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 Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Grzegorz Mikułowski ◽  
Rafał Wiszowaty
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Experimental Verification ◽  
Load Capacity ◽  
Mechanical Energy ◽  
Specific Situation ◽  
Engineering Structures ◽  
Piston Cylinder ◽  
Proposed Model ◽  
Energy Absorbers

Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA), which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.

scholarly journals On Probability Characteristics for a Class of Queueing Models with Impatient Customers

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 594 ◽  
Author(s):  
Yacov Satin ◽  
Alexander Zeifman ◽  
Alexander Sipin ◽  
Sherif I. Ammar ◽  
Janos Sztrik
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Markov Model ◽  
Queueing Models ◽  
Impatient Customers ◽  
Numerical Examples ◽  
Markovian Queue ◽  
Proposed Model ◽  
System Characteristics ◽  
Individual Requirement

In this paper, a class of queueing models with impatient customers is considered. It deals with the probability characteristics of an individual customer in a non-stationary Markovian queue with impatient customers, the stationary analogue of which was studied previously as a successful approximation of a more general non-Markov model. A new mathematical model of the process is considered that describes the behavior of an individual requirement in the queue of requirements. This can be applied both in the stationary and non-stationary cases. Based on the proposed model, a methodology has been developed for calculating the system characteristics both in the case of the existence of a stationary solution and in the case of the existence of a periodic solution for the corresponding forward Kolmogorov system. Some numerical examples are provided to illustrate the effect of input parameters on the probability characteristics of the system.

Integrated dynamic cell formation with operator assignment and inter-cell layout problems: A mathematical model

2015 ◽  
Vol 231 (9) ◽  
pp. 1658-1669 ◽  
Author(s):  
Saeed Sadeghi ◽  
Mohammad Ali Forghani ◽  
Masoud Seidi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Manufacturing System ◽  
Cellular Manufacturing ◽  
Cell Formation ◽  
Cellular Manufacturing System ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Cell ◽  
Operator Assignment

Designing a cellular manufacturing system involves four major decisions: cell formation, cellular layout, operator assignment and cellular scheduling which should be considered, simultaneously. This article presents a new mathematical model to solve the cell formation, operator assignment and inter-cell layout problems, concurrently. The objectives of proposed model are minimization of inter–intra cell part movements, machine relocation cost and operator-related issues including hiring, firing, training and salary costs. Two numerical examples in both small and large sizes are optimally solved by the Lingo software to verify and validate the proposed mathematical model. Also, a sensitivity analysis is performed to analyze the behavior of operators in different production periods.

Feasible Solution of Profile-Shift Coefficient for Involute Internal Gear Pair in Zero-Tooth-Difference Mechanism

2010 ◽  
Vol 118-120 ◽  
pp. 830-835
Author(s):  
Shi Jie Wang ◽  
Chi Zhang
Keyword(s):  
Mathematical Model ◽  
Feasible Solution ◽  
Additional Constraint ◽  
Gear Pair ◽  
Shift Coefficient ◽  
Coupling Relationship ◽  
Pumping System ◽  
Gear Mechanism ◽  
Relationship Of ◽  
Internal Gear

Zero-tooth-difference internal gear mechanism is applied in thrust-eccentric gear coupling designed particularly for oil-submerged motor driven progressing cavity pumping system. The petroleum output of pump depends on the distance (eccentricity) between the canters of external and internal gears proportionally, while the eccentricity is affected by the profile-shift coefficient (abbreviated hereafter as PSC). Larger PSC can increase the amount of eccentricity but decrease the strength of gear, especially for small numbers of teeth. The optimum coupling relationship of radial and tangential PSC is just what to be found here. The work presented in this paper focuses on a method for determining the PSC of gears in the mechanism. The domain of initial values is prepared at first based on developed mathematical model. Then, according to tooth profile engagement equation and additional constraint conditions, a reasonable set of PSC is approached for different eccentricities. Moreover, the PSC can be modified and readjusted with optimum method until satisfied result is obtained finally.

scholarly journals Mathematical model and characteristics analysis of crossed-axis helical gear drive with small angle based on curve contact element

