Structured Method to Reconfigure the Fatigue of Mechanical Products such as HKS in a Refrigerator

To determine the fatigue lifetime of a system such as a car, refrigerator, etc., parametric Accelerated Life Testing (ALT) can be used as an arranged way to find out its reliability and failure mechanisms a when it is subjected to continual loads The process includes: (1) parametric ALT used to establish the BX life, (2) load evaluation for designing an accelerated life test(s), (3) a tailored representative of ALTs with design adjustments, and (4) an appraisal of whether system gets to the goal for the BX lifetime. A generalized life-stress failure approach with an accelerated factor, and sample size formulation are proposed. An organized reliability approach, such as parametric ALT, can help the designer to find product defects having an effect on reliability as computed by the improvement in life, LB, and the decreasing in failure rate, λ in the design stage. As a consequence, manufacturers can stop recalls from failures of their products when introduced into the marketplace. A hinge kit system (HKS) in a domestic refrigerator that needed to be redesigned was provided as an example. After a tailored set of parameter ALTs, the HKS with design changes were expected to realize the life aim – B1 life ten years.


Introduction
To be competitive in the global market, traditional mechanical product, such as household refrigerator, can need to be redesigned to include new scientific knowledge and quality to meet the appeal of customers.If a new system is pushed to the open market with inadequate testing that imitates end-users' use patterns of the system, there is the possibility for inappropriate failures of the system in the field.These failures can unpleasantly affect the awareness of the product quality made by the manufacturer.Since the 1970's, it has been acknowledged that there is a significant gap between the consumer's desire for reliability and its implementation by companies in their products.To stop having expected design defects in the marketplace, the notable qualities of a newly devised product might be evaluated in the developing phases of the product before it is introduced into the market.Evolving a product worked by machinery thus involves an organized method which embodies reliability quantitative (RQ) specifications [1,2].Fatigue is the significant cause of failure in most components, comprising about 80 to 90% of failures in the field [3].Fatigue shows itself in cracks which usually begin from tall stress regions -channels, holes, narrow exteriors, etc., in mechanical systems.As result of material displacement, fatigue is the degradation of a material produced by cyclic dynamic loading from its end-user usage.This failure can cause disastrous results in a system so that it would result in a wound or death of an end-user.Significant studies have been conducted on low-cycle fatigue, especially in the domain of turbine engines.It includes a measure, such as the stress proportion, R (=σmin/σmax), manifested as the relation of the maximum cyclic stress to the minimum cyclic stress.Employing this parameter as an accelerated factor (AF) in ALT, can help find the design faults such as a high stress raiser in the system worked by machinery.Engineers often identify design defects and correct them by employing Taguchi's procedure or design of experiments (DOE) [4].DOE is an arranged process to find the link between components during its manufacture.The DOE's objective is to find that the factors are devised in the most advantageous manner for the working conditions (or surrounding).DOE is accomplished for some design factors that may affect the system.Its capacity is explained by analysis of variance (ANOVA).Taguchi's way can be used to assess the reliability of a design.It tries to discover the most advantageous design where the ''noise'' factor does not have any effect on the design.However, DOE including Taguchi's way may not necessarily identify which factors are crucial to reduce failures such as fatigue failure without numerous mathematical computations.Thus, the method cannot produce the optimal design.Engineers may design the mechanical product using the strength of materials as design way [5].A current study also designates that a crucial element in fracture mechanics called fracture toughness could be utilized as an attribute of material strength.With the development of quantum mechanics, engineers have been able to identify that the failure in a product can happen from nanoscale/microscale voids discovered unexpectedly in metal alloys and/or engineering plastics.However, because limited sample sizes and testing time are employed, current way also can not reproduce the imperfects of components due to the fatigue which happens by customers in the marketplace.A life-stress approach unified with a (quantum) mechanics technique could be used to find imperfections or cracks because failures typically happen stochastically in the regions of large stress.Another possible tool that engineering utilize is finite element analysis (FEA) [6].This approach assumes that unsuccessfulness may be identified by (1) precise (Lagrangian or Newtonian) modeling; (2) evaluating the reaction for the load by building the stress/strain; (3) using well-proven approach such as rain-flow counts, and (4) deducing system successfulness by Palmgren -Miner ' s supposition.Executing this process may give some ready estimations of failure.However, this process cannot accurately replicate fatigue failure produced by material imperfections such as micro-voids, narrow surfaces, etc.This paper provides parametric ALT as an approach with general application that can produce a reliability quantitative (RQ) statement.With this approach, assignment of test cycles can be estimated and product defects can be identified so the fatigue life of the product can be improved.This procedure is suitable to applications to a wide range of mechanical products such as cars, airplanes, construction machines, etc. that have failures due to material deformation.The approach covers: (1) an ALT procedure produced on BX lifetime, (2) load examination, (3) tailored set of ALTs with modifications, and (4) a decide of whether the system gets to the aimed BX lifetime.To achieve the functionality for ALT, it is required to evaluate a newly designed system or product in the market to attain the aimed life.A quantum-conveyed time-to-failure model and sample size formulation are recommended.As an example of the approach, the process of redesigning HKS in a domestic refrigerator was used in this paper

