Fatigue Life Analysis of Remanufactured Radial Rolling Bearing with the Replaced Loading Zone

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Introduction
Te purpose of rolling-bearing remanufacturing is to excavate the remaining life of bearings whose bearing parts (mainly the rings) are not fully used.Rolling-bearing remanufacturing has a longer history than generalized remanufacturing and has formed a series of system documents in the long process of development [1].Te concept of bearing remanufacturing was frst presented in September 1974, when Stanley presented a report entitled "bearing feld inspection and refurbishing" at the Symposium on Propulsion System Structural Integration and Engine Integrity, held at the Naval Post Graduate School in Monterey [2].Te U.S. Army Aviation Systems Command held a symposium named "bearing restoration by grinding seminar" in St. Louis from May 20 to 21,1976.After the meeting, the U.S. Army Aviation Systems Command summarized these reports and issued USAAVSCOM-TR-76-27 [3], which marks the remanufacturing of rolling bearings as a systematic project.NASA released the frst report on bearing remanufacturing in 1976, TM-X-73440 [4].In the 21 st century, the ecological deterioration caused by carbon dioxide emissions has attracted more and more attention.Te scale of the rolling-bearing remanufacturing industry is developing rapidly.Bearing manufacturers have set up specialized remanufacturing factories one after another.Te typical manufacturers include SKF [5][6][7], Schaefer [8,9], and Timken [10][11][12].
Due to the particularity of the raceway remanufacturing method, the rolling bearing cannot return to the original design life after remanufacturing but can only return the bearing life to the original life curve, as shown in Figure 1.Te calculated rated life curve in the fgure refers to the theoretical life curve established according to the bearing application condition in the process of bearing selection.In practical application, due to installation factors, environmental pollution, insufcient lubrication, and other factors, the actual life often deviates from the predicted life value.According to Timken's statistics, only 10% of the bearing used in heavy industry can reach the rated fatigue life L 10 .Bearing remanufacturing can efectively restore its life.On the other hand, the fatigue life of remanufactured bearings can still be calculated by the statistical method after remanufacturing when a batch of bearings has reached their fatigue life.Te remanufacturing level of rolling bearing varies and metal removal of the raceway varies, which will directly afect the fatigue life of bearings after remanufacturing.Many studies have focused on the fatigue life of remanufactured bearings.NASA released the life analysis report TN D-8486 of remanufactured bearing in 1977 [14].In 1987, an analytical report TM-88871 [15] was published on the efect on fatigue life owing to metal removal on raceways by NASA.Zaretsky and Branzai [16] summarized the life calculation of remanufactured bearings again at the Society of Tribologists and Lubrication Engineers Annual Meeting and Exhibition in 2014 based on NASA TM-2005-212966 [17].Zamzam et al. [18] analyzed the rolling contact fatigue of remanufactured bearings by polishing.Chen et al. [13] proposed a new class IV remanufacturing method based on the remanufacturing of large-size radial bearing rollers and the fatigue life of cylindrical roller bearings by the new remanufacturing method is verifed by experiments.Matthew [19] studied the problem of bearing remanufacturing to prolong life and improve performance.Darisuren et al. [20] researched the relationship between the remanufacturing process and fatigue life of spherical roller bearings.
None of the abovementioned studies on fatigue life of remanufactured bearings has paid attention to the replacement of the loading zone.According to the practical application of replacing the loading zone for radial bearing after manufacturing, the fatigue life factors of diferent remanufacturing levels with replacement of the loading zone are calculated in this paper.Te results of case studies show that the life factors of the radial bearing with the replacement of the loading zone are increased and the increased range varies according to diferent remanufacturing levels, with a maximum increase of 12% according to the calculations in this paper.

