Detection of Fault in Rolling Element Bearing using Condition Monitoring by Experimental Approach

Transcription

1 Detection o Fault in Rolling Element Bearing using Condition Monitoring by Experimental Approach Sakshi Kokil (1) Mechanical Dept NBN Sinhgad School o Engineering Pune (M.S.), India. Assist. Pro. M. M. Shah Mechanical Department BRACT s VIT college Pune (M.S.), India. (3) (2) Pro. S. Y. Gajjal Mechanical Department NBN Sinhgad School o Engineering. Pune (M.S.), India. Pro. S. D. Kokil (4) Mechanical Dept SSVPS Polytechnic Dhule (M.S.), India Abstract Rolling element bearings are requently encountered in rotating machine due to their load carrying capacity and low riction characteristics. The complexity o loading mechanism in bearing shows its eect in the orm o distributed and local deects. Deects in bearing causes catastrophic ailure and Hertzian contact stresses, which increases the vibration level in the machine. Eicient unctioning o machine critically depends on good health o employed rolling bearings. Hence, health monitoring o rolling element bearing through their vibration responses is a vital issue. There are various techniques or vibration analysis such as wear debris analysis, oil analysis, temperature method and condition monitoring. Most o the work attempted in various papers was condition monitoring done by time domain and requency domain method. Some o the work ocused on time domain analysis, they compared stastical parameters o time domain signals with shat speeds. In ew papers the work ocused on characteristic ault requency o bearing in requency domain analysis. In this dissertation work an experimental test rig is built to acquire vibration levels o deective bearing and also the requency domain analysis is carried out by FFT analyzer to compare the vibration amplitudes on characteristic ault requency o bearing. The eect o rotational speed, deect position and load on the diagnostics o rolling element bearing deects is investigated. Vibration signatures o these parameters are compared and sensitivity o vibration analysis is studied. Overall vibration increases in presence o local deects and dynamic radial loads. Keywords Condition monitoring, rolling element bearing, requency domain analysis. I. INTRODUCTION Fault detection o the rolling element bearing, has been gaining importance in recent years because o its detrimental inluence on the reliability o the machines. Vibration signature analysis is the most commonly used in aultdetection technique employed in bearing systems. Detection o the ault and its severity are two important steps or eatures o a condition monitoring system. Lie o a machine component is determined by the severity o the ault in bearing. It is crucial, especially in critical systems, where continuous operation is generally unavoidable. In industrial applications, these bearings are considered as critical mechanical components and a deect in such a bearing causes malunction and even lead to catastrophic ailure o the machinery. Deects in bearings may arise during use or during the manuacturing process such as crack damage, spalling, corrosion, atigue ailure, etc. Thereore detection o these deects is important or condition monitoring as well as quality inspection o bearings. Bearing deects are classiied into localized and distributed. The localized deects include cracks, pits and spalls caused by atigue on rolling suraces. The other categories o distributed deects include surace roughness, waviness, and misaligned races and o size rolling elements. These deects may result rom manuacturing error and abrasive wear. Vibration monitoring o rolling element bearing is done by generally condition monitoring. Because condition monitoring is versatile technique, can detect almost all source o vibration. It includes use o FFT analyzer. Many researchers contributed in condition monitoring area. By reviewing some o research papers it was ound that vibration analysis can be done by numerical and experimental approach. Mao Kunli, Wu Yunxin [1] ocused on experimental approach to signal analysis. It describes the use o vibration measurements by a periodic monitoring system or monitoring the condition o rolling element bearing o the centriugal machine. This paper proposed basic method o vibration diagnosis upon rolling bearing as requency analysis. Dierent deect position such as outer race, inner race and ball has its corresponding ault characteristic requency. Experimental set up consisted o motor driven shat. That shat was supported by two support bearing and one test bearing. Rotor was placed on motor driven shat. Accelerometer to measure 859

