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The Influence of Tool Tolerances on the Gear Quality of a Gear Manufactured

by an Indexable Insert Hob

Conference Paper · September 2013

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 technical

The Influence of Tool Tolerances on the

Gear Quality of a Gear Manufactured
by an Indexable Insert Hob
Mattias Svahn, Lars Vedmar and Carin Andersson
Recently, a new type of hob with carbide inserts has been introduced, providing higher cutting speeds,
longer tool life and higher feed rates when compared to re-grindable, high-speed steel hobs. But with this
kind of hob, new challenges occur due to positional errors of the cutting edges when mounted on the tool.
These errors lead to manufacturing errors on the gear teeth which must be controlled. In this paper, the
tooth quality of a gear manufactured by hobs with different quality classes is analyzed using a simulation
model in combination with Monte Carlo methods.

Introduction Visalis et al (Ref. 4), presents the software tooth quality for the corresponding hob
The most common and economical module HOB3D for CAD systems, where quality class is determined. The input to
method to produce involute gears — both the un-deformed chip geometry and the the simulation software is provided by an
spur and helical — is by hobbing. Hobs manufactured tooth surface are mod- analysis of the cutting tooth deviations of
have been — until now — mainly re- eled. These works do not consider any a commercial hob with inserts.
grindable, high-speed steel (HSS) with manufacturing errors due to the tool or Using the Monte Carlo method (Ref.
additional coatings such as TiN, TiCN, machine settings. Chiu et al (Ref. 5) com- 8), the expected gear tooth quality can be
etc. Today’s new type of hob with carbide puted the manufactured tooth surface by determined by this simulation tool and
inserts is advantageous to HSS hobbing modeling the hobbing process with intro- with hob geometry generated by prede-
with its ability to increase cutting speed duced eccentricity to the hob axis. Svahn termined statistical functions. The aim
and feed rate while prolonging tool life. et al (Ref. 6) modeled the manufactured of the study is to identify which param-
However, one obstacle to overcome is to gear tooth hobbed with errors introduced eters are influencing gear tooth quality
fulfil the requirements for hobbing accu- to the manufacturing process. for this new tool concept, and to show
rate gears for high-performance appli- In this paper a simulation tool is used that these types of results can be provided
cations while using hobs with inserts. based on a mathematical, geometric without costly, time consuming — and
The geometry and the positioning of the model where the hobbed tooth surface often impossible — experimental testing.
inserts must be highly accurate for the can be determined in three dimensions The use of simulation tools to analyze
hob to comply with the tight tolerances (Ref. 7). The cutting teeth of the hob can the gear hobbing process can be a great
of, for example, DIN 3968 (Ref. 1). In the be individually positioned in the axial benefit to tool developers in finding out
literature (Ref. 2) it is stated that hob- and in the radial direction, compared to which tolerances and other parameters
bing in industrial applications achieves their nominal positions. This is done by are of importance, and in manufacturing
gear quality according to DIN in the 8-11 using results from measurements of an an involute gear within given tolerances.
range, and grade 7 in less frequent appli- actual hob or applying continuous prob- In this study, the focus is on the radial
cations. However, there is little experi- ability density functions. Utilizing this and the axial errors from the nominal
ence of the gear quality achieved using simulation model it is possible to com- position of these inserts. The shape of the
the new type of indexable insert hobs, pute the gear tooth surface topography inserts, the tool body and generating pro-
due possibly to errors of the inserts and manufactured by hobs of different tol- cess will otherwise be considered perfect.
the higher feed rates that they are capable erance classes. By applying gear tooth The results in this study are based on the
of operating at. The purpose of this study deviation standards, the expected gear numerical values listed in Table 1.
is to analyze the impact of possible errors
of the hob geometry on the manufactured Table 1 Nomenclature and numerical example
gear tooth. Basic Rack Gear
Normal module mn = 4.75 mm Number of teeth z = 56
Previous work in modeling the manu-
Normal pressure angle αn = 20° Face width b = 50 mm
factured gear tooth geometry encompass- Helical angle β = 21.5° Hob
es, for example, the work of Michalski Tip addendum ht = 7.50 mm Number of entrances g = 1
(Ref. 3) that, by use of CAD environment Tip radius rt = 1.63 mm Lead angle λ = 2.37°
and logical material removal to deter- Protuberance p = 0.1 mm Total number of cutting teeth N = 120
mine the manufactured tooth flanks, and Cutting teeth per revolution N = 12

This paper was first presented at the 2013 VDI International Conference on Gears, Technical University of Munich, Garching, Germany, and is reprinted here with VDI permission.