Classification of Rolling-Bearing Remanufacturing
Te method of rolling-bearing remanufacturing includes but is not limited to the scope of generalized remanufacturing.Generalized remanufacturing mainly includes additive manufacturing technology, combined with machining to restore the size and shape accuracy of the parts.Coors et al. [21] investigated the wear behavior of additively welded cladding layers on less wear-resistant base materials.Finally, he discovered that additive manufacturing processes can be used to clad less wear-resistant base materials and achieve high wear resistance, making it possible to exploit the advantages of surface coatings under severe wear conditions.But the remanufacturing of rolling bearings is diferent from the generalized remanufacturing, and the diference is mainly refected in the remanufacturing of raceways.Due to the huge alternating stress between the contact pair of rolling elements and raceways in the work, the raceways remanufactured by using additive technology are difcult to meet the application needs of rolling bearings.At present, the method of removing materials is widely used to remanufacture bearings.Te object of rolling-bearing remanufacturing is the bearing that has been used or stored for a long time.Because of the diferent storage status, the diferent number of use cycles, and the diferent application conditions, the condition of rolling bearing to be remanufactured varies greatly.When the bearing is remanufactured, its remanufacturing level should be determined frst.Diferent remanufacturing levels mean that there are diferences in the methods and contents of remanufacturing, which has a direct impact on the fatigue life of remanufactured bearings.Terefore, the classifcation methods of remanufacturing used in practical applications are introduced frst.
At present, there is no universally accepted standard for the classifcation of bearing remanufacturing.Te active classifcation methods are based on the enterprise 2 Journal of Engineering documents of bearing remanufacture factories and the research report of NASA.Remanufacturing classifcations from typical factories as well as NASA are listed in Table 1.
Te classifcation details are diferent as can be seen in Table 1.SKF divides the remanufacturing level into fve levels in the form of class I-class IV [5]; Schaefer FAG divides the remanufacturing level into four levels according to level I-level IV [8]; Timken divides the remanufacturing level into three levels according to type I-type III [11]; and NASA [17] divides the remanufacturing level into four levels according to level I-level IV.Diferent remanufacturing levels involve distinct remanufacturing procedures.Te following provides a concise overview of the procedures associated with each remanufacturing level based on NASA's remanufacturing classifcation.Level I is the remanufacturing level to inspect used bearings or bearings in long-term stock to confrm whether they still meet the requirements of drawings or if bearings with minor defects are partially polished or grinded to restore bearing performance.Level II refers to the remanufacturing level of replacing the rolling element and cage when necessary and the polishing of raceways to restore bearing performance, and the thickness of metal removal on the raceway is less than 13 µm.Level III refers to the remanufacturing level of raceway grinding and replacing of enlarged rollers to restore bearing performance, and the thickness of metal removal on the raceway is 76 µm and 300 µm for bearings with outer diameter less or greater than 400 mm.Level IV means the remanufacturing level of replacing a new ring.

Rolling Contact Fatigue and Replacement of the Loading Zone
In the application of rolling bearings, the external load is transferred to the rolling elements through the ring, which causes huge contact stress between the rolling elements and the raceway.Periodic alternating stress on rolling element surfaces and raceways causes rolling contact fatigue.Te area which bears the load is defned as the loading zone.Due to the efect of the clearance of the radial bearing, only some area in the circumference direction of the fxed ring is subjected to alternating stress.

Efect of Loading Zone Replacement on Fatigue Life.
Taking the application of deep-groove ball bearings as an example, the schematic diagram of loading zones (both original and new) and the contact profle under external load P are illustrated in Figure 2. In Figure 2(a), the outer ring of the bearing is fxed and the inner ring rotates at angular velocity ω i .Gr is the radial clearance of the bearing.Because of the combined infuence of load and motion, the whole inner raceway is the loading zone, while only the lower part of the outer raceway is the loading zone.Te size of the loading zone on the outer raceway is afected by the clearance, while the larger the clearance, the smaller the loading zone is.Continuous action of periodic alternating stress will cause stressing of the metal on the raceway surface.Te stressed depths of raceways are indicated as x i and x o on section A-A in Figure 2(b), respectively.Te replacement of the loading zone refers to the use of the raceway area which has not been stressed as the new loading zone in the next application cycle as shown in Figure 2(a).For example, the inner ring is the rotating ring and the outer ring is the fxed ring, and when the bearing is subjected to radial force, the rotating ring is stressed as a whole, but only a part of the fxed ring is stressed; the stressed part is called the loading zone, and the unstressed part is called the nonloading zone.After the bearing runs for a certain period of time, the inner ring and the outer ring are remanufactured at diferent levels according to the degree of damage and the nonloading area of the outer ring is used as the new loading zone when the bearing is reinstalled after remanufacturing.Ball bearings and roller bearings have the same principle; the only diference is the contact form.
Te fatigue life of bearing will decrease to a certain extent after material stressing according to TM-2005-212966 [17].Te fatigue life of rolling bearings is a comprehensive characterization parameter of the life of internal and external raceways and rolling elements.A replaced loading zone means that the fxed ring raceway is not stressed and the fatigue life of the fxed ring will not decrease.Ten, the fatigue life of bearing will be diferent.Te fxed ring (the outer ring in Figure 2(a)) is rotated 180 degrees in the circumferential direction to enter a new application cycle.In the new application cycle, the life of the inner raceway decreases, but the life of the outer raceway is the same as that of the new bearing, which will lead to the increase of the life of the remanufactured bearing system, as shown in Figure 3.

