Uncertainty Considerations in the Dynamic Loading and Failure of Spur Gear Pairs1

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Fisseha M. Alemayehu ◽  
Stephen Ekwaro-Osire
Keyword(s):  
Spur Gear ◽  
Design Parameters ◽  
Dynamic Factor ◽  
Performance Measurements ◽  
Random Loading ◽  
Pair Model ◽  
Multibody Dynamic ◽  
Gear Systems ◽  
Rigid Multibody ◽  
Analysis Of Performance

Gears and gear systems, like any other mechanical system, are subjected to design parameter, and loading uncertainties emanating from inherent randomness, manufacturing, and assembly errors. The traditional deterministic approach to the design of such systems overlooks these uncertainties. This work presents a novel probabilistic multibody dynamic analysis (PMBDA) that enhances the deterministic design practice of gears and gear systems. A contact based, rigid multibody spur gear pair model with random loading, and design parameters has been developed. An advanced mean based on fast probability integration method was implemented to perform a reliability analysis of performance measurements: dynamic factor, root bending stress, and fatigue life of gears. Probabilistic sensitivity analysis of these performance functions to several random variables was also determined. In addition to revealing system reliability or probability of failure, the PMBDA approach also helps designers to consider certain variables critically.

Uncertainty Considerations in the Dynamics of Gear-Pair

2012 ◽  
Author(s):  
Fisseha M. Alemayehu ◽  
Stephen Ekwaro-Osire
Keyword(s):  
Parameter Uncertainty ◽  
Traditional Approach ◽  
Design Parameters ◽  
Dynamic Factor ◽  
Gear Pair ◽  
The Novel ◽  
Gear Design ◽  
Pair Model ◽  
Multibody Dynamic ◽  
Gear Systems

Gears and Gear systems are subjected to uncertainty of design parameters and loading caused by inherent conditions, measurement and manufacturing errors. Hence, the motivation of this work is to improve the deterministic design practice of gears and gear systems. A probabilistic rigid multibody dynamic gear-pair model with design and load uncertainties has been developed and analyzed. Rigid gear-pair model was developed in multibody dynamics software ADAMS and parameter uncertainty and probabilistic analysis was performed from separate probabilistic software called NESSUS. To perform the probabilistic multibody analysis, ADAMS and NESSUS were interfaced using MATLAB. The effect of parameter uncertainty on dynamic factor, DF of a gear pair was investigated. The sensitivity of DF to five uncertain loading and design parameters were also determined. This paper has demonstrated the importance of the novel PMBD modeling approach to gear design and dynamic factor analysis. The method has brought a new dimension of design approach of gears and gear systems than traditional approach that considers a certain empirically defined dynamic rating factors. In addition to revealing system reliability or under-performance through probability of failure, it also helps designers to consider certain variables critically through the sensitivity results.

Effect of design parameters on stresses occurring at the tooth root in a spur gear pressed on a shaft

2021 ◽  
pp. 095440892199529
Author(s):  
Fatih Güven
Keyword(s):  
Internal Pressure ◽  
Tangential Stress ◽  
Spur Gear ◽  
Design Parameters ◽  
Interference Fit ◽  
Gear Design ◽  
Compact Design ◽  
Fit Tolerance ◽  
Moderate Stress ◽  
Good Agreement

Gears are commonly used in transmission systems to adjust velocity and torque. An integral gear or an interference fit could be used in a gearbox. Integral gears are mostly preferred as driving gear for a compact design to reduce the weight of the system. Interference fit makes the replacement of damaged gear possible and re-use of the shaft compared to the integral shaft. However, internal pressure occurs between mating surfaces of the components mated. This internal pressure affects the stress distribution at the root and bottom land of the gear. In this case, gear parameters should be re-considered to assure gear life while reducing the size of the gear. In this study, interference fitted gear-shaft assembly was examined numerically. The effects of rim thickness, profile shifting, module and fit tolerance on bending stress occurring at the root of the gear were investigated to optimize gear design parameters. Finite element models were in good agreement with analytical solutions. Results showed that the rim thickness of the gear is the main parameter in terms of tangential stress occurring at the bottom land of the gear. Positive profile shifting reduces the tangential stress while the pitch diameter of the gear remains constant. Also, lower tolerance class could be selected to moderate stress for small rim thickness.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Using Dynamic Analysis for Compact Gear Design

1998 ◽  
Author(s):  
Ping-Hsun Lin ◽  
Hsiang Hsi Lin ◽  
Fred B. Oswald ◽  
Dennis P. Townsend
Keyword(s):  
Dynamic Response ◽  
Bending Strength ◽  
Three Dimensional ◽  
Spur Gear ◽  
Dynamic Factor ◽  
Operating Speed ◽  
Gear Design ◽  
Dynamic Factors ◽  
Speed Range ◽  
Response Change

