Abstract
This paper presents a probabilistic design approach for the Gerber bending fatigue failure rule using sensitivity-based analysis. The design model parameters are considered as random variables that are characterized by mean values and coefficients of variation (covs). The coefficient of variation of a design parameter is obtained by using first order Taylor series expansion for strength and stress in a stress-based fatigue design. A reliability factor is determined based on the coefficients of variation and a failure probability. The reliability factor is then used for design sizing and analysis. Probabilistic design allows a quantification of risk that is not possible with deterministic design approaches. This risk quantification can help to avoid over- or under-design problems while ensuring that safety and quality levels are economically achieved. Over design requires more resources than necessary and leads to costly products. Avoiding over-design helps to conserve product materials and reduce manufacturing resources, machining accuracy, quality control, and processing. Under-designed products are prone to failures, making the products unsafe and unreliable. This increases the risks of product liability lawsuits, customer dissatisfaction, and even accidents. This study shows a 51% reduction in component size without compromising desired reliability and hence a possible 51% reduction in component mass and cost. Therefore, significant savings in product cost can be obtained through probabilistic design. Probabilistic design seems to be the most practical approach in product design due to the inherent variability associated with service loads, material properties, geometrical attributes, and mathematical design models. It is becoming the preferred design method because over- or under-design can be avoided while still ensuring the safety of a product.
Highlights
In today’s market environment, quality is taken for granted
A probabilistic fatigue design approach based on the Gerber failure rule has been presented
The model design parameters use mean values to estimate expected design results while the reliability of the design is evaluated using the coefficients of variation of the design parameters
Summary
In today’s market environment, quality is taken for granted. A quality product is associated with rare unexpected and unpleasant events which result from uncertainties in design. Customers are usually satisfied if a product performs as expected or better (“Understanding Probabilistic Design”). Designing a quality product is of paramount importance for product market success. In traditional or deterministic design, safety or design factors are usually subjectively assigned in product design so as to assure reliability. This method of design can sometimes be crude. The safety factor method does not give insight about individual variation or the actual margin of safety in a design (Koch, 2002). Because of the difficulty of relating safety factor and product safety quantitatively, some prefer the term design factor to safety factor (Mott, 2008)
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