Study on the pitch curve with minimal rotary inertia for the noncircular gears

2017 ◽  
Vol 232 (15) ◽  
pp. 2666-2673
Author(s):  
Xin Zhang ◽  
Shouwen Fan
Keyword(s):  
Mathematical Model ◽  
Calculus Of Variations ◽  
Design Method ◽  
High Load ◽  
Rotary Inertia ◽  
Slow Response ◽  
Numerical Examples ◽  
General Mathematical Model ◽  
Noncircular Gears ◽  
Pitch Curve

Aimed at the high load and slow response of the noncircular gears design, a general mathematical model for designing the pitch curve with minimal rotary inertia of the noncircular gear is proposed by resorting to kinematics principle and calculus of variations. To achieve the closure design, the constraint conditions and smoothness characteristics of N-lobed noncircular gear pitch curve with minimal rotary inertia are established and calculated analytically. In addition, the unified design method of the conjugate pitch curves with minimal rotary inertia for the noncircular gears is given in this paper. Unclosed and closed N-lobed conjugate pitch curves that satisfy the desired transmission requirements can be easily solved by using the proposed method, and each lobe has identical profile to ensure the periodical motion of the pitch curves. Numerical examples are implemented in computer and demonstrate the feasibility of the above method.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals Design of Vegetable Pot Seedling Pick-up Mechanism with Planetary Gear Train

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Zhipeng Tong ◽  
Gaohong Yu ◽  
Xiong Zhao ◽  
Pengfei Liu ◽  
Bingliang Ye
Keyword(s):  
Design Method ◽  
Planetary Gear ◽  
Gear Train ◽  
Dimensional Synthesis ◽  
Planetary Gear Train ◽  
Key Points ◽  
Physical Prototype ◽  
Noncircular Gears ◽  
Pitch Curve ◽  
Parameter Values

Abstract It has been challenging to design seedling pick-up mechanism based on given key points and trajectories, because it involves dimensional synthesis and rod length optimization. In this paper, the dimensional synthesis of seedling pick-up mechanism with planetary gear train was studied based on the data of given key points and the trajectory of the endpoint of seedling pick-up mechanism. Given the positions and orientations requirements of the five key points, the study first conducted a dimensional synthesis of the linkage size and center of rotation. The next steps were to select a reasonable solution and optimize the data values based on the ideal seedling trajectory. The link motion was driven by the planetary gear train of the two-stage gear. Four pitch curves of noncircular gears were obtained by calculating and distributing the transmission ratio according to the data. For the pitch curve with two convex points, the tooth profile design method of incomplete noncircular gear was applied. The seedling pick-up mechanism was tested by a virtual prototype and a physical prototype designed with the obtained parameter values. The results were consistent with the theoretical design requirements, confirming that the mechanism meets the expected requirements for picking seedlings up. This paper presents a new design method of vegetable pot seedling pick-up mechanism for an automatic vegetable transplanter.

Study on Meshing Characteristic and CAM Technology of Eccentric Involute Gears

2012 ◽  
Vol 479-481 ◽  
pp. 917-920
Author(s):  
Yong Ping Liu ◽  
Peng Fei Meng ◽  
Chi Bing Hu
Keyword(s):  
Design Method ◽  
Shape Design ◽  
Digital Manufacturing ◽  
Transmission Characteristics ◽  
Systemic Theory ◽  
Theoretical Design ◽  
Parameterized Modeling ◽  
Involute Gears ◽  
Noncircular Gears ◽  
Pitch Curve

According to the meshing principle of noncircular gears, the meshing characteristic and digital manufacturing technology of eccentric involute gears is studied. Based on analyzing the parameterized modeling of pitch curve, transmission characteristics and convex-concave property on eccentric involute gears, the transmission feasibility of this type gear is proved. Through tooth shape design, CAM calculation and processing simulation, the validity and manufacturability of theoretical design method on this type gear is proved. The research results can provide more systemic theory basis for the design, manufacture, measure and application of eccentric involute gears.

