**1. Introduction**

Because of the competitiveness in the global market, manufacturers must continually innovate and improve their products. Often, this involves new technologies and design features for the product that must be quickly delivered to the marketplace. However, without sufficient testing or anticipation of how the features may be used or misused, the introduction of these new features may increase failures of the product in the field and negatively impact the company's image. These added attributes are often requested or desired by consumers, and companies strive to include these features in new design specifications for the product. The features for the newly designed mechanical product may not be evaluated entirely before being introduced into the market. Thus, any defects may only show themselves as performance issues once the product is in the marketplace. Reliability quantitative (RQ) specifications using proper methodology should be included and evaluated in the product design that meets its expected life before it will be released [1–4].

**Citation:** Woo, S.; O'Neal, D.L.; Woldemichael, D.E.; Atnaw, S.M.; Tulu, M.M. Improving the Fatigue of Newly Designed Mechanical System Subjected to Repeated Impact Loading. *Metals* **2021**, *11*, 139. https://doi.org/10.3390/met11010139

Received: 16 December 2020 Accepted: 4 January 2021 Published: 12 January 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Mechanical systems such as automobiles, airplanes, and refrigerators [5] convert forms of energy to achieve a specific function (movement of the automobile or airplane and cooling for the refrigerator). The energy conversion requires forces and movement of components, which eventually produce the desired functions with multiple system mechanisms. In the process, mechanical systems are typically subjected to repeated loads. Most mechanical products are made of multi-module structures. If the modules are properly designed and assembled, mechanical systems can work properly and perform their planned functions. For example, in utilizing the vapor-compression refrigeration cycle, a domestic refrigerator is used to cool or freeze food. The refrigerator evaporator provides cooled air to both the refrigerator and freezer sections. A refrigerator has multiple subsystems—Door, cabinet, drawers and shelves, control system, compressor, motor, water supplying device, heat exchangers, and other various components. The total number of parts might be as high as 2000. The product lifetime is targeted to have no less than a B20 life 10 years. As a refrigerator consists of 8 to 10 modules (see Figure 1a) and each module may contain as many as 100 components, the lifetime target of each module needs to have a B1 life of 10 years. The product lifetime of the system is determined by the module with the shortest life, which is module #3 in Figure 1b.

(**b**) Product lifetime *LB* and failure rate *Ώ*s

**Figure 1.** Product lifetime with multi-modules decided by newly designed module (**a**) Classification of multi-module refrigerator; (**b**) Product lifetime *LB* and failure rate *λ*s.

To avoid the failure of a mechanical system in the field [6,7], it should be designed to robustly endure or survive whatever usage conditions the customers subject the system. Design faults should be recognized and altered by statistical methodology [8] or reliability testing [9] before a commercially manufactured goods is released. However, the statistical methodology and subsequent testing may require large numbers of computations for an optimum solution but may not identify the ultimate failures that may occur in the field by consumers. If there are design faults that cause an inadequacy of strength (or stiffness) when a system is subjected to repeat loading, the system will fail before its expected lifetime due to fatigue failure. American Society for Testing and Materials (ASTM) procedures typically require large samples, skilled personnel, testing apparatus arranged by data acquisition systems, etc. Thus, discovering possible mechanical failures such as fatigue can involve time-consuming and costly testing procedures [10–13]. To recognize these limitations, there have been numerous attempts to systematically evolve fatigue testing [14]. It is difficult to estimate the lifetime cycles of problematic parts in multi-module products where failures rarely occur in the field due to design flaws.

An alternative method, based on reliability block diagrams [15], is where the accelerated life testing (ALT) could be scrutinized [16–24]. It includes test planning for the product, failure mechanics, accelerated procedures, sample size equation, etc. Elsayed [25] categorized physics/statistics, statistical, and physics/experimental-based models for assessment. Meeker [26] proposed numerous feasible recommendations to organize an ALT. Carrying out an ALT [27,28] requires numerous concepts such as the BX life for the product test plan based on reliability engineering, a life-stress model, sample size equation, and fracture mechanics [29–32] because failure may occur suddenly from the frail components in a system. Contemporary experimental methods may fail to reproduce the design defects. These methods may evaluate insufficient part samples in multi-module products and may not identify the failure(s) that actually happen in the marketplace.

To implement the optimal design of a mechanical system, engineers have relied on traditional design approaches such as strength of materials [33]. A recent fracture mechanics study proposed that the crucial elements might be fracture toughness as an alternative of strength as an applicable material property. As quantum mechanics has been used in electronic technology, designers have identified system failures from micro-void coalescence (MVC) and noted a grea<sup>t</sup> number of metallic alloys or numerous engineering plastics [34]. To determine the failure phenomena of a mechanical system, a better lifestress model might be combined with the traditional design approaches and applicable methodology of identifying the failure of electronic parts due to small cracks or preexisting defects. This approach would not be feasible to model using current finite element methods (FEMs) [35].

To better identify product failures in the marketplace, there is another engineering perspective that incorporates the FEM [36]. Many engineers believe that rare system failures might be evaluated by: (1) Mathematical modeling utilizing Newtonian or Lagrangian techniques; (2) obtaining the system stress/strain from the time response for (dynamic) loads; (3) making use of the rain-flow counting method for von-Mises stress [37,38]; and (4) approximating system damage by Palmgren–Miner's rule [39]. Nevertheless, utilizing a systematic method that can give closed-form, precise solutions would involve utilizing numerous assumptions that might not identify multi-module system failures, due to material defects such as micro-voids and contacts when subjected to loads.

This study introduces a parametric ALT as a systematic reliability method that can generate the RQ specifications such as mission time for identifying and modifying the design faults of newly designed mechanical systems. It incorporates: (1) An ALT plan formed on system BX lifetime, (2) a load examination for ALT, (3) customized ALTs with the alterations, and (4) an assessment of whether the last design(s) of the system fulfills the objective BX lifetime. A newly designed hinge kit system (HKS) in a domestic refrigerator subjected to repeated impact loading is provided as an example.
