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.

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.

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.

Reconsideration of the LogiX Gear Using a General Mathematical Model of Composite Gear Profiles

1992 ◽  
Author(s):  
Y. C. Tsai ◽  
H. L. Chang
Keyword(s):  
Mathematical Model ◽  
Necessary Conditions ◽  
Pressure Angle ◽  
General Mathematical Model ◽  
Zero Values ◽  
Specific Sliding ◽  
Gear Profile ◽  
Logix Gear ◽  
The Ideal

Abstract A general mathematical model is derived for describing the conjugate tooth profiles and meshing properties of composite gears. Via a typical gear parameter, the pressure angle, necessary conditions that determine the continuity of composite gears in tooth geometry and meshing properties are introduced. The peculiarity of the presented model is that composite gears can be parametrically characterized by the specific functions in terms of pressure angle. An example is demonstrated that the discontinuity in composite gears will be efficiently and logically solved. In this paper the LogiX gear, a special composite gear which consists of many segmental “S” curves in gear profiles and possesses zero values of relative curvature and specific sliding at the joints of connected segmental profiles, will be parametrically investigated by this model. The “ideal” LogiX gear profile, theoretically, is constructed by infinite numbers of segmental profiles such that it may have infinite numbers of zero values of relative curvature and specific sliding. However, this “ideal” LogiX gear profile is characterized as a linear parametric profile that is a monotonous curve substantially and no more has infinite numbers of the zero values. Finally, many parametric gears which own power relative curvature and specific sliding than that of the “ideal” LogiX gear profile are presented.

Compensating analysis of a double circular-arc helical gear by computerized simulation of meshing

2001 ◽  
Vol 215 (7) ◽  
pp. 759-771 ◽  
Author(s):  
C-K Chen ◽  
C-Y Wang
Keyword(s):  
Mathematical Model ◽  
Helical Gear ◽  
Tooth Contact Analysis ◽  
Angular Misalignment ◽  
Circular Arc ◽  
Numerical Examples ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Computerized Simulation

A mathematical model of a stepped double circular-arc helical tooth profile with two centre offsets is developed. The conditions of gear meshing that reflect manufacturing and assembly errors are simulated. The locations of bearing contact and the contact path pattern of mating tooth surfaces are determined by tooth contact analysis (TCA). By applying the proposed mathematical model and TCA, single error impact can be determined. To compensate for offset and angular misalignment, the authors propose an adjustable bearing whereby transmission errors can be minimized. The investigation is illustrated with several numerical examples.

MODELING OF THE DYNAMIC PROCESS RELEASE OF STUCK DRILLING TOOLS BY HYDRO-PULSE METHOD

2019 ◽  
pp. 94-103
Author(s):  
K. H. Levchyk ◽  
M. V. Shcherbyna
Keyword(s):  
Mathematical Model ◽  
Dynamic Process ◽  
Drilling Fluid ◽  
Pulse Method ◽  
Geometrical Parameters ◽  
Technical Solution ◽  
Rock Layer ◽  
Drilling Tool ◽  
Drilling Tools ◽  
Drill Pipes

A technical solution is proposed for the elimination the grabbing of drilling tool, based on the use of energy due to the circulation of the drilling fluid. The expediency eliminating the grabbing drilling tool using the hydro-impulse method is substantiated. A method of drawing up a mathematical model for the dynamic process of a grabbing string of drill pipes in the case of perturbation of hydro-impulse oscillations in the area of the productive rock layer is developed. The law of longitudinal displacements arising in the trapped string is obtained, which allows choosing the optimal geometrical parameters of the passage channels and the frequency rotational of shutter for these channels. Recommendations for using this method for practical use have been systematized.

scholarly journals A Mathematical Model of a Differential Drive with a Limited Gear Ratio

2021 ◽  
Vol 54 ◽  
pp. 699-711
Author(s):  
Andrey Efimov ◽  
Oleg Polushkin ◽  
Sergey Kireev ◽  
Marina Korchagina
Keyword(s):  
Mathematical Model ◽  
Gear Ratio ◽  
Differential Drive

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

scholarly journals Experimental Investigation of Tandem Blade Cascades With Double-Circular ARC Profiles

1985 ◽  
Author(s):  
Wu Guochuan ◽  
Zhuang Biaonan ◽  
Guo Bingheng
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Mach Number ◽  
Total Pressure ◽  
Incidence Angle ◽  
Axial Direction ◽  
Geometrical Parameters ◽  
Optimal Conditions ◽  
Turning Angle ◽  
Circular Arc

24 double circular are tandem blade cascades of three different chord-ratios were investigated under different displacements in peripheral and axial direction. The inlet Mach number was 0.3. The Reynolds number based on blade chord was 2.7×105. The characteristics of the tandem blade cascades, such as the dependence of turning angle and coefficient of total pressure loss on incidence angle were obtained. The ranges of main geometrical parameters under optimal conditions were recommended.

scholarly journals Theoretical Modeling, Design and Simulation of an Innovative Diverting Valve Based on Coanda Effect

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 103
Author(s):  
Giancarlo Comes ◽  
Carlo Cravero
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Computational Fluid Dynamics ◽  
Additive Manufacturing ◽  
Water Flow ◽  
Coanda Effect ◽  
Geometrical Parameters ◽  
Convex Wall ◽  
Fluidic Device ◽  
Coandǎ Effect

The present work is focused on the study of an innovative fluidic device. It consists of a two-ways diverter valve able to elaborate an inlet water flow and divert it through one of the two outlets without moving parts but as a result of a fluctuation of pressure induced by two actuation ports, or channels. Such apparatus is named Attachment Bi-Stable Diverter (ABD) and is able to work with the effect of the fluid adhesion to a convex wall adjacent to it, this phenomenon is known as Coanda Effect; it generates the force responsible for the fluid attachment and the consequent deviation. The main purpose of this work is to develop a knowhow for the design and development of such particular device. A mathematical model for the ABD has been developed and used to find the relationships between the geometrical parameters and the operative conditions. A configuration has been designed, simulated with a computational fluid dynamics approach. A prototype has been printed with and additive manufacturing printer and tested in laboratory to check the effective working point of the device.

A MATHEMATICAL MODEL OF THE PHYSICAL GROWTH MECHANISM AND GEOMETRICAL CHARACTERIZATION OF GROWING FORMS

2011 ◽  
Vol 04 (01) ◽  
pp. 35-53 ◽  
Author(s):  
YURI K. SHESTOPALOFF
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Growth Mechanism ◽  
Growth Suppression ◽  
Physical Growth ◽  
Geometrical Parameters ◽  
Growth Equation ◽  
Software Application ◽  
Multicellular Organisms

The article introduces a mathematical model of the physical growth mechanism which is based on the relationships of the physical and geometrical parameters of the growing object, in particular its surface and volume. This growth mechanism works in cooperation with the biochemical and other growth factors. We use the growth equation, which mathematically describes this mechanism, and study its adequacy to real growth phenomena. The growth model very accurately fits experimental data on growth of Amoeba, Schizosaccharomyces pombe, E.coli. Study discovered a new growth suppression mechanism created by certain geometry of the growing object. This result was proved by experimental data. The existence of the growth suppression phenomenon confirms the real workings and universality of the growth mechanism and the adequacy of its mathematical description. The introduced equation is also applicable to the growth of multicellular organisms and tumors. Another important result is that the growth equation introduces mathematical characterization of geometrical forms that can biologically grow. The material is supported by software application, which is released to public domain.

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