Parametric Transition as a Spiral Curve and Its Application in Spur Gear Tooth with FEA
The exploration of this paper will focus on the Cshaped
transition curve. This curve is designed by using the concept
of circle to circle where one circle lies inside other. The degree of
smoothness employed is curvature continuity. The function used in
designing the C-curve is Bézier-like cubic function. This function has
a low degree, flexible for the interactive design of curves and
surfaces and has a shape parameter. The shape parameter is used to
control the C-shape curve. Once the C-shaped curve design is
completed, this curve will be applied to design spur gear tooth. After
the tooth design procedure is finished, the design will be analyzed by
using Finite Element Analysis (FEA). This analysis is used to find
out the applicability of the tooth design and the gear material that
chosen. In this research, Cast Iron 4.5 % Carbon, ASTM A-48 is
selected as a gear material.
[1] K. G. Baass, "The use of clothoid templates in highway design,"
Transportation Forum 1, 1984, pp. 47-52.
[2] D. J. Walton, and D. S. Meek, "Planar G2 transition between two circles
with a fair cubic Bézier curve," J. Computer Aided Design, 31, 1999, pp.
857-866.
[3] D. J. Walton, and D. S. Meek, "The use of cornu spirals in drawing
planar curves of controlled curvature," J. Computational and Applied
Mathematics, 25, 1989, pp. 69-78.
[4] D. J. Walton, D. S. Meek, and J. M. Ali, "Planar G2 transition curves
composed of cubic Bézier spiral segments," J. Computational and
Applied Mathematics, 157, 2003, pp. 453-476.
[5] D. J. Walton, and D. S. Meek, "Curvature extrema of planar parametric
cubic curves," J. Computational and Applied Mathematics, 134, 2001,
pp. 69-83.
[6] D. J. Walton, and D. S. Meek, "A planar cubic Bézier spiral," J.
Computational and Applied Mathematics, 72, 1996, pp. 85-100.
[7] Z. Habib, and M. Sakai, "G2 planar cubic transition between two circles
with shape control," J. Computational and Applied Mathematics, 223,
2009, pp. 133-144.
[8] Z. Habib, and M. Sakai, "Circle to circle transition with a single cubic
spiral," Proc. Int. Conf. on Visualization, Imaging, and Image
Processing, ACTA Press, 2005, pp. 691-696.
[9] Z. Habib, and M. Sakai, "G2 planar cubic transition between two
circles," Int. J. Computer Mathematics, 80, 2003, pp. 959-967.
[10] I. Juhász, "Cubic parametric curves of given tangent and curvature," J.
Computer Aided Design, 25, 1998, pp. 1-9.
[11] J. M. Ali, H. B. Said, and A. A. Majid, "Shape control of parametric
cubic curves," Proc. Fourth Int. Conf. CAD/CG, 1995, pp. 161-166.
[12] B. W. Bair, "Computer aided design of elliptical gears," J. Mechanical
Design, 124, 2002, pp. 787-793.
[13] G. I. Sheveleva, A. E. Volkov, and V. I. Medvedev, "Algorithm for
analysis of meshing and contact of spiral bevel gears," J. Mechanism
and Machine Theory, 42, 2006, pp. 198-215.
[14] A. Belsak, and J. Flasker, "Method for detecting fatigue crack in gears,"
J. Theoretical and Applied Fracture Mechanics, 46, 2006, pp. 105-113.
[1] K. G. Baass, "The use of clothoid templates in highway design,"
Transportation Forum 1, 1984, pp. 47-52.
[2] D. J. Walton, and D. S. Meek, "Planar G2 transition between two circles
with a fair cubic Bézier curve," J. Computer Aided Design, 31, 1999, pp.
857-866.
[3] D. J. Walton, and D. S. Meek, "The use of cornu spirals in drawing
planar curves of controlled curvature," J. Computational and Applied
Mathematics, 25, 1989, pp. 69-78.
[4] D. J. Walton, D. S. Meek, and J. M. Ali, "Planar G2 transition curves
composed of cubic Bézier spiral segments," J. Computational and
Applied Mathematics, 157, 2003, pp. 453-476.
[5] D. J. Walton, and D. S. Meek, "Curvature extrema of planar parametric
cubic curves," J. Computational and Applied Mathematics, 134, 2001,
pp. 69-83.
[6] D. J. Walton, and D. S. Meek, "A planar cubic Bézier spiral," J.
Computational and Applied Mathematics, 72, 1996, pp. 85-100.
[7] Z. Habib, and M. Sakai, "G2 planar cubic transition between two circles
with shape control," J. Computational and Applied Mathematics, 223,
2009, pp. 133-144.
[8] Z. Habib, and M. Sakai, "Circle to circle transition with a single cubic
spiral," Proc. Int. Conf. on Visualization, Imaging, and Image
Processing, ACTA Press, 2005, pp. 691-696.
[9] Z. Habib, and M. Sakai, "G2 planar cubic transition between two
circles," Int. J. Computer Mathematics, 80, 2003, pp. 959-967.
[10] I. Juhász, "Cubic parametric curves of given tangent and curvature," J.
Computer Aided Design, 25, 1998, pp. 1-9.
[11] J. M. Ali, H. B. Said, and A. A. Majid, "Shape control of parametric
cubic curves," Proc. Fourth Int. Conf. CAD/CG, 1995, pp. 161-166.
[12] B. W. Bair, "Computer aided design of elliptical gears," J. Mechanical
Design, 124, 2002, pp. 787-793.
[13] G. I. Sheveleva, A. E. Volkov, and V. I. Medvedev, "Algorithm for
analysis of meshing and contact of spiral bevel gears," J. Mechanism
and Machine Theory, 42, 2006, pp. 198-215.
[14] A. Belsak, and J. Flasker, "Method for detecting fatigue crack in gears,"
J. Theoretical and Applied Fracture Mechanics, 46, 2006, pp. 105-113.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51775", author = "S. H. Yahaya and J. M. Ali and T.A. Abdullah", title = "Parametric Transition as a Spiral Curve and Its Application in Spur Gear Tooth with FEA", abstract = "The exploration of this paper will focus on the Cshaped
transition curve. This curve is designed by using the concept
of circle to circle where one circle lies inside other. The degree of
smoothness employed is curvature continuity. The function used in
designing the C-curve is Bézier-like cubic function. This function has
a low degree, flexible for the interactive design of curves and
surfaces and has a shape parameter. The shape parameter is used to
control the C-shape curve. Once the C-shaped curve design is
completed, this curve will be applied to design spur gear tooth. After
the tooth design procedure is finished, the design will be analyzed by
using Finite Element Analysis (FEA). This analysis is used to find
out the applicability of the tooth design and the gear material that
chosen. In this research, Cast Iron 4.5 % Carbon, ASTM A-48 is
selected as a gear material.", keywords = "Bézier-like cubic function, Curvature continuity, Cshapedtransition curve, Spur gear tooth.", volume = "4", number = "8", pages = "594-7", }