scholarly journals Mathematical model and geometrical design method of noncircular face gear with intersecting axes

2021 ◽  
pp. 095440622199070
Author(s):  
Dawei Liu ◽  
Zhenzhen Lv ◽  
Bingbing Li
Keyword(s):  
Mathematical Model ◽  
Fourier Series ◽  
Design Method ◽  
Experimental Results ◽  
Transmission Mechanism ◽  
Design Parameters ◽  
Cnc Milling ◽  
Face Gear ◽  
Pitch Curve ◽  
The Mathematical Model

In order to establish the design method of a noncircular face gear (NFG) with intersecting axes, the meshing theory of this gear is investigated based on the principle of space gear meshing. A generalized approach for designing closed pitch curve of the NFG with intersecting axes was proposed based on Fourier series. The mathematical model of the NFG generated by a shaper cutter was established. The fundamental design parameters of the gears were defined, with the principle for determining their values discussed. The prototype of a NFG was machined by 5-axis CNC milling and the motion rule was tested. Experimental results verify the feasibility of the innovative transmission mechanism and the correctness of the mathematical model of NFG with intersecting axes.

A GENERAL CAD/CAM MODEL FOR APT-LIKE ROTARY MILLING CUTTERS

2015 ◽  
Vol 39 (3) ◽  
pp. 669-678
Author(s):  
Chang-Tzuoh Wu ◽  
Nien-Te Liu
Keyword(s):  
Mathematical Model ◽  
Differential Geometry ◽  
Design Method ◽  
Systematic Design ◽  
Cad Cam ◽  
Helical Groove ◽  
Nc Machine ◽  
General Mathematical Model ◽  
Cam Model ◽  
Geometry And Kinematics

This paper presents a general mathematical model for NC-machining an APT-LIKE rotating cutter. The design model of cutting-edge and helical groove is also developed by using the principles of differential geometry and kinematics. Based on the envelope condition, approaches for solving the inverse problems that are related to the manufacturing models are also presented. The velocities of the cutter in the radial and axial directions are then determined based on the gouging avoidance of grooves. The results of the numerical experiment indicate that the proposed systematic design method by using 2-axis NC machine setup is feasible and reliable.

Avoidance of Cutter Retracting Interference in Noncircular Gear Shaping Through 4-Linkage Model

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Fangyan Zheng ◽  
Hua Lin ◽  
Xinghui Han ◽  
Mingde Zhang ◽  
Weiqing Zhang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Cutting Process ◽  
Cutting Experiment ◽  
Noncircular Gears ◽  
Pitch Curve ◽  
Gear Shaping ◽  
Linkage Model

Gear shaping, a widely used machining method for circular gears, was generalized to noncircular gears in recent works using a 3-linkage machine tool. As the pitch curve normals of noncircular gears change constantly in processing, angles may exist between the pitch curve normals and the cutter relieving direction, bringing in turn cutter retracting interference. Regarding this, the paper proposes a 4-linkage shaping method. Through linkage motion of 4 machine tool axes, noncircular gear pitch normals are along the cutter relieving direction, avoiding completely cutter retracting interference. On such basis, a mathematical model is first established, the cutting process is then discussed and a cutting experiment is finally carried out, proving the validity of the proposed method.

