International Journal o Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:03 106 A study on the Accelerated Lie Test Coupled with Computation or Lie Prediction o Product According to Wear and Damage So Young Hwang 1, Hyunsoo Jeong 1 and Naksoo Kim 1 1 Sogang University, Department o Mechanical Engineering, Seoul, 121-742, South Korea Corresponding Author: Naksoo Kim, nskim@sogang,ac.kr Abstract-- In order to guarantee the reliability o the product, an accurate lie prediction process is required. Proposed accelerated lie test coupled with computation analysis can predict the lie o product quantitatively rom the design stage. By understanding the mechanism o the product, the characteristic o the ailure can be identiied and represented by wear model and damage model. Then test response prediction unction according to acceleration actor can be obtained utilizing computation analysis. From the test response prediction unction, product lie prediction unction can be determined by deining the quantitative ailure. To veriy the reliability o proposed procedure, it is applied to predict the lie o rerigerator door. In this case, the cause o the ailure is the wear o hinge. The wear depth o the experiment and computation showed less than 5% dierence. For cross validation, lie o bearing is also predicted. 1. INTRODUCTION As industrial technology is advanced, developing new product in short time has become important actor. In addition, the reliability o new product has emerged as a major issue. The new products that are currently developed are designed to be operable or decades. Thereore the reliability test to guarantee the lie o new product is essential. Many researches have been done on reliability test because the time consumed to run the test has critical eect on the new product development period.[1] Generally accelerated lie test is conducted to shorten the test period since it is impossible to test the lie with actual use condition. Accelerated lie test is carried out in cruel condition compare to actual use condition. The degree o harshness is deined as acceleration actor. There are various kinds o stress that can be imposed during accelerated lie test and it is important to select the right stress type that its to the product. Many researches that investigate the eiciency o the accelerated lie test according to the stress type are conducted. Nelson et al.(1980) proposed step stress model and analysis method when accelerated lie test is perormed using constant stress type.[2] Shaked et al.(1983) researched on eicient acceleration condition to ind the lie o the product and conirmed that step stress type is more eicient than the constant stress type.[3] Srivastava et al.(2011) imposed various type o stress and proved that step stress type is proper or cutting destruction system.[4] Investigations about basic procedure o accelerated lie test or the type o stress has been done since 1980. Recently, studies about the material properties and analysis technique o accelerated lie test result are conducted. Mettas and Vassiliou (2004) studied analyzing method by dividing the stress actors.[5] Mohammadian and Ait- Kadi(2010) investigated three kinds o approach to analyze the results.[6] Bunea and Mazzuchi(2006) proposed a model that can analyze the data rom very small amount o sample[7] while Rajkumar et al.(2011) proposed and conirmed that there are speciic accelerated lie test models according to material properties. [8] Lee et al.(2012) designed accelerated test condition to understand the riction characteristic o FKM elastomer and predicted the lie rom the test.[9] Chao Zhang et al.(2013) has proposed analysis model to predict the lie o solid lubricated bearings which is very important component in aerospace ield. Also an experiment is carried out to prove the analysis model. [10] However in order to carry out the accelerated lie test, completed sample is required. Yet it will take some time to get whole product that is completely manuactured. Also products that are manuactured these days have complex system which complicates to predict the lie through accelerated lie test. In addition, lie predicted by accelerated lie test has limitations since the test is perormed in harsh condition and not actual use condition. Thereore in this study, accelerated lie test coupled with computation is proposed which can predict the lie quantitatively with only ew actual tests. Along with proposal, conirmation is made on the possibility o predicting lie with various conditions. Then accelerated lie test coupled with computation can be utilized to ensure the reliability o product lie rom the design stage. This can maximize the eiciency o design period. 2. THEORETICAL BACKGROUND In order to predict the lie o the product according to wear and damage using accelerated lie test coupled with computation, the behavior o wear and damage have to be representable in applied stress condition through simulation. To represent the wear and damage with inite element method, proper characterizing model is required.
