scholarly journals Research and Manufacturing of Oval Gear Pair Applied in Rotor of a Roots Type Compressor

2021 ◽  
Vol 31 (5) ◽  
pp. 31-38
Keyword(s):  
Mathematical Model ◽  
Theoretical Calculation ◽  
Tooth Profile ◽  
Transmission Ratio ◽  
Design Parameters ◽  
Gear Pair ◽  
Cylindrical Gear ◽  
Special Cases ◽  
Oval Gear

This study presents a method of shaping the tooth profile of an oval gear pair with the modified cycloid profile of the ellipse. The driving oval gear was shaped by a rack cutter with the profile of an improved cycloid, and the tooth profile of the driven oval gear was shaped by a shaper cutter to ensure that gear pair will mesh accurately with a function of transmission ratio. Mathematical model of the oval gear pair was established according to the theory of the non-circular gear with consideration to the conditions of the design parameters to avoid undercutting and tooth distribution of the oval gear. An improved pair of cycloid oval gears is designed and manufactured according to the results of the theoretical calculation. Furthermore, this gear pair is specifically applied to a Roots-type compressor to demonstrate its applicability in special cases where the traditional cylindrical gear pair cannot be replaced.

Research on Mathematical Modeling and Kinematic Simulation of Elliptic Family Gears

2013 ◽  
Vol 579-580 ◽  
pp. 300-304 ◽  
Author(s):  
Lian Xia ◽  
Da Zhu Li ◽  
Jiang Han
Keyword(s):  
Performance Analysis ◽  
Tooth Profile ◽  
High Order ◽  
Numerical Control ◽  
Gear Pair ◽  
Cylindrical Gear ◽  
Kinematic Simulation ◽  
Cad Modeling ◽  
Pure Rolling ◽  
Pitch Curve

Elliptic family gears are commonly used in non-circular gears, which include elliptic gear, high-order gear, elliptic deformed gear and high-order deformed gear, thereinto high-order deformed gear can include the elliptic family gears through adjust its order and deformed coefficient. Because non-circular gear has different tooth profile in different position of pitch curve and there is difference in the left and right tooth profile of the same gear tooth, thus the CAD modeling of non-circular gear is difficult for these characteristics; but the precise model of non-circular gear has important significance to the realization of numerical control machining, kinematic simulation and relevant mechanical analysis. This paper deduce the corresponding pure rolling mathematical model based on the pure rolling contact theory that cylindrical gear and non-circular gear mesh in the end face, and realize the CAD modeling of non-circular straight and helical gears by letting the cylindrical gear and non-circular gear make solid geometry operation, which is suitable for pitch curve with convex and concave. The non-circular gear shaping methods with equal polar and equal arc length are simulated by setting different discrete polar angles, and the transmission ratio curve and the angular acceleration curve of driven gear are get through the kinematic simulation of gear pair, which realize the transmission performance analysis of elliptic family gear pair. The above research results can be applied to the modeling and kinematic performance analysis of other non-circular gears.

Study on the compound transmission mechanism of the curve-face gear based on screw theory

2017 ◽  
Vol 232 (17) ◽  
pp. 3115-3124 ◽  
Author(s):  
Chao Lin ◽  
Yanqun Wei ◽  
Zhiqin Cai
Keyword(s):  
Screw Theory ◽  
Transmission Mechanism ◽  
Tooth Surface ◽  
Design Parameters ◽  
Gear Pair ◽  
Face Gear ◽  
Cylindrical Gear ◽  
Cam Mechanism ◽  
Conjugate Surfaces ◽  
Curve Face

The compound transmission mechanism of curve-face gear is a new type of gear transmission based on the cam mechanism and the curve-face gear pair. It combines the transmission characteristics of the cam mechanism and noncircular bevel gear. When the compound transmission mechanism of curve-face gear is engaged in the meshing transmission, the rotating center of the cylindrical gear is fixed and used as the driving wheel, and the curve-face gear can generate the helical motion around the axis. In this paper, the meshing characteristics and motion laws of the compound transmission mechanism of the curve-face gear are studied based on the theory of screw. Based on the meshing theory of gears, the coordinate system of conjugate surfaces is established, the basic meshing theory and equation are obtained. On this basis, combined with the principle of the cam, the transmission principle is analyzed by the screw theory. The tooth surface equation of the compound transmission mechanism of curve-face gear is deduced based on the meshing theory and the related knowledge of geometry. The motion law of the curve-face gear and the change of the motion law with the change of the basic parameters of the gear pair with different design parameters are calculated and analyzed. An experimental platform is built to verify the law of motion, and the experimental results are compared with the theoretical values. The correctness of the theoretical analysis is verified, which provides a new way for the research of the compound transmission mechanism of the curve-face gear.