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110162
Author(s):  
Dong Liang ◽  
Sheng Meng ◽  
Rulong Tan
Keyword(s):  
Mathematical Model ◽  
Small Angle ◽  
Performance Test ◽  
Load Capacity ◽  
Helical Gear ◽  
Contact Element ◽  
Gear Pair ◽  
Manufacturing Method ◽  
Gear Drive ◽  
Milling Method

To improve load capacity and transmission characteristics of crossed-axis helical gear drive, a generation approach of the gear pair with small-angle based on the curve contact element is proposed. Contact principle based on spatial curve meshing relationships is introduced and geometric models of tooth profiles are developed according to a pair of mated conjugate curves. Furthermore, a mathematical model of crossed-axis helical gear drive with small-angle is established. Numerical examples are illustrated for this research using the 10° shaft angle, and the computerized simulation is also developed based on the solid models. According to gear geometry and finite element method, general characteristics including undercutting conditions, sliding ratios and contact stress for tooth profiles are analyzed. Comparisons with crossed-axis involute gears are also carried out. Finally, the gear prototype is processed using the gear milling method and a basic performance test is conducted. Analysis results show that the new gear pair has well contact characteristics. Further studies on the dynamic analysis and precision manufacturing method will be carried out.

scholarly journals Mathematical Modeling of a Supply Chain with Imperfect Transport and Two-Echelon Trade Credits

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
A. Thangam
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Supply Chain ◽  
Trade Credit ◽  
Delay Period ◽  
Credit Period ◽  
Numerical Examples ◽  
Proposed Model ◽  
Replenishment Policy ◽  
Trade Credits

Although a smoothly running supply chain is ideal, the reality is to deal with imperfectness in transportations. This paper tries to propose a mathematical model for a supply chain under the effect of unexpected disruptions in transport. Supplier offers the retailer a trade credit period and the retailer in turn offers his customers a permissible delay period. The retailer offers his customers a credit period and he receives the revenue from to , where is the cycle time at the retailer. Under this situation, the three cases such as , , and are discussed. An EPQ-based model is established and retailer's optimal replenishment policy is obtained through mathematical theorems. Finally, numerical examples and sensitivity analysis are presented to felicitate the proposed model.

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.

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 General mathematical model of the roadmap fight against cartels

2019 ◽  
pp. 36-41
Author(s):  
Yu. G. Vasin ◽  
T. Yu. Rudaya
Keyword(s):  
Mathematical Model ◽  
Probabilistic Models ◽  
Proposed Model ◽  
The Social ◽  
General Mathematical Model ◽  
Road Maps ◽  
The Subject ◽  
State Programs ◽  
Constituent Elements ◽  
Forecast Function

The article offers a description of the general algorithm for the formation of a mathematical (stochastic) model of countering cartels as a massive negative social and legal phenomenon. The specified model allows to realize (calculate) the forecast function is a necessary element of state programs (“road maps”) to counter illegal manifestations. The formation of a mathematical model should be preceded by a stage of theoretical modeling, which establishes the constituent elements and relationships of the subject of study. It is proved that the prognostic model of the social-legal phenomenon should be based on the provisions of probability theory. A specific technique is proposed for calculating a system of stochastic indicators (mathematical expectation and standard deviation) of the corresponding model on a single methodological basis. Proposals were made for forecasting methods in relation to quantitative probabilistic models of fighting cartels. The importance of the constant (periodic) verification of the initial statistical data and the correct interpretation of the results of prediction calculations is substantiated. The directions of the practical use of the proposed model for the creation of a comparative monitoring system for the cartelization of the EAEU product markets are proposed.

scholarly journals Design, Analysis And Experimental Study Of Worm And Worm Gear Pair For Plug Valve Application

2020 ◽  
Author(s):  
Abhijeet P Shah ◽  
Yuvraj Jadhav
Keyword(s):  
Mathematical Model ◽  
Experimental Study ◽  
Dynamic Analysis ◽  
Load Capacity ◽  
Design Procedure ◽  
Design Analysis ◽  
Worm Gear ◽  
Gear Pair ◽  
Plug Valve ◽  
Mathematical Model Analysis

Abstract The design procedure, load capacity, mathematical model, analysis of worm and worm gear for plug valve has not been investigated, which is a great barrier for the users. This research focuses on addressing these issues by design of gear, developing mathematical model, dynamic analysis of gear and experimental study to find out efficiency of worm gear for plug valve application.

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