• Journal of the Korean Society for Precision Engineering
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• v.15 no.5
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• pp.85-92
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• 1998

This present paper describes a mathematical model of profile shifted elliptical gears, and this model is based on the concepts of envelope theory and conjugate geometry between the blank and the straight-sided rack cutter. The geometric model of the rack cutter includes working regions generating involute curves and fillets for trocoidal curves, and furthermore the addendum modified coeff. is considered for avoiding undercutting. The addendum modified coeff. is changed linearly along with pitch curves and must be the same absolute value at both major semi-axis and minor semi-axis. If undercutting is at all pronounced, the undercut tooth not only are weakened in strength, but lose a small portion of the involute adjacent to the base circle, then this loss of involute may cause a serious reduction in the length of contact. A very effective method of avoiding undercutting is to use the so-called profile shifted gearing. Non-undercutting condition is examined with the change of eccentricity and addendum modified coeff. in elliptical gears and then the minimum number of tooth is proposed not to gernerate undercutting phenomenon.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.572-577
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• 1997

This present paper describes a mathematical model of profile elliptical gears, and this model is based on the concepts of envelop theory and conjugate geometry between the blank and the straight-sided rack cutter. The geometric model of the rack cutter includes working regions generating involute curves andd fillets for trocoidal curves, and furthermore the addendum modified coeff,is considered for avoiding undercutting. The addendum modified coeff, is changed linearly along with pitch curves and must be the must be the same absolute value at both major semi-axis and minor semi-axis. If undercutting is at all pronounced, the undercut tooth not only are weakened in strength, but lose a small portion of the involute adjacent to the base circle, then this loss of involute may ncause a serios reduction in the length of contact. A very effective method of avoiding undercutting is to use the so-called profile shifted gearing. Non-undercutting conditon is examined with the change of eccentricity and addendum modefied coeff. in elliptical gears and then the minimum number of tooth is proposed not to gernerate undercutting phenomenon.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.154-162
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• 1991

In this study, the simulation program is developed where the tooth profile error in internal gear shaping is calculated considering several factors which affect it. This factors are the circular feed of the pinion cutter, the interference by the geometric conditions of the cutter and the internal gear, the deviation from the theoretical involute profile of the cutter and the eccentricity of the cutter and the internal gear. With this program, the effects are investigated which the geometric conditions and the cutting conditions in internal gear shaping have on the tooth profile error of the internal gear. The condition for the minimization of it is derived and then the results of simulation are adequately verified by measurements of internal gears cut by a pinion cutter.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.2
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• pp.296-303
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• 1987

The composite gear which is composed of involute curve and circular arc has been studied. In the vicinity of pitch point, its profile is an involute curve, and in the dedenum, a circular arc. The curve in the dedendum is generated by the circular arc of the mating gear. Though the available range between minimum and maximum radius of circular arc can be given by existing tooth profile equation, there was no formulation which relates design parameters to the desired radius. It is attempted to get the formula for the radius of circular arc as a function of design parameters, such as unwounded angle, number of teeth, module, and pressure angle. The radius of circular arc, the chordal tooth thickness at working root circle, nominal bending stress, Hertz stress and contact ratio obtained from derived formula are compared with those of the existing design criteria. And these are compared with those of involute gear.