_{1}

Parametric Accelerated Life Testing (ALT) was used to improve the reliability of ice-maker system with a fractured helix upper dispenser in field. By using bond graphs and state equations, a variety of mechanical loads in the assembly were analyzed. The acceleration factor was derived from a generalized life-stress failure model with a new load concept. To reproduce the failure modes and mechanisms causing the fracture, new sample size equation was derived. The sample size equation with the acceleration factor also enabled the parametric accelerated life testing to quickly reproduce early failure in field. Consequently, the failure modes and mechanisms found were identical with those of the failed sample. The design of this testing should help an engineer uncover the design parameters affecting the reliability of fractured helix upper dispenser in field. By eliminating the design flaws, gaps and weldline, the B1 life of the redesign of helix upper dispenser is now guaranteed to be over 10 years with a yearly failure rate of 0.1% that is the reliability quantitative test specifications (RQ).

Reliability describes the ability of a system or module to function under stated conditions for a specified period of time [

The product reliability function can be quantified from the expected product lifetime L_{B} and failure rate l in

This equation is applicable below about 20 percent of cumulative failure [

However, it may not be easy to identify all failure modes attributable to the particular design because the failure modes in the mechanical systems come from repetitive stresses which may not be found in its initial testing or design. Refrigeration system modules such as ice-maker system need to be robustly designed to withstand a variety of loads. Consequently, the ice-maker system determines the control factors (or design parameters) to endure the noise factors (or stresses) so the system properly works. Such reliability targeting is known to be conventionally achieved through the Taguchi methods (SDE) and the statistical design of experiment [

In this study we present a new parametric Accelerated Life Testing (ALT) method that can improve the reliability of fractured helix upper dispenser in field. This new accelerated testing methodology [

design parameters.

As seen in

In the marketplace, one part in ice-maker system was cracking or fracturing (see

An ice-maker system in a refrigerator consists of multiple parts―AC auger motor, ice bucket, ice tray, and lever. They can be put together as a subassembly and have an

input and output for ice harvest. As parameters and required input, robust design schematic of ice-maker employs two experimental arrays: one for the control array (design) and the other for the noise array (loads). Optimizing over the control factors, optimal design data can be reduced to a signal (output)-to-noise (load) ratio. As there are multiple parts in ice-maker system, ultimately, it is designed to harvest ice (see

Where these parts might receive mechanical overloads in ice-making process, there are two cases―the crushed or fused ice. Depending on the customer usage conditions, the mechanical load of the icemaker is low because it is operated without fused or webbed ice. Fused or webbed ice will form in the tray when they do not dispense ice in cubed mode for long time.

Another case is crushed ice. It involves several kinematic or mechanical processes: 1) the filtered water is pumped through a tap line that is supplying the ice tray; 2) the cold air in the heat exchanger chills the tray; 3) after ice is made, the cubes are harvested, stocking the bucket until it is full; and 4) a crusher breaks the cubed ice in the crushed mode. When the customer pushes the lever by force, the crushed ice is dispensed in its mode.

The bond graph can be conventional in state space representation to group terms by state variables. The modeling (or state equation) of ice bucket assembly can be expressed as

The mechanical stress of the ice bucket assembly depends on the disturbance load T_{D} in Equation (2).

If there is a void such as structural design flaw - 2 mm gap and weldline where the

loads are applied, the structure subjected to repetitive stress can fracture at that location (see

Failure of helix upper dispenser can happen when the strength of materials composing the system structures yield with the loads applied to it. The load could be higher than the system was designed for or the material could be insufficient to handle repetitive loads to which it is subjected. That is, failure occurs when the stress is greater than the material strength, or when the material cannot withstand the loads.

The design engineer would want to move the void in the structure to a location away from where the stress (or load) is applied. A reliability engineer should seek to redesign the structure to either: 1) move the loads, or 2) change the material shape and type to withstand the load.

To derive the life-stress model for helix upper dispenser, the time to failure (TF) can be estimated from the McPherson’s derivation [

The first term on the right hand side of Equation (3) is the load and the second term is the internal energy. The internal (or external) stress in a product is difficult to quantify and use in accelerated testing. It is necessary to modify Equation (3) into a more applicable form. Thus, stresses in crushing ice may come from the torque. Because there is no temperature change, its portion of second term can be neglected.

From the time-to-failure in Equation (3), the acceleration factor can be defined as the ratio between the needed accelerated stress levels and those found under typical operating conditions. The acceleration factor (AF) can be modified to include the load from Equation (3):

Under severe testing (or accelerated) conditions, the refrigeration system subjected to a duty cycle will experience a shortened module lifetime [

As seen in

In targeting the reliability of the refrigerator, there are three cases: the new design maintains a modified module, new module, and similar module to the prior design on the basis of market data. Ice-maker module is indeed the modified one to the prior design because design flaws―2 mm gap and weldline will be eliminated. In targeting the reliability of the modified module, the field data are often used as a reference.

