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1、<p><b> 軸承壽命分析</b></p><p><b> 摘 要</b></p><p> 自然界苛刻的工作條件會導(dǎo)致軸承的失效,但是如果遵循一些簡單的規(guī)則,軸承正常運轉(zhuǎn)的機會是能夠被提高的。在軸承的使用過程當(dāng)中,過分的忽視會導(dǎo)致軸承的過熱現(xiàn)象,也可能使軸承不能夠再被使用,甚至完全的破壞。但是一個被損壞的軸承,會留下它為什
2、么被損壞的線索。通過一些細(xì)致的觀察工作,我們可以采取行動來避免軸承的再次失效。</p><p> 關(guān)鍵詞:軸承 失效 壽命</p><p> 1 .軸承失效的原因</p><p> 軸承失效有以下多種原因,然而軸承的壽命實驗卻是所有機械實驗中最有意義的。實驗者必須控制實驗過程以確保結(jié)果。其他的失效模式在Tallian[19.2]中有詳細(xì)論述。下邊幾段就詳細(xì)論述
3、了可以影響壽命試驗結(jié)果的幾種失效模式。</p><p> 23章中,從EHL的觀點討論了潤滑條件對壽命試驗結(jié)果的影響,同時還有其他的潤滑條件會影響實驗的結(jié)論,首先是潤滑劑的接觸面積,受到軸承的尺寸,轉(zhuǎn)速,潤滑劑的流動性等因素的影響,潤滑劑在軸承表面形成的潤滑層的厚度一般小于0.05~0.5um,大于這個薄層厚度的固體微粒會殘留在接觸面上,從而劃傷潤滑溝道和軸承的滾動面。從而大大縮短軸承的耐用性。關(guān)于這點Sayl
4、es和MacPherson以及其他人都有詳細(xì)的論證。</p><p> 因此,為了確保實驗結(jié)果我們必須選用合適等級的潤滑劑。潤滑劑的選擇由工況決定,實驗時也如此。如果工況選擇的范圍不確定,就必須考慮到接觸面積對實驗結(jié)果的影響。</p><p> 23章中討論了不同的接觸面積對軸承失效壽命實驗結(jié)果的影響。</p><p> 潮氣是影響潤滑結(jié)果的另一個重要因素,長
5、時間在水中和油中被腐蝕不但對外觀質(zhì)量有影響,還會影響到滾動表面的軸承壽命。關(guān)于這點Fitch等人[19.7]有過論證。而且,即使是僅有50~100PPM(百萬分之一)的水汽含量也會產(chǎn)生有害影響,甚至產(chǎn)生表面看不出痕跡的腐蝕。這是由于軸承的溝道和滾動面之間會產(chǎn)生氫脆現(xiàn)象,從23章中也可以看出在潤滑實驗中濕氣是如此重要的一個因素。因此在軸承壽命的試驗結(jié)果中必須考慮到潮氣的影響。為了降低對壽命減少的影響,潮氣的含量最多不能超過40PPM。&l
6、t;/p><p> 潤滑劑的化學(xué)成分也是需要考慮的。大多數(shù)商業(yè)潤滑油包含許多為特定目的而開發(fā)的專有添加劑。例如,為了提高抗磨損性能,為了能達(dá)到極限壓力,或者耐熱性,還可以在邊際潤滑油膜的情況下提供邊界潤滑還能為邊界潤滑提供一個邊界潤滑層。這些添加劑同時也能即時的或者逐漸地影響滾動軸承的耐用性。為了避免添加劑成為加速壽命試驗的條件,我們必須小心以確保測試潤滑劑的添加劑不會受到惡化。為了保證同組產(chǎn)品壽命試驗的結(jié)果有連貫
7、性,最好在整個壽命試驗中都用同一供應(yīng)商的標(biāo)準(zhǔn)潤滑劑。</p><p> 為了得到一個合理的結(jié)果,統(tǒng)計學(xué)要求做很多組壽命試驗。因此一個軸承的壽命試驗需很長的時間。實驗人員必須保證整個實驗過程的連續(xù)性,由于任何微小的變化都會影響實驗結(jié)果,因此這個過程是很復(fù)雜的。甚至這些微小的變化在造成重大變化之前都不會被注意到。一旦發(fā)生這樣的情況,就沒機會補救了。只能在更好的控制條件下重新做實驗。</p><p
8、> 比如說:添加劑的穩(wěn)定性會影響到整個實驗的條件?,F(xiàn)在已經(jīng)知道了一些添加劑在長期使用時會造成大量的額外損耗。這些易退化的添加劑會影響軸承表面的潤滑條件,從而影響軸承的壽命。</p><p> 一般的對潤滑劑做化學(xué)檢測時是不會檢測添加劑的成分的。因此,如果一種潤滑劑用于長時間的軸承壽命實驗的話,生產(chǎn)者應(yīng)該定期更換實驗的樣品,比如一年一次。用來詳細(xì)評估潤滑劑的使用要求。</p><p&g
9、t; 實驗時還要控制的是適當(dāng)?shù)臏囟?。潤滑層(油膜)的厚度對溫度的影響是相?dāng)敏感的,大多數(shù)裝機實驗是在標(biāo)準(zhǔn)的工業(yè)環(huán)境下進(jìn)行的,在這一年實驗時間中環(huán)境溫度變化是非常大的。同時,個別軸承受溫度變化的影響是會影響到整個系統(tǒng)的常規(guī)的制造公差的。因此,所有軸承受溫度變化的影響會直接影響到壽命試驗數(shù)據(jù)的準(zhǔn)確性。因此為了保證實驗數(shù)據(jù)的連貫性,必須監(jiān)控并實時調(diào)節(jié)每個軸承的使用溫度。因此對于軸承壽命試驗時±3ºC的溫度公差被認(rèn)為是可接
10、受的。</p><p> 用于軸承壽命試驗的硬件裝備的磨損是另一個需要監(jiān)控的恒量。用于重載實驗的軸和軸承的內(nèi)圈都會受到很大的載荷。反復(fù)拆裝軸承會對軸的表面產(chǎn)生損害。這樣的改變會影響幾何形狀的。軸外徑和軸承內(nèi)徑都會受腐蝕的影響。腐蝕是由于震動產(chǎn)生的微粒被氧化而產(chǎn)生的。這樣也會減少軸承壽命試驗的時間。同時這樣的機構(gòu)也會在裝配面上產(chǎn)生重大的幾何形變,從而影響軸承內(nèi)徑,最終成為降低壽命的重要原因。</p>
11、<p> 軸承缺陷的檢測也是壽命試驗的重要考察因素。軸承缺陷最早是由原材料上的微小裂紋引起的。這樣的缺陷在實驗中是沒法檢測的。為了檢測這個缺陷就需要使這個缺陷遞增到能影響軸承參數(shù)的數(shù)量級別。比如說噪音,溫度,震動等缺陷。可以在系統(tǒng)中應(yīng)用這些技術(shù)方法來檢驗缺陷。而具有這樣能力的系統(tǒng)可以從早期就檢測出在多樣化工作條件復(fù)雜系統(tǒng)中用來測試用的缺陷軸承。而當(dāng)前還沒有一個單一的系統(tǒng)能檢測出所有的軸承缺陷。因此將來有必要選擇一種能在軸承
12、受到微小的傷害之前就停下機器的監(jiān)控系統(tǒng)。</p><p> 缺陷遞增的速率是相當(dāng)重要的。如果在實驗結(jié)束時缺陷的程度和理論計算出的是一致的,唯一的區(qū)別就是實驗中對缺陷的檢測總是落后于理論計算的。標(biāo)準(zhǔn)的軸承鋼在耐久性實驗中缺陷的遞增速度是相當(dāng)快的。而且這個遞增還不是主要因素,考慮到有代表性的耐久性實驗的數(shù)據(jù)都是經(jīng)統(tǒng)計學(xué)分析后得到的。有的也不一定,比如一些表面硬度不同的鋼材或是專為實驗用生產(chǎn)的鋼材。因此在分析結(jié)果的時
