Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 3159-0040 Vol. 2 Issue 2, February - 2015 Development of 400 Newton Spring Weighing Machine Olayinka O. Awopetu1, Tunji J. Erinle1 and Olaoluwa J. Fasan1 1Department of Mechanical Engineering, Federal University of Technology, Akure, Ondo State, Nigeria. [email protected]; [email protected]; [email protected]

Abstract- The weighing machine has spring the pinion. The indicator scale consists of the pointer wire diameter ퟑ 퐦퐦 with ퟐퟎ 퐜퐨퐢퐥퐬 and external and dial; in which the dial is calibrated in weight units diameter ퟑퟎ 퐦퐦. The objectives of this work are to and thus the pointer gives an indication of the weight develop and determine the performance acting on the springs. evaluation of the mechanical spring weighing Scale or Balance weighing either mechanical or machine of ퟒퟎퟎ 퐍퐞퐰퐭퐨퐧(퐍) that will be of high electronic device commonly used in households, resolution and easily operated with simple scientific laboratories, businesses and industry to mechanism. The performance of the weighing measure the weight or mass of an object or machine was done with simple standard weights substance. Spring device made of an elastic material of different loads placed on the weighing machine that undergoes a significant change in shape or The test carried out gave one revolution and deformation, under an applied load. Springs are used full scale deflection at maximum load ퟓퟎ 퐝퐞퐠퐫퐞퐞퐬 in spring balances for weighing, for the storage of of ퟒퟎퟎ 퐍 (ퟒퟎ 퐤퐠) with initial sensitivity of ퟏ 퐝퐞퐠퐫퐞퐞 mechanical energy and also used to absorb impact. deflection caused by a load of ퟏퟎퟎ 퐠. The modulus ퟐ The specific form of a spring depends on its use. A of rigidity of the spring used, 퐆퐬퐭퐞퐞퐥 = ퟖퟎ 퐆퐍/퐦 . weighing spring is normally wound as a helix and its The spring weighing machine is for the weighing elongation is proportional to the applied force, so that of bulky materials or packed piece in the the spring can be calibrated to measure this force. laboratory. The efficiency of the machine is ퟗퟑ %. The weight of an object may be determined by Keywords- Development, Spring, Weighing, using either a comparative method, as with a Machine, Efficiency. chemical-laboratory balance or by measuring the gravitational force directly by means of a spring scale. I. INTRODUCTION The deflection of a spring scale depends on the local A mechanical spring weighing machine of gravitational attraction. Weighing is performed by 400 Newton(N) is to be designed, fabricated and comparison and is independent of the specific tested for laboratory purpose. The weighing machine magnitude of the local gravitational attraction, consists of casing cabinet, helical coil spring, dial (Encarta Encyclopedia, 2009). indicator scale, pointer, rack and pinion gear. If the Weighing and measuring are an important and result of the weighing system is to be meaningful often vital part of our existence. Our bodies, the food these two requirements must be met in the act of we eat and all the products we use as an integral part measurement: the standard which is used for of modern living, have been weighed and measured at comparison must be accurately defined and some stage in their development hence the weighing commonly accepted and the procedure and apparatus measurement is the act of the result of a qualitative employed for obtaining the comparison must be comparison between a pre-defined standard and an provable. unknown magnitude, (Beekwith and Roy, 1985). The mechanical weighing systems employ the Mechanical weighing machine systems originated three basic elements of measuring systems: Detecting in Egypt, and were used as early as 500B.C. The and measuring elements (transducer) which detects earliest devices were of the cord and equal arm type the physical variable to be measured (measurand) traditionally used to symbolized justice. Unequal arm and converts the signal in to a more usable form; balances were apparently first used; this device called intermediate stage which modifies the signal from the a Danish steelyard was described by Aristotle (384- transducer so that a desirable output is available and 3222B.C) in the mechanics, (Sirohi, 1991). Balance is indicating or recording device. accomplished by moving the beam through the loop of The spring represents the transducer as it converts cord, which acts as the fulcrum point, until balance is the weight of the physical quantity into a mechanical obtained. displacement of the springs. The rack and pinion About 2000 years ago the ancient Romans gearing constitutes the intermediate stage as a developed the steelyard. Like the equal-arm balance, relatively small displacement at the end of the springs the steelyard consists of a beam supported by a is amplified to give a relatively large displacement of