Abstract This paper presents procedures for designing compact spur gear sets with the objective of minimizing the gear size. The allowable tooth stress and dynamic response are incorporated in the process to obtain a feasible design region. Various dynamic rating factors were investigated and evaluated. The constraints of contact stress limits and involute interference combined with the tooth bending strength provide the main criteria for this investigation. A three-dimensional design space involving the gear size, diametral pitch, and operating speed was developed to illustrate the optimal design of spur gear pairs. The study performed here indicates that as gears operate over a range of speeds, variations in the dynamic response change the required gear size in a trend that parallels the dynamic factor. The dynamic factors are strongly affected by the system natural frequencies. The peak values of the dynamic factor within the operating speed range significantly influence the optimal gear designs. The refined dynamic factor introduced in this study yields more compact designs than AGMA dynamic factors.

Dynamic analysis of uncertain spur gear systems

2021 ◽  
Vol 150 ◽  
pp. 107280
Author(s):  
Sha Wei ◽  
Fu-Lei Chu ◽  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Dynamic Analysis ◽  
Spur Gear ◽  
Gear Systems

Effect of Design Parameters on Lubrication Behavior of Spur Gear Pairs

2017 ◽  
Author(s):  
Yanfang Liu ◽  
Qiang Liu ◽  
Peng Dong
Keyword(s):  
Power Loss ◽  
Elastohydrodynamic Lubrication ◽  
Spur Gear ◽  
Design Parameters ◽  
Curvature Radius ◽  
Gear Pair ◽  
Sliding Velocity ◽  
Rolling Velocity ◽  
Lubrication Performance ◽  
Meshing Process

An involute spur gear pair meshing model is firstly provided in this study to achieve relevant data such as rolling velocity, sliding velocity, curvature radius etc. These data are needed in a transient, Newtonian elastohydrodynamic lubrication (EHL) model which is provided later. Based on these two models, the behavior of an engaged spur gear pair during the meshing process is investigated under dynamic conditions, film thickness, pressure, friction coefficient etc. could be achieved through the models. Then, power loss under certain operating condition is calculated. Relationship between power loss and lubrication performance is also analyzed.

scholarly journals The Lubricant Churning Loss in Spur Gear Systems

1973 ◽  
Vol 16 (95) ◽  
pp. 881-892 ◽  
Author(s):  
Yasutsune ARIURA ◽  
Taku UENO ◽  
Teruo SUNAGA ◽  
Shigemi SUNAMOTO
Keyword(s):  
Spur Gear ◽  
Gear Systems

Probabilistic Performance of Helical Compound Planetary System in Wind Turbine

2015 ◽  
Vol 10 (4) ◽  
Author(s):  
Fisseha M. Alemayehu ◽  
Stephen Ekwaro-Osire
Keyword(s):  
Wind Turbine ◽  
Multibody Systems ◽  
Planetary System ◽  
Design Parameters ◽  
Wind Turbine Gearbox ◽  
New Approach ◽  
Highly Nonlinear ◽  
Multibody Dynamic ◽  
Input Variables ◽  
Maintenance Process

The dynamics of contact, stress and failure analysis of multibody systems is highly nonlinear. Nowadays, several commercial and other analysis software dedicated for this purpose are available. However, these codes do not consider the uncertainty involved in loading, design, and assembly parameters. One of these systems with a combined high nonlinearity and uncertainty of parameters is the gearbox of wind turbines (WTs). Wind turbine gearboxes (WTG) are subjected to variable torsional and nontorsional loads. In addition, the manufacturing and assembly process of these devices results in uncertainty of the design parameters of the system. These gearboxes are reported to fail in their early life of operation, within three to seven years as opposed to the expected twenty years of operation. Their downtime and maintenance process is the most costly of any failure of subassembly of WTs. The objective of this work is to perform a probabilistic multibody dynamic analysis (PMBDA) of a helical compound planetary stage of a selected wind turbine gearbox that considers ten random variables: two loading (the rotor speed, generator side torque), and eight design parameters. The reliability or probabilities of failure of each gear and probabilistic sensitivities of the input variables toward two performance functions have been measured and conclusions have been drawn. The results revealed that PMBDA has demonstrated a new approach of gear system design beyond a traditional deterministic approach. The method demonstrated the components' reliability or probability of failure and sensitivity results that will be used as a tool for designers to make sound decisions.

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