wheel

Unit

 No. of teeth, z

17

80

-

 Gear ratio, u

3,529 41

mm

 Normal module, m n

8,467

°

 Normal pressure angle, α n

25

°

 Helix angle, β

15,5

mm

 Centre distance, α

339,727

mm

 Face width, b

152,4

mm

 Tip diameter, d a

169,212

544,132

mm

 Profile shift coefficient, x

0,172 0

0,001 5

-

 

Page 19 - 10th line - replace ... (14), and ISO 6336-3:2006, Eq. (7). with ... (11), and ISO 6336-3:2006, Eq. (8).

Page 19 - sixth line from below - replace Using the nominal ... with Using the reference ...

 

Page 20 - fourth line - replace ... Fig. 9). with ... Fig. 9.

Page 20 - fifth line - replace ... 5.3.3.2, and ...  with ... 5.4.3.2, and ...

Page 20 - fifth line from below - replace ... Fig. 7, with ... Fig. 4,

Page 20 - second line from below - replace ... 1,428 ...  with ... 1,3355 ...

Page 20 - second line from below - replace ... 1,324 ...  with ... 1,677 ...

Page 20 - incorrect set of equations

 

For contact stress:

                                                 (1)                                                          (2)

 

                                                 (3)                                

 

For bending stress:

                                             (4)                                                            (5)

 

                                                  (6)

 

 

Page 20: correct set of equations

 

For contact stress:

                                               (7)                                                            (8)

 

                                                  (9)

For bending stress:

                                             (10)                                                          (11)

 

                                                 (12)

 

                                                                                                                          Tab. 4.

Replacing ... 1,428 with ... 1,3355 - incorrect first row

 

 

 

 

 

Stress

cycles in

30 years

 

N

 

 

Face load

factor

 

KHβ

 

Contact

stress

 

σH ∙ SH

N/mm2

 

Life factor

 

ZNT

 

Cycles to

failure

 

N f

 

Damage

parts

 

Ui

(N/N f)

 

 

 

 

 

 

 

 

 

 

 

 

Tab. 5.

Correct first row

 

 

 

 

 

Stress

cycles in

30 years

 

n

 

Face load

factor

 

KHβ

 

Contact

stress

 

σH ∙ SH

N/mm2

 

Life factor

 

ZN

 

Cycles to

failure

 

N

 

Damage

parts

 

Ui

(n/N)

 

 

 

 

 

 

 

 

 

 

 

 

 

Tab. 5.

Replacing ... 1,324 with ... 1,677 - incorrect first row

 

 

 

 

 

Stress

cycles in

30 years

 

N

 

 

Face load

factor

 

KFβ

 

Bending

stress

 

σF ∙ SF

N/mm2

 

Life factor

 

YNT

 

Cycles to

failure

 

N f

 

Damage

parts

 

Ui

(N/N f)

 

 

 

 

 

 

 

 

 

 

 

Tab. 6.

Correct first row

 

 

 

 

 

Stress

cycles in

30 years

 

n

 

 

Face load

factor

 

KFβ

 

Bending

stress

 

σF ∙ SF

N/mm2

 

Life factor

 

YN

 

Cycles to

failure

 

N

 

Damage

parts

 

Ui

(n/N)

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 4.  Wöhler damage curve for bending: corrected curve (dashed) of the spectrum and one value of the scale y2

 

 

3.2. ISO 6336, Part 6: conclusion

 

Lifetime calculations of gear pairs for a given safety factor are standard requests when they are being designed or checked. The standard ISO 6336 - 6 makes progress towards satisfying these demands. But, despite some minor confusion and mistakes, it is a very useful tool for designers. To this extent, this article seeks to improve the readability of this part of the standard ISO 6336, while taking into account Technical Corrigendum 1 (2007).

 

 

References

 

1.           ISO 6336 - 3:2006(E). Calculation of Load Capacity of Spur and Helical Gears - Part 3: Calculation of Tooth Bending Strength.

2.           ISO 6336 - 6:2006(E). Calculation of Load Capacity of Spur and Helical Gears - Part 6: Calculation of Service Life Under Variable Load.

3.           DIN 3990.  Tragfähigkeitsberechnung von Stirnrädern.

4.           DIN 3960. Begriffe und Bestimmungsgrößen für Stirnräder (Zylinderräder) und Stirnradpaare (Zylinderradpaare) mit Evolventenverzahnung. [In English: Terms and Parameters for Spur Gears (Cylindrical Gears) and Pairs of Spur Gears (Pairs of Cylindrical Gears) with Involute Toothing.]

5.           Linke H. 2010. Stirnradvezahnung. [In English: Spur]. Munich: Carl Hanser Verlag München. ISBN: 978-3-446-41464-8.

6.           Litvin F., A. Fuentes. 2004. Gear Geometry and Applied Theory (Second Edition). Cambridge: Cambridge University Press. ISBN: 0-521-81517-7.

 

 

Received 14.03.2018; accepted in revised form 29.05.2018

 

 

Scientific Journal of Silesian University of Technology. Series Transport is licensed under a Creative Commons Attribution 4.0 International License



[1] Faculty of Mechanical Engineering, VŠB-TU Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic. Email: milos.nemcek@vsb.cz.