2 vibration signals were mounted at 4 dierent positions. Output o accelerometer sent to data acquisition system (DAQ). FFT analyzer processes data rom DAQ in requency domain. Bearing with deect present on outer race was analyzed. Graphs were plotted in requency domain. Ater analysis o graph and comparing it with theoretical outer race pass requency, peaks were observed. So vibration analysis can be able to detect location o ault. Using vibration diagnosis, such common bearing aults as crushing, crack, indentation, wear can be detected eectively. When ball passes through deect creates impact signal. By this impact source o ault can be detected. Bearing race pass requency calculated by theoretical ormula. K. Yavanarani1, G. S. Simon Sundara Raj[2] proposed wavelet-based vibration analysis or deense applications. Vibration signal recording was carried out on bearings o MSL engine test bed. The Integrated Circuit Piezoelectric (ICP) accelerometer was used to record data related bearing. Experimental set up consisted eight accelerometers (ive uni-axial and three tri-axial) possessing high sensitivity and wide range o measurement. The Discrete Wavelet Transorm (DWT) o the vibration signal computed using the Fast Wavelet Transorm (FWT). Time domain and requency domain data were recorded and compared. The Spectral Analysis using FFT provides inormation about the requency content o the raw data but ails to provide time localization o the spectral components. So to overcome this drawback short term Fourier transorm (STFT) and wavelet transorm was employed and ound that it can clearly detect multi resolution deect. Paper reported, it is possible to diagnose the state o operation or the evolution o aults in the bearing by observing the amplitudes o vibration and the requency spectrum under dierent loading conditions. Pro. Dr. Zahari Taha, Nguyen Trung Dung[3] did signal analysis o single point deect by inite element analysis. To monitor the condition o a bearing, a SKF 1206 ETN9 sel-aligning ball bearing is used in this study. The inite element method is adopted to observe the dynamic response o the structure. The housing and outer raceway structures are discredited into and node linear tetrahedron elements, respectively. The experimental setup consisted o lathe spindle on which test bearing was mounted. A deect is created intentionally on the outer raceway o the bearing with the size o 2 mm in diameter and depth using Electrical Discharge Machining (EDM). Accelerometer was mounted on test bearing and output signal given to DAQ system. Signals recorded in time and requency domain analysis. I there is a peak at outer race pass requency, it can be concluded that there is a deect on the outer raceway o the bearing. It is observed that in both simulation and experiment, the deect on the bearing can be detected. However, the squared magnitudes are dierent and the one in simulation is slightly larger. M Amarnath, R Shrinidhi, A Ramachandra, S B Kandagal[4] predicted vibration signal analysis o antiriction bearing. The test rig consists o a shat with central rotor, which is supported on two bearings. An induction motor coupled by a lexible coupling drives the shat. The cylindrical roller bearing is tested at constant speed o 1400 rpm with radial load o 230 N. Cylindrical roller bearing type with outer race and roller deects. Two-channel FFT analyzer was used to monitor vibration signals rom good and deective bearings. Three types o bearing deects on inner race, outer race and roller deects were studied. Initially good bearing was ixed in the test rig and signals were recorded using FFT analyzer, shock pulse meter and spike energy analyzer. The good bearing was replaced by deective bearing and signals were recorded or each one o the case separately under the same standard condition. Time domain analysis and requency domain analysis were carried out. Time waveorm indicates severity o vibration in deective bearings. Frequency domain spectrum identiies amplitudes corresponding to deect requencies and enables to predict presence o deects on inner race, outer race and rollers o antiriction bearings. R B Sharma, Yogesh Sharma [5] compared experimental results and CAE results o deective and deect ree bearings. The experimental investigation or the mode shapes and the critical requencies o the cracked bearing have been obtained rom the experimental test rig setup and the mode shapes experimental step up. The bearing used or this work is o single cylinder SI engine o Herohonda 100 cc. the material o bearing was stainless steel. Experimental set up consisted o motor driven shat o which test bearing was mounted. The bearing is mounted in between the DC motor and Eddy Current Dynamometer. DAQ card was provided or urther signal analysis and Lab- View sotware was used to interpret signal in time domain analysis. A numerical simulation o the bearing is perormed using ANSYS, and practical investigations were carried out to veriy the proposed measurement approach. First mode shape and second mode shape were plotted