Like module D listed in

Modules | Market Data | Expected Reliability | Targeted Reliability | |||||
---|---|---|---|---|---|---|---|---|

Yearly Failure Rate, %/yr | B_{x} Life, yr | Yearly Failure Rate, %/yr | B_{x} Life, yr | Yearly Failure Rate, %/yr | B_{x} Life, yr | |||

A | 0.35 | 2.9 | Similar | x1 | 0.35 | 2.86 | 0.10 | 10 (x = 1.0) |

B | 0.24 | 4.2 | New | x5 | 1.20 | 0.83 | 0.15 | 10 (x = 1.5) |

C | 0.30 | 3.3 | Similar | x1 | 0.30 | 3.33 | 0.10 | 10 (x = 1.0) |

D | 0.31 | 3.2 | Modified | x2 | 0.62 | 1.61 | 0.10 | 10 (x = 1.0) |

E | 0.15 | 6.7 | Modified | x2 | 0.30 | 3.33 | 0.15 | 10 (x = 1.5) |

Others | 0.50 | 2.0 | Similar | x1 | 0.50 | 2.00 | 0.40 | 10 (x = 4.0) |

Product (Total) | 1.9 | 5.4 | - | - | 3.27 | 3.06 | 1.00 | 10 (x = 10) |

yearly failure rate was 0.31%/year and lifetime, L_{B1} was 3.2 years. To respond a customer claims, new target for ice-maker system was set to be L_{B1} 10 years with 1.0 yearly failure rate and the ice-maker system is determined by the lifetime of the helix upper system.

To derive the sample size equation, probability concept in reliability engineering should be understood. The Cumulative Distribution Function (CDF) in the Weibull function can be expressed as:

The Weibull reliability function, R(t), is expressed as:

The characteristic life h_{MLE} from the Maximum Likelihood Estimation (MLE) can be derived as:

If the confidence level is 100(1 - a) and the number of failures, r, is expected to be r ³ 1, then the characteristic life, h_{a}, can be estimated from Equation (14):

Presuming there are no failures, the p-value is a and ln(1/a) is mathematically

equivalent to the Chi-Squared value,_{a}, would then be represented as:

Equation (8) is established for all cases r ³ 0 and can be redefined as follows:

To evaluate the Weibull reliability function, the characteristic life can be converted into L_{B} life as follows:

After a logarithmic transformation, Equation (11) can be expressed as:

If the estimated characteristic life of p-value a, h_{a}, in Equation (10), is substituted into Equation (12), we obtain the B_{X} life equation:

Because most accelerated lifetime testing typically has a small number of samples, the number of failures would not be as much as that of the sample size.

If Equation (14) is substituted into Equation (13), the B_{X} life equation becomes an inequality and can be written as follows:

The sample size equation with the number of failures can also be modified as follows:

For a 60% confidence level, the first term,

a Taylor expansion. These approximations transform the general sample size equation to the following:

If the acceleration factor, AF, from Equation (4) is added into the planned testing time, Equation (24) can be modified to include AF. When the target reliability ? failure rate l and lifetime L_{B} are given, this equation will be used to carry out parametric accelerated life testing:

Generally, the operating conditions for the mechanical ice bucket assembly in an icemaker are −15˚C to −30˚C temperature, 0% - 20% relative humidity, and 0.2 - 0.24 G vibration.

The dispenser is used an average of approximately 3 - 18 times per day in the United States. Under maximum use for 10 years, the dispenser incurs about 65,700usage cycles (

Assume that the shape parameter was 2, the test cycles and the numbers of samples calculated from Equation (18) were 42,000 cycles and 10 pieces, respectively. The parametric ALT for helix upper dispenser was designed to ensure a B1 of 10 years life with about a 60% level of confidence that it would fail less than once during 42,000 cycles.

When the controller outside the chamber gives the start signal, the auger motor rotates the clamp helix dispenser, the helix upper dispenser and the blade dispenser. To apply the maximum disturbance torque TD, two parts―the helix upper dispenser and the band clamper―were bolted together to slip them. At this point, the rotating blade dispenser will impact the fixed helix upper dispenser to the maximum mechanical disturbance torque (1.47 kN・cm). Depending on the operating condition of the equipment, the blade dispenser will provide maximum torque to the helix upper dispenser 4 - 6 times in 5 seconds.

value in the previous ALT is 2.0. However, the final value confirmed on the Weibull plot was 4.8. As the ratio of characteristics life, h_{1}/h_{2}, gives the acceleration factor, AF is approximately 2.2 on the Weibull plot.

