Reliability Analysis and Design of Epicyclic Gear Trains

1979 ◽  
Vol 101 (4) ◽  
pp. 625-632 ◽  
Author(s):  
S. S. Rao
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Design Criterion ◽  
Gear Train ◽  
Design Parameters ◽  
Analysis And Design ◽  
Input Shaft ◽  
Reliability Based Design ◽  
Epicyclic Gear ◽  
Gear Trains

The concepts of system reliability are applied for the structural reliability analysis and design of epicyclic gear trains. The reliability analysis is based on the representation of an epicyclic gear train as a series-parallel network. The power transmitted, the speed of the input shaft, the center distance between the gear pairs and the permissible stresses are assumed to be random variables following normal distribution. The layout of the gears and the speed ratios are assumed to be known. The face widths of the gears are taken as random design parameters. The design criterion is that the reliability of the gear train either in bending or surface wear failure mode at any of the output speeds must be equal to a specified value. The design of an epicyclic transmission system which gives four forward speeds and one reverse speed is considered for illustration. The results of the reliability-based design of the gear train are compared with those of the conventional deterministic design.

A Study on Structural Design of Huge Barge Structures Based on Collapsing Behavior and Reliability Analysis

2003 ◽  
Author(s):  
Shinji Katsura ◽  
Hiroo Okada ◽  
Koji Masaoka ◽  
Takashi Tsubogo
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Estimation Method ◽  
Bending Moment ◽  
Irregular Waves ◽  
Elastic Response ◽  
Design Parameters ◽  
Reliability Based Design ◽  
Calculation Results

This paper deals with the limit state and reliability analysis of huge barge structures (HBS) which are supposed floating refuse storage and incineration plant based on collapsing behavior analysis in irregular waves as a part of studies on structural reliability-based design methods. First, a limit state and reliability analysis method is shortly presented for the buckling and ultimate collapse strength of deck, bulkhead and bottom panels of HBS. Next, a simplified method is briefly introduced for collapsing behavior and reliability analysis of HBS under extreme sea loads by using a developed system combined with a finite element method and plastic node method using hexahedral element models. Moreover, a simplified estimation method is shortly introduced for the probabilistic load model considering the hydro-elastic response of the structure in irregular waves. Finally, dominant limit state modes of 1,000m-class HBS under combined loads with bending moment, shearing force and lateral pressure are obtained by applying the above methods. Then, the features of the collapsing behavior and reliability level are investigated by using above calculation results. Effects of statistical values such as reduction of thickness due to corrosion, yield stress and design parameters are also investigated using sensitivity analysis.

Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
High Velocity ◽  
Mechanical Energy ◽  
Gear Train ◽  
Recursive Method ◽  
Gear Pair ◽  
Simple Method ◽  
Epicyclic Gear ◽  
Thick Line ◽  
Gear Trains ◽  
Isomorphic Graphs

Epicyclic gear trains (EGTs) are used in the mechanical energy transmission systems where high velocity ratios are needed in a compact space. It is necessary to eliminate duplicate structures in the initial stages of enumeration. In this paper, a novel and simple method is proposed using a parameter, Vertex Incidence Polynomial (VIP), to synthesize epicyclic gear trains up to six links eliminating all isomorphic gear trains. Each epicyclic gear train is represented as a graph by denoting gear pair with thick line and transfer pair with thin line. All the permissible graphs of epicyclic gear trains from the fundamental principles are generated by the recursive method. Isomorphic graphs are identified by calculating VIP. Another parameter “Rotation Index” (RI) is proposed to detect rotational isomorphism. It is found that there are six nonisomorphic rotation graphs for five-link one degree-of-freedom (1-DOF) and 26 graphs for six-link 1-DOF EGTs from which all the nonisomorphic displacement graphs can be derived by adding the transfer vertices for each combination. The proposed method proved to be successful in clustering all the isomorphic structures into a group, which in turn checked for rotational isomorphism. This method is very easy to understand and allows performing isomorphism test in epicyclic gear trains.

Meshing Efficiency Analysis of Two Degree-of-Freedom Epicyclic Gear Trains

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Essam Lauibi Esmail
Keyword(s):  
Reference Frame ◽  
Power Efficiency ◽  
Power Flow ◽  
Flow Direction ◽  
Efficiency Analysis ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Two Degree Of Freedom

The concept of potential power efficiency is introduced as the efficiency of an epicyclic gear train (EGT) measured in any moving reference frame. The conventional efficiency can be computed in a carrier-moving reference frame in which the gear carrier appears relatively fixed. In principle, by attaching the reference frame to an appropriate link, torques can be calculated with respect to each input, output, or (relatively) fixed link in the EGT. Once the power flow direction is obtained from the potential power ratio, the torque ratios are obtained from the potential power efficiencies, the particular expression of the efficiency of the EGT is found in a simple manner. A systematic methodology for the efficiency analysis of one and two degree-of-freedom (DOF) EGTs is described, and 14 ready-to-use efficiency formulas are derived for 2DOF gear pair entities (GPEs). This paper includes also a discussion on the redundancy of the efficiency formulas used for 1DOF GPEs. An incomplete in the efficiency formulas in previous literature, which make them susceptible to wrong application, is brought to light.