and their behavior was observed. Deect type was triangular notch o 12mm each side and 14mm base side, depth o crack was 27mm approximately. The model is evaluated or the FEM analysis under the modal analysis head, to know the resulting undamental requency o the cracked crankshat using ANSYS The comparison is drawn in between the experimental investigation and the modal analysis using CAE methodology o the bearing with & without crack. The results obtained rom the simulation are approximately validates by the experimental ones. This study is useul to provide the saety eatures against the catastrophic ailures o bearing because the analysis o condition o bearing may be evaluated with the help o CAE based modal analysis using modeling the same model o bearing with deect as comparison with the size & nature o deect o bearing in practical real ground. The experimental and the simulation results were quite very closer to each other. Abhay Utpat [6] compared vibration signal by experimental and numerical approach. ANSYS is used or analyzing signals by numerical method. In numerical approach, whole bearing was modeled and imported in ANSYS. Analysis is carried out by assuming bearing as a mass spring model. Graphs were plotted in time and requency domain analysis or deected and deect ree bearings. In experimental approach, experimental set up developed with the help o belt drive arrangement. Shat carrying test bearing and support bearing is driven by motor by belt and pulley arrangement. Support bearing were kept deect ree. Only radial load is applied with the help o load cell. Vibration signal was acquired by piezo-electric accelerometer and output was ed to FFT analyzer or requency domain analysis o signal. Deect ree bearing, bearing with inner race deect and bearing with outer race deect were compared by experimentally and numerically. Further comparison is done by comparing FEA results and experimental results. Result analysis was carried out or various dierent actors such as comparison between deect 860

3 ree and deected bearing, comparison between deects present on outer race and inner race in requency domain. During comparison o deected and deective bearing, change in peak amplitude was observed. From graph it was noted that vibration amplitude varies with change in deect position. Rise in vibration amplitude was observed due to which outer raceway deect ound to be more severe than inner raceway deect or constant load and constant rpm. Also vibration signal varies with deect size or constant load and constant rpm. Vibration signal or dierent radial load but constant deect size and rpm did not show drastic change. U.A.Patel, Shukla Rajkamal [7] studied FEA model o deect ree and deective bearing. Author s ocus was on study o vibration signals o deective bearing by numerical method in ANSYS. In numerical method whole bearing assembly is modeled in PRO-E. Model was meshed in ANSYS with the help o tetrahedron 4-node SOLID element. First modal analysis was perormed or application o load and then dynamic analysis was carried out by assuming bearing as spring mass model. Cylindrical deect on outer raceway was modeled. Resulted signals were plotted in requency domain i.e. graph o amplitude o vibration versus requency. Deect size selected 0.2mm^3. The natural requency o system was around 34Hz. Experimental set-up consisted o shat driven by motor. Shat supported a rotor carried two support bearing and one test bearing. Accelerometer was mounted on test bearing which supplies signal to FFT gives signal in requency domain data. Results o both experimental data and numerical data or deected and deect ree bearing were compared. Author reported that inite element method can used to detect presence o ault. Vibration analysis is sensitive to presence o deect. Small dierence was observed between experimental and numerical result due to complexity o modeling bearing is involved. Author also noted dierent values o damping coeicients at dierent shat speeds and graph o amplitude o vibration versus damping coeicients is plotted. From graph it was ound that, with increase in damping coeicients and increase in damping ratio amplitude o vibration decreases. So by varying dierent values o damping ratio and damping coeicients jerks in bearing can be eliminated. While dierent speeds with constant radial load and deect size vibration amplitude ound to be increased. Hence, vibration signal analysis is sensitive change in deect position, change in rpm, change in deect size, presence o deect. Also, whole bearing model can be meshed in ANSYS or detail signal analysis in numerical method. In numerical method, meshing, selection o element while meshing is very important part during signal analysis. Overall vibration analysis is versatile technique as it can detect source o vibration. Condition monitoring can be