13、候就必須考慮是標(biāo)準(zhǔn)的軸承鋼還是專門的實驗用鋼材。</p><p> 耐久性實驗最后結(jié)果的有效性是由元素-金相分析驗證的。軸承會通過高倍光學(xué)顯微鏡,高倍電子掃描顯微鏡,高倍電子顯微鏡,化學(xué)元素分析等多種方法來分析。生產(chǎn)時出現(xiàn)的會導(dǎo)致缺陷的元素以及殘留在表面發(fā)生化學(xué)變化以后會導(dǎo)致缺陷的元素(如S,P等有害元素)等都會影響軸承的壽命。這些檢驗方法都是用來保證實驗得出的數(shù)據(jù)是真實有效的。Tallian將所有軸承失效的黑
14、白圖片匯編起來【19.8】,可以為判斷各種類型的失效提供依據(jù)。現(xiàn)在Tallian已經(jīng)將其更新為【19.9】,其中加入了彩色圖片。</p><p> 元素-金相實驗可以提供一個精確的證據(jù),使實驗結(jié)果處于可控制情況下,同時檢測有疑點和爭議的地方。當(dāng)軸承從試驗機上取下來的時候可以現(xiàn)做一個初步的研究,將會在30倍顯微鏡下觀察失效的部分。而正常的顯微圖片請看19.2~19.6中的圖片。、</p><p
15、> 圖19.2是球軸承溝道的表面失效圖片。圖19.3是滾子軸承溝道由于未校準(zhǔn)而造成表面開裂的圖片。圖19.4是一個球軸承由于外圈表面銹蝕而導(dǎo)致外圈開裂的圖片。圖19.5是表面凹陷殘骸的詳細(xì)圖片。圖19.6是一個由于熱變形造成的內(nèi)圈游隙變化的圖片。</p><p> 最后的4張圖片不是用正確的實驗方法得到的有效的失效模式。然而,這些錯誤的數(shù)據(jù)需要從有效的失效數(shù)據(jù)中剔除掉,從而得到能正確評估壽命試驗的有效數(shù)
16、據(jù)。</p><p> 2 .避免失效的方法</p><p> 解決軸承失效問題的最好辦法就是避免失效發(fā)生。這可以在選用過程中通過考慮關(guān)鍵性能特征來實現(xiàn)。這些特征包括噪聲、起動和運轉(zhuǎn)扭矩、剛性、非重復(fù)性振擺以及徑向和軸向間隙。</p><p> 扭矩要求是由潤滑劑、保持架、軸承圈質(zhì)量(彎曲部分的圓度和表面加工質(zhì)量)以及是否使用密封或遮護(hù)裝置來決定。潤滑劑的粘度
17、必須認(rèn)真加以選擇,因為不適宜的潤滑劑會產(chǎn)生過大的扭矩,這在小型軸承中尤其如此。另外,不同的潤滑劑的噪聲特性也不一樣。舉例來說,潤滑脂產(chǎn)生的噪聲比潤滑油大一些。因此,要根據(jù)不同的用途來選用潤滑劑。</p><p> 在軸承轉(zhuǎn)動過程中,如果內(nèi)圈和外圈之間存在一個隨機的偏心距,就會產(chǎn)生與凸輪運動非常相似的非重復(fù)性振擺(NRR)。保持架的尺寸誤差和軸承圈與滾珠的偏心都會引起NRR。和重復(fù)性振擺不同的是,NRR是沒有辦法
18、進(jìn)行補償?shù)摹?lt;/p><p> 在工業(yè)中一般是根據(jù)具體的應(yīng)用來選擇不同類型和精度等級的軸承。例如,當(dāng)要求振擺最小時,軸承的非重復(fù)性振擺不能超過0.3微米。同樣,機床主軸只能容許最小的振擺,以保證切削精度。因此在機床的應(yīng)用中應(yīng)該使用非重復(fù)性振擺較小的軸承。</p><p> 在許多工業(yè)產(chǎn)品中,污染是不可避免的,因此常用密封或遮護(hù)裝置來保護(hù)軸承,使其免受灰塵或臟物的侵蝕。但是,由于軸承內(nèi)外
19、圈的運動,使軸承的密封不可能達(dá)到完美的程度,因此潤滑油的泄漏和污染始終是一個未能解決的問題。</p><p> 一旦軸承受到污染,潤滑劑就要變質(zhì),運行噪聲也隨之變大。如果軸承過熱,它將會卡住。當(dāng)污染物處于滾珠和軸承圈之間時,其作用和金屬表面之間的磨粒一樣,會使軸承磨損。采用密封和遮護(hù)裝置來擋開臟物是控制污染的一種方法。</p><p> 噪聲是反映軸承質(zhì)量的一個指標(biāo)。軸承的性能可以用不
20、同的噪聲等級來表示。</p><p> 噪聲的分析是用安德遜計進(jìn)行的,該儀器在軸承生產(chǎn)中可用來控制質(zhì)量,也可對失效的軸承進(jìn)行分析。將一傳感器連接在軸承外圈上,而內(nèi)圈在心軸以1800r/min的轉(zhuǎn)速旋轉(zhuǎn)。測量噪聲的單位為anderons。即用um/rad表示的軸承位移。</p><p> 根據(jù)經(jīng)驗,觀察者可以根據(jù)聲音辨別出微小的缺陷。例如,灰塵產(chǎn)生的是不規(guī)則的噼啪聲;滾珠劃痕產(chǎn)生一種連續(xù)
21、的爆破聲,確定這種劃痕最困難;內(nèi)圈損傷通常產(chǎn)生連續(xù)的高頻噪聲,而外圈損傷則產(chǎn)生一種間歇的聲音。</p><p> 軸承缺陷可以通過其頻率特性進(jìn)一步加以鑒定。通常軸承缺陷被分為低、中、高三個波段。缺陷還可以根據(jù)軸承每轉(zhuǎn)動一周出現(xiàn)的不規(guī)則變化的次數(shù)加以鑒定。</p><p> 低頻噪聲是長波段不規(guī)則變化的結(jié)果。軸承每轉(zhuǎn)一周這種不規(guī)則變化可出現(xiàn)1.6~10次,它們是由各種干涉(例如軸承圈滾道
22、上的凹坑)引起的??刹煊X的凹坑是一種制造缺陷,它是在制造過程中由于多爪卡盤夾的太緊而形成的。</p><p> 中頻噪聲的特征是軸承每旋轉(zhuǎn)一周不規(guī)則變化出現(xiàn)10~60次。這種缺陷是由在軸承圈和滾珠的磨削加工中出現(xiàn)的振動引起的。軸承每旋轉(zhuǎn)一周高頻不規(guī)則變化出現(xiàn)60~300次,它表明軸承上存在著密集的振痕或大面積的粗糙不平。</p><p> 利用軸承的噪聲特性對軸承進(jìn)行分類,用戶除了可以
23、確定大多數(shù)廠商所使用的ABEC標(biāo)準(zhǔn)外,還可確定軸承的噪聲等級。ABEC標(biāo)準(zhǔn)只定義了諸如孔、外徑、振擺等尺寸公差。隨著ABEC級別的增加(從3增到9),公差逐漸變小。但ABEC等級并不能反映其他軸承特性,如軸承圈質(zhì)量、粗糙度、噪聲等。因此,噪聲等級的劃分有助于工業(yè)標(biāo)準(zhǔn)的改進(jìn)。</p><p> BEARING LIFE ANALYSIS</p><p><b> ABSTRAC
24、T</b></p><p> Nature works hard to destroy bearings, but their chances of survival can be improved by following a few simple guidelines. Extreme neglect in a bearing leads to overheating and possibly