scholarly journals Meshing principle analysis of 3-DOF involute spherical gear

2020 ◽  
Vol 213 ◽  
pp. 02029
Author(s):  
Baichao Wang ◽  
Xue Zhang ◽  
Litong Zhang ◽  
Xianting Lu
Keyword(s):  
Mathematical Model ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Gear Pair ◽  
Tooth Surfaces ◽  
Three Degree Of Freedom ◽  
Relationship Of ◽  
The Mathematical Model ◽  
Spherical Gear

In this paper, a mathematical model of meshing motion of three degree of freedom involute spherical gear pair is constructed. The mathematical model can realize continuous meshing transmission between gear pairs without transmission principle error. Based on the meshing principle and motion analysis of the gear, the tooth profile of the spherical gear is designed by combining the two tooth surfaces of the involute ring gear and the hemispherical bevel gear. According to the conjugate motion relationship of spherical gear pair, a mathematical model of arc tooth surface of hemispherical bevel gear is established, and the mathematical description of the tooth profile of spherical gear is completed by combining the equation of ring tooth surface. It provides the basis and Reference for the meshing design of ball gear.

Computerized Tooth Profile Generation and Undercut Analysis of Gears Manufactured With Pre-Shaving Hobs

2009 ◽  
Vol 16-19 ◽  
pp. 1278-1282
Author(s):  
Xiang Wei Kong ◽  
Jing Zhang ◽  
Meng Hua Niu
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Design Parameters ◽  
Gear Teeth ◽  
The Mathematical Model

This paper investigated the feature of pre-shaving hob contour and the generated gear tooth profile. By tooth generation method, a complete geometry of the gear tooth can be mathematically derived in terms of the design parameters of the pre-shaving hob cutter. The mathematical model consisted of equations describing the generated fillet and involute profiles. The degree of undercutting and the radii of curvatures of a fillet were investigated by considering the model. Finally, a computer program for generating the profile of the gear teeth was developed by simulating the cutting methods. The methods proposed in this study were expected to be a valuable guidance for pre-shaving hob designers and manufacturers.

Mathematical Model and Surface Deviation of Cylindrical Gears With Curvilinear Shaped Teeth Cut by a Hob Cutter

Volume 3 ◽  
2004 ◽  
Author(s):  
Jui-Tang Tseng ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Design Parameters ◽  
Cutting Mechanism ◽  
Cylindrical Gear ◽  
Tooth Gear ◽  
Surface Deviations ◽  
Tool Setting ◽  
Surface Deviation ◽  
Cutter Design

The generating motion of a cylindrical gear with curvilinear shaped teeth cut by a CNC hobbing machine is proposed. Based on the cutting mechanism and the gear theory, the surface equation of this kind of gear is developed as a function of hob cutter design parameters. Computer graphs of the curvilinear-tooth gear are presented based on the developed gear mathematical model, and the tooth surface deviations due to machine-tool setting with nominal radius of circular tooth trace are also investigated.

scholarly journals Evaluation and Optimization of the Oil Jet Lubrication Performance for Orthogonal Face Gear Drive: Modelling, Simulation and Experimental Validation

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1935 ◽  
Author(s):  
Yu Dai ◽  
Feiyue Ma ◽  
Xiang Zhu ◽  
Qiao Su ◽  
Xiaozhou Hu
Keyword(s):  
Mathematical Model ◽  
Volume Fraction ◽  
Tooth Surface ◽  
Design Parameters ◽  
Gear Pair ◽  
Face Gear ◽  
Gear Drive ◽  
Lubrication Performance ◽  
Jet Nozzle ◽  
Oil Jet

The oil jet lubrication performance of a high-speed and heavy-load gear drive is significantly influenced and determined by the oil jet nozzle layout, as there is extremely limited meshing clearance for the impinging oil stream and an inevitable blocking effect by the rotating gears. A novel mathematical model for calculating the impingement depth of lubrication oil jetting on an orthogonal face gear surface has been developed based on meshing face gear theory and the oil jet lubrication process, and this model contains comprehensive design parameters for the jet nozzle layout and face gear pair. Computational fluid dynamic (CFD) numerical simulations for the oil jet lubrication of an orthogonal face gear pair under different nozzle layout parameters show that a greater mathematically calculated jet impingement depth results in a greater oil volume fraction and oil pressure distribution. The influences of the jet nozzle layout parameters on the lubrication performance have been analyzed and optimized. The relationship between the measured tooth surface temperature from the experiments and the corresponding calculated impingement depth shows that a lower temperature appears in a situation with a greater impingement depth. Good agreement between the mathematical model with the numerical simulation and the experiment validates the effectiveness and accuracy of the method for evaluating the face gear oil jet lubrication performance when using the impingement depth mathematical model.