eectively used to dierentiate between signals or dierent deect sizes, dierent deect positions, and change in load. There are various approaches to vibration based condition monitoring which are experimental, numerical, theoretical and analytical. II. METHEDOLOGY OF VIBRATION ANALYSIS Vibration analysis works on principle that, whenever a local deect on element interacts with its mating element abrupt changes in the contact stresses at interace which generates pulse o very short duration [11]. The periodic impacts occur at ball-passing requency that is characteristic deect requencies, which can be estimated rom the bearing geometry and the rotational speed. The vibration signal o a deected bearing produces impact when ball passes through deect. These deect requencies are calculated with the help o the Fast Fourier Transorm (FFT) spectrum. A. Time Domain Analysis Time domain technique is easiest and simplest technique to analyze the vibration signal waveorm. Peak-to-peak amplitude is measure rom the top o the positive peak to the bottom o the negative peak. Root mean square (RMS), measures the overall level o a discrete signal [7]is given by, RMS(x) = N x 2 (1) Where, N is the number o discrete points and represents the signal rom each sampled point. The resultant RMS values are compared with recommended values to determine the condition o a bearing however, this method is not sensitive to detect small or early-stage deects. The crest actor is the ratio o peak acceleration over RMS. Value o the crest actor or good bearing is approximately ive. At advance stages o material wear, bearing damage propagates, RMS increases, and crest actor decreases. Kurtosis is another important parameter to indentiy the health o bearing. The equation to calculate the value o kurtosis is given by: K= N n 1 2 x( n) ^4 N.( )^2 Where, x (n) is the time series, μ is the mean value o the data, σ 2 is the variance o the data and N is the total number o data points. A good surace inish bearing has a theoretical kurtosis o 3, and when the surace inish deteriorates value o kurtosis increases, but kurtosis is insensitive to loads and speeds. Kurtosis value, Crest actor, Impulse actor and Clearance actor are non-dimensional statistical parameters. Impulse and Clearance actors have similar eects like Crest actor and Kurtosis value. Impulse actor, Kurtosis value, Crest actor and Clearance actor are all sensitive to incipient atigue spalling. Peak-to-peak value, RMS, Crest actor and kurtosis are only shows the damage at the ball bearing but do not give inormation about the location o deect e.g. inner race, outer race, cage or the roller. B. Time- Frequency Domain Analysis Time-requency domain techniques have capability to handle both, stationary and non- stationary vibration signals. This is the main advantage over requency domain techniques. Time requency analysis can show the signal requency components, reveals their time variant eatures. A number o time-requency analysis methods, such as the Short-Time Fourier Transorm (STFT), Wigner-Ville Distribution (WVD), and Wavelet Transorm (WT), have been introduced. STFT method is used to diagnosis o rolling element bearing aults. Local deects or wear cause periodic impulses in acoustic emission and vibration signals. The amplitude and period o these impulses are determined by shat rotational speed, ault location, and bearing dimensions. The requencies o these impulses, considering dierent deect locations [1]. I the shat rotational requency per (2) 861

4 second is Fs, the number o balls/rollers in the bearing is Z, the ball/roller diameter is d, the pitch diameter o the bearing is D, and the contact angle is β (β = 0 or a radial bearing), then the rotational requency o a rolling element, r and the rotational requency o the ball cage with a stationary outer race, Fbcsor are expressed as 1) The requency o rolling element bearing making contact with a certain point on inner race i z d r 1 cos 2 D 2) The requency o rolling elements making contact with a certain point on outer race o z d r 1 cos 2 D 3) The requency o rolling elements spinning around their own axes b r D d 1 cos ^2 2 d cos D 4) The requency o cage spinning c r d 1 cos 2 D From above ormulae bearing race pass requencies or outer race and inner race is tabulated below Table 1. Bearing race-pass requencies The setting on VFD is done in such a way that 50 Hz corresponds to 1410rpm and 140 Hz corresponds to 4000rpm.VFD is chosen as it possesses advantages that it is simple, compact and posses lexible ranges o speeds. Also recent trend in industry is to use VFD. Given experimental set up includes accelerometer mounted on bearing housing as shown in ig. This accelerometer converts vibrating orce into electrical signal. This signal is given to DAQ (Data Acquisition System) which processes given signal and FFT analyzer