48 GEAR TECHNOLOGY | July 2014

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Figure 1 Deviation of inserts of hob, where ∆r is the radial displacement and ∆a is the axial displacement. Related measured quantities in
DIN 3968 are frk and fe.

Generation of Hobs cutting tooth deviation Δa and Δr are hob are tested by a null-hypothesis using
The hob used in this study is an index- presented in Figure 1, together with mea- the Ç 2 - test. The measured distribution
able, insert hob; individual inserts are sured quantity fe and frk from DIN 3968. complies with a normal distribution in
assembled on the tool body. The posi- The statistical distribution of the posi- both cases at the 5% significance level
tion of the cutting edges, which are the tional error must be known to be able to (Figs. 2, 3). This allows that the inserts
boundaries of these inserts, is affected apply the Monte Carlo method. Knowing follow a normal distribution; it is now
by the geometry of the inserts and their the statistical distribution enables genera- assumed that the positional errors of the
positioning on the tool body. Overly large tion of new hobs based on this distribu- inserts for all hobs in this study comply
deviations will directly affect the tooth tion within the same or other tolerance with normal distribution.
quality of the hobbed gear tooth nega- range. These hobs are then to be used Considering now only these deviations
tively. In order to manufacture a gear as input to the simulation software later being present, different hob classes can
with satisfactory quality, these deviations described, where the gear tooth topogra- be generated by positioning the inserts
must be controlled. phy and the gear quality manufactured by according to a normal density probability
The DIN 3968 standard for single- different hob quality classes can be deter- function. The position of each individual
start hobs (Ref. 1) measures the hob in 17 mined. insert is random, but confirms the given
steps and, depending on normal module A commercial hob with carbide inserts probability functions. For a hob with nor-
mn, classifies the hob in the quality class- is control-measured using a CNC mea- mal module mn = 4.75 mm, the tolerance
es AA through to D, with AA being the suring center, Zeiss CenterMax with soft- levels for different hob classes, accord-
most accurate hob. The measuring pro- ware packages Calypso and Gear Pro Hob. ing to DIN 3968 (Ref. 1), are defined in
cedure of hobs is well described in VDI/ The distribution of the axial and the radi- Table 2.
VDO (Ref. 9) and by Goch (Ref. 10). The al deviations of the cutting edges of the

Figure 2 CDF: plot, radial deviation of inserts. Figure 3 CDF: plot, axial deviation of inserts.

July 2014 | GEAR TECHNOLOGY 49

 technical

Simulation of the Manufacturing Table 2 Tolerance levels of a single-start hob with normal module mn = 4 - 6.3 mm
Hob class
Process AA A B C
To isolate manufacturing errors that arise frk [μm] 20 32 63 125
to only the prescribed positional errors fe [μm] 6 10 20 40
of the tool inserts and to determine the
impact of these errors on the manufac- Table 3 Gear tooth quality according to DIN 3962, for a gear with normal module mn = 3.55 - 6 mm
tured gear tooth, a simulation model and width b = 40 - 100 mm (- not presented)
is used. With this model, developed by Gear quality
5 6 7 8 9 10 11 12
Vedmar (Ref. 7), the hobbed tooth sur-
fg± - - 10 14 20 32 50 80