Rolling Contact Fatigue of Rolling Bearings.
Te contact types commonly observed in rolling bearings are point contact and line contact, as illustrated in Figure 4. Te contact state of deep-groove ball bearing is the typical point contact as can be seen in Figure 4(a).Te contact point expands to an ellipse when applied with the external load P. When the ball contacts with the inner and outer raceways, one is in contact with the outer circle and the other is in contact with the inner circle.Te diference of the coincidence degree results in the diference of the contact ellipse.In Figure 4(a), a is the half length of the contact ellipse between the inner raceway and the ball, b is the half width of the contact ellipse between the inner raceway and the steel ball, and a′ and b′ are the half length and half width of the contact ellipse between the outer raceway and the steel ball, respectively.Te contact state of cylindrical roller bearing is the typical line contact as can be seen in Figure 4(b).a and b are the half length and half width of the contact ellipse between the outer raceway and the cylindrical roller, respectively, and b′ is the half width of the contact ellipse between the inner raceway and the cylindrical roller.
Te contact area between rolling elements and raceways are very small, which results in huge contact stress between rolling elements and raceways.Te material of a certain depth under the efective area of the load is afected by stress.Te contact area of inner and outer raceways is diferent, so the depth of stress on the raceway surface is diferent.Fatigue failure of the contact surface is a statistical phenomenon, which is related to the volume of the material under stress, so the stress depth directly afects the fatigue life of the internal parts of rolling bearings [22].Rolling contact fatigue is characterized by metal particles falling of from the surface of the raceway or rolling elements.For a well-lubricated bearing, the exfoliation begins with a crack below the surface and then extends to the surface, eventually forming a pit or exfoliation on the surface of the loading area.
Lundberg and Palmgren [23] considered that orthogonal shear stress τ 0 was the origin of fatigue crack and put forward an equation for calculating the fatigue life of bearings.Chalsma and Zaretsky [24] revised Lundberg's life calculation equation by using maximum shear stress τ 45    4 Journal of Engineering instead of orthogonal shear stress τ 0 , as shown in the following equation: In equation ( 1), S is the survival probability and c is the stress life index, e is the slope of Weibull distribution, N is the bearing life counted by the number of stress cycles, and V is the volume of being stressed.According to the study of Lundberg and Palmgren [23,24], e is equal for the point contact and for the line contact.
Te fatigue life of the raceways can be obtained as follows: In equation (2), L i and L o are the lives of inner and outer raceways, respectively, and A is the life factor infuenced by the raw material.

Life Factors of Remanufactured Raceways in Rolling Bearing
Diferent remanufacturing levels correspond to diferent techniques in the remanufacturing process, and the fatigue life of the remanufactured raceway will be infuenced by diferent techniques directly.Ten, the life factors of raceways after remanufacturing are discussed separately according to whether the stressed surface material is removed or not.

Life Factor of the Remanufactured Raceway without Metal
Removing.Te used times of rolling bearings which will be remanufactured are various.For convenience, L 10 is chosen as the used time for bearings which will be remanufactured in the following discussion.According to the defnition of rating life, when a batch of bearings work for a certain time, 10% of the bearings fail, while the remaining 90% of the bearings do not fail; then, the certain time is defned as rating life L 10 .
Te remaining 90% bearings are remanufactured and there is no metal which will be removed from the raceway.Based on the defnition of rating life, the new L 10 of remanufactured batch bearings is equivalent to L 19 of original batch bearings, namely, In equation (3), F is the failure probability.Ten, the survival probability is In equation ( 4), S is the survival probability.Ten, the new L 10 (original L 19 ) of remanufactured batch bearings can be obtained by the Weibull theory [25] as follows: In equation (5), k is the material-related life impact factor.
Te life factor of the remanufactured raceway without metal removing can be expressed as follows: In equation ( 6), LF p is the life factor of the remanufactured raceway without metal removing (polish only).
Te reliability involved in calculating the life factor by equation ( 6) is 90%.Reliability requirements of rolling bearings vary under diferent application conditions.Zaretsky and Branzai [17] calculated life factors of rolling bearing with diferent reliability as listed in Table 2. Te calculation method of the data in Table 2 is the same as the method mentioned in this paper, so the data in Table 2 can be directly quoted in calculating fatigue life of raceways.