interprets signal in requency domain waveorm. Fig. 1. Experimental set-up A set up consists o 1 HP at 1410rpm three-phase induction motor and output shat which is mounted on table. Radial load is applied on test bearing by spring thimble nut arrangement. Test bearing is mounted in between two support bearing. The support bearings are deect ree bearings and the test bearings are deective. A piezo-electric accelerometer with magnetic base is mounted on the housing o the test bearing. The accelerometer is connected to FFT Analyzer which processes the time signals. The output o analyzer is connected to computer which has the relevant hardware and the Lab-View sotware to acquire the data. Cylindrical deect created by EDM rom 1mm to 3mm diameter sized deect is analyzed. Deep groove single row ball bearing is preerred. Load is varied rom 424N to 724N while speed is varied rom 1400, 1500 upto 2400 rpm. Focus o experimental approach was on requency domain analysis. III. EXPERIMENTAL APPROACH Experimental set up consists o motor driven spindle on which two support bearings and one test bearing are mounted. Deects on bearing are created by EDM. Fig. 1 shows experimental setup. Most o researchers used belt and pulley arrangement or driving spindle on which test bearing is mounted. But it was ound that belt and pulley arrangement will act as another source o vibration due to slight misalignment and this will corrupt vibration signal. Hence in this set up, gear coupling is used to connect motor shat and spindle carrying test bearing. Load is applied with the help o spring thimble nut arrangement. One revolution o thimble nut spring gets compressed in radial direction corresponds to 212N. Load arrangement is done with the help o spring and thimble nut because load application should be easy and compact arrangement. VFD is used to get variety o speeds. IV. MEASUREMENTS OF VIBRATION AMPLITUDES The support bearings are deect ree bearings and the test bearings are deective. A piezo-electric accelerometer with magnetic base is mounted on the housing o the test bearing. The amplitudes o vibrations o test bearings are measured at dierent speeds, loads and deect sizes on outer ring as well as inner ring o bearings under ollowing dierent conditions. i) At constant speed & radial load with variations in deect sizes. ii) At constant deect size & radial load with variations in speed. iii) At constant deect size and speed with variations in radial load at test bearing.signals are acquired in requency domain and interpreted in proper ormat. 862

5 V. RESULTS AND DISCUSSIONS Experimental amplitudes o vibrations are measured at various speeds, loads and or dierent deect sizes on outer and inner ring o bearings. For deect present on outer race with deect size 2mm, 2.5mm and 3mm at 1800 rpm vibration amplitudes observed 0.005g, g and 0.08g respectively. Fig. 1, ig. 2, ig. 3 shows vibration amplitudes when deect present on outer race deect present at load 424N with 1800rpm having deect sizes 2mm,2.5mm and 3mm. Like this dierent vibration amplitudes are measured by variation o deect sizes, deect position, speed o shat which is tabulated in table 2. Graphs o some acquired signals are shown in ig.1-7. When deect is present on inner race with deect sizes o 2mm at 1500rpm, 1800rpm and 2400rpm vibration amplitude is noted as g, 0.001g and g as shown in ig. 6 and ig.7. While deect is present on inner race with deect size 2mm at 1800rpm load is varied rom 424N, 530N, 636N and 742N and vibration amplitude noted as 0.001g, g, g and g respectively. These requencies are measured at characteristic ault requencies or bearing race pass requencies. Because principle behind vibration analysis is that, whenever a local deect on element interacts with its mating element abrupt changes in the contact stresses at interace which generates pulse o very short duration. The periodic impacts occur at ball-passing requency that is characteristic deect requencies, which can be estimated rom theoretical ormula mention in previous section. Eorts have been taken about measuring o above vibration signals with 2-3 dierent types o accelerometer. It was ound that not much dierence was there in vibration amplitudes. Slight changes may have occurred due to change in load zone. Sr. no. Deect size Mm Location o Deect Inner race/outer race RPM Deect Free New Bearing mm/s 2 Experimental Theoretical 1 2 Outer race Outer race 3 3 Outer race 4 2 Outer race Outer race 6 3 Outer race 7 2 Inner race 8 2 Inner race 9 2 Inner race 10 2 Inner race 11 2 Inner race Force=530N 12 2 Inner race Force=636N 13 2 Inner race Force=742N 14 1 Outer race Table 2. Experimental vibration amplitude Approx 104Hz with amplitude 105Hz 0.005g Hz with amplitude g 105Hz Hz amplitude 0.08g 105Hz Hz amplitude 0.08g 105Hz Hz amplitude 0.012g 105Hz Hz amplitude 0.082g 105Hz Hz amplitude g 137.5Hz Hz amplitude 0.001g 165Hz Hz amplitude g 220Hz Hz amplitude 0.001g 165Hz Hz amplitude g 165Hz Hz amplitude g 165Hz Hz amplitude g 165Hz Hzamplitude 0.007g 144Hz 863

