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52070-467995SRI RAMAKRISHNA INSTITUTE OF TECHNOLOGY, COIMBATORE-10(Approved by AICTE, New Delhi – Affiliated to Anna University, Chennai)center-629920UNIT II- BALANCINGTUTORIAL 1A rotating shaft carries three unbalanced masses of 4kg, 3kg and 2.5kg at radial distances of 75mm, 85mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The second and third masses are in the planes at 200mm and 375mm from the plane of the first mass. The angular positions are measured counter-clockwise from the reference line along x axis and viewing the shaft from the first mass end.The shaft length is 800mm between bearings and the distance between the plane of the first mass and the bearing at that end is 225mm.Determine the amount of the counter masses in the planes at 75mm from the bearings for the complete balance of the shaft. The first counter mass is to be in a plane between the first mass and the bearing and the second mass in a plane between the third mass and the bearing at that end.Given Data:m1 = 4 kgr1 = 75mm θ1 = 45°m2 = 3 kgr2 = 85mmθ2 = 135°m3 = 2.5 kgr3 = 50mmθ3 = 240°Solution:Plane Diagram and Space Diagram: PlaneMass(kg)Radius(m)Force (mr) kg.mDistance From RP (m)Couple(kg.m2)X(RP)mx0.0750.075 mx00140.0750.3000.1500.045230.0850.2550.3500.08932.50.0500.1250.5250.065Ymy0.0400.040my0.6500.026myCouple Polygon:0.026my=74.34/1000my=0.07434/0.026my= 2.859 kgθy=148.84+180°θy=328.84°Force Polygon:0.075 mx=23.24/10mb =0.2324/0.075my= 3.1 kgθy=74.74+180°θy=254.74°TUTORIAL 2A shaft carries four masses of magnitude 200kg, 300kg, 400kg and 200kg respectively and revolving at radii 80mm, 70mm, 60mm and 80mm in planes measured from 1 at 300mm, 400mm and 700mm. The angles between the cranks measured anticlockwise are 1 to 2 is 45°, 2 to 3 is 70° and 3 to 4 is 120°. The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 100mm between X and Y is 400mm and Between Y and D is 200mm. If the balancing masses revolve at a radius of 100mm fine their magnitudes and angular positions.Given Data:m1 = 200 kgr1 = 80 mm θ1 = 0°m2 = 300 kgr2 = 70 mmθ2 = 45°m3 = 400 kgr3 = 60 mmθ3 = 115°m4 = 200 kgr4 = 80 mmθ4 = 235°To Find:Magnitude of X = mx Magnitude of Y = my Angular Position of X = θx Angular Position of Y = θySolution:Plane Diagram & Space Diagram: PlaneMass(kg)Radius(m)Force (mr) kg.mDistance From RP (m)Couple(kg.m2)12000.08016-0.100-1.6X(RP)mx0.1000.100 mx0023000.070210.2004