25、seizure or, at worst, an explosion. But even a failed bearing leaves clues as to what went wrong. After a little detective work, action can be taken to avoid a repeat performance.</p><p> KEY WORDS: bearing
26、s, failures , life</p><p> 1 .WHY BEARINGS FAIL</p><p> An individual bearing may fail for several reasons; however, the results of an endurance test series are only meaningful when the test b
27、earings fail by fatigue-related mechanisms. The experimenter must control the test process to ensure that this occurs. Some of the other failure modes that can be experienced are discussed in detail by Tallian [19.2]. Th
28、e following paragraphs deal with a few specific failure types that can affect the conduct of a life test sequence.</p><p> In Chapter 23, the influence of lubrication on contact fatigue life is discussed fr
29、om the standpoint of EHL film generation. There are also other lubrication-related effects that can affect the outcome of the test series. The first is particulate contaminants in the lubricant. Depending on bearing size
30、, operating speed, and lubricant rheology, the overall thickness of the lubricant film developed at the rolling element-raceway contacts may fall between 0.05 and 0.5 m . Solid particles and damage</p><p>
31、Therefore, filtration of the lubricant to the desired level is necessary to ensure meaningful test result. The desired level is determined by the application which the testing purports to approximate. If this degree of f
32、iltration is not provided, effects of contamination must be considered when evaluating test results. Chapter 23 discusses the effect of various degrees of particulate contamination, and hence filtration, on bearing fatig
33、ue life.</p><p> The moisture content in the lubricant is another important consideration. It has long been apparent that quantities of free water in the oil cause corrosion of the rolling contact surfaces
34、and thus have a detrimental effect on bearing life. It has been further shown by Fitch [19.7] and others, however, that water levels as low as 50-100 parts per million(ppm) may also have a detrimental effect, even with n
35、o evidence of corrosion. This is due to hydrogen embrittlement of the rolling element and r</p><p> The chemical composition of the test lubricant also requires consideration. Most commercial lubricants con
36、tain a number of proprietary additives developed for specific purposes; for example, to provide antiwear properties, to achieve extreme pressure and/or thermal stability, and to provide boundary lubrication in case of ma
37、rginal lubricant films. These additives can also affect the endurance of rolling bearings, either immediately or after experiencing time-related degradation. Care must be tak</p><p> The statistical nature
38、of rolling contact fatigue requires many test samples to obtain a reasonable estimate of life. A bearing life test sequence thus needs a long time. A major job of the experimentalist is to ensure the consistency of the a