Notions of Reliability for ALT
Mechanical systems in products such as refrigerators, automobiles, airplanes, etc. utilize power to generate mechanical advantages of the system through various mechanisms.Most systems that include machinery have subsystems (or module) structures.If the subsystem (or multi-module) are correctly constructed, systems operated by the machinery can perform its own arranged tasks.For example, a refrigerator is composed of about 2000 parts.The desired product lifetime of a refrigerator can be expected to be a B20 life ten years.A refrigerator can be divided into 8 to 10 modules (or 20 units) with each unit possessing 100 components.Consequently, the life of each unit might be aimed to be B1 life ten years.The product life is determined by any modules that might have design flaws.To perform ALT, BX lifetime as an index of product life is necessitated.BX life, LB, can be defined as the time period in which X percent of a product population is expected to fail.In other words, a `BX life Y years' is another way to state the product life.It helps resolve the accumulative failure rate of a system and can be a response to market requirements for reliability.For example, if the product life has B20 life 10 years, 20% of the population will have unsuccessful during ten years of operation time.

Developing an all-inclusive testing scheme for parametric ALT
Reliability is indicated as the latent qualities of a system to effectively work under a set of required circumstances for a stated period of time.It is represented graphically as the "bathtub curve" as seen in Figure 1.The curve manifests the failure rate as a function of time after the product has been introduced.The typical bathtub curve has three divisions with respect to time.divisions.First, there is a declining failure rate in the initial product life (β < 1).In the second division, there is a continuous failure rate (β = 1).In the third division, there is a increasing failure rate to the ending of the life in a product (β > 1).If a product is introduced into the field and follows the bathtub, it will have a difficult time accomplishing a desired result in the market because of the higher failure rates in its inceptive introduction.Manufacturers would then need to improve the system design by increasing the reliability goals for the newly designed system to (1) minimize untimely failures during the early times after introduction of the product, (2) drop the random failures in the expected life of the product, and (3) enhance the product's expected life in the market.If the product reliability is improved and the products has a longer lifetime, then, its failure rate in the field may drop and the company's reputation enhanced.For such situations, the bathtub would then be transformed to the line without a curve (indicated by the dashed line in figure 1) where the failure rate is low throughout the anticipated life of the system.
where R is reliability, f is the density function, and λ is the failure rate.If Equation (2) takes is expressed as an integral, the X% cumulative failure, F(LB), at T = LB is given as: ) Presuming that T1 will be the period of the earliest failure, the reliability, R(t), may also be determined: where m is the Poisson parameter that may be stated as t (mean) If the system design is upgraded, the failure rate in the field might drop and the product lifetime increases.The product reliability may be shown as [7]: where Equation ( 6) is valid in less than 20% of accumulative failures, F().If a designer specifies the product life, LB, they can then identify any defects and modify the design by ALT to achieve the require LB.For example, the HKS discussed below as a case study can be considered as an altered module to the original design because there were some design changes in it.To respond to the demands of the end-user, the new life objective of the HKS was specified to be B1 life ten years.

