Performance evaluation of force transducers

Transcription

1 Indian Journal of Pure & Applied Physics Vol. 50, February 2012, pp Performance evaluation of force transducers Harish Kumar 1,2 * & Chitra Sharma 3 1 CSIR-National Physical Laboratory, New Delhi University School of Engineering & Technology, Guru Gobind Singh Indraprastha University, New Delhi 3 Indira Gandhi Institute of Technology, New Delhi * harishkec@gmail.com Received 29 September 2011; revised 29 November 2011; accepted 7 December 2011 The performance evaluation of the developed ring shaped force transducers of capacity 20 and 50 kn for tension and compression modes has been studied. The force transducers have been metrologically characterized according to the calibration procedures based on the standards ISO and IS (reaffirmed 2003). The factors contributing to the uncertainty of the force transducers and methodology for computing the uncertainty of force transducers have been discussed. The 50 kn dead weight force machine with uncertainty of force applied (best measurement capability, bmc) ± 0.003% (k = 2) has been used for metrological characterization of force transducers. The force transducers qualify the class 00 per the standard ISO and class 0 as per IS (reaffirmed 2003), hence, may be used as force transfer standards. Keywords: Force transducer, IS (reaffirmed 2003), ISO Introduction The force transducers play a very important role in various applications directly or indirectly. The applications may be like verification of material testing machines, electronic weighing balance, weighing of aircrafts, thrust measurement of jet or rocket engines, monitoring the components of cutting forces in different machining processes like turning, milling, drilling, morphological study etc. There is wide range of force transducers available for capacities ranging from few newtons to mega newtons. The typically used force transducers may be like ring shaped, elliptical dynamometers type, strain gauged load cells or frequency based tuning fork type. Ring shaped force transducers are quite common and used on a large scale since the inception in The conventional ring shaped force transducers are composed of an elastic ring, made up of steel alloy and an axial deflection measuring system like dial gauges, micrometer or vibrating reed 1-3. But, now the ring shaped force transducers have been developed in form of strain gauged force transducers and various attempts have proved for its worth. The metrological performance evaluation of ring shaped force transducers of capacity 20 and 50 kn in tension and compression modes using different calibration procedures based on different standards like ISO and IS (reaffirmed 2003) have been investigated in the present paper. The factors according to the standard procedure have been considered while evaluating the metrological performance of the force transducers and results have been reported Experimental Details The force transducers have been calibrated according to the calibration procedures based on the standards ISO and IS (reaffirmed 2003). The standard procedures include the application of force at different angular positions and consider deviation due to factors like repeatability error, reproducibility error, interpolation error, zero error and resolution error while evaluating the uncertainty of the force transducer. The force machine of 50 kn dead weight (bmc ± 0.003%, k=2) has been used for metrological investigations of force transducers. The 50 kn dead weight force has been designed and developed by More House Corporation, USA and has been installed in National Physical Laboratory, New Delhi, India in The dead weight force machine employs precisely calibrated and traceable stainless steel dead weights of nominal force values ranging from 0.5 to 5 kn taking also the effect of local values of gravity and buoyancy correction for the applied force by the dead weight force machine. The main components of the dead weight force machine are the loading hanger, sets of dead weights and a rigid main frame supporting these

