提升機(jī)制動系統(tǒng)(液壓盤式制動器)設(shè)計(jì)
提升機(jī)制動系統(tǒng)(液壓盤式制動器)設(shè)計(jì),提升機(jī)制動系統(tǒng)(液壓盤式制動器)設(shè)計(jì),提升,晉升,機(jī)制,系統(tǒng),液壓,制動器,設(shè)計(jì)
河南理工大學(xué)萬方科技學(xué)院
萬方科技學(xué)院
本科畢業(yè)論文（英文翻譯）
院（系部） 機(jī)械與動力工程系
專業(yè)名稱 機(jī)械設(shè)計(jì)制造及自動化
年級班級 2008級機(jī)制04班
學(xué)生名稱 高 金 濤
指導(dǎo)老師 張 躍 敏
Reflections regarding uncertainty of measurement, on the results of a Nordic fatigue test interlaboratory comparison
Magnus Holmgren, Thomas Svensson, Erland Johnson, Klas Johansson
Abstract This paper presents the experiences of calculation and reporting uncertainty of measurement in fatigue testing. Six Nordic laboratories performed fatigue tests on steel specimens. The laboratories also reported their results concerning uncertainty of measurement and how they calculated it. The results show large differences in the way the uncertainties of measurement were calculated and reported. No laboratory included the most significant uncertainty source, bending stress (due to misalignment of the testing machine, “incorrect” specimens and/or incorrectly mounted specimens), when calculating the uncertainty of measurement. Several laboratories did not calculate the uncertainty of measurement in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM) [1].
Keyword Uncertainty of measurement, Calculation, Report, Fatigue test, Laboratory intercomparison
Definitions R Stress ratio Fmin/Fmax · F Force (nektons) · A and B Fatigue strength parameters · s and S Stress (megapascals) · N Number of cycles.
Introduction
The correct or best method of calculating and reporting uncertainty of measurement in testing has been the subject of discussion for many years. The issue became even more relevant in connection with the introduction of ISO standards, e.g. ISO17025 [2]. The discussion, as well as implementation of the uncertainty of measurement concept, has often been concentrated on which equation to use or on administrative handling of the issue. There has been less interest in the technical problem and how to handle uncertainty of measurement in the actual experimental situation, and how to learn from the uncertainty of measurement calculation when improving the experimental technique. One reason for this may be that the accreditation bodies have concentrated on the very existence of uncertainty of measurement calculations for an accredited test method, instead of on whether the calculations are performed in a sound technical way. The present investigation emphasizes the need for a more technical focus.
One testing area where it is difficult to do uncertainty of measurement calculations is fatigue testing. However, there is guidance on how to perform such calculations, e.g. in Refs. [3, 4]. To investigate how uncertainty of measurement calculations are performed for fatigue tests in real life, UTMIS (the Swedish fatigue network) started an interlaboratory comparison where one of the most essential parts was to calculate and report the uncertainty of measurement of a typical fatigue test that could have been ordered by a customer of the participating laboratories. For cost reasons, customers often ask for a limited number of test specimens but, at the same time, they request a lot of information about a large portion of the possible stress-life area [from few cycles (high stresses) to millions of cycles (low stresses) and even run-outs]. The way the calculation was made should also be reported. The outcome concerning the uncertainty of measurement from the project is reported in this article.
Participants
Six Nordic laboratories participated in the interlaboratory comparison: one industrial laboratory, two research institutes, two university laboratories and one laboratory in a consultancy company. Two of the laboratories are accredited for fatigue testing, and a third laboratory is accredited for other tests. Each participant was randomly assigned a number between 1 and 6, and this notification will be used in the rest of this paper.
Experimental procedure
The participants received information about the test specimens (without material data), together with instructions on the way to perform the test and how to report the results.
The instructions were that tests should be performed as constant load amplitude tests, with R=0.1 at three different stress levels, 460, 430 and 400 Map, with four specimens at each stress level, at a test frequency between 10 and 30 Hz, with a run-out limit at cycles and in a normal laboratory climate ( and relative humidity). This was considered as a typical customer ordered test.
