scholarly journals The Mathematical Model of Curve-Face Gear and Time-Varying Meshing Characteristics of Compound Transmission

2021 ◽  
Vol 11 (18) ◽  
pp. 8706
Author(s):  
Yanan Hu ◽  
Chao Lin ◽  
Shuo Li ◽  
Yongquan Yu ◽  
Chunjiang He ◽  
...  
Keyword(s):  
Screw Theory ◽  
Point Contact ◽  
Transmission Ratio ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Pair ◽  
Surface Geometry ◽  
Face Gear ◽  
Meshing Characteristics ◽  
Curve Face

The curve-face gear pair is a new type of gear pair with variable transmission ratio for spatial finite helical motion. In this paper, mathematical models of a new developed curve-face gear were simplified and obtained directly by the standard shaper. The subsequent studies on the curve-face gear compound transmission characteristics were further analyzed by the combinations of the principle of space gearing and screw theory. Firstly, the conjugate tooth surface geometry as well the point contact traces of curve-face gears were derived. Secondly, the geometric relationships between gear pair and the corresponding meshing characteristics were evaluated by several basic geometric elements, including instantaneous screw, axodes, striction curve, and conjugate pitch surface. Based on that analysis, it was found that the tooth contact normal was reciprocal to the instantaneous twist, which demonstrated that the conjugate motion with the desired transmission ratio could be realized in current curve-face gear compound transmission. Moreover, the time-varying slip characteristics of the curve-face gear pair were also revealed, that is, rolling and sliding action coexist at all contact on the tooth surfaces. In brief, this work provided the theoretical basis for following researches on machining curve-face gear with standard shaper.

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.

Contact fatigue model and life prediction of the compound motion curve-face gear pair

2020 ◽  
Vol 44 (3) ◽  
pp. 440-451
Author(s):  
Chao Lin ◽  
Peilu Li ◽  
Chunjiang He ◽  
Qingkun Xing
Keyword(s):  
Fatigue Life ◽  
Crack Growth ◽  
Contact Fatigue ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Fatigue Model ◽  
Contact Fatigue Life ◽  
Five Axis ◽  
Curve Face

Different from the common face gear pair fixed rotation motion between intersecting axes, the compound transmission of the curve-face gear is a new motion form, which can convert rotational motion into rotation and movement motion. To solve the contact fatigue life problem of this new motion form gear pair, a new contact fatigue life calculation method of the compound transmission curve-face gear pair was proposed. Based on the space gear engagement principle and the fracture mechanics theory, the theoretical contact fatigue model of the curve-face gear composite transmission was established. Considering that the contact load for every tooth is time-varying in the half-period of the curve-face gear, the contact fatigue life stage of the curve-face gear was divided into crack initiation and crack growth, and the crack growth fatigue life for each tooth was calculated using the finite element method. The curve-face gear pair was processed in the five-axis NC machining center and the compound transmission experiment platform of the curve-face gear was set up to measure the tooth surface dynamic contact stress, and the overall life of the curve-face gear was predicted. The comparison analysis between theoretical and experimental results verified the correctness of the theoretical contact fatigue calculation model.

scholarly journals Meshing characteristics of a sphere–face gear pair with variable shaft angle

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985951 ◽  
Author(s):  
Lei Liu ◽  
Jinzhao Zhang
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Contact Points ◽  
Shaft Angle ◽  
Meshing Characteristics ◽  
Curvature Interference

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

Research on the Discrete Algorithm of Tooth Surface for a Curve-Face Gear

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Zhiqin Cai ◽  
Chao Lin
Keyword(s):  
Gear Tooth ◽  
Theoretical Data ◽  
Surface Characteristics ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Distribution Law ◽  
Discrete Algorithm ◽  
Generating Method ◽  
Curve Face

Abstract The curve-face gear pair is a new type of face gear pair with a variable transmission ratio. Concerning the complexity of its tooth surface, based on the coordinate transformation principle and the spatial meshing theory, a discrete algorithm of this tooth surface was proposed. The determination rule of the limiting points on the tooth surface was analyzed by introducing the generating method and tooth surface characteristics of this gear tooth. Through the corresponding limiting angles and the distribution law of the contact line, the gear tooth surface was discretized, and the theoretical data points of the tooth surface were obtained. The variations in gear tooth surface in a meshing cycle and under different parameters were analyzed. By comparing the virtual tooth model and the corresponding rolling experiment, the correctness of the tooth surface discrete algorithm of the curve-face gear was verified.