2 KUMAR & SHARMA: PERFORMANCE EVALUATION OF FORCE TRANSDUCERS 87 components and the pneumatic system for loading and unloading the weights. The force in range kn may be applied in either mode (tension and compression). A high resolution digital indicator, DMP 40 (HBM Germany make) has been used. Though, the resolution could be used as fine as mv/v, mv/v has been used and the excitation voltage was kept 5 V throughout the study IS (reaffirmed 2003) The calibration process is as follows: The digital indicator has been switched on for warm up and stabilization. The no load output (before taring) and the calibration signal were noted. Before the application of the calibration forces, the force proving instrument was preloaded thrice to its maximum capacity and kept at full load for 90 s. The calibration of the force proving instrument has been done in tension/compression mode. The calibration was carried out by applying one series of calibration forces in ascending order from 10% to 100% in steps of 10% in tension/ compression at 0 degrees. The force proving instrument was subjected to the full load once for about 90 s each time before starting the calibration to the new position i.e. at 180 and 360 degrees. Between the loadings, readings corresponding to no load after waiting at least 30 s for the return to zero were noted. The uncertainty of measurement of the force proving instrument involves the deviations due to zero error, repeatability error, resolution error and the uncertainty of measurement of force due to the force calibrating machine. w 2 (res) (a/ 3) 2 = a 2 /3, where a = f r /2 f c Relative Interpolation Deviation (%), Triangular shaped probability distribution, type B error, factor 6 w 2 (int) (a/ 6) 2 = a 2 /6, where a = f c /2 w c (tra) relative combined standard uncertainty [w 2 (rep) + w 2 (zer) +w 2 (res) + w 2 (int)] 1/2 W (tra) relative expanded uncertainty = kw c(tra) W (bmc) BMC of force calibrating machines [±0.025% (k=2) in present study] W (k=2) Overall uncertainty of measurement force proving instrument [W 2 (tra) +W 2 (bmc)] 1/2 The findings are shown in Figs 1 and 2. A typical calculation is presented in Table ISO The calibration process is as follows: The digital indicator was switched on for 30 min to warm up and stabilization. The no load output (before taring) and the calibration signal were noted. Fig kn Force Transducer as per IS (reaffirmed 2003) The uncertainty of the force transducers 5,8-10 been calculated as follows: has Relative Zero Deviation (%), Rectangular w 2 (zer) (a/ 3) 2 = a 2 /3, where a = f o /2 f o b Relative Repeatability Deviation (%), U shaped probability distribution, type B error, factor 2 w 2 (rep) (a/ 2) 2 = a 2 /2, where a = b/2 f r Relative Resolution Deviation (%), Rectangular shaped probability distribution, type B error, Fig kn force transducer as per IS (reaffirmed 2003)

3 88 INDIAN J PURE & APPL PHYS, VOL 50, FEBRUARY 2012 Before the application of the calibration forces, the force transducer was preloaded thrice to its maximum capacity and kept at full load for 90 s. The values at no load, full load and no load after removing the full load is noted. The calibration of the force transducer has been done in tension mode as well as in compression mode. The calibration was carried out by applying two series of calibration forces in ascending order from 10% to 100% in steps of 10% at initial position, considered initial position as 0 o. Two series of calibration forces have been applied at rotation positions 120 o and 240 o. The force transducer was subjected to the full load once for about 90 s each time before starting the calibration to the new position i.e. 120 and 240. Between the loadings, readings corresponding to no load after waiting at least for 30 s for the return to zero were noted. The uncertainty of measurement of the force transducer involves the relative deviations due to zero error, repeatability error, reproducibility error, resolution error, interpolation error and the uncertainty of measurement of force due to the force machine (bmc of force standard machine). The uncertainty of the force transducers 6,8,9 has been calculated as follows: f o Relative zero deviation (%), Rectangular w 2 (zer) (a/ 3) 2 = a 2 /3, where a = f o /2 b Relative repeatability deviation (%), Rectangular probability distribution, type B error, w 2 (rep) (a/ 3) 2 = a 2 /3, where a = b/2 c Relative reproducibility deviation (%), U factor 2 w 2 (rpr) (a/ 2) 2 = a 2 /2, where a = c/2 f r Relative resolution deviation (%), Rectangular w 2 (res) (a/ 3) 2 = a 2 /3, where a = f r /2 f c Relative interpolation deviation (%), Triangular shaped probability distribution, type B error, factor 6 w 2 (int) (a/ 6) 2 = a 2 /6, where a = f c /2 w c (tra) relative combined standard uncertainty [w 2 (rep) + w 2 (rpr) + w 2 (zer) +w 2 (res) + w 2 (int)] 1/2 W (tra) relative expanded uncertainty = kw c(tra)

