IJSRP JUNE 2012 Online Print Version - IJSRP.ORG

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International Journal of Scientific and Research Publications, Volume 2, Issue 6, June <strong>2012</strong> 47 ISSN 2250-3153 International Statistical Institute, 45:295-300. [11] David, H. A., & Galambos, J., (1974). ―The asymptotic theory of concomitants of order statistics‖. Journal of Applied Probability, 11:762- 770. [12] David, H. A., & Nagaraja, H. (2003). ―Order Statistics”. John Wiley & Sons, New York, 3rd edition. [13] Feller, W. (1966). ―An Introduction to Probability Theory and its Applications‖.Volume 2. Wiley, New York. [14] Filus, J. K., & Filus, L. Z. (2006). ―On some new classes of multivariate probability distributions‖. Pakistan J. Statistics, 21(1):21-42. [15] Hanif, S. (2007). ―Concomitants of Ordered Random Variables‖. Ph.D Thesis, National College of Business Administration & Economics, Lahore. [16] Nagaraja, H. N. (1988). ―Record values and related statistics: A review‖. Communication in Statistics: Theory and Methods, 17:2223–2238. [17] Nevzorov, V. B. (1988). ―Records‖. Theory of Probability and its Aplications, 32:201-228. [18] Shahbaz, S., & Shahbaz, M. Q. (2011). ―The trivariate pseudo Rayleigh distribution‖. World Applied Sciences Journal, 12(12):2279-2282. [19] Shahbaz, S., & Shahbaz, M. Q. (2010). ―On bivariate concomitants of order statistics for pseudo exponential distribution‖. Middle East J. Scientific Research, 6(1):22-24. [20] Shahbaz, S., Shahbaz, M. Q., & Mohsin, M. (2009b). ―On concomitants of order statistics for bivariate pseudo exponential distribution‖. World Applied Sciences Journal, 6(8):1151-1156. [21] Shahbaz, S., & Ahmad, M. (2009a). ―Concomitants of order statistics for bivariate pseudo Weibull distribution‖. World Applied Sciences Journal, 6(10):1409-1412. [22] Tahmasebi, S., & Behboodian, J. (2010). ―A short note on entropy ordering property for concomitants of order statistics‖. World Applied Sciences Journal, 9(3):257-258. AUTHORS First Author – Kishore K. Das, M. Sc., Ph.D Department of Statistics, Gauhati University, Guwahati, Assam, India Second Author – Bhanita Das, M. Sc., Ph.D Department of Statistics, Gauhati University, Guwahati, Assam, India Third Author – Bhupen K. Baruah, M. Sc., Ph.D . . Department of Chemistry, Gauhati University, Guwahati, Assam, India www.ijsrp.org
International Journal of Scientific and Research Publications, Volume 2, Issue 6, June <strong>2012</strong> 48 ISSN 2250-3153 Design and Stress Analysis of Watt and Porter Governor *Ravindra Singh Rana, **Rajesh Purohit, *Alok Singh *Assistant Professor Department of Mechanical Engineering M.A.N.I.T, Bhopal (M.P.), India **Associate Professor Department of Mechanical Engineering M.A.N.I.T, Bhopal (M.P.), India Abstract- The function of the governor is to maintain the speed of an engine within specified limits whenever there is a variation of load.. This device can be used in almost all vehicles. The objective our investigation to identify the stress concentration areas, areas which are most susceptible to failure when governor is rotating about its axis, also the value of these stresses is measured. This analysis is carried out with the help of PRO E. The displacement of the various elements of the SPINDLE from the base is also calculated and the graphs are plotted. Effect of the ―WEIGHT OF THE ARMS‖ is the major area of concern for our study and all the calculations are done considering the weight of the arms. Weight of the arms acts on the centroid of the arms and when the governor assembly rotates, centrifugal force starts acting on the centroid of the arms and tends to deflect the arms, this deflection or bending is to be minimized. In our work, we have done the Stress analysis on a particular configuration of governor assembly and then various materials are suggested on a theoretical basis. Index Terms- PRO E, Spindle, Weight of the Arms. A I. INTRODUCTION Governor, or speed limiter, is a device used to measure and regulate the speed of a machine, such as an engine. A classic example is the centrifugal governor, also known as the watt. [1-3] Centrifugal governors were used to regulate the distance and pressure between millstones in windmills since the 17th century. Early steam engines employed a purely reciprocating motion, and were used for pumping water an application that could tolerate variations in the working speed. It was not until the Scottish engineer James Watt introduced the rotative steam engine, for driving factory machinery, that a constant operating speed became necessary. Between the years 1775 and 1800, Watt, in partnership with industrialist Matthew Bolton, produced some 500 rotati-vebeam engines. At the heart of these engines was Watts self-designed "conical pendulum" governor: a set of revolving steel balls attached to a vertical spindle by link arms, where the controlling force consists of the weight of the balls. Building on Watts design was American engineer Willard Gibbs who in 1872 theoretically analyzed Watts‘s conical pendulum governor from a mathematical energy balance perspective. During his graduate school years at Yale University, Gibbs observed that the operation of the device in practice was beset with the disadvantages of sluggishness and a tendency to overcorrect for the changes in speed it was supposed to control. The objective our investigation to identify the stress concentration areas, areas which are most susceptible to failure when governor is rotating about its axis, also the value of these stresses is measured. Analysis is carried out with the help of PRO E. The displacement of the various elements of the SPINDLE from the base is also calculated using PRO E and the graphs are plotted. Different materials for different parts are used that are theoretically justified. II. MATERIALS FOR DIFFERENT PARTS 2.1 Spindle and Arms: The spindle of the governor is made of STAINLESS STEEL. The properties of stainless steel are given below: Physical Properties, Density= 0.29 lbs/in3(8.03 g/cm3) ,Modulus of Elasticity ksi (MPa) 28.0 x 103 (193 x 10^3) in tension 11.2 x 103 (78 x 10^3) in torsion. STAINLESS STEEL is used because of its high MODULUS OF ELASTICITY in tension and the high modulus of elasticity in tension means high bending strength, which is the major cause for failure of the spindle, it is for this reason that stainless steel is used for the design of spindle. Apart from that the Corrosion resistant property of stainless steel and its stress concentration corrosion resistance justify the use of stainless steel for both spindle and arms. 2.2 Base: The base of the governor assembly is made up of Fe30. This material is used because it has very good Vibrations Damping capacity. It is a prerequisite for the governor or any machine that the base should be stable and it should not vibrate, it is for this reason that Fe30 is used. 2.3 Sleeve and Head: The sleeve of the governor is made up of BRONZE. Sleeve is that part of governor which moves relatives to spindle so there is always FRICTION associated with it, and when there is friction, then when the sleeve is moving upwards friction acts downwards and retards its speed and when it moves downwards friction acts upwards, in this way for a given height of governor there are two speeds on the controlling curve which results in the INSTABILITY of the governor. The friction of the governor is therefore be kept as low as possible, Bronze is a material which is self-lubrication and it has very low coefficient of friction. 2.4 Pins and Bushes: Self-lubricating bushings (lubrication free bushings) are made up of one of two basic compositions: PTFE-Based Metal-Polymer Materials Thermoplastic-Based Metal-Polymer Materials III. DESIGN OF GOVERNOR 3.1 Design of Watt Governor: The Design of Watt Governor involves determining the Minimum and maximum speed of the Governor. The minimum speed occurs when the sleeve is at its rest or initial position. www.ijsrp.org
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