39、pplied test conditions throughout the entire test period. This process is not simple because subtle changes can occur during the test period. Such changes might be overlooked until their effects become major. At that tim
40、e it is often too late to salvage the</p><p> For example, the stability of the additive packages in a test lubricant can be a source of changing test conditions. Some lubricants have been known to suffer a
41、dditive depletion after an extended period of operation. The degradation of the additive package can alter the EHL conditions in the rolling content, altering bearing life. Generally, the normal chemical tests used to ev
42、aluate lubricants do not determine the conditions of the additive content. Therefore if a lubricant is used for enduranc</p><p> Adequate temperature controls must also be employed during the test. The thic
43、kness of the EHL film is sensitive to the contact temperature. Most test machines are located in standard industrial environments where rather wide fluctuations in ambient temperature are experienced over a period of a y
44、ear. In addition, the heat generation rates of individual bearings can vary as a result of the combined effects of normal manufacturing tolerances. Both of these conditions produce variations in operatin</p><p
45、> The deterioration of the condition of the mounting hardware used with the bearings is another area requiring constant monitoring. The heavy loads used for life testing require heavy interference fits between the be
46、aring inner rings and shafts. Repeated mounting and dismounting of bearings can produce damage to the shaft surface, which in turn can alter the geometry of a mounted ring. The shaft surface and the bore of the housing a
47、re also subject to deterioration from fretting corrosion. Fretting</p><p> The detection of bearing failure is also a major consideration in a life test series. The fatigue theory considers failure as the i
48、nitiation of the first crack in the bulk material. Obviously there is no way to detect this occurrence in practice. To be detectable the crack must propagate to the surface and produce a spall of sufficient magnitude to
49、produce a marked effect on an operating parameter of the bearing: for example, noise, vibration, and/or temperature. Techniques exit for detecting fa</p><p> The rate of failure propagation is therefore imp
50、ortant. If the degree of damage at test termination is consistent among test elements, the only variation between the experimental and theoretical lives is the lag in failure detection. In standard through-hardened beari
51、ng steels the failure propagation rate is quite rapid under endurance test conditions, and this is not a major factor, considering the typical dispersion of endurance test data and the degree of confidence obtained from
52、statistical </p><p> The ultimate means of ensuring that an endurance test series was adequately controlled is the conduct of a post-test analysis. This detailed examination of all the tested bearings uses