Classification identification and modification of the pitch curve with nondifferentiable points for N-lobed noncircular gear

2016 ◽  
Vol 230 (19) ◽  
pp. 3556-3567 ◽  
Author(s):  
Xin Zhang ◽  
Shouwen Fan
Keyword(s):  
Calculus Of Variations ◽  
Lagrange Equation ◽  
Numerical Examples ◽  
Novel Method ◽  
Simulation Results ◽  
Pitch Curve ◽  
Outer Contact ◽  
Identification Model

A novel method for the design of discretionary N-lobed pitch curve and intermittent N-lobed pitch curve is presented. And a general formulation for classification identification model of the pitch curve with nondifferentiable points for N-lobed noncircular gear ( N-LNG) is proposed. The formulation is based on the differentiable principle. In particular, the steepest rotation modification model and method of the pitch curve with discontinuous points for any type of N-LNG are established by resorting to fundamentals of the calculus of variations. The modification model can be calculated via the Euler–Lagrange equation, and its conjugate pitch curves which contain outer contact and inner contact can be obtained in general by using the principle of noncircular gear meshing. This identification and modification model and method are implemented in several numerical examples, and simulation results demonstrate that the pitch curve with nondifferentiable points for N-LNG can be effectively identified and modified.

Modeling of the Meshing of Trochoidal Profiles With Clearances

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Lozica Ivanović ◽  
Goran Devedžić ◽  
Saša Ćuković ◽  
Nenad Mirić
Keyword(s):  
Mathematical Model ◽  
Gear Ratio ◽  
Geometrical Parameters ◽  
Circular Arc ◽  
Numerical Examples ◽  
Gerotor Pumps ◽  
General Mathematical Model ◽  
Height Change ◽  
Gear Profile ◽  
Profile Development

This paper explains development of the general mathematical model of trochoidal gearing that can be applied for gerotor pumps and cyclo reducers. The model analyzes geometry and physics of the gearing pair in trochoidal pump where the outer gear has one tooth more than the inner gear. The inner gear profile is described by peritrochoid equidistance and the outer gear profile by circular arc. Mathematical model of gearing with clearances is based on the principle of an ideal profile development. Minimum clearance height between teeth profiles in relation to instantaneous gear ratio is determined. The influence of gear profile geometrical parameters on gearing process, clearance height change, and pulsation of drive moment is analyzed and presented in numerical examples. Obtained results can be used for the design of the trochoidal gearing where accurate and silent operation is required.

scholarly journals Mathematical Model and Geometrical Design Method of Noncircular Face Gear with Intersecting Axes

2020 ◽  
Author(s):  
Dawei Liu ◽  
Zhenzhen Lv ◽  
Guohao Zhao
Keyword(s):  
Mathematical Model ◽  
Fourier Series ◽  
Design Method ◽  
Transmission Mechanism ◽  
Design Parameters ◽  
The Novel ◽  
Face Gear ◽  
Simulation And Experiment ◽  
Pitch Curve ◽  
The Mathematical Model

Abstract In order to establish the design method of a noncircular face gear (NFG) with intersecting axes, the meshing theory of this gear is investigated based on the principle of space gear meshing. A generalized approach for designing closed pitch curve of the NFG with intersecting axes is proposed based on Fourier series. The mathematical model of the NFG generated by a shaper cutter is established. The fundamental design parameters of the gears are defined, with the principle for determining their values discussed. The results of simulation and experiment verify the feasibility of the novel transmission mechanism and the correctness of the mathematical model of NFG with intersecting axes.

A Study on the General CAD Model for Rotary Milling Cutters

2015 ◽  
Vol 764-765 ◽  
pp. 176-180
Author(s):  
Chang Tzuoh Wu ◽  
Chien Hung Liu ◽  
Nien Te Liu
Keyword(s):  
Mathematical Model ◽  
Differential Geometry ◽  
Analytical Solution ◽  
Design Method ◽  
Cad Model ◽  
Systematic Design ◽  
Helical Groove ◽  
Nc Machine ◽  
General Mathematical Model ◽  
Geometry And Kinematics

This paper presents a general mathematical model for NC-machining an APT-LIKE rotating cutter. The design model of cutting-edge and helical groove are also developed by using the principles of differential geometry and kinematics. The analytical solution for the resolution profile of helical groove has also been developed. The results of numerical experiment indicate that the proposed systematic design method by using 2-axis NC machine setup are feasible and reliable.

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