Deviation
face topography is determined in three ff± 7 10 14 20 28 45 71 125

[μm]
dimensions by using analytical, paramet- fH 2 - 10 14 20 28 45 71 110
ric, differentiable functions. By compar- ff 2 7 9 12 18 28 45 63 110
ing the hobbed tooth surface with the
ideal smooth gear tooth geometry, devia- tooth topography after manufacturing just after hobbing to ensure controlled
tions from the manufacturing process can by these hobs. An example of the results finished results. If the gear tooth is man-
be analyzed. from the simulation model is presented ufactured with protuberance, the gear
To use this simulation tool to deter- in Figure 4, showing gear teeth manu- tooth quality has no information if the
mine the manufacturing errors due to factured using a perfect hob and a hob of amount of grinding stock accounts for
imperfections of the hob, hobs are gen- quality class B with grinding stock. the manufacturing errors. This will then
erated by choosing the tolerance levels Using a hob allows manufacturing of not guarantee that the finished tooth
according to DIN 3698. It is assumed gears with or without protuberance. In surface is not impaired. In the simula-
that the positional error of the inserts the case of protuberance, the gear tooth tion model this is, however, possible; this
complies with normal distribution — i.e., is manufactured with grinding stock. The could give an indication of the necessary
N (μ,σ2). Hobs are now generated using remaining material in the involute region amount of protuberance needed for the
probability density function N (0, is to be removed in a subsequent refin- specific hob class. The material remov-
Ti/1.96), where Ti is the tolerance for the ing process, such as grinding or skiving. al rate is far greater in hobbing than in
respective hob quality class. These hobs The gear quality is determined after an any refining process, so minimizing the
are then used as input to the simulation eventual refining process, but the same grinding stock would lead to less time-
model to determine the expected gear types of measurements are also applied consuming refining steps. As the main

Figure 4 Hobbed gear tooth from simulation model manufactured by a hob with protuberance = 0.1 mm.

Figure 5 Inspection charts of manufactured gear tooth for the profile and the lead deviations.

50 GEAR TECHNOLOGY | July 2014

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objective is to find the correlation of the
quality class between the hob and the
gear tooth, measurements will be restrict-
ed to after hobbing and no considerations
are taken to any finishing process.
After manufacturing, measurements of
the gear tooth are drawn on inspection
charts. These charts can be used to deter-
mine alignment and form deviations for
both the profile and the lead. In the Volvo
group standard (Ref. 11), these deviations
are defined as fgα for profile alignment and
ffα for profile form deviation; fHβ for lead
alignment and ffβ for lead form deviations.
A stylus tracks the tooth surface at des-
ignated lines. For profile deviations the
probe starts at sscp (start control point),
records tooth deviations and ends at secp
(end control point), where s = √r2 – rb2 and
rb is the base circle radius. This is nor-
mally performed in the middle of the
face width. fgα and ffα are defined in Figure Figure 6 Result from simulation where the profile deviations are plotted with varying hob
classes. On the left ordinate, the gear tooth deviation, and on the right ordinate,
5, where point A is specified tip relief. the gear quality, is plotted.
The lead deviations are measured of the
whole face b at the line s = (sscp + secp)/2.
A mean line of first order least square is
established within the evaluation area
0.8b. The mean line is then extrapolated
over the whole width b and fHβ and ffβ are
defined (Fig. 5).
The quantitative measure of these
tooth deviations quantifies the gear tooth
quality by using DIN 3962–Part 1 (Ref.
12) and Part 2 (Ref. 13), depending on
the normal module mn and the face width
b of the gear.

Results
To determine the quality grade of the
hob needed to manufacture gears within
given tolerance, and what deviation of
the inserts impacts the gear quality most,
simulations are performed with differ-
ent hob grades. For each hob class, eight
hobs are generated to manufacture one
gear each; and for every gear four dia- Figure 7 Result from simulation where the lead deviations are plotted with varying hob classes.
metrically positioned gear teeth are con- On the left ordinate, the gear tooth deviation, and on the right ordinate, the gear
quality, is plotted.
trol-measured using gear tooth devia-
tion standards. This is performed for two Table 4 Gear tooth quality classes achieved in simulations for different hob classes, presented
feed rates; the more conventional feed for two feed rates; mean/maximum quality is considered
Hob class
rate S = 3.5 mm/rev for HSS hobs and the
AA A B C
higher feed rate S = 8.0 mm/rev which ∆a ∆r ∆a ∆r ∆a ∆r ∆a ∆r
hobs with carbide inserts are capable of. S = 3.5 mm / rev <7/7 7/8 7/8 8/9 8/9 9/10 9/11 10/11
In Figures 6 and 7 the profile and lead S = 8.0 mm / rev 10/11 10/11 10/11 10/11 10/12 10/12 11/>12 11/>12
deviations are presented. These are sepa-
rated to only axial deviations of inserts
in the left column and only radial devia-
tions of inserts in the right column. The