6 Fig.3 vibration amplitude when deect o 3mm and speed o 1800rpm. Fig.1 vibration amplitude when deect at outer race o 2mm with load 424N and speed o 1800rpm Fig. 2. vibration amplitude when deect at outer race o 2.5mm with load 424N and speed o 1800rpm Fig.3 vibration amplitude when deect o 3mm at outer race with load 424N and speed o 1800rpm. 864

7 Fig.4 vibration amplitude when deect present at outer race o 2mm with load 424N and speed o 2400 rpm Fig. 5 vibration amplitude when deect present at outer race o 2.5mm with load 424N and speed o 2400rpm Fig. 6 vibration amplitude when deect present at outer race o 3mm with load 424N and speed o 2400rpm 865

8 Fig. 7 vibration amplitude when deect present at outer race o 2mm with load 424N and speed o 1500rpm CONCLUSION When deect is present on outer race at constant orce 424N and 1800 rpm vibration level varies with increase in deect size. It is observed that, vibration amplitude increases with increase in size o deect. When deect is present on inner race at constant speed 1800 rpm and deect size 2mm vibration level varies with change in load.. It is observed that, vibration amplitude decreases with increase in load. When at constant speed and constant load but deect positions are compared that is vibration amplitudes o deect present on inner race and outer race is compared, it is ound that vibration amplitude at inner race is slightly less than that o outer race. Hence, outer race deect is more severe. Condition monitoring can be done by time domain and requency domain technique. Time data graphs are acquired and observed. It was ound that, data extraction rom time domain signals is very diicult because it can detect presence o ault but unable to detect exact location. In requency domain analysis vibration amplitudes can be compared at bearing race pass requency. It was observed that, requency domain analysis can be eectively used to detect the various sources o ault. Numerical approach o inite element analysis o bearing can successully detect change in deect size o bearing by comparing values o energy dissipated. In some cases, inite element analysis is unable to provide rotation requency to the bearing due to complex dynamic behavior. In experimental approach, proposed test rig eectively helps to compute sensitivity o vibration signatures or dierent source o vibration in bearing. ACKNOWLEDGMENT Authors are thankul to Mechanical department and guide or their extended help to complete this paper. REFERENCES [1] Mao Kunli1, Wu Yunxin, Fault Diagnosis o Rolling Element Bearing Based on Vibration Frequency Analysis, Third International Conerence on Measuring Technology and Mechatronics Automation,2011 [2] K. Yavanarani1, G. S. Simon Sundara Raj, S. Sheena Christabel, J.Vijayaraghavan, Multi Resolution Analysis or Bearing Fault Diagnosis,IEE, [3] Pro. Dr. Zahari Taha, Nguyen Trung Dung Rolling Element Bearing Fault Detection with a Single Point Deect on the Outer Raceway Using Finite Element Analysis, Asia Paciic Industrial Engineering and Management Systems Conerence, December 2010 [4] M Amarnath,, R Shrinidhi,, A Ramachandra,,S B Kandagal Prediction o Deects in Antiriction Bearings using Vibration Signal Analysis IE(I) Journal-MC, September 2004 [5] R B Sharma, Yogesh Sharma, Comparison o Vibration and Cae Techniques or the Condition Monitoring O Rolling Element Bearings, (IJERA) ISSN: , March 2014 [6] Abhay Utpat, Vibration signature analysis o deective deep groove ball bearings by numerical and experimental approach ISSN : IJMER, June 2013 [7] U.A.Patil, Shukla Rajkamal Vibrational analysis o sel align ball bearing having a local deect through FEA and its validation through experiment ISSN: May-June 2012 [8] Hasan Ocak,Smet Bayram,H. Metin, Vibration analysis based localized bearing ault diagnosis under dierent load conditions, September 15-16th [9] H.Metin Ertunç Hasan Ocak Muhammet Merdoğlu Samet Bayram Mesut Çavuş, Vibration Analysis Based Localised Bearing Fault Diagnosis under Dierent Load Conditions International Workshop on Research and Education in Mechatronics, September 2011 [10] Design o Machine Elements ; Alex Vallance & V. L. Doughtie; Mc- Graw Hill; Edition 3 [11] Zeki Kiral, Hira Karagulle, Simulation and analysis o vibration signal generated by rolling element bearing with deects ELSEVIER, January 2003 [12] Zeki Kiral, Hira Karagulle Vibration analysis o rolling element bearings with various deects under the action o an unbalanced orce,elsevier, July 2005 [13] M. Kaczorowski, A neural network approach or ball bearing lie prognosis, Project Report, Mechanical and Industrial Engineering Department, University o Massachusetts-Amherst, May