### Abstract

In this work, a mathematical model of an elastic conjugate element is presented, using envelope theory and a deviation function. A basic deformation curve in a two-dimensional system is defined, and determined by the maximum deformation of the originally generated curve. The set of these points of maximum deformation in the moving coordinate frame determines the deviation of the originally generated curve. The degree of deviation is described by a deviation function. A deviation function is chosen to reshape the originally generated curve. The reshaped curve is called a basic deformation curve. If the basic deformation curve is known, an envelope associated with them can be determined. The results are applied to rotary gear pump design. The reshaped curve is superior to the originally generated curve. The reshaped curve has lower deformation, von-Mises stress, and greater bending strength than the originally generated curve. This investigation indicates that envelope theory and deviation function can avoid singular points of conjugate elements, using an example.

Original language | English |
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Pages (from-to) | 262-274 |

Number of pages | 13 |

Journal | Mechanism and Machine Theory |

Volume | 42 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Mar 1 |

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### All Science Journal Classification (ASJC) codes

- Bioengineering
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications

### Cite this

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*Mechanism and Machine Theory*, vol. 42, no. 3, pp. 262-274. https://doi.org/10.1016/j.mechmachtheory.2006.04.009

**Applying envelope theory and deviation function to tooth profile design.** / Yang, Hsueh-Cheng Yang.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Applying envelope theory and deviation function to tooth profile design

AU - Yang, Hsueh-Cheng Yang

PY - 2007/3/1

Y1 - 2007/3/1

N2 - In this work, a mathematical model of an elastic conjugate element is presented, using envelope theory and a deviation function. A basic deformation curve in a two-dimensional system is defined, and determined by the maximum deformation of the originally generated curve. The set of these points of maximum deformation in the moving coordinate frame determines the deviation of the originally generated curve. The degree of deviation is described by a deviation function. A deviation function is chosen to reshape the originally generated curve. The reshaped curve is called a basic deformation curve. If the basic deformation curve is known, an envelope associated with them can be determined. The results are applied to rotary gear pump design. The reshaped curve is superior to the originally generated curve. The reshaped curve has lower deformation, von-Mises stress, and greater bending strength than the originally generated curve. This investigation indicates that envelope theory and deviation function can avoid singular points of conjugate elements, using an example.

AB - In this work, a mathematical model of an elastic conjugate element is presented, using envelope theory and a deviation function. A basic deformation curve in a two-dimensional system is defined, and determined by the maximum deformation of the originally generated curve. The set of these points of maximum deformation in the moving coordinate frame determines the deviation of the originally generated curve. The degree of deviation is described by a deviation function. A deviation function is chosen to reshape the originally generated curve. The reshaped curve is called a basic deformation curve. If the basic deformation curve is known, an envelope associated with them can be determined. The results are applied to rotary gear pump design. The reshaped curve is superior to the originally generated curve. The reshaped curve has lower deformation, von-Mises stress, and greater bending strength than the originally generated curve. This investigation indicates that envelope theory and deviation function can avoid singular points of conjugate elements, using an example.

UR - http://www.scopus.com/inward/record.url?scp=33846419479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846419479&partnerID=8YFLogxK

U2 - 10.1016/j.mechmachtheory.2006.04.009

DO - 10.1016/j.mechmachtheory.2006.04.009

M3 - Article

AN - SCOPUS:33846419479

VL - 42

SP - 262

EP - 274

JO - Mechanism and Machine Theory

JF - Mechanism and Machine Theory

SN - 0374-1052

IS - 3

ER -