www.jmest.org JMESTN42350443 47 Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 3159-0040 Vol. 2 Issue 2, February - 2015 fulcrum, and weight measurements are made by fundamental principle of design has been maintained, balancing a known weight on one side of the fulcrum although there have been many variations to against an unknown weight on the other side of the accommodate user need. Since the 1907 there has fulcrum. The Roman steelyard, in which the fulcrum is been acceleration development of semi-self-indicating fixed so that suspended loads have a constant and fully self-indicating weighing machine designed to movement arm and are counter balance by a reduce or obviate the tedium of handling multiplicity of moveable poise, is probably of slightly less antiquity weight for weighing. Self-indicating and most semi- than the bismar. The principle of the Roman steelyard self-indicating weighing machine afford for weighing is applied to modern steelyard used by butchers and different quantities of goods in successive operation is incorporated in improved form in platform and by Grif, (Helcalfe, 1975). weighbridge. Until the end of the eighteen century, Modern balances that use the same principles as very large steelyard was used for weighing carts. The the equal-arm balance and the steelyard can make steelyard, often as much a 20ft long, was suspended very precise weight measurements. Precision from a gantry or beam projecting over the highway balances used in scientific laboratories can measure and capable was of being raised or lowered by means the weight of small amounts of material down to the of a block and tackle winch. The steelyard was nearest 1 millionth of a gram (3.53 hundred millionths lowered until chains suspended from the load hook of an ounce). Such weighing devices are enclosed in could fasten to a cart from which the horse had been glass or plastic to prevent wind drafts and temperature untarnished. The whole was then raised, slowly and variations from affecting the measurements. Other laboriously, until the cart was clear off the ground. mechanical scales in use today include pendulum Poise was moved along the bars, until an operator scales and spring scales. In a pendulum scale, a who could walk along a platform below the steelyard platform is connected to a weighted pendulum. When established equipoise; innkeepers often owned these an object is placed on the platform, the weighted carts steelyards, (Jain, 1990). pendulum swings out to the side to balance the load; The Turnpike Act of 1741 authorised road trustee a needle attached to the pendulum indicates the to erect at toll gates “any cranes machine or engine weight. In a spring scale, a platform is connected to a which they shall judge for weighing of carts, wagon or spring, which either stretches or compresses to other carriage” and charged them to levy toll balance a load placed on the platform. A needle according to weight and to apply revenue to the repair whose position depends on the extent to which the of roads. Although this act increased the number of spring is stretched or compressed indicates the weight cart steelyard, the inconveniences of weighing by of the load. spurred inventor help to device some laborious and II. MATERIALS AND METHODS expedition manner of weighing. It has been claimed for Eayre and Yeomas in 1739, they invented the Materials selection platform of weighing machine, but John Wyath in 1741constructed the first compound level platform The choice of components used for this development of 400 N spring weighing machine is scaled and his first weighbridge was erected at the Birmingham workhouse. Next, in chronological order, based on the following factors: Efficiency of came the spring balance, Richard Salter, (1760), equipment, Simplicity of design and Cost. Table 1 shows the materials criteria for the selection. Progenitor of the firm of George Salter and co. Ltd., of west Bromwich, is known to have been making spring Table 1: Materials Selection in 1760 and to have made a barrel spring balance, Machine (Sirohi, 1991). S/N Material Unit Criteria Part About the year 1770, early in the nineteenth century, Augustus Siebel and Marriott H. in 1946 Readily weldable, low strength , high ductility, invented the bow spring balance. The latter form of Pivot Mild resistant and indicator was for many years used in 1. 1 hardenable surface, good shaft steel platform machines supplied by Henry Pooley in 1947, heat treatment and cold used in Great Britain. In the one on the left, the semi- workings circular charts acts a pendulum. In the one on the High compressive strength, right the triangle members has a similar function; both good damping include the plumb bob and cord to serve as an index, Helical Mild 2. 4 characteristics, high (Haslam, et al, 1970) spring steel torsional strength and low Counter scales of the Roberval type in 1906 were first made at the beginning of the nineteenth century tensile strength and weighing machines of the Beranger pattern were Readily weldable, low made at about the middle of the century, (Robert, strength , high ductility, Mild 1992). These patterns have undergone but little 3. Frame 1 hardenable surface, good steel change construction to this day. Automatic weighers heat treatment and cold for the handling of grains were first used in Great Britain at the beginning of the twentieth century. The workings