July 2014 | GEAR TECHNOLOGY 51

 technical

positional error of the cutting edges, giv-

ing the different hob classes, complies
with given distribution function, here
N (μ,σ2). The outcome from the simula-
Table 5 The minimum amount of grinding stock needed for each hob class for the feed rates tion model will also yield a distribution.
considered
Amount of protuberance, p[μm] In these plots, 95% of the set of the tooth
AA A B C deviation are comprised by the colored
S = 3.5 mm / rev 20 20 30 50 bracket, and the mean value is presented
S = 8.0 mm / rev 30 30 45 65 by the black line. On the left ordinate in
each plot, the measured quantity is pre-
sented and on the right ordinate the cor-
responding gear tooth quality according
to DIN 3962 Part 1 and Part 2.
The gear tooth quality is determined by
the maximum deviation:
(1)
Qmax = max(Q (fgα,max), Q (ffα,max), Q (fHβ,max),
Q (ffβ,max))

For the gear geometry in this study

(Table 1), the corresponding gear qual-
ities for the resulting tooth deviations
from simulations are given in Table 3.
Using the results in Figures 6 and 7, the
gear quality according to Equation 1 is
given in Table 4.
As earlier mentioned, the presented
measurements do not consider if the
amount of grinding stock is adequate
to ensure that the involute region is
Figure 8 Inspection chart over profile and lead for a gear; hobbed at the feed rate S = 8.0 mm/rev.
On the left, results from industrial hobbing machine; and right, results from simulation not impaired after subsequent refining
are presented. steps. This is, however, possible in the
described simulation model. The amount
of protuberance needed for each hob
class in this example is given in Table 5.
This means the gear in this study will be
correct for all hob quality classes using a
hob with protuberance p = 0.1 mm.

Experimental Verification
To verify the results from the simulation
model, they are compared with a gear
manufactured using an industrial hob-
bing machine, i.e., a Liebherr LC 380.
The hob used in this verification was
control- measured, and the positional
error of the inserts in the axial and in
the radial direction was used as input to
the simulation model. The gear manu-
factured — in both experiments and in
simulation — was control-measured for
alignment and form deviations, accord-
ing to previous section. The results from
Figure 9 Gear tooth quality vs. axial feed rate of hob for different hob classes. these measurements are presented graph-
ically (Fig. 8) and in measured quantity
Table 6 Gear tooth deviations, results from experiments and simulations (Table 6).
Tooth deviation, mean value of four diametrically positioned teeth.
fgα [μm] ffα [μm] fHβ [μm] ffβ [μm]
The shape of the curves corresponds
manu. sim. manu. sim. manu. sim. manu. sim.
remarkably well for both profile and lead.
S = 8.0 mm/rev -15 7.3 31 26.2 1 2.7 21 38.3 There is, however, a systematic alignment