Life Factor of the Remanufactured Raceway with Metal
Removing.It is necessary to remove some metal on the surface of the raceway in levels II, III, and IV remanufacturing, as discussed in Section 1. Removals of the strengthened material have an impact on fatigue life of the raceway.Schematic of normalized maximum shearing stress τ 45 as a function of normalized depth below the raceway surface showing the efect of metal removal in redistributing stress is shown in Figure 5.According to Figure 5, the stress distribution state is changed by polishing or grinding.τ 45 in the fgure is normalized and is equal to 1 when the depth of the stressed material is the same as the position of the maximum shear stress.
Assuming the depth of material removal is x and it is further assumed that the metal at depths greater than Z 45 are not stressed.Terefore, after material removal, metals have not been subject to stress cycles which can be expressed as follows: In formula (7), (a) is the calculation formula of point contact type bearings and (b) is the calculation formula for linear contact type bearings.a is the major semiaxis of the contact ellipse, l L is the equivalent width of the contact region, and l t is the length of the raceway contact area.
After material removal, metals have a stressed volume of In equation ( 8), (a) and (b), respectively, represent the stress volume under the raceway for point contact type bearings and linear contact type bearings after removing metal materials.
Each of the stressed volumes contributed to the life of the entire raceway having a stressed volume defned in the following equation: (a), In equation ( 9), (a) and (b), respectively, represent the life of the stressed part and the unstressed part.
Harris [22] derived the relationship between individual component life and system life.Te life of the entire volume from equation ( 9) can be further defned from the Lundberg-Palmgren equation, equation ( 6), where It is uncertain which ring is fxed in bearing application.Te inner and outer rings are described by fxed and rotating rings.According to the abovementioned analysis, the fatigue life of the fxed ring will be the same as that of the new ring after replacing the loading zone and the fatigue life of the rotated ring will be changed.Ten, equation ( 10) becomes In equation (11), L v ′ is the fatigue life of the rotated ring.Te life factor of the remanufactured raceway with metal removing can be defned as follows: In equation ( 12), LF g is the life factor of the remanufactured raceway with metal removing (polish and grinding), and L v is the original fatigue life of the rotated ring.

Fatigue Life of Remanufactured Bearing with Replacement of the Loading Zone.
A bearing is a system of multiple components each with a diferent life, and the life of the system is diferent from the life of an individual component in the system.Te relationship between rolling bearing system and rings can be expressed as in the following equation: In equation ( 13), L R is the fatigue life of the bearing system after remanufacturing and L u is the fatigue life of the fxed ring.
Te life factor of the remanufactured bearing can be defned as follows: In equation ( 14), LF R is the life factor of the remanufactured bearing system.
Te calculation process of life factors of bearings with diferent remanufacturing degrees can be clearly described by the fowchart shown in Figure 6.
Te above describes the calculation methods of the life factors of bearings at diferent remanufacturing levels.Te life factor can intuitively refect the diference between the fatigue life of the bearing considering the replacement of the loading zone and the fatigue life obtained by the active calculation method, and the diference comes from whether the fxed ring is stressed or not after the bearing is remanufactured.Te method proposed in this paper can improve Journal of Engineering the coincidence between the theoretical life and the actual life of the bearing.

Case Studies
Te analysis in this paper is a theoretical research of fatigue life for remanufactured bearings.Te fatigue life of rolling bearings is a statistical problem, so it is difcult to verify the research results of this study by using experimental methods.Terefore, the following selected cases are calculated theoretically and compared with the results of previous calculation methods to verify the results.

Life Factors of Diferent Remanufacturing Levels.
Assuming that there are 1000 sets of bearings of various types, the life of the inner ring L 10i is 1400 hours and that of the outer ring L 10o is 3000 hours; the fatigue life of the bearing systems can be calculated by the Lundberg-Palmgren equation [23], and it is equal to 1,000 hours.Assuming that the bearing works well, 10% of the bearings (100 sets) will fail after 1,000 hours according to the defnition of fatigue life.900 of the 1000 sets of bearings that have not failed can be remanufactured.Depending on the conditions of the bearings after application, it is possible to remanufacture the bearings in level I, II, III, or IV.Te life factor is calculated according to diferent remanufacturing levels as shown in the following section.