Failure mechanics and accelerated testing for redesign
As there is a design imperfection in the system or product, it can be unsuccessful before its expected life.Pinpointing the failure can be accomplished through reliability testing such as ALT.A designer can then redesign the mechanical product such as HKS to achieve the desired lifetime.The main challenged in reliability testing is discovering the cause(s) of the untimely failures of the system.Achieving the desired life requires identifying the failure type and resolving some coefficients that describe the failure.First, the life-stress (LS) prototype that integrates stresses and reaction parameters is arranged.This formulation may describe many failures such as those created by fatigue in a system worked by machinery.Because product failure often starts from the state of having reality of imperfections at the atomic/microscopic level when these defects are susceptible to repetitive loads, the life-stress type from such prospective might be expressed.Namely, fatigue failures can start from material imperfections, such as electron/voids that emerge at the nano level and then evidence themselves at the microscopic or macro level.Using a quantum point of view, it can be defined as transport such as the diffusion of shallow level dopants in silicon.First, imagine an electric particle limited to go only in x orientation from x = 0 to x = a.Schrodinger wave governing equation is expressed as: where m is electron mass, h is Planck quantity, V is potential energy,   is wave function,   is energy.The boundary circumstances are:   → 0   → ∞, 2)   = 0 at walls.Equation ( 6) is resolved: where ( + ) = (), a is (periodic) intervening time, n is principal quantum number Transport processes are defined as [8]:  =  (8) where J is a kind of flux, X is stated as an exerting force, L is a transport numerical quantity.For example, the succeeding processes are solved to employ for solid-state diffusion of impurities in silicon which is employed in semi-conductor: 1) electro-migration-induced voiding, 2) build-up of chloride ions, and 3) trapping of electrons or holes.
If electro-magnetic force, , is engaged, the impurities such as material void constructed by electronic movement is directly carried because the energy barrier of junction is less elevated in location, phaseshifted, distorted, etc.The junction function, J, could be expressed as [9]: where B is constant, a is interim between atomic particles,  is exerted field, k is Boltzmann's quantity, Q is energy, and T is temp.If Equation ( 9) takes the reverse, (generalized) stress type can be expressed as The hyperbolic sine expression in Equation ( 10) may be defined as: (1) at earliest () −1 in low effect, (2) () − in central effect, and (3) (  ) −1 in high effect.As raised testing is executed in the middlecategorized effect, Equation ( 10) is redefined as: ) As power is explained as the multiplication of effort and flows, stresses can start from effort such as force in a system.So, Equation (11) may be differently defined as the more generic expression: (12) Product imperfections may be exhibited during elevated forces being exerted on the material/system.In Equation ( 12), the acceleration factor (AF) may be defined as the proportional amount between the elevated forces for an accelerated test compared to those for normal operation.The AF may be expressed as: To attain the assigned time (or cycle) for the ALT from the targeted BX life, the sample size associated with the AF can be expressed as [10]: In ALTs, the design defects of the system worked by machinery can be pinpointed to attain the desired life for the component or system.

Case study: redesign of the HKS
To comfortably operate the door in a household refrigerator, a HKS with a spring-damper mechanism was framed.In launching the new HKS, it involved to observe potential design imperfections that may create unexpected failures and assess the HKS reliability.The major components in the HKS is composed of HKS cover , oil damper , cam , shaft , and spring . as seen in figure 2. In the market, the HKS pieces in a household refrigerator were cracking and fracturing due to fatigue and some design defects.To reproduce the utilization and load conditions of real end-user in the marketplace, engineers need to identify that reliability tests are involved.A company might optimally and robustly design the mechanical product to ensure it operates to the end of its anticipated life.If there are the design imperfections, the product can be unsuccessful before its expected lifetime.Thus, the HKS's actual life expectancy relies on the most problematic components.To replicate the troublesome components in the structure and alter them necessitates using an organized reliability way.It covers as follows: 1) load study returned from the field, 2) performing ALTs with modifications, and 3) confirming if life objective is achieved.Established on the customer usages in the marketplace, the HKS can then be exposed to similar loads due to door operating (open/closing) tests.As the HKS door unit is a simple structure, it can be modelled with a force and moment balance (figure 3).

