Abstract
Dependency on deterministic design techniques without attention to inherent process variations and uncertainties in gear design and manufacturing processes can lead to unreliable results and affect the performance of a gearing system. A better understanding of the impact of uncertainty associated with the system input on the system output can be achieved by including reliability techniques to accomplish a reliable design methodology. This emerged the need to consider the probabilistic behavior of the stress distribution on the gear tooth during the design phase. The present effort reports on the application of the SSI theory within the context of a “Design for Reliability” approach in support a detailed gear design methodology for the evaluation the tooth-root strength with FEM-based verification. The SSI theory is formulated to predict the effect of the root fillet generated by a rack or hob tool with and without protuberance on the gear system reliability. The results obtained from the probabilistic analysis strongly agreed with the FEM’ results across a range of different gear tooth fillet profiles. A quantitative assessment of the investigated gear sets showed the highest tooth-root stress was associated with the lowest tip radius of the generating tool. This approach helps with making the decision by quantifying the impact of stress and strength variations during the gear design stage.
Highlights
Traditional deterministic design approaches compensate for uncertainties through the use of empirical safety factors, which do not provide sufficient information to achieve optimal use of available resources in terms of material, manufacturing and operational costs [1]
Comparison of these cases indicates that bending stress distribution increases with the root fillet that is generated by small cutter tip radius as in case (1) and the effective stresses for the four cases calculated by Finite Element Method (FEM) are closer to those obtained by the probabilistic design method
The Stress-Strength Interference (SSI) theory as a probabilistic design tool was applied to examine the influence of root fillet contour on the gear tooth strength for four gear sets with different fillet profiles
Summary
Traditional deterministic design approaches compensate for uncertainties through the use of empirical safety factors, which do not provide sufficient information to achieve optimal use of available resources in terms of material, manufacturing and operational costs [1]. Components resulting from such conventional design methods are either over-safe leading to wastage of resources or unsafe leading to unexpected failures They fail to provide the necessary understanding of the variability associated with the properties of materials, manufacturing tolerances and in-service loading. Gears are generally designed based on endurance (fatigue characteristics) design standards They should be selected and shaped to either endure a “nominal” i.e. rated load condition or unlimited load cycles. The detailed geometry of the fillet influences the maximum bending stresses developed at the root of the gear tooth and is determined by the gear cutting manufacturing process and cutting tool dimensions [8]. The SSI theory as a probabilistic design tool will be used to examine the influence of root fillet contour on the gear tooth strength for four gear sets with different fillet profiles
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