Life Factor of Level I Remanufactured Bearings. If the
bearing is remanufactured at level II, the fatigue life of the rotating ring can be obtained by equation ( 6) and the fatigue life of the bearing system can be obtained by equation (13).When the inner and outer rings are fxed rings, respectively, the life factor of the remanufactured bearing by level I is  Journal of Engineering calculated by using equation ( 14) and the results are listed in equation (15).
In equation ( 15), the subscript I means level I remanufacturing, the subscript Rvi means the fxed outer ring and rotated inner ring, and Rvo means the fxed inner ring and rotated outer ring.

Life Factor of Level II Remanufactured Bearings.
Assuming that the bearing needs to be remanufactured of level II, part of the metal on the raceway is removed.Each of the stressed volumes contributed to the life which can be obtained by equation (9).For the convenience of subsequent comparison, the material removal rate of the following calculation is 5% as in the literature [23].
Assuming that the inner ring is a rotating ring, then In equation ( 16), the subscript xvi means the unstressed volume of the rotated inner ring and the subscript (1 − x) vi means stressed volume of the rotated inner ring.
Te life of the inner ring is derived from equation ( 11) as follows: In equation (17), the subscript vi means the rotated inner ring and the fxed outer ring.
When the inner ring is a rotating ring, the life of the bearing can be obtained from equation (13) as follows: In ( 18), the subscript II means level II remanufacturing and the subscript Rvi means the fxed outer ring and the rotated inner ring.
Similarly, when the outer ring is a rotating ring, the life of the bearing can be obtained from equation (13) as well, as follows: In equation (19), the subscript Rvo means the fxed inner ring and the rotated outer ring.
Ten, the life factor of the remanufactured bearing by level II is calculated as follows:

Life Factor of Level III Remanufactured Bearings.
Calculation procedure for level III remanufacturing is the same as level II, but the material removal rate of level III is more than that of level II.For the convenience of subsequent comparison, the material removal rate of the following calculation is chosen 20% as the same in reference [17].
Ten, the life factor of the remanufactured bearing by level III is calculated as follows: In equation ( 21), the subscript III means level III remanufacturing.

Life Factor of Level IV Remanufactured Bearings.
Te life factor of the remanufactured bearing by level IV is calculated as follows: In equation ( 22), the subscript IV means level IV remanufacturing.
Te bearing life is assumed reasonably and the life factor is calculated by the method proposed in this paper.It is found that the bearing life factor increases with the increase of the remanufacturing level and gradually approaches 1. Tis is because both the removal of stressed materials and the replacement of new parts have a positive impact on bearing life.At the same remanufacturing level, the life factor when the inner ring is a fxed ring is greater than that when the inner ring is a rotating ring.

Comparison with Endurance Data of Diferent Bearings.
Harris analyzed endurance data of 7935 bearings in reference [26].Te data are from 2 helicopter manufacturers, 3 aircraft engine manufacturers, and the U.S. Government agency-sponsored technical reports [27].Te data comprised deep-groove radial ball bearings, angular-contact ball bearings, and cylindrical roller bearings of 62 rolling bearing sets.Tese data are plotted in Figure 6 using the number of bearings failed rather than the number of bearings in a set.Vlcek et al. [28] established a simple algebraic relation for the upper and lower L 10 life limits considering the number of bearings failed and the limits are also plotted in Figure 7.
Te actual life of most bearings is much greater than the upper L 10 life as can be seen in Figure 7. 47 sets of bearings would result in lives that would statistically be no diferent than that of new bearings if subject to levels I-III rework.Te 4 sets of deep-groove ball bearings in the border can be subject to level IV rework to bring them into an acceptable range.Also, the life factors with the replaced loading zone are listed in Table 3. Te data in Table 3 show that the life factors of remanufactured bearing which subject to levels II-IV rework will be near 1 if we replace the loading zone in application.
Te resultant L 10 life should fall between the maximum and minimum values if the rework life is no diferent from the calculated life.If, however, the L 10 life is greater than the maximum variation L 10 life, then the true life is probably greater than the calculated.However, it can be found from Figure 7 that the actual L 10 of a large number of bearings is greater than the theoretical maximum L 10 .Tis indicates that the life of the bearing after remanufacturing may be greater than the theoretical life because the loading zone needs to be replaced when the bearing is reinstalled after remanufacturing.