www.jmest.org JMESTN42350443 48 Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 3159-0040 Vol. 2 Issue 2, February - 2015 D Readily weldable, low T = W × (Khurmi and Gupta, 2004) (6) strength , high ductility, 2 Load Mild 4. 1 hardenable surface, good Energy stored, E for helical spring subjected to carrier steel heat treatment and cold an axial load, W workings 훕 2 E = 퐬 (7) Rack and Mild Machinable, highly ductile, 4G 5. pinion steel good heat treatment E = Energy stored, J/m3 Mild Machinable and good 6. Bushing 4 Design Analysis of Gear steel strength Spring Mild Base on design application, a mild steel rod of 7. High strength 35 diameter will be suitable for the spur gear (pinion). support steel This diameter represent Addendum circle diameter. A Bolt and Mild 0 8. High strength standard pressure angle of 20 for full depth involute nut steel system is used and a module, m of 1.5. Design Analysis of the Spring Weighing Addendum circle diameter (Outside diameter of the Machine pinion) (DO) = 35 mm The design analysis was determined using Addendum = 1m = 1 × 1.5 = 1.5 mm equation (1) to (22) and table 2 shows the calculated Dedendum = 1.25m = 1.25 × 1.5 = 1.875 mm value of the equations. Tooth thickness = 1.5708m = 1.5708 × 1.5 = Design Analysis for Helical Spring 2.3562 mm D C = (Shigley and Mischke, 2001) (1) Working depth = 2m = 2 × 1.5 = 3 mm d 4C −1 0.615 Total depth (Addendum + Dedendum ) = 2.25m = K = + (2) 4C −4 C 2.25 × 1.5 = 3.375 mm C = spring index Clearance = 0.25m = 0.25 × 1.5 = 0.375 mm D = Mean diameter of spring, mm Filet radius at root = 0.4m = 0.4 × 1.5 = 0.6 mm d = Diameter of wire, mm Pitch circle diameter of the pinion (DP) = DO − 2 × Addendum = 35 − 2 × 1.5 = 32 mm K = Wahl factor Circular pitch, PC = π m = 1.5π = 4.712 mm The maximum torsional (shear) stress, 훔 due 퐬 0 to maximum load, W to be weighed Pressure angle = ∅ = 20 8WD Determination of number of teeth of the pinion, 훕퐬 = K (Shigley and Mischke, 2001) (3) πd3 퐓퐏 2 τ = maximum torsional stress, N/m DP s T = (Khurmi and Gupta, 2004) (8) P m W = maximum load, N For Pinion: Base circle radius, Rb = rP cos ∅ = The linear deflection, 훅 of the spring due to D P cos ∅ axial load, W 2

8WC3n Determination of number of teeth of the rack, δ = (Holowenko, et al, 1983) (4) Gd 퐓퐑 W = axial load, N The transmission ratio between the pinion and the rack is 2: 1 δ = linear deflection, mm DR 2 T = = 2 T (9) G = modulus of rigidity, N/m R m P