We conclude that these methodologies are valid to reproduce the fielded failures because (1) the location and shape of the fractures in both market and ALT results are extremely similar; and (2) on the Weibull plot, the shape parameters of the ALT results, b_{1} and market data, b_{2}, are very similar. It also might represent the load states in field and parametric ALT. This approach was very effective in reproducing the fracture of the product from the marketplace.

The fracturing and cracking of both the fielded products and the ALT results occur in the contact area of the blade dispenser, where was the design flaw―2 mm gap. Due to the design defects between the blade dispenser and helix upper dispenser, the impact (1.47 kN×cm) of the blade dispenser generated the high stress against the helix upper dispenser. The concentrated stress of the blade dispenser is approximately 36.9 kPa, based on finite element analysis (FEA). When the blade dispenser, made of stainless steel, meets the polycarbonate helix upper dispenser at a right angle in −30˚C, it will be fractured near the impact area of the helix upper dispenser.

Based on failure analysis and first ALT, the design flaw―2 mm gap was the root cause of the fractured helix upper dispenser in ice-maker system. The missing design parameters for the helix upper dispenser were modified as follows: 1) the design flaws (C1: gap reduction, 1.2 → 0.0 mm), 2) the shape of blade dispenser (C2), and 3) the weld line (C3) (see

All samples in the first ALT (n = 10) failed within 11,600 cycles as shown in _{1} 10 years. The confirmed values of AF and b in

For the second ALT, the test sample number and required testing cycles recalculated in Equation (18) was 6 pieces and 54,000 cycles. In result all samples were failed within 38,000 cycles, as shown in _{1} 10 years.

In the third ALT results, the samples did not crack and fracture until 75,000 cycles of parametric ALT. The reliability quantitative test specifications (RQ) of a mechanical structure meet that newly designed samples do not fail within the target life of B1 10 years. The design improvements of eliminating the gap and reinforcing the ribs were very effective in enhancing the reliability of the sample (see

1^{st} ALT | 2^{nd}ALT | 3^{rd}ALT | |
---|---|---|---|

Initial Design | Second Design | Final Design | |

In 54,000 Cycles, Fracture of helix is less than 1. | 170 cycles: 1/10 (10%) 5200 cycles: 1/10 (20%) 7780 cycles: 2/10 (40%) 8800 cycles: 2/10 (60%) 11600 cycles: 4/10 (100%) | 17,000 cycles: 1/6 (17%) 25,000 cycles: 3/6 (67%) 28,200 cycles: 1/6 (83%) 38,000 cycles: 1/6 (100%) | 54,000 Cycles: OK 75,000 Cycles: OK |

Helix Structure | |||

Material and specification | PC + SUS (t = 1.2) GAP: 2 mm | PC + SUS (t = 1.2) GAP: 0 mm | PC + SUS (t = 1.2) GAP: 0 mm Added rib on side and front of helix |

shows the graphical results of an ALT plotted in a Weibull chart.

To improve the reliability of ice-maker system with the fractured helix upper dispenser in field, we have examined the failure analysis for fractured helix upper dispensers and carried out the parametric ALTs with various design improvements. The following general conclusions were obtained:

1) Based on the claimed marketplace product returns and ALT reproduction, the root causes of ice-maker system with the failed helix upper dispenser in field came from the fragile structure of the helix upper dispenser. Specific flaws were found to be 2 mm gap, the weldline, and the impact of the stainless steel blade dispenser on the polycarbonate helix upper dispenser.

2) The critical controllable design improvements involved gap elimination and rib reinforcement. These were shown to be effective in enhancing the reliability of ice- maker system with the helix upper dispenser fractured in field.

3) After a sequence of parametric ALTs, the samples did not crack and fracture until 75,000 cycles of parametric ALT. The reliability quantitative test specifications (RQ) of a mechanical structure meets because newly designed samples do not fail within the target life of B1 10 years.

4) The failure analysis of the failed product and three rounds of ALT were very effective in reproducing the ice-maker system with the fractured helix upper dispenser claimed in the marketplace and in improving its reliability.

The new reliability design methodology could be applied to other mechanical systems, including automobile gear trains and engines, construction equipment, forklifts, washing machines, vacuum cleaners, and motor fan systems. We recommend that the missing or improper controllable design parameters on these systems should be studied for reliability design. These parameter studies might include failure analysis, load analysis, and a tailored series of accelerated life tests.

Woo, S.-W. (2016) Reliability Design of Ice-Maker System Subjected to Repetitive Loading. Engineering, 8, 618-632. http://dx.doi.org/10.4236/eng.2016.89056