Results and Discussion
Te life factors of remanufactured bearings whether the loading zone is replaced or not are shown in Figure 8. Te life factors according to diferent calculating methods and diferent fxed rings can be seen in Figure 8(a).Te life factors of the bearings without replacement of the loading zone are from reference [17], while the life factors' replacement of the loading zone is from this paper.Te deviation between the calculation method proposed in this paper and the active calculation method can be seen in Figure 8(b).According to the data comparison in the fgure, the following results are obtained: (1) With the increase of the remanufacturing level, the life factor of remanufacturing improves step by step regardless of whether the loading zone is replaced or not.Tis growth trend is determined by the classifcation method of remanufacturing.Te higher the remanufacturing level, the more stressed materials removed and the more new parts replaced, which has a positive impact on bearing life.(2) Regardless of whether the fxed ring is the inner ring or the outer ring, the bearing life factor after considering the replacement of the loading zone is higher than that obtained by the active calculation method.Tis is because after remanufacturing, the loading area needs to be replaced and the fxed ring is not stressed at this time, so its life should be the same as the life of the new ring.Tis is the most critical part of this paper and also the core theoretical content that is diferent from the existing research results.Considering that the bearing fatigue life after changing the loading zone is closer to the actual situation, the life factor calculation method proposed in this paper is better than the active calculation method.(3) Te life factors of remanufactured bearings with diferent fxed rings are also quite diferent when the loading zone is replaced.Te cause of this diference lies in the diference of the coincidence degree between the rings and the rolling element as analyzed in part 3.2.(5) For level I and II remanufactured bearings, whether to consider replacing the loading zone has a great impact on the bearing life, but for level III and IV remanufactured bearings, whether to consider replacing the loading zone has almost no impact on the bearing life because a large number of stress materials are removed, which has a positive impact on the bearing life.

Conclusion
(1) Te research object of this paper is radial bearing.For thrust bearings or thrust-radial bearings, the whole circumferential direction of both fxed and rotating rings is the loading zone, so the results of this paper are not applicable.(2) In this paper, the life of inner and outer raceways of bearings is assumed, and the life of the bearing system is calculated through this assumed life; thus, the life coefcient of remanufactured bearings is obtained.(3) Radial bearings are widely used in various rotating machinery, but there is a lack of research on the life of remanufactured bearings by replacing the loading zone, which leads to a huge deviation between the actual life and the theoretical life, which is not conducive to the application of bearings in engineering practice.Te research results of this paper are a supplement to the active calculation method of bearing life and can reduce the deviation between the actual life and the theoretical life of the bearing.Te research results of this paper are a supplement to the active calculation method of bearing life and can reduce the deviation between the actual life and the theoretical life of the bearing.

Recommendations and Future Directions
(1) Reference 14, reference 21, and this paper all calculate the bearing life factor by assuming the bearing life and metal removal rate, which lacks test verifcation.However, bearing life is a complicated statistical problem, and bearing researchers should verify their conclusions through experiments as much as possible.Te life curves of remanufactured bearings considering the replacement of load zones also need to be supplemented by life tests to facilitate practical engineering applications.(2) Raceway fatigue of rolling bearings (especially industrial bearings under heavy load conditions) is an unavoidable problem in its application practice, and it is also the root problem that causes the big diference between bearing remanufacturing and general remanufacturing.For heavy and large bearings, the material that needs to withstand the alternating periodic stress only accounts for a small part of the whole bearing material; if the raceway is separated from the bearing as a whole, it provides great convenience for the bearing remanufacturing.

Figure 3 :
Figure 3: Life curve of remanufactured rolling bearings with the replaced loading zone.

Figure 4 :
Figure 4: Contact form of ball bearing and roller bearing.(a) Point contact.(b) Line contact.

x2Figure 5 :
Figure 5: Schematic of normalized maximum shearing stress τ 45 as a function of normalized depth below the raceway surface showing the efect of metal removal in redistributing stress.

Table 1 :
Classifcation and details of bearing remanufacturing.

Table 2 :
Life factors of the remanufactured raceway with diferent reliability.

Table 3 :
Life factors of diferent remanufactured bearings.Te deviations between the life factors obtained by diferent calculation methods are volatile.As can be seen in Figure8(b), the biggest deviation in case studies is level II remanufacturing with the fxed outer ring, which is 11.3%.Te smallest deviation in case studies is level IV remanufacturing with fxed inner rings, which is 0.3%.Te mean deviation of various remanufacturing levels is 6.55%.Tis is the result of the combined efect of the remanufacturing level and the coincidence degree.