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CSME 2024/12
Volume 45 No.6
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517-531
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Generation, Modeling, and Analysis of Curvilinear Cylindrical Gear Drive Featuring Predesigned Fourth-Order Transmission Error and Cosine Tooth Profile
Cheng-Kang Lee a and Yung-Chang Cheng b
aDepartment of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung, Taiwan 833301, ROC.
bDepartment of Mechatronics Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan 824005, ROC.
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Abstract:
This study proposes an innovative curvilinear
cylindrical gear drive characterized by a predesigned
fourth-order transmission error and a cosine tooth
profile. The predesigned fourth-order transmission
error not only absorbs linear transmission errors but
also contributes to a smoother overall motion curve.
The cosine tooth profile helps reduce the minimum
number of teeth without undercutting. This research
begins by establishing the generation methods and
mathematical models for both the curvilinear pinion
and gear. A set of nonlinear simultaneous equations,
consisting of fifteen unknowns and fifteen equations,
is then formulated based on tooth contact conditions
and the predesigned fourth-order transmission error
condition. The differential evolution algorithm and
Newton's method are subsequently employed to
conduct a global search and local refinement of the
unknowns, leading to precise design solutions for the
generating motion parameters. Tooth Contact
Analysis (TCA) theory is applied to verify that the
actual transmission error aligns perfectly with the
predesigned fourth-order transmission error and to
confirm that the contact ellipses and bearing contacts
are centrally located on the tooth surface. Finally, to
further validate the theoretical accuracy, CAD/CAM
technology and a four-axis computer numerical
control (CNC) machine are used to fabricate a
curvilinear cylindrical gear drive. After inspecting the
bearing contact positions using red ink, it is
confirmed that the actual contact situation
corresponds with the theoretical results.
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Keywords: curvilinear cylindrical gear, cosine tooth profile, fourth-order transmission error, CAD/CAM, four-axis computer numerical control (CNC) machining.
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*Corresponding author; e-mail:
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©
2024
CSME , ISSN 0257-9731
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