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What is the difference between pressure angle and operating
pressure angle?
qUESTIon
operatigPressureAgle
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name (if you wish toremain anonymous, no problem)
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Answer provided by John Mayhan, Xtek, Inc.
Thepressure angle of a standard gear is defined as the
angleformed by a line tangent to the pitch circle, and the line
nor-mal to the tooth profile at the pitch circle. The profile angle
isdefined as the angle formed by the line tangent to the tooth
sur-face, and the line normal to the pitch surface at a
specifiedpitchpoint. The profile angle is determined by the tool
used to form
the involute curvature of the gear teeth. For a standard
gearprofile, these angles are equal (Fig. 1).
The operatingpressure angle is defined as the angle formedby the
line tangent to both base circle diameters of the matinggears, and
the line normal to their intersecting pitch circles. Itis common to
design mating gears with base circles that dif-fer from the
standard dimensions, and that operate at centerdistances different
from the standard center distance. In thesecases the pressure angle
generated by the tool will differ fromthe pressure angle at which
the gears will operate (Fig. 2).
John Mayhan, vice president, engineering for Xtek Inc.;11451
Reading Road; Cincinnati, Ohio 45241;
Phone: (513) 733-7993.
Fgure 1 Stanar gear profle wth equal angles (Fgures
courtesyXtek, inc.).
Fgure 2 A pressure angle generate by the tool wll er rom
thepressure angle at whch the gears wll operate.
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Answer provided by Dr. Hermann J. Stadtfeld, Gleason Corp.
If a cylindrical gear with a certain positive addendum
modifi-cation is mated with a cylindrical gear having the same
amountof negative addendum modification (V0 gearing), then the
cen-ter distance will be the same as that of a gear set with no
modi-fications (module times half the sum of pinion and gear
teeth).The pitch lines in both cases (no modification or a V0
profileshift) will be the same, and the pitch diameter is, in both
cases,calculated as module times the number of teeth. The
relation-ship between the two pitch diameters (or the pitch radii)
isequal to the relationship of the tooth count of the two mem-
bers (ratio). For involute gearing, the pitch circle is
definedfrom the location, where the two interacting surfaces show
nosliding, but pure rolling. This is where the line of
engagementintersects the center connecting line, as shown in the
involutedevelopment in Figure 1. R1a (Fig. 1) is the pitch radius,
and thepressure angle is defined between the orthogonal to the line
ofengagement and the pitch radius R1a in the pitch point.
Fgure 1 Lne o engagement an pressure angle (Fgures
courtesyGleason Corp.).
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3/358 GEAR TECHNOLOGY | May 2013[www.geartechnology.com]
ask the expert
If one of the two cylindrical gears has anaddendum modification
(Fig. 2) and themate does not, then the center distancechanges. It
is calculated as module timeshalf the sum of pinion and gear teeth,
plusmodule times (where is the addendummodification factor or
profile shift factor).It is interesting that in such a scenario
the
original pitch circles of the two gears losetheir function. The
interaction of the invo-lutes of two differently profile-shifted
gears(not V0gearing) will lead to a new line ofengagement (Fig. 3;
red line of engagementfor a+a) and a new working pitch pointbetween
them where the sliding velocity is zero and the rela-tionship
between the radii from the center of the two gears tothat point is
again equal to the relationship of the tooth count ofthe two
members (ratio).
The new profile dividing line is calledthe operating pitch line.
The pressure
angle, which was based on the nominalpitch lines during the
manufacturing of theindividual gears, can now be determined atthe
operating pitch line location. In Figure2, the pressure angle can
be found in thepitch point, and the operating (or work-ing)
pressure angle is defined in the work-ing pitch point. Figure 3
clearly shows thedifference between the two lines of engage-ment
(which is equal to the differencebetween the pressure angle and the
oper-ating pressure angle). The operating pres-
sure angle is more relevant to the gear setsoperating
performance and is also requiredto calculate the bearing forces.
The pres-sure angles of the tools are independentfrom operating
conditions, but reflect thenominal pressure angles.
Dr. Stadtfeld is Gleason Corp. vice president, bevel
geartechnology, R&D
Fgure 2 Prncple o aenum mofcaton (or profle sht X).
Fgure 3 Ptch pont an workng ptch pont ater center stance
change.
dr. Hermann The Expert Statel, rawng nvolute an ptch lne.
pressure angle
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