Mathematical Model and Surface Deviation of Cylindrical Gears With Curvilinear Shaped Teeth Cut by a Hob Cutter

2004 ◽  
Vol 127 (5) ◽  
pp. 982-987 ◽  
Author(s):  
Jui-Tang Tseng ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Design Parameters ◽  
Cutting Mechanism ◽  
Cylindrical Gear ◽  
Cylindrical Gears ◽  
Tooth Gear ◽  
Surface Deviations ◽  
Surface Deviation ◽  
Cutter Design

The generating motion of a cylindrical gear with curvilinear shaped teeth cut by a CNC hobbing machine is proposed. On the basis of the cutting mechanism and the gear theory, the surface equation of this type of gear is developed as a function of hob cutter design parameters. Computer graphs of the curvilinear-tooth gear are presented based on the developed gear’s mathematical model, and the tooth surface deviations due to machine-tool settings with nominal radius of circular tooth traces are also investigated.

Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured With Shaper Cutters

1998 ◽  
Vol 120 (1) ◽  
pp. 92-99 ◽  
Author(s):  
Shinn-Liang Chang ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Contact Line ◽  
Relative Velocity ◽  
Tooth Profile ◽  
Gear Pair ◽  
Line Method ◽  
Envelope Method ◽  
Noncircular Gears

Pitch curves of a conjugate noncircular gear pair are derived based on kinematic considerations. A method for considering the inverse mechanism relationship and the equation of meshing, is proposed here to derive a complete mathematical model of noncircular gears manufactured with involute-shaped shaper-cutters. The proposed method is similar to the contact line method and the envelope method, but is easier to apply to the determination of tooth profiles. A computer program is developed for generation the tooth profile with backlashes. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Finally, modified elliptical gears are presented to illustrate the tooth profile generation when the proposed mathematical model is applied, and to investigate the phenomenon of tooth undercutting.

scholarly journals Research and manufacture of external non-circular gear-pair with improved cycloid profile of the ellipse

2021 ◽  
Vol 4 (2) ◽  
pp. first
Author(s):  
Thai Hong Nguyen ◽  
Trung Thanh Nguyen ◽  
Viet Hoang Nguyen
Keyword(s):  
Mathematical Model ◽  
Tooth Profile ◽  
Gear Pair ◽  
Design Scheme ◽  
Profile Design ◽  
The Mathematical Model ◽  
Gear Profile

Non-circular gears (NCGs) are known as an alternative to conventional mechanical mechanisms in continuous speed converters. In which, the gear profile is the factor that directly affects the performance and quality meshing of the non-circular gear. However, the types of curves that are being used to generating profiles of the non-circular gears still exist limited in meeting the conditions of undercutting and uniformity of tooth sizes at different positions on the centrode. To optimize the profile of the non-circular gear, the paper presents a new profile in which the traditional involute profile of the non-circular gears is replaced by an improved cycloid curve of the ellipse. The mathematical model of new profile of non-circular gear is formed by eccentric circular shaper cutter with the improved cycloid of the ellipse in accordance with the theory of gearing in consideration of undercutting conditions. Based on the mathematical model established by this research, a program was written in Matlab. On that basis, a pair of non-circular gear was designed and fabricated experimentally on a wire breaker to verify the theory. The results show that with the new tooth profile design scheme, the shortcomings of uneven teeth on the non-circular gear of the traditional studies when using the involute profile of the circle have been overcome.

scholarly journals Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Qi Zhang ◽  
Guang Wen ◽  
Shuang Liang ◽  
Qin Tong ◽  
Li Hou ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Contact Stress ◽  
Surrogate Model ◽  
Kriging Model ◽  
Design Parameters ◽  
Theoretical Formula ◽  
Kriging Surrogate Model ◽  
Cylindrical Gear ◽  
Pressure Angle ◽  
Tooth Width

Given the absence of a theoretical formula to analyze the influence of parameters on the contact stress of cylindrical gear with arc tooth, an explicit mathematical model of cylindrical gear with arc tooth between the design parameters and the contact stress is established based on Kriging surrogate model. The parameters of the variation function of Kriging model are optimized by using the whale optimization algorithm (WOA), and the explicit mathematical model accuracy between the design parameters and the contact stress of the gear is in turn optimized by the improved Kriging surrogate model. The influence of design parameters on the contact stress of cylindrical gear with arc tooth is analyzed based on the established mathematical model. The proposed algorithm was realized via the programming platform MATLAB; the simulation results indicate that the precision evaluation indexes (the correlation coefficient (R2), root mean square error (RMSE), and the relative maximum absolute error (RMAE)) of the proposed Kriging model are improved, in addition to the error range which is narrowed from (−2, 4) to (0, 3). As the tooth width, modulus, pressure angle, and tooth line radius increased, the contact stress of the cylindrical gear with arc tooth gear declined, which was negatively correlated with the design parameter. The amplitude of contact stress of the cylindrical gear with arc tooth was the largest due to the change of tooth radius, followed by the change of modulus, while the influence of tooth width was less. Finally, the influence of modulus-tooth line radius interaction and pressure angle-tooth line radius interaction on contact stress of cylindrical gear with arc tooth was significant.

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