Results and discussion
For an expected life cycle for ten years, the HKS is expected to experience about 36,500 utilization cycles for the worst-case operating conditions.The HKS impact is 1.10kN which was the estimated largest force employed by the customer.For the ALT with the raised weight of the door, the HKS impact was 2.76kN.Utilizing an accumulative damage quantity, λ, of 2.0, the AF was estimated to be 6.3 in Equation (18).The testing cycles utilized in parametric ALT for the assigned sample size and life objective were computed from Equation (14).For six samples and a life target of B1 life 10 years, the allotted time were 24,000 cycles.This ALT may be designed to attain B1 life ten years if it was failed less than once for 24,000 cycles.
In the first ALT, the HKS housing fractured at 3,000 and 15,000 cycles (figure 4).The shaping and site of the unsuccessfulness in the ALT were close to those seen in the market.The HKS in both the market and 1 st ALT test samples fractured in its housing.The design defects of the HKS started from no support structure in its housing having no ribs.If there were design faults in the structure where the loads were employed, the fracturing of HKS happened before its expected life.The repeated forces exerted in combination with the product imperfections can have been the source of the fracturing of the HKS.Thus, the fragile HKS housing had to be reinforced.The notch (Figure 6) was completely detached and the corner was rounded inside and outside.Strengthened ribs also were bolted on the decks and housing (figure 5).In dissembling the problematic HKS samples, there was spilled oil from the damper (Figure 7) found at 15,000 cycles.This failure started from leakage around an o-ring in the sealing structure and Teflon, which had a spacing of 0.5mm.It was guessed that there could be intervention between the Teflon and o-ring.To create a firm seal between the o-ring and Teflon and also have suitable strength for the exerted impact, the sealing structure in oil damper was changed as seen in figure 6.In the 2 nd ALT, the cover of the HKS fractured at 8000, 9000, and 14,000 cycles.The HKS for the second ALT failed from the poor selection of material used for the HKS cover.The HKS cover was made of plastic (Figure 8).This plastic HKS cover began to be cracking and fracturing at its ends.As an action plan, the material for the hinge kit cover was changed from plastic to Al die casting (figure 7).
7th International Conference of Engineering Against Failure Journal of Physics: Conference Series 2692 (2024) 012039 To survive the expected repeated impacts from use in the market, the HKS design was revised: (1) the HKS housing was strengthened, C1 (Figure 6); (2) the sealing structure of the damper was altered, C2 (Figure 7); (3) the material of HKS cover, C3, was modified from plastic to aluminum (Figure 8).With these modifications, the refrigerator could be operated to assure the reliability needed in the product life because there were no issues until 24,000 mission cycles.Over the course of three ALTs, the lifetime of HKS was ensured to be B1 life ten years with a cumulated failure rate of 1%.

Conclusions
To refine the design of new system worked by machinery such as HKS, parametric ALT is proposed as an organized method as follows: 1) ALT plan, 2) load investigation, 3) a tailored of ALTs with changes, and 4) a judgement of the design demands of the HKS to acquire they were achieved.An HKS in a domestic refrigerator was employed as a case research to illustrate the implementation of this process.
In 1st ALT, the HKS failed in the fracture of its housing and the spilled oil damper.In the 2 nd ALT, the cover fracturing of the HKS occurred.After ALT testing with changes, the HKS were settled to be an expected B1 life ten year.

Figure 2 .
Refrigerator and mechanical components of HKS

Figure 3 .
Figure 3. Model with a straightforward force and moment of HKS.As the customer uses the door in a household refrigerator, the impact stress due to the door weight is concentrated on the HKS.The moment balance around the HKS can be defined as  0 =   ×  =  0 =  0 ×  (15) As the raised weight of the door end was expected to grow the impact of the HKS, the moment equation around the HKS may be defined as ∑  =   ×  +   ×  =  1 =  1 ×  (16) With similar environmental circumstances, the life-stress type in Equation (12) can be redefined as:  = () − =  − = ( × ) − = () − (17) where A and B are constant.The accelerated factor in Equation (13) will then become:  = (  1  0 )  = (  1  0 )  = (  1 ×  0 )  = (  1  0 )

Figure 4 .
Figure 4. Unsuccessful HKS from the market and in the first ALT