International Journal o Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:03 107 Wear occurs when there is a riction orce between two contacted objects repeatedly. Wear can remove material and this leads to operation error. Thereore it is important to understand the variables that generate wear and predict the wear phenomenon. There have been many researches to embody wear behavior and recently this has been applied to numerical method such as inite element method. [11] The racture caused by material damage is divided into ductile and brittle racture according to accompanied strain. In this paper, the process o ductile racture is considered as the material damage mechanism. One o the characteristics o ductile racture is that the material goes through signiicant amount o plastic deormation beore racture. When the ractured plane o ductile material is observed under a microscope, iber with ininitesimal pool as i tiny tensile test is perormed can be seen. Fracture starts with tiny void initiation. These voids are generated around the inclusions or pre-exists. Voids grow and unite each other to generate crack and this lead to racture. Simply put, the process o cavity nucleation, growth and coalescence reaches to racture. In this chapter, two models are investigated. Archard wear model relecting the hardness and the stress condition and Gurson-Tvergaard-Needleman (GTN) ductile racture model which represents the plastic deormation and damage. 2.1 Wear model Wear is inluenced by many actors such as property o material, structures, environment and operating condition. Archard insisted that there is a need o some kind o theory which relates the wear ratio and load given. Also Archard explained that the theory have to represent the eective structure o wear and came up with Archard equation as Eq. (1). [12] V F s H N k (1) V is the volume o the wear. s, FN and H is sliding distance, normal load and hardness o wear surace respectively. k represents the non-dimensional ratio o the wear. Generally, the wear is predicted using Archard equation. In this equation, amount o wear is proportional to sliding distance and the load and inverse proportional to the hardness o the wear surace. Archard wear loss is associated with only the hardness, and wear loss observed and measured in the experiment is constant. Thereore the material hardness is an important variable to determine contact wear o material.[13] However as many researches are done, modiied Archard equations that its to the material characteristics are used. Rabinowicz classiied the wear type into severe (galling) wear, moderate wear and burnishing wear according to the k value rom Archard equation. Then a equation that represents the state rom moderate wear to burnishing wear is proposed.[14] Greenwood and Williansom considered the roughness o the contact surace and modiied the wear model. [15] In this research, modiied Archard model shown in Eq. (2) is used. This equation had increased the degree o reedom or each variable which is applicable according to material characteristics. a b Pv W k dt (2) c H W is the amount o wear. For v, P, H and k is eed rate, normal pressure, hardness o wear surace and nondimensional wear ratio respectively. Constants a, b and c are the degree o reedom o each variables. In this study, general values are used: as a=1, b=1 and c=2. 2.2 Damage model Recently, modiied Gurson model is used to obtain the result which agree with experiments and include the eect o void nucleation and coalescence. Tvergaard (1981) added three tuning parameters q 1, q 2 and q 3 to predict the strain at racture accurately and proposed modiied yield condition as shown in Eq. (3). Tvergaard had revised the equation through experiment data and ound that when q 1 = 1.5, q 2 = 1 and q 3 = 2.25, reasonable racture can be predicted. 2 e * 3 m *2 2q1 cosh q2 1 q 3 0 (3) y 2 y Also, Tvergaard and Needleman (1984) considered the modiied volume raction * = * () according to void volume raction to explain the void coalescence as shown in Eq. (4). i * F c c ( c) i c c i F c and is critical value o void volume raction and racture void volume racture respectively. These are material constants o racture model. As shown in Eq. (4), when the void volume raction is below the critical value, void volume raction is applied as eective void volume raction as it is. However it is over the critical value, the eect o hydrostatic stress is increased and the value increases rapidly. In this case, plasticity instability is promoted. The relation o void nucleation and the growth can be described as Eq. (5). pl pl 1 A (5) growth nucleation kk e 2 pl n 1 e n A exp s 2 2 s n n c (4) (6)
International Journal o Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:03 108 Eq. (5) distinguishes the void nucleation and the growth while Eq. (6) represents the probability distribution o void nucleation. The lower case letter n is the average while s n stands or standard deviation o standard normal distribution o A/ n. 3. ACCELERATED LIFE TEST COUPLED WITH COMPUTATION 3.1 Mechanism First step is to understand the cause o the ailure. In order to ind the cause o the ailure, mechanism o the component must be understood. Then speciic actors that aect the ailure o the component can be determined such as temperature, humidity, and load. In case o rerigerator door, the lie is predicted according to the delection o the door. As shown in Fig.1, when the door is opened or closed, the door is rotating around the axis o the rotation. Then the weight o the door and the stu inside the door apply the load. I the load is applied, the hinge ixed in rotation axis and the hinge ixed on cabinet contacts and rotates. Then the wear and damage occurs on the hinges which result in door delection. Thereore the cause o the ailure is the wear and damage on the hinge. Hinge looks as shown in Fig.2. There are our set o hinge at each corner o the rerigerator. Thereore as the door opening is repeated, hinge wears out which result in delecting the door. The main actors that assumed to increase the wear and damage on the hinge are the load. Thereore the eective stress actors are the load and rpm. Fig. 1 Failure mechanism o hinge Fig. 2. Hinge in rerigerator door 3.2 Accelerating test condition Ater selecting the eective stress actors, accelerating test condition must be determined. It is to ind the inluence o each stress actors and deine acceleration actor (AF) which is the amount o acceleration. I there are multiple actors, inluence o each actor should be tested independently. Then relation between actors to the ailure must be deined. In case o door hinge, acceleration actor is the load. Thereore AF can be represented as shown in Eq.(7) 1 AF R N F (7) Total revolution R (8) N 1 N 1 represents the number o cycle at measurement. As shown in Eq.(8), R is the value dividing total cycle to N 1. 3.3 Test response prediction ucntion Test response prediction unction is tendency o response to number o cycle at speciic accelerated condition. For ailure o the component, most o the response will be the wear or wear related values. Thereore, response according to cycle must be determined. For example, when load o 2.8kg is applied on the hinge, reduction in height according to the cycle is shown in Fig.3 3.4 Lie prediction unction At speciic stress condition, test response prediction unction can be determined. I the test response predictions or other stress conditions are obtained, test response unction according to AF can be determined. Then by applying the reerence value o the ailure, lie prediction unction can be obtained. For example, when the reerence value o the rerigerator door delection is 5 mm, it means that height reduction o hinge must be 5 mm. Then or each stress condition, lie as the number o cycle can be calculated. From this result, the lie curve can be achieved.
