© 2012 GETview
Limit ed. All right s reserved
14
4.0 S
PUR
G
EAR
D
ESIGN
4.1 Modeling of Spur Gear
Tr aditional spur gear s have the teeth w hich ar e str aight and par allel to the axis of the shaft that conveys the gear Mott, 2003. Nor mally, the teeth have an involute for m w her e this for m can be acted as in
contacting the teeth Mott, 2003. Figur e 8 show s a schematic and r elated ter minology for spur gear
Figure 8: Some of the terms in spur gear Price, 1995.
Based on Figur e 8, an inner cir cle and an outer cir cle can be dr aw n, and smaller cir cles can be fitted w ithin their boundar ies, as show n in Figur e 9. This r esulting str uctur e w ill be used to design a pr ofile
tooth of the spur gear .
Figur e 9: A new basis model of desi gning a spur gear tooth.
4.2 Single Tooth Design uses an S-Shaped Transition Curve
By applying the segmentation of divisions, tw o segments ar e divided to cr eate this single tooth. This is because an S-shaped cur ve has the beginning point at the tangent of base cir cle and ending at the tangent
of the outside circle. For the fir st segment, the inputs ar e c = {-0.398, 0.689}, c
1
= {0, 0.795},
α = 0.6667π
r adian,
β = 0.5π radian,
r = r
1
= 0.206 ar e used, w hile for segment tw o, the inputs ar e c = {0.398, 0.689},
c
1
= {0, 0.795},
α = 0.3333π radian, β = 0.5π radian and other parameters remain the same as in segment
one. Then, h and k ar e deter mined to be 0.2779 and 0.3780 in accor dance w ith the inputs and theor ies above. Notice that, the value of h and k is similar in both segments. Figur e 10 show s the design of the
tooth and its segmentation using an S-shaped tr ansition cur ve.
Figur e 10: Single tooth of spur gear using an S-shaped tr ansit ion cur ve left and i ts segment ation r ight.
4.3 Single Tooth Design uses a C-Shaped Spiral Curve
In this case, Figur e 9 is modified to suit the elements i n designing a C-shaped spir al cur ve Subsection 3.3. The small cir cles ar e dr aw n at the inter section of tw o circles. For this cur ve, it needs four segments
to design a single tooth of the spur gear . Segment one consists of c = {-0.398, 0.689}, c
1
= {-0.247, 0.725},
α = 0.05556π radian, β = 0.6667π radian,
r = 0.206 and r
1
= 0.05. The values of k and shape par ameter s,
λ
,
λ
1
ar e computed by using the Eqs. 3, 10, 11, and 12. We found that k = 0.1431 w her eas
λ
and
λ
1
ar e equal to 2.7695 and 0.3619, r espectively. For segment tw o, the inputs ar e c = {0, 0.795}, c
1
= {-0.247, 0.725},
β = 1.5π radian whi
le the r est is exactly the same as in segment one. This time, k and shape par ameter s,
λ
,
λ
1
ar e found to be 0.2449, 2.1279 and 0.5343, r espectively. These tw o segments have a
© 2012 GETview
Limit ed. All right s reserved
15
CATI A V5
Develop t he solid mo del of t he spur
gear
CATI A V5
All co ord inat es ar e joi ned using
spl ine package
CATI A V5
Coor dinat es defin it ion in accor d ance t o th e t oo th
pro file in Wo lfr am Mat hem at ica 7.0
W ol f ram M athemat ica 7 .0
Ap ply t he cu rve th eo ries in d esigni ng t he t oo th
pr ofi le o f th e spur gear
symmetr ical cur ve w hich can be defined as mir r or ing or balancing to segment thr ee and four . Thus, segment thr ee and four have the similar shape to segment one and tw o, r espectively Du Sautoy, 2009.
Figur e 11 show s the design of the tooth and its segmentation using this C spiral cur ve. Next, w e w ill apply the single tooth designs using both developed cur ves in or der to design a solid model of the spur gear .
Figur e 11: Single tooth of spur gear using a C-shaped spir al cur ve left and it s segmentat ion r ight.
4.4 S Transition and C Spiral as the Shaped Curves in Solid of Spur Gear