52 GEAR TECHNOLOGY | July 2014

[www.geartechnology.com]
 7. Vedmar, L. “A Parametric Analysis of the Gear
error present on all gear teeth for the pro- be minimized if the expected gear tooth Surface Roughness after Hobbing,” ASME
file. For the lead errors, the form error is deviations can be controlled. Journal of Mechanical Design, Vol. 132, pp.
overestimated in simulations compared The gear tooth is manufactured with 111004–1–111004–8, 2010.
to experiments. grinding stock by introducing protuber- 8. Kalos, H. Malvin. Monte Carlo Methods, 2009,
2nd Edition, Wiley-VCH.
ance to the tool. If the protuberance is 9. VDI/VDE 2606: Measurement of Gearing Tools;
Conclusions and Discussions minimized this will promote the finishing Measuring of Hobs, pp. 1–46, 2010.
In this paper it is shown that the gear operations. 10. Goch, G. “Gear Metrology,” CIRP
tooth topography and the corresponding There are other parameters determining Annals – Manufacturing Technology, Vol. 52,
Issue 2, pp. 659–695, 2003.
quality, manufactured by different hob the quality of the gear in addition to those 11. Volvo Group Standard, STD 5082, 81:
quality classes, can be determined using presented in this study. Here, only the Deviations and Inspection Methods for
a developed simulation model (Ref. 7). form and the alignment deviations of the Cylindrical Gears with Involute Gear Teeth, pp.
Here, errors in the cutting edge position gear tooth are considered. In DIN 3962, 1–23, 2007.
12. DIN 3962: Tolerances for Cylindrical Gear
are introduced, so that the cutting teeth there are also pitch error, concentricity, Teeth–Part 1, 1978.
deviate in the axial and the radial direc- etc. that are not considered in the quality 13. DIN 3962: Tolerances for Cylindrical Gear
tions when compared to their nominal grading of the gears in this study. The sim- Teeth–Part 2, 1978.
positions. ulations show good agreement with exper-
The results show very good agreement imental results but additional deviations to
with experimental results (Fig 8.; Table the hob cutting teeth may be introduced
6). Conclusions that can be drawn are for even better agreement, such as rotation
that radial deviations impair the gear of the inserts of the hob. This type of error
tooth more than the axial deviation of the is more probable to insertable hobs than
inserts. The effect is only slight and most conventional HSS hobs, and is not includ-
noticeable for the low feed rate, more ed in the hob standards.
specific fgα, fHβ and ffβ in Figures 6 and 7. Ac k n o w l e d g e m e nt . T h i s s t u d y
For the low feed rate considered in this has been performed as a part of the
study, both the mean value and the dis- GEORGH research project, financed by
persion of the alignment and the form SSF/ProViking. This research is carried
errors differ significantly between hob out within the Sustainable Production For Related Articles Search
classes. But for the higher feed rate, the Initiative (SPI). The tool and its specifica-
gear tooth will be manufactured with tions were provided by Sandvik Coromant indexable
same quality grade for the hob classes AA AB and testing and measurements at www.geartechnology.com
and A. The alignment and form errors were conducted at Volvo Construction
will differ in small degree but are still Equipment. The support is gratefully
classified in the same quality grade. An acknowledged by the authors.
explanation is due to the higher feed rate.
With increasing feed rate the distance References
between the feed marks will increase, 1. DIN 3968: Tolerances for Single Start Hobs for
Involute Spur Gears, 1960.
resulting in larger gear tooth deviations 2. Enroy, R. Gear Hobbing, Shaping and
and inferior gear tooth quality. However, Shaving – A Guide to Cycle Time Estimating
the positional error of the inserts between and Process Planning, 1990, 1st Edition, SME–
the hob classes AA and A impair the gear Society of Manufacturing Engineers. Carin Andersson is an
3. Michalski, J. and L. Skoczylas. “Modelling the Associate Professor at the
tooth quality less than the feed rate. Even Tooth Flanks of Hobbed Gears in the CAD Division of Production and
using a perfect hob, the expected gear Environment,” Int’l. J. Adv. Manuf. Technol. Vol. Materials in the Department
tooth quality will not improve signifi- 36, pp 746-751, 2008. of Mechanical Engineering,
4. Vasilis, D. V. Nectarios and A. Aristomenis. Lund University, Sweden.
cantly. Figure 9 presents the result from
“Advanced Computer Aided Design
the simulation model showing how the Simulation of Gear Hobbing by Means of Mattias Svahn is a Ph. D
gear tooth quality is affected by the feed Three-Dimensional Kinematics Modelling,” student at the Division of
rate. At the lower feed rate, suitable for ASME Journal of Manufacturing Science and Machine Elements in the
HSS hobs, there is a significant difference Engineering, Vol. 129, pp911-918, 2007. Department of Mechanical
5. Chiu, H., Y. Umezaki and Y. Ariura. “An Engineering, Lund
in gear quality achieved for the different Improvement of the Tooth Profile Accuracy University, Sweden.
hob classes. However, for the higher feed of a Hobbed Gear by Adjusting the Hob
rate the gear quality converges resulting Eccentricity,” JSME International Journal, Vol.
in the same quality gear tooth for an A, 32 No. 1, pp. 131–135, 1989. Lars Vedmar is an
6. Svahn, M., L. Vedmar and C. Andersson. Associate Professor at
AA and a perfect hob. “Tooth Deviations of an Involute Helical Gear the Division of Machine
The amount of grinding stock need- Manufactured in a Simulated Hobbing Process Elements in the Department
ed to account for manufacturing errors, with Introduced Errors,” 1st International of Mechanical Engineering,
Lund University, Sweden.
such as tool errors and feed marks, may Conference on Virtual Machining Process
Technology, 2012.

July 2014 | GEAR TECHNOLOGY 53

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