Cycloid Drives With Machining Tolerances

1989 ◽  
Vol 111 (3) ◽  
pp. 337-344 ◽  
Author(s):  
J. G. Blanche ◽  
D. C. H. Yang
Keyword(s):  
High Efficiency ◽  
Dynamic Instability ◽  
Torque Ripple ◽  
Gear Train ◽  
Space Applications ◽  
Input Shaft ◽  
Epicyclic Gear ◽  
Speed Reducer ◽  
Planet Gear ◽  
Gear Mechanism

The cycloidal speed reducer, or cycloid drive, is an epicyclic gear train in which the profile of the planet gear is an epitrochoid and the annular sun gear has rollers as its teeth. The cycloid drive has very high efficiency and small size, in comparison with a conventional gear mechanism, making it an attractive candidate for limited space applications. On the other hand, in this type of transmissions there exist two major drawbacks, namely, backlash and torque ripple. Backlash, the angle through which the output shaft can rotate when the input shaft is held fixed, has a degrading effect on the output accuracy. Torque ripple, the variation in mechanical advantage as the input shaft rotates, causes vibrations and could lead to dynamic instability of the machinery. If the cycloid drive were manufactured to the ideal dimensions, there would be no backlash nor torque ripple. However, in reality, there will always be some machining tolerances. In this paper an analytical model is developed which models the cycloid drive with machining tolerances. Consequently, the effect of machining tolerances on backlash and torque ripple are investigated. It is found that both the backlash and the torque ripple are inherent periodic functions of the input crank angle.

Reliability Based Design Optimisation of a “No Burst” High Pressure Pipeline

2002 ◽  
Author(s):  
Graham Stewart ◽  
Caroline Roberts ◽  
Ian Matheson ◽  
Malcolm Carr
Keyword(s):  
High Pressure ◽  
Structural Reliability ◽  
Design Stage ◽  
Design Parameters ◽  
Extreme Value Distributions ◽  
Reliability Based Design ◽  
Pressure Pipeline ◽  
Pipeline Wall ◽  
High Pressure Pipeline ◽  
Pipeline Design

The design philosophy of a pressure-protected subsea pipeline is intimately linked to the reliability of the Pressure Protection System (PPS) and to the probability of burst of the pipeline if it is exposed to full wellhead shut-in pressure. A reliability based design approach is presented that allows the pipeline wall thickness (and cost) to be reduced under the philosophy that the pipeline will “not burst” in the event of PPS failure. This paper describes how uncertainties in the pipeline design parameters may be initially modelled statistically to allow structural reliability techniques to be adopted at the design stage (before the pipe is manufactured). It further addresses how correlation of these parameters can be included and their extreme value distributions developed, which is particularly relevant as the length of the tieback increases. A method to incorporate inspection inaccuracy is also presented. The initial estimates of the design parameters necessarily err on the conservative side. These can be later updated when manufacturing data is available.

Reliability Analysis of Foundation Pit by Improved Response Surface Method

2011 ◽  
Vol 147 ◽  
pp. 197-202 ◽  
Author(s):  
Jiang Zhou ◽  
Jing Cao ◽  
Yu He ◽  
Jie Song
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Structural Reliability ◽  
Lateral Displacement ◽  
Limit State ◽  
Uniform Design ◽  
Design Parameters ◽  
State Function ◽  
Foundation Pit ◽  
Improved Response Surface Method

Lacking of explicit limit state function (LSF) will result large quantities of computational efforts for a FEAM based structural reliability analysis. An improved response surface (RS) method is proposed to analyze the failure probability of foundation pit through combining uniform design (UD) and non-parametric regression (NPR). Deferent levels of design parameters are first delicately selected according to UD and then FEAM is used to analysis corresponding pit response parameters including maximum lateral displacement of wall, settlement of ground, safety factor of overall stability, safety factors of against overturning, heave and piping. The RS relationship is then established through NPR based on inputs and responses. At last, a direct Mont Carlo Simulation is carried out to obtain the probability density function of response parameters.