International Journal o Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:03 109 Fig. 3. Height reduction according to number o cycle 4. COMPUTATION TECHNIQUES Advantage o accelerated lie test coupled with computation is that the lie o a component can be predicted with ew actual tests. In order to ensure the result, reliability o the computation must be validated. Usually, accelerated lie test is done or more than thousand cycles. So it is impossible to simulate every cycle. Thereore updating algorithm is needed. As shown in Fig.4, wear and damage can be updated. First, material properties and damage model parameters can be obtained rom the basic material evaluation test such as tensile test. For wear model parameter k, it can be determined by constant stress condition experiment and step stress condition experiment by reverse engineering. For step stress condition, stress is increased by certain number o cycle. Then or every measured cycle, the amount o wear and damage can be updated as shown in Fig.4. In case o hinge, the experiment setup is prepared as shown in Fig.5. This machine repeatedly contacts the hinge and rotates. In order to control the load, weight is applied at the top o the machine. As a result the computed decrement o height and the experiment shows good agreement as shown in Fig.6. The dierence is within 5%. Thereore the lie o the rerigerator door can be estimated to be 17 years, when door is assumed to be opened 30 times a day. Fig. 4. Flow chart o updating wear and damage Fig. 5. Experiment setup
International Journal o Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:03 110 Fig. 6. Comparison between computation and test 5. VALIDATION In order to ensure that proposed accelerated lie test coupled with computation can be applied to other components as well, ball bearing is selected. When ball bearing is used, the dimension must be precise. Otherwise the rotation o the axis has run out. Thereore, it is important or bearings to maintain the precision. However, when bearing is used or long time, wear and spalling occurs on the roller and the race which aects the precision. In this chapter, lie o bearing according to decrement o height is predicted. The cause o the bearing reduction in height is the load. Thereore, eective stress condition is due to the load. In order to ind the proper k value o the wear model, test machine is built as shown in Fig.7 (a). There are load cells to measure the load given by the oil pump. (Fig.7 (b)) As a result, when k is selected as shown in Table.1, the dierence between experiment and simulation was less than 2%. Then according to applied load, the lie o the bearing according to reerence value o 0.5 mm reduction in height is obtained. As shown in Fig.8 ew experiments are done and rest o the conditions are predicted using computation. To ensure the predicted lie curve, a condition that is close to actual use condition is experimented. As a result, it showed good agreement. (a) (b) Fig. 8. Bearing lie curve 6. CONCLUSION By applying analytical techniques to the conventional accelerated lie test, acceleration lie test coupled with analysis is established. It can evaluate the reliability o the product in short time. In order to validate the acceleration lie test coupled with analysis, wear experiment is perormed and its result and the analysis result is compared to veriy the validity. Acceleration lie test coupled with analysis predicts the lie o the product rom the product development stage which can validate the reliability beorehand and reduce the development time. When there is no method to quantiy the cause o ailure in general accelerated lie test, acceleration lie test coupled with analysis can predict the lie quantitatively by using analytical technique. Thereore by selecting the ailure criterion and representing the mechanism with inite element method, even the lie o the product with complicated system can be predicted and shorten the developing time. Fig. 7. Bearing wear test machine (a) Full machine (b) Loadcell Table I Dierence between experiment and simulation result or wear depth Parameter Test result Simulation result Wear coeicient K Decrement o height (per 10,000 revolution) 0.0548 [mm] 0.0533 [mm] 3.989e-09 ACKNOWLEDGEMENT This work was supported by Sogang University (Grant no. 201210031). REFERENCES [1] Jung, Joo, and Jeong (2012) Investigation into the Worst Stress Condition or an Accelerated Lie Test o a Compressor in Rerigerators - Acceleration Factor and the Reducible Test Time under High Temperature. Journal o the Korean Society or Power System Engineering, Vol. 16, No.3, pp. 44-50. [2] Nelson, W. (1980) Accelerated Lie Testing - Step-Stress Models and Data Analyses Reliability. IEEE Transactions, Vol. R-29, No.2, pp. 103-108. [3] Shaked, M. and N.D. Singpurwalla (1983) Inerence or step-stress accelerated lie tests. Journal o Statistical Planning and Inerence, Vol. 7, No.4, pp. 295-306.
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