53、high-magnification optical inspection, higher-magnification scanning electron microscopy, metallurgical and dimensional examinations, and chemical evaluations as required. The characteristics of the failures are examine
54、d to establish their origins and the residual surface conditions are evaluated for indications </p><p> The post-test analysis is, by definition, after the fact. To provide control throughout the test serie
55、s and to eliminate all questionable areas, the experimenter should conduct a preliminary study whenever a bearing is removed from the test machine. In this portion of the investigation each bearing is examined optically
56、at magnifications up to 30 for indications of improper or out-of-control test parameters. Examples of the types of indications that can be observed are given in Figs. 19.2-19.6.</p><p> Figure 19.2 illustra
57、tes the appearance of a typical fatigue-originated spall on a ball bearing raceway. Figure 19.3 contains a spalling failure on the raceway of a roller bearing that resulted from bearing misalignment, and Fig. 19.4 contai
58、ns a spalling failure on the outer ring of a ball bearing produced by fretting corrosion on the outer diameter. Figure 19.5 illustrates a more subtle form of test alteration, `where the spalling failure originated from t
59、he presence of a debris dent on the surf</p><p> The last four failures are not valid fatigue spalls and indicate the need to correct the test methods. Furthermore, these data points would need to be elimin
60、ated from the failure data to obtain a valid estimate of the experimental bearing life.</p><p> 2 .AVOIDING FAILURES</p><p> The best way to handle bearing failures is to avoid them.This can b
61、e done in the selection process by recognizing critical performance characteristics.These include noise,starting and running torque,stiffness,non-repetitive run out,and radial and axial play.In some applications, these i
62、tems are so critical that specifying an ABEC level alone is not sufficient.</p><p> Torque requirements are determined by the lubricant,retainer,raceway quality(roundness cross curvature and surface finish)
63、,and whether seals or shields are used.Lubricant viscosity must be selected carefully because inappropriate lubricant,especially in miniature bearings,causes excessive torque.Also,different lubricants have varying noise
64、characteristics that should be matched to the application. For example,greases produce more noise than oil.</p><p> Non-repetitive run out(NRR)occurs during rotation as a random eccentricity between the inn
65、er and outer races,much like a cam action.NRR can be caused by retainer tolerance or eccentricities of the raceways and balls.Unlike repetitive run out, no compensation can be made for NRR.</p><p> NRR is r
66、eflected in the cost of the bearing.It is common in the industry to provide different bearing types and grades for specific applications.For example,a bearing with an NRR of less than 0.3um is used when minimal run out i