n = Number of spring coils For Rack: Base circle radius, Rb = rR cos ∅ = D R cos ∅ The spring of 20 active turns is to be used for the 2 spring weighing machine Design Analysis of Shaft for Pinion 2δ θ = (5) Weight of the pinion, W (N) D P 2 θ = angular deflection, degree WP = 0.00118TPbm (10) Torque or twisting moment, T due to the axial b = face width of the gear teeth, mm 0.912 load, W y = 0.154 – (for 200 full depth involute system) (11) TP www.jmest.org JMESTN42350443 49 Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 3159-0040 Vol. 2 Issue 2, February - 2015 y = tooth form factor (for 200 full depth involute system) Table 2: Design Analysis σ = σ × C (12) Equations w a V S/N Equations Results No. σa = Allowable static stress for steel untreated 2 D = 140 N/mm 1 C = 1 10 d CV = Velocity factor 4C − 1 0.615 2 K = + 2 1.145 V = Pitch line velocity 4C − 4 C 3 8WD 1.3 C = (13) 3 훕퐬 = K 3 2 V 3+V πd3 GN/m 8WC3n WT = σwb PC y (Lewis equation) (14) 4 δ = 4 0.3 m Gd W = Tangential load(N) T 2δ 5 θ = 5 20⁰ Using equation of motion to determine the pitch D line velocity, V D 6 T = W × 6 6 Nm V2 = U2 + 2aS (15) 2 2 훕퐬 5.3 MJ/ S 7 E = 7 3 4G m = tooth space of the pinion which is the distance moved DP 21 8 T = 8 by the rack P m teeth 2 D 42 a = acceleration due to gravity = 9.81 m/s 9 T = R = 2 T 9 R m P teeth W =W / Cos⁡∅ (16) N T 2 10 WP = 0.00118TPbm 10 0.8 N W =Normal load N 0.912 y = 0.154 – Load on the bearing of the pinion shaft. It is the 11 TP 11 0.11 0 radial load, Wr (for 20 full depth involute system) W = W sin⁡∅ (17) 130 r N 12 σ = σ × C 12 w a V MN/m2 The resultant load, WR (N) 3 2 2 ⁰ 13 C = 13 0.93 WR=√ [(WN) + (WP) ] + 2 × WN × WP × (Cos⁡20 ) (18) V 3 + V

Bending moment on the shaft due to the resultant 14 WT = σwb PC y (Lewis equation) 14 1016 N load, M (N) b 0.22 15 V2 = U2 + 2aS 15 Mb=WR × distance between the centre of pinion m/s and the centre of bearing 16 WN =WT / Cos⁡∅ 16 1081 N Torsional moment on the shaft due to tangential 17 Wr= WN sin⁡∅ 17 370 N load, Mt (N) WR=√ [(WN) 2 + (WP) 2] + 2 × WN × WP 18 18 1082 N Mb=WR × SP (19) × (Cos⁡20⁰)

SP = distance between the centre of pinion and the 19 Mb=WR × SP 19 40 Nm centre of bearing 20 Mt = WT × DP/2 20 16 Nm Mt = WT × DP/2 (20) 21 Te = √ [(Mb) 2+ (Mt) 2] 21 43 Nm Equivalent Twisting moment, Te 2 2 22 d3= (16 Te) /π x τ 22 15 mm Te = √ [(Mb) + (Mt) ] (Khurmi and Gupta, 2004) (21) 3 Calibration of Scale d = (16 Te) /π x τ (22) The materials needed for the calibration of a new d = shaft diameter, mm scale of mechanical weighing machine as follows: τ = shear stress of the shaft material without key = 56 N/mm2 Standard weight of 1 kg to 40 kg were needed and Protractor marking tools

The following procedures were followed in calibrating the scale of simple weighing machine such as:

i. Take where the deflector rested as reference point without load. ii. Mark that point as zero.