A Study of the Duality Between Epicyclic Gear Trains and Beam Systems

2006 ◽  
Author(s):  
Gordon P. Pennock ◽  
Jeremiah J. Alwerdt
Keyword(s):  
Gear Train ◽  
Specific Design ◽  
Beam System ◽  
Dual Beam ◽  
Epicyclic Gear ◽  
Angular Velocities ◽  
Gear Trains ◽  
Design Requirements ◽  
Primary Contribution ◽  
Insight Into

This paper provides geometric insight into the duality between the kinematics of epicyclic gear trains and the statics of beam systems. The two devices have inherent geometrical relationships that allow the angular velocities of the gears in a gear train to be investigated from a knowledge of the forces acting on the dual beam system, and vice-versa. The primary contribution of the paper is the application of this duality to obtain the dual beam system for a given compound epicyclic gear train. The paper develops a systematic procedure to transform between the first-order kinematics of a gear train and the statics of the dual beam system. This provides a simple and intuitive approach to study the speed ratios of an epicyclic gear train and the force ratios of the dual beam system. The speed ratios are expressed in terms of kinematic coefficients, which are a function of the position of the input gear and provide insight into the gear train geometry. Several numerical examples of simple and compound epicyclic gear trains are presented to demonstrate the simplicity of the proposed approach. The analytical equations that are developed in the paper can be incorporated, in a straightforward manner, into a spreadsheet that is oriented towards an epicyclic gear train satisfying specific design requirements.

Cycloid Drives With Machining Tolerances: Part I — Kinematic Analysis

1987 ◽  
Author(s):  
J. G. Blanche ◽  
D. C. H. Yang
Keyword(s):  
High Efficiency ◽  
Dynamic Instability ◽  
Torque Ripple ◽  
Gear Train ◽  
Space Applications ◽  
Design Synthesis ◽  
Input Shaft ◽  
Epicyclic Gear ◽  
Speed Reducer ◽  
Gear Mechanism

Abstract The cycloidal speed reducer, or cycloid drive, is an epicyclic gear train in which the profile of the planet gear is an epitrochoid and the annular sun gear has rollers as its teeth. The cycloid drive has very high efficiency and small size, in comparison with a conventional gear mechanism, making it an attractive candidate for limited space applications. On the other hand, in this type of transmissions there exist two major drawbacks, namely, backlash and torque ripple Backlash, the angle through which the output shaft can rotate when the input shaft is held fixed, has a degrading effect on the output accuracy. Torque ripple, the variation in mechanical advantage as the input shaft rotates, causes vibrations and could lead to dynamic instability of the machinery. If the cycloid drive were manufactured to the ideal dimensions, there would be no backlash nor torque ripple. However, in reality, there will always be some machining tolerances. In this paper an analytical model is developed which models the cycloid drive with machining tolerances. This model is used in Part II of this investigation to determine the effect of machining tolerances on backlash and torque ripple. As a result, simple and practical equations for design synthesis of this type of drives are formulated.

Nomographs for Kinematics, Statics and Power Flow Analysis of Epicyclic Gear Trains

2009 ◽  
Author(s):  
Essam L. Esmail ◽  
Hamed A. Hussen
Keyword(s):  
Electric Motor ◽  
Power Flow ◽  
Automatic Transmission ◽  
Flow Analysis ◽  
Gear Train ◽  
Innovative Design ◽  
Epicyclic Gear ◽  
Power Split ◽  
Gear Trains ◽  
Flow Through

A new methodology for constructing multi-axes nomographs is developed. Using this methodology, a unified general formulation for computing velocities and torques of any epicyclic-type transmission train is presented. To demonstrate and apply the new technique, Ravigneaux automatic transmission is used to show how the velocities, the torques and the power flow through the train can be simultaneously visualized on a single nomograph. The present methodology is judged to be more efficient than other methods and than the three-ax nomograph methodology. Using this methodology an innovative design of two-input transmission with only one electric motor/generator (MG) and without any rotating clutches is presented. The proposed design provides some of the benefits and flexibility of a power-split design by using the conventionally available Ravigneaux gear train in a simpler mechanical layout which makes the design compact, mechanically simple, and operationally flexible.

Determination of the Optimum Partial Factors in Structural Reliability Analysis

1998 ◽  
Vol 05 (02) ◽  
pp. 169-180 ◽  
Author(s):  
D. H. Li ◽  
C. Y. Tang ◽  
M. Jie ◽  
Albert H. C. Tsang ◽  
Y. C. Tsim
Keyword(s):  
Objective Function ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Optimization Method ◽  
Design Criterion ◽  
Resistance Force ◽  
Reliability Design ◽  
Structural Reliability Analysis ◽  
Live Loads ◽  
Partial Factor

In this paper, an optimization method is used to determine the values of partial factors in structural reliability analysis. Once the proper objective function is defined, a group of optimum partial factors, which enable the objective function to take its minimum value, will need to be determined. In the present study, two kinds of objective function are considered. The conditions that have to be satisfied for optimum partial factors of these two kinds of objective function are then derived. In both cases, the result shows that the partial factors of both dead and live loads should satisfy the same proportional expression and should be inversely proportional to the partial factor of resistance force. A simple beam is used as an example to illustrate the computations involved. It is found that the design concept proposed in this paper leads to a design criterion similar to that which applies to the conventional deterministic method. Thus, this concept can be easily used in practice. The illustrative example shows that the values of the dead load and live load have a significant effect on the reliability design criteria.

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