67、s needed,such as in disk—drive spindle motors.Similarly,machine—tool spindles tolerate only minimal deflections to maintain precision cuts.Consequently, bearings are manufactured with low NRR just for machine-tool applic
68、ations.</p><p> Contamination is unavoidable in many industrial products,and shields and seals are commonly used to protect bearings from dust and dirt.However,a perfect bearing seal is not possible because
69、 of the movement between inner and outer races.Consequently,lubrication migration and contamination are always problems.</p><p> Once a bearing is contaminated, its lubricant deteriorates and operation beco
70、mes noisier.If it overheats,the bearing can seize.At the very least,contamination causes wear as it works between balls and the raceway,becoming imbedded in the races and acting as an abrasive between metal surfaces.Fend
71、ing off dirt with seals and shields illustrates some methods for controlling contamination.</p><p> Noise is as an indicator of bearing quality.Various noise grades have been developed to classify bearing p
72、erformance capabilities.</p><p> Noise analysis is done with an Ander-on-meter, which is used for quality control in bearing production and also when failed bearings are returned for analysis. A transducer
73、is attached to the outer ring and the inner race is turned at 1,800rpm on an air spindle. Noise is measured in andirons, which represent ball displacement in μm/rad.</p><p> With experience, inspectors can
74、identify the smallest flaw from their sound. Dust, for example, makes an irregular crackling. Ball scratches make a consistent popping and are the most difficult to identify. Inner-race damage is normally a constant high
75、-pitched noise, while a damaged outer race makes an intermittent sound as it rotates.</p><p> Bearing defects are further identified by their frequencies. Generally, defects are separated into low, medium,
76、and high wavelengths. Defects are also referenced to the number of irregularities per revolution.</p><p> Low-band noise is the effect of long-wavelength irregularities that occur about 1.6 to 10 times per
77、revolution. These are caused by a variety of inconsistencies, such as pockets in the race. Detectable pockets are manufacturing flaws and result when the race is mounted too tightly in multiple jaw chucks.</p><
78、;p> Medium-hand noise is characterized by irregularities that occur 10 to 60 times per revolution. It is caused by vibration in the grinding operation that produces balls and raceways. High-hand irregularities occur
79、at 60 to 300 times per revolution and indicate closely spaced chatter marks or widely spaced, rough irregularities.</p><p> Classifying bearings by their noise characteristics allows users to specify a nois
80、e grade in addition to the ABEC standards used by most manufacturers. ABEC defines physical tolerances such as bore, outer diameter, and run out. As the ABEC class number increase (from 3 to 9), tolerances are tightened.
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