www.jmest.org JMESTN42350443 50 Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 3159-0040 Vol. 2 Issue 2, February - 2015 iii. Then add standard weight of 1kg, the IV. CONCLUSION deflector will move, mark where the deflector stop. The mechanical spring weighing machine iv. Repeat the procedure above for other developed could meet the requirements of the user different weight until 40 kg weight is placed and also being that it is simple, strong, durable, portable and mark at that point on the scale. affordable. It will be very useful for the weighing of bulky materials or packed piece in the laboratory. The Find the degree of deflection in between each machine parts can be obtained locally and it can work weight increases from to kg 1 10 for longer period of time if the mechanism is well 35 kg gives 3600 (1 revolution deflection) maintained. 360 1 kg = = 10.30deflection REFERENCES 35 0 [1] Adams, O. E and Paul, H. B. (1983). Machine Therefore 40 kg gives 1 revolution and 50 Design. Published in Moscow, 3rd Edition, pp. deflection (The scale will look like a dial indicator 263. scale) [2] Beekwith, G. T. and Roy, D. M. (1985). “Standard Since 1 kg = 1000 g of Measurement”, Mechanical Measurement, 1000g For 10deflection, we have = 97g Published in Pittsburgh, 5th Edition, pp. 173. 10.3 approximately 100 g [3] Encarta Encyclopedia, (2009). "Scale (weighing), weight and spring." Microsoft Encarta. Redmond, Therefore, it will take as from 100 g weight of load WA. for the deflection to move. When it is less than 100 g weight of load there will be no deflection. [4] Haslam, J. A., summers, G. R and Williams, D. (1977), “Determination of Errors” Engineering III. RESULTS AND DISCUSSION Instrumentation and Control. 5th Edition, Testing the mechanical weighing machine developed Published in India, pp. 58-60. in order to verify its overall performance which is the [5] Hetcalfe, T. J., F.I.W.M.A, (1975). Weighing load carrying capacity of the machine. Materials were Machine, the Institute of Weight and weighed for the testing with different loads placed on Measurement Administration. the weighing machine. The readings taken were given in Table 3 and Fig. 1 shows the variation of the test of [6] Holowenko, A. R. Hall, A. S and Laughtin, H. G. the machine. Therefore, the efficiency of the machine (1983). Spring Design Schaum’s Outline of was determined using equation (23). Theory and Problems of Machine Design, McGram Hill Publishing Company Singapore, pp. Table 3: Testing Data 255-266. Test Measured Valued (kg) [7] Jain, R. K. (1990). “Error in Measuring Instrument”, 1 36.5 Mechanical and Industrial Measurement, Khanna Publishers, 8th Edition. (Revised and enlarged), 2 37.1 India, pp. 15-16. 3 36.8 [8] James, B. H., Martin, J. Siegel et al (1989). 4 37.5 Mechanical Design for Machine, 2nd Edition, Average measured reading (kg) Published in Michigan, pp. 201-240. 36.5 +37.1+36.8+37.5 147.9 [9] Khurmi R. S. and Gupta J. K. (2004) A Textbook of = = = 37.0 kg 4 4 Machine Design. Eurasia Publishing House (P) Average measured value Ltd. Ram Nagar, New Delhi -110055. Efficiency = × 100 (23) Actual capacity of the mchine [10] Redford, G. D. (1975). “Bolt design”, Mechanical 37 Engineering Design the Macmillan Press Ltd, 2nd Efficiency = × 100 40 Edition, England, pp. 144-154. Efficiency = 93 % [11] Robert, L. M. (1992). “Stress Analysis”, Machine Elements in Mechanical Design Macmillan

38 Publishing Company. 2nd Edition, New York, pp. 37.5 70-74. 37 [12] Shigley, J. E and Mischke, C. R. (1989). 36.5 Deflection and Stiffness, Mechanical Engineering 36 McGraw Hill Book Company, 5th Edition. New Weighing Mass Weighing TEST 1 TEST 2 TEST 3 TEST 4 York, pp. 91, 459-676. Testing [13] Shigley, J. E. and Mischke, C.R. (2001). Mechanical Engineering Design. 6th Edition, pp.

Fig. 1: Variation of measured Value 600, pp. 835, pp. 842 www.jmest.org JMESTN42350443 51 Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 3159-0040 Vol. 2 Issue 2, February - 2015 [14] Sirohi, R. S. (1991). Basic Concept of [15] Spots, M. F. (1988). Design of Machine Element, Measurement, Mechanical Measurements, Wiley Prentice Hall of India, 6th Edition, pp.591. Western Limited, 3rd Edition, New Delhi, pp.3-5.

APPENDICES

Plate 1: Fabrication Phase 1

Plate 2: Fabrication Phase 2

Fig. 2: Orthographic Projection of the Spring Weighing Machine

Plate 3: Fabrication Phase 3

Fig. 3: Isometric Projection of the Spring Weighing Machine.

Plate 4: Fabrication Phase 4

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Plate 5: Fabrication Phase 5

Plate 6: Fabrication Phase 6

Plate 7: Assembly

Plate 8: Spring Weighing Machine

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