Research on the time-varying characteristics and alications of curve-face gear pair

2016 ◽  
pp. 501-508 ◽  
Author(s):  
Z.Q. Cai ◽  
C. Lin ◽  
Y. Liu ◽  
X.L. Zhao
Keyword(s):  
Time Varying ◽  
Gear Pair ◽  
Face Gear ◽  
Curve Face

Analysis of tooth contact and transmission errors of curve-face gear

2016 ◽  
Vol 231 (19) ◽  
pp. 3579-3589 ◽  
Author(s):  
Chao Lin ◽  
Chunjiang He
Keyword(s):  
Contact Line ◽  
Contact Point ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Generating Method ◽  
Mathematical Equations ◽  
Curve Face

The authors have established the mathematical equations for the tooth surface of non-circular gear and curve-face gear based on the external generating method with the same shaper cutter. The paper covers the derivation of contact line on both non-circular gear and curve-face gear, the derivation of contact point on curve-face gear, the transmission functions with errors of alignment, the analysis of transmission errors and the comparison between curve-face gear pair and normal face gear pair. The developed theory is verified by experiment.

scholarly journals Tooth bending stress analysis of high speed curve face gear of composite transmission

2021 ◽  
Vol 22 ◽  
pp. 20
Author(s):  
Yongquan Yu ◽  
Chao Lin ◽  
Yanan Hu
Keyword(s):  
High Speed ◽  
Normal Load ◽  
Engineering Application ◽  
Tooth Surface ◽  
Gear Pair ◽  
Bending Stress ◽  
Contact Ratio ◽  
Face Gear ◽  
Cylindrical Gear ◽  
Curve Face

To promote the engineering application of composite transmission of high speed curve face gear, which consists of a cylindrical gear and a high speed curve face gear, the analysis of tooth bending stress should be taken into consideration. High speed curve face gear pair is a new type of curve face gear pair. Combined with the principle of high speed cam and curve face gear pair transmission, it can transfer the axial/rotation composite motion and power between two intersecting shafts. Based on the gear engagement principle, the gear meshing coordinate system was established and the fundamental of the high speed composite transmission was expounded. Combined with the tooth profile equation of generating gear, the tooth surface equation of high speed curve face gear was gained. Tooth force, contact ratio and normal load distribution were calculated. Then the tooth bending stress of high speed curve face gear during the transmission was calculated and analyzed in detail. Influence of basic parameters on tooth bending stress was discussed. Finally, the simulation and measurement experiment of tooth bending stress was carried out. By the comparison analysis of simulation, experiment and theory, the correctness of tooth bending stress calculation method was verified, which has important guiding significance for the further research of high speed curve face gear of composite transmission.

Vibration-based fault diagnosis of helical gear pair with tooth surface wear considering time-varying friction coefficient under mixed EHL condition

2021 ◽  
pp. 1-16
Author(s):  
Siyu Wang ◽  
Rupeng Zhu
Keyword(s):  
Dynamic Response ◽  
Hydrodynamic Lubrication ◽  
Helical Gear ◽  
Calculation Model ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Pair ◽  
Surface Wear ◽  
Mesh Stiffness ◽  
Helical Gear Pair

Abstract Based on “slice method”, the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elasto-hydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

Optimal Tooth Modifications in Hypoid Gears

2004 ◽  
Vol 127 (4) ◽  
pp. 646-655 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and optimal diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in (Simon, V., 2000, “Load Distribution in Hypoid Gears,” ASME J. Mech. Des., 122, pp. 529–535) the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the diameter of the cutter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

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