The Analysis and Modeling for Nutation Drives with Double Circular-Arc Helical Bevel Gears

2006 ◽  
pp. 949-954 ◽  
Author(s):  
Bing Gu ◽  
Ligang Yao ◽  
Guo Wu Wei ◽  
Ying Jie Cai ◽  
Jian S. Dai
Keyword(s):  
Circular Arc ◽  
Bevel Gears

Mathematical Modeling and Simulation of the External and Internal Double Circular-Arc Spiral Bevel Gears for the Nutation Drive

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Ligang Yao ◽  
Bing Gu ◽  
Shujuan Haung ◽  
Guowu Wei ◽  
Jian S. Dai
Keyword(s):  
Mathematical Modeling ◽  
Numerical Control ◽  
Tooth Surface ◽  
Circular Arc ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Nc Simulation ◽  
Helical Angle ◽  
Nc Milling ◽  
Spiral Bevel

The purpose of this paper is to propose a pair of external and internal spiral bevel gears with double circular-arc in the nutation drive. Based on the movement of nutation, this paper develops equations of the tooth profiles for the gear set, leading to the mathematical modeling of the spiral bevel gear with a constant helical angle gear alignment curve, enabling the tooth surface to be generated, and permitting the theoretical contacting lines to be produced in light of the meshing function. Simulation and verification are carried out to prove the mathematical equations. Numerical control (NC) simulation of machining the external and internal double circular-arc spiral bevel gears is developed, and the spiral gears were manufactured on a NC milling machine. The prototype of the nutation drive is illustrated in the case study at the end of this paper.

Research on NC Technologies of Loxodromic Normal-Arc Bevel Gear

2014 ◽  
Vol 621 ◽  
pp. 570-575
Author(s):  
Su Zhen Wu ◽  
Jing Wang ◽  
Xue Liang Sui
Keyword(s):  
Planning Process ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Circular Arc ◽  
Primary Condition ◽  
Bevel Gears ◽  
New Type ◽  
Machining Planning ◽  
Relationship Of

Normal circular-arc spiral bevel gear is a new type gear based on Bertrand conjugation principle. Normal circular-arc bevel gear selects directrix on the basis of paying attention to machining planning process. When the directrix serves as loxodrome, the formed tooth profile surface not only has fine transmissibility like general arc bevel gear, but also is convenient to machining. Starting with differential geometry, the geometry nature and inner relationship of Bertrand conjugation surface are studied. Then the normal circular-arc surface id put forward which is a typical Bertrand surface; the conjugation theory of loxodrome normal circular-arc bevel gears is studied. The characters of loxodrome line are analyzed. The tooth profile of loxodrome normal circular-arc bevel gears, the primary condition the directrix line must be satisfied, the relative curvature of the conjugating surfaces, the relations between non-interventional condition and curvature axle of the directrix line is provided; the NC machining theory of normal circular-arc bevel gears is studied, including the designing and manufacture of the tool, the movement of the machine, the adjustment of the tool under the condition of tangency and non-interventional condition and so on.

Modeling of Error Analysis Simulation of Normal Circular Arc Bevel Gear Transmission

2013 ◽  
Vol 589-590 ◽  
pp. 606-610 ◽  
Author(s):  
Guo Jun Dong ◽  
Ming Wang
Keyword(s):  
Contact Zone ◽  
High Speed ◽  
High Strength ◽  
Helix Angle ◽  
Transmission Error ◽  
Angle Error ◽  
Circular Arc ◽  
Bevel Gears ◽  
Operation Test ◽  
Simulation Results

The normal circular arc bevel gears are used in industrial areas of high speed, high bearing and high strength widely. A mathematical simulation model is built and it can analyze transmission error and contact zone of normal circular arc bevel gears. In this model, the instantaneous engaging points of gear pair are transformed into the least-values of rotary angles of corresponding points between two gears along the final motion, so this method is very simple and effective. Under the condition of existing helix angle error, transmission error and contact zone of a pair of normal circular arc bevel gears are simulating analyzed. At last, the operation test of contact zone of gears indicates gears transmission is stable and the gears contact zones are largely in line with the simulation results.

Transmission Ratio Analysis and Controllable Tooth Profile Modeling for the Nutation Drive with Double Circular-Arc External and Internal Spiral Bevel Gears

2010 ◽  
Vol 97-101 ◽  
pp. 3128-3134 ◽  
Author(s):  
Zheng Lin ◽  
Li Gang Yao ◽  
Shu Juan Huang
Keyword(s):  
Three Dimensional ◽  
Tooth Profile ◽  
Transmission Ratio ◽  
Circular Arc ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Three Dimensional Modeling ◽  
Spiral Bevel ◽  
Comparative Results ◽  
Profile Modeling

This paper proposes an approach for calculating the transmission ratio of nutation drive based on the working principle of the nutation movements. Then, the analysis of the influences for the nutation angle on the transmission ratio is carried out. The controllable tooth profile modelling for external and internal spiral bevel gears with double circular-arc is proposed. Based on the proposed tooth profile modeling, the three dimensional modeling and virtual assembly of the nutation drive have been further completed. Finally, the kinematical simulation is preceded in the simulating system and the comparative results have been accomplished between the simulation results and the theoretical ones of the transmission ratio.

scholarly journals Dynamic modal analysis of double-sided meshing nutation drive with double circular arc spiral bevel gears

2020 ◽  
Vol 11 (1) ◽  
pp. 115-123
Author(s):  
Zheng Lin ◽  
Ligang Yao ◽  
Zhiyu Xie
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Transmission Error ◽  
Drive System ◽  
Nonlinear Dynamic Model ◽  
Circular Arc ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Meshing Stiffness ◽  
Spiral Bevel

Abstract. In order to reduce the vibration of the double-sided meshing nutation drive with double circular arc spiral bevel gears, the dynamic modal of the nutation system is analyzed. The bending-torsional-axial coupling nonlinear dynamic model of the double-sided meshing nutation drive system with time-varying meshing stiffness, meshing damping, transmission error and tooth backlash is established, and the equation of motion of the system is derived. The natural frequencies and corresponding modal modes of the nutation system are calculated, and the effects of the average meshing stiffness of gears and the bearing support stiffness of nutation gears on the modal of the system are analyzed. The modal analysis of double circular arc spiral bevel gears is carried out, and the ten order natural frequencies and their corresponding modes are obtained. The results show that the nutation drive system and the double circular arc spiral bevel gears do not resonate during transmission.

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