4 KUMAR & SHARMA: PERFORMANCE EVALUATION OF FORCE TRANSDUCERS 89 W (bmc) BMC of force calibrating machines [±0.025% (k=2)] in the present study W (k=2) Overall uncertainty of measurement force proving instrument [W 2 (tra) +W 2 (bmc)] 1/2 The findings 4 are shown in Figs 3 and 4. A typical calculation is presented in Table 2. 3 Results and Discussion The ring shaped force transducers of capacity 20 and 50 kn in tension and compression mode have been developed using the elastic theories of thin rings. The force transducers have been metrologically characterized using the 50 kn dead weight force machine and the calibration procedure based on the standard ISO and IS (reaffirmed 2003). The uncertainty of measurement of the force transducers has been computed by taking relative deviation into account due to factors like repeatability error, reproducibility error, zero error, resolution error, interpolation error and bmc of the force standard machine. The uncertainty has been evaluated as per guidelines of standard procedures and guidelines for uncertainty measurement. Typical excel sheets have shown the calculations for uncertainty measurement for 20 kn force transducer as per the Fig kn force transducer as per ISO Fig kn force transducer as per ISO

5 90 INDIAN J PURE & APPL PHYS, VOL 50, FEBRUARY 2012 standard procedures discussed. The force transducers have been found to exhibit good metrological results with uncertainty of measurement ± 0.025% (k = 2), confirming to class 00 as per the ISO and 0.033% (k=2), confirming to class 0 as per IS (reaffirmed 2003) for both modes i.e. tension and compression mode. 4 Conclusions The metrological performance of ring shaped force transducers of capacities 20 and 50 kn developed according to the standard calibration procedures based on standards ISO and IS (reaffirmed 2003) using the force standard machine of 50 kn (bmc ± 0.003%, k=2) has been studied. The uncertainty of the force transducer is found to be ± 0.025% (k = 2) as per ISO and 0.033% (k=2) as per IS (reaffirmed 2003), respectively, which includes the relative deviations due to the factors as per standard procedures. The force transducers confirm to class 00 and class 0 as per ISO , IS (reaffirmed 2003), respectively and are suitable for use as force transfer standard. Acknowledgement Authors express their sincere thanks to Prof R C Budhani, Director, National Physical Laboratory, New Delhi, India, Dr A K Bandyopadhyay, Head, Apex Level Standards and Industrial Metrology Group, National Physical Laboratory, New Delhi, India and Prof Nupur Prakash, Director, Indira Gandhi Institute of Technology, Delhi, India. Authors also express their sincere thanks to Mr. Anil Kumar, Head, Mass Standard Group, Apex Level Standards and Industrial Metrology Group, National Physical Laboratory, New Delhi, India. References 1 Kumar Harish, Sharma Chitra & Kumar Anil, International J Engng Sci & Tech, 3(2) (2011) Rehman M A & Rehman S, J Institution of Engineers (India) Mechanical Engineering Division, 88 (2007) Harish Kumar, Chitra Sharma & Kumar Anil, J Scientific & Industrial Res, 70 (7) (2011) Calibration of force proving instruments used for verification of uniaxial testing machines, ISO Calibration of Force Proving Instrument, IS (reaffirmed 2003). 7 Kumar Harish, Kumar Anil & Yadav Poonam, Measurement Sci Rev, 11(2), (2011) International Standards Organization (1995), Guide for Expression of Uncertainty in Measurement, ISO GUM Document. 9 Guidelines for Estimation & Expression of Uncertainty in Measurement, NABL 141 Metallic materials Calibration of Force Proving Instrument, IS (re-affirmed 2004). 10 Kumar Harish & Kumar Anil, NCSLI Measure The Journal of Measurement Science, 6 (2) (2011) 64.