The test results were to be used to calculate estimates of the two fatigue strength parameters, A and B, according to linear regression of the logs and long variables, i.e.. The reported result should include both the estimated parameters A and B and the uncertainties in them due to measurement errors. The report should also include the considerations and calculations behind the results, especially those concerning uncertainty of measurement.
Several properties were to be reported for each specimen. The most important one was the number of cycles until fracture or if the specimen was a run-out (i.e. survived for cycles).
The tests were to be performed in accordance with ASTM E-466–96 [5] and ISO5725-2 [6]. ASTM E-466-96 does not take uncertainty of measurement into account;
However, ASTM E-466-96 mentions that the bending stress introduced owing to misalignment must not exceed 5% of the greater of the range, maximum or minimum stresses. There are also requirements for the accuracy of the dimensional measurement of the test specimen.
All participants used hydraulic testing machines. The test specimens were made of steel (yield stress 375–390 Map, and tensile strength 670–690 Map, tabulated values). The test specimens were distributed to the participants by the organizer.
Results
The primary laboratory results that should be compared are the estimated Whaler curves. In order to present all results in the same way, the organizer transformed some of the results. The Whaler curves reported by the participants are shown in Fig. 1.
It can be seen that there are considerable differences between laboratories. An approximate statistical test shows a significant laboratory effect. Material scatter alone cannot explain the differences in the Whaler curves.
In order to investigate if the laboratory effect was solely caused by the modeling uncertainty, we estimated new parameters from the raw data with a common algorithm. We then chose to use only the failed specimens and to make the minimization in the logarithmic life direction. The results are shown in Fig. 2. A formal statistical significance test was then made, and the result of such a test shows that the differences between the laboratories shown in Fig. 1 could be attributed only to modeling.
Uncertainty of measurement calculations
One of the most important objectives with this investigation was to compare the observed differences between laboratory test results with their estimated uncertainties of measurement. The intention was to analyze the uncertainty analyses as such, and to compare them to the standard procedure recommended in the ISO guide: Guide to the Expression of Uncertainty in Measurement (GUM) [1].
The laboratories identified different sources of uncertainty and treated them in different ways. These sources are the load measurement, the load control, the superimposed bending stresses because of misalignment and the dimensional measurements. Implicitly, laboratory temperature and humidity, specimen temperature and corrosion effects are also considered. In addition, the results show a modeling effect. The different laboratory treatments of these sources are summarized in Table 1.
Specific comments on the different laboratories
All laboratories gave their laboratory temperature and humidity, but did not consider these values as sources of uncertainty, i.e. the influence of temperature and humidity was neglected. This conclusion is reasonable for steel in the temperature range and humidity range in question [7].
Laboratory 1. The uncertainty due to the applied stress was determined taking load cell and dimensional uncertainties into account. The mathematical evaluation was made in accordance with the GUM. Specimen temperature was measured, but was implicitly neglected. The modeling problem was mentioned, but not considered as an uncertainty source. Laboratory 2. The report contains no uncertainty evaluation. The uncertainties in the load cell and the micrometer are considered, but neglected with reference to the large material scatter. Specimen temperature was measured. Modeling problems are mentioned by a comment regarding the choice of load levels.
Laboratory 3. The report contains no uncertainty evaluation. However, the accuracy of the machine is given and the load was controlled during the tests to be within specified limits. The bending stresses were measured on one specimen, but their influence on the fatigue result was not taken into consideration. Laboratory 4. The uncertainties in the load cell and the dimensional measurements are considered in an evaluation of stress uncertainty. The method for the evaluation is not in accordance with the GUM method, but was performed by adding absolute errors. The bending stress influence and the control system deviations are considered, but not included in the uncertainty evaluation. The failure criterion is mentioned and regarded as negligible, and corrosion is mentioned as a possible source of uncertainty. Laboratory 5. Uncertainties in the load cell and the load control were considered, and the laboratory stated in the report that the evaluation of the load uncertainty was performed according to the CIPM method. Laboratory 6. No report was provided, but only experimental results and a Whaler curve estimate.
No laboratory reported the uncertainty in the estimated material properties, the Whaler parameters, but at most the uncertainty in the applied stress. The overall picture of the uncertainty considerations is that only uncertainty sources that are possible to estimate from calibration reports were taken into account in the final evaluation.
Fig. 1 All experimental results and estimated Whole curves from the different laboratories
Number of cycles to failure
One important source that several laboratories mentioned is the bending stresses induced by misalignment in the testing machine, incorrectly mounted test specimens or “incorrect” specimens. The amount of bending stress was also estimated in some cases, but its influence on the uncertainty in the final Whole curve was not investigated.
The results from this experimental investigation show that there are different ways of determining the Whole curve from the experimental result. One problem is the surviving specimens, the run-out results. Four laboratories used only the failed specimens’ results for the curve-fit, one laboratory neglected all results at the lowest level, and one laboratory included the run-outs in the estimation. Another problem is the mathematical procedure for estimating the curve. Common practice, and the recommendation in the ASTM standard, is that the curve should be estimated by minimizing the squared errors in log life, i.e. the statistical model is
, (1)
Where e is a random error, assumed to have constant variance, and where log stands for the logarithm with base 10. E can be interpreted as the combination of at least two types of errors: namely (1) a random error due to the scatter in the material properties, and (2) a measurement error due to uncertainties in the measurement procedures.
Fig. 2 All experimental results and estimated Whole curves using the common procedure
Number of cycles to failure
Table 1 Sources of uncertainty and laboratory treatment
C The laboratory report considers the source explicitly or implicitly, N the laboratory report neglects the source, A the laboratory report takes the source into account in the uncertainty of measurement calculation
Where e is a random error, assumed to have constant variance, and where log stands for the logarithm with base 10. E can be interpreted as the combination of at least two types of errors: namely (1) a random error due to the scatter in the material properties, and (2) a measurement error due to uncertainties in the measurement procedures. Stress was minimized, which led to a model discrepancy as discussed in the following.
Discussion
Experimental results
Most laboratories performed estimations of the Whaler curve parameters. Visual comparison of their estimated curves suggests differences, and a statistical test verified the conclusion that there is a statistically significant laboratory effect. A closer study of each participant’s procedure for determining the Whaler curve shows that the differences seem to be caused by different modeling of the curve.
Since the test was intended to simulate a customer ordered test, some specific problems occurred. First, the number of test specimens is limited and therefore one should be careful when drawing conclusions from the results, since the scatter is considerable in fatigue and the number of specimens are limited.
Another problem that occurred was that, since run-outs were wanted, two different failure criteria (failure mechanisms) were used to halt the test: fracture of the test specimen or cycles. In the latter case, the use of the equation may cause problems, see later.
The investigator then looked at whether any laboratory differences remained after excluding the model interpretation effects. This was accomplished in two ways:
Namely, firstly by direct comparison of the experimental fatigue lives obtained, and secondly by using the same estimating procedure on all data sets. This therefore tested whether any laboratory differences remained or not. The first comparison was done on the two higher load levels. For these, no statistically significant differences were found. The second comparison, which included the failures
On the lowest level, verified the result. Since the variation between laboratories is larger than the variation within a laboratory no statistically significant variation within a laboratory can be distinguished from the total
Variation in material.
The conclusion is that no systematic errors in measurements were detected, but different modeling techniques give significant differences in the results. This in fact indicates that when different fitting models are used different quantities are measured even though they have the same name. Before any agreement is reached about the way of reporting fatigue data, it is of utmost importance that the modeling procedure is clearly defined in the test report. It is very important for the laboratories’ customers to be aware of this fact and, when requesting a test, to ask for a preferred modeling procedure as well as to be aware of the modeling procedure used by the laboratory when using fatigue data in design.
Uncertainty evaluation
All laboratories made some considerations regarding the uncertainties of measurement. However, none of them evaluated uncertainties for the resulting Whole parameters, but only for the applied stress. However, none of the measurement uncertainties reported are unrealistic considering the factors taken into account, this is based inexperience. Since the specimens were destroyed during the tests it is not possible to separate the material variation from the repeatability. An estimate of the combined measurement uncertainty and the variation in material is
About 30% of the lifetime and the major contribution are from the material variation and therefore one conclusion is that the measurement uncertainty in this test could be neglected during this test. This is not true for all fatigue tests and it is therefore anyhow interesting to study how the participants treated measurement uncertainty.
Only one participant used the method recommended by the ISO guide GUM. This is surprising, since European accreditation authorities have recommended the GUM for several years. Among the uncertainty sources that were identified by the laboratories, only load cell measurement uncertainties and dimensional measurement uncertainties were taken into account. Important sources such as misalignment and load control were identified by some participants but were not included in the evaluation of stress uncertainty. Apparently only calibrated devices were considered for the overall uncertainty, and other sources, more difficult to evaluate, were excluded. No motivation for these exclusions can be found in the reports.
One participant rejected the uncertainty evaluation with reference to the large scatter in fatigue lives. Our overall conclusion from the laboratory comparisons, that there are no detectable systematic effects, may be seen as verification of this rejection, but it is questionable if this was an obvious result beforehand. In contrast, for instance, uncertainties due to misalignment are not obviously negligible in comparison with the material scatter, and should be considered in an uncertainty analysis.
This investigation, together with other observations [8, 9], shows problems with the introduction of the ISO17025 requirement for uncertainty of measurement statements. The reasons for this may be that the uncertainty of measurement discussion during recent years has concentrated very much on which equation to use and on administrative aspects, e.g. whether the uncertainty of measurement should always be reported directly in the report, or only when the customer requests it, etc., instead of on the ‘real’ technical issues. Hopefully, the introduction of the pragmatic ILAC-G17:2002, a document about the introduction of the concept of uncertainty of measurement in association with testing [10], will improve the situation.
Conclusions
The way to define, calculate, and interpret uncertainty of measurement and to use it in Whaler-curve determination is poorly understood among the participants, in spite of the fact that they consist of a group with significant experience
Of fatigue testing, and that some of them were also accredited for fatigue tests. An important overall tendency is that the laboratories only include uncertainty
Sources that are easily obtained, e.g. from calibrated gauges where calibration certificates exist.
關(guān)于北歐的疲勞實(shí)驗(yàn)室的比較—測量結(jié)果不確定值的反映
摘要：這篇論文介紹了關(guān)于疲勞檢測的不確定性的計(jì)算和報(bào)告的實(shí)驗(yàn)。6個(gè)北歐實(shí)驗(yàn)室對鋼性元件進(jìn)行了疲勞實(shí)驗(yàn)，他們也報(bào)告了疲勞測量不確定性的結(jié)果和計(jì)算方法。實(shí)驗(yàn)結(jié)果表明大量的測量不確定性結(jié)果是可以計(jì)算和報(bào)告的。沒有實(shí)驗(yàn)室包括最重要的不確定源，當(dāng)它們進(jìn)行不確定值的計(jì)算時(shí)，有幾個(gè)實(shí)驗(yàn)室沒有計(jì)算符合從指導(dǎo)到結(jié)果的測量的不確定性值。
關(guān)鍵詞：測量，計(jì)算，不確定性報(bào)告，疲勞測試，聯(lián)合實(shí)驗(yàn)室
介紹：計(jì)算和報(bào)告測量的不確定性值的最好或者正確的方法一直是許多年來討論的問題,隨著ISO(例如ISO17025)的引進(jìn)這個(gè)問題更加突出。關(guān)于測量的不確定性值的討論和鑒定與這個(gè)問題息息相關(guān)。在發(fā)展實(shí)驗(yàn)技術(shù)的時(shí)候已經(jīng)有很少人對技術(shù)問題和在實(shí)驗(yàn)條件下如何處理測量的不確定性值和如何從測量的不確定性值可以學(xué)到什么感興趣了。這種現(xiàn)象可能的一個(gè)原因是合格的物體已經(jīng)集中在用精確的方法計(jì)算測量的不確定性值上，而不是集中在用這種方法是不是合理的問題上了。目前的方法集中在一種更加科學(xué)的方法上。
對測量的不確定性值計(jì)算比較困難的一個(gè)領(lǐng)域是疲勞測量。但是，對于這樣的計(jì)算有一個(gè)指導(dǎo)，研究如何確定測量不確定性值的方法是研究現(xiàn)實(shí)生活中物體的疲勞檢測。瑞典疲勞網(wǎng)站開設(shè)了一家聯(lián)合實(shí)驗(yàn)室公司，它的最重要的一部分就是計(jì)算和報(bào)告重要疲勞實(shí)驗(yàn)的不確定性值，這些實(shí)驗(yàn)是由實(shí)驗(yàn)室的參與者進(jìn)行的。最重要的原因是顧客們索要有限個(gè)測量模型，同時(shí)，他們也需要大量的信息。所用的計(jì)算方法也要報(bào)告，關(guān)于工程測量的不確定性值的結(jié)果也在這篇文章中報(bào)告。
六個(gè)北歐的實(shí)驗(yàn)室都參加了這個(gè)聯(lián)合實(shí)驗(yàn)室，一個(gè)工業(yè)實(shí)驗(yàn)室，兩個(gè)研究院，兩個(gè)大學(xué)實(shí)驗(yàn)室，一個(gè)咨詢公司實(shí)驗(yàn)室。其中兩個(gè)實(shí)驗(yàn)室研究疲勞實(shí)驗(yàn)，第三個(gè)研究其他的實(shí)驗(yàn)，每個(gè)參與者被隨意指派1—6的編號，這個(gè)報(bào)告被用在這篇文章的其他部分。
實(shí)驗(yàn)程序：
參與者收到了沒有數(shù)據(jù)的材料模型，及其如何進(jìn)行測量和如何報(bào)告結(jié)果的信息。要求是在固定載荷下進(jìn)行多次實(shí)驗(yàn)，用半徑為1mm的在三種壓力（460，430，400MP）下，每種壓力下都進(jìn)行試驗(yàn)的4種模型，頻率在10---30Hz之間，在室溫下旋轉(zhuǎn)5百萬轉(zhuǎn)。這就是客戶要求的測量。
這種測量結(jié)果被用來計(jì)算兩個(gè)物體的疲勞增長的參數(shù)，A和B,和由于測量錯(cuò)誤而引起的不確定性值，報(bào)告的結(jié)果應(yīng)該包括A和B的結(jié)果和這種不確定性值，在結(jié)果的后面尤其是這些不確定性值每個(gè)模型的這幾種特性都應(yīng)該報(bào)告。最重要的是模型達(dá)到疲勞時(shí)的周期數(shù)，或者是模型報(bào)廢的周期數(shù)。做這個(gè)測量時(shí)ASTM E-466-96、ISO-5725-2.、ASTM E-466-96并沒有考慮到測量的不確定性值，由于誤差不能超過最大和最小值的范圍的百分之五，所以，ASTM-466-96參照彎曲壓力，對模型的測量也有一些精度要求。所有的參加者都用液壓疲勞機(jī)，測量模型是由鋼制成的，它的表面的壓力范圍是375-390Mp,拉伸力壓強(qiáng)的范圍是670-690Mp.測量模型由組織者分發(fā)給參加者。
結(jié)果：
為了用同一種方法表示出所有的結(jié)果，初級實(shí)驗(yàn)結(jié)果應(yīng)該用Whole表格來進(jìn)行比較，參與者報(bào)告的Whole表格見圖1。它顯示了各實(shí)驗(yàn)室之間的顯著的差別。一個(gè)大概統(tǒng)計(jì)的實(shí)驗(yàn)結(jié)果表明了各實(shí)驗(yàn)室的顯著差別，分散的材料不能單獨(dú)解釋W(xué)hole表格的區(qū)別，為了研究各實(shí)驗(yàn)室的差別是否是因?yàn)槟Ｐ偷牟淮_定造成的，我們比較了由原始數(shù)據(jù)得出的新數(shù)據(jù)，當(dāng)我們使用那些不合格的模型時(shí)，對結(jié)果進(jìn)行對數(shù)運(yùn)算后，結(jié)果如2圖所示。以前的統(tǒng)計(jì)結(jié)果和這次的結(jié)果比較可得結(jié)果如圖1所示。
測量計(jì)算得不確定性
這個(gè)研究的重要過程之一就是比較各實(shí)驗(yàn)室之間的估計(jì)的測量不確定性的差別。目的就是分析測量的不確定性，參照ISO標(biāo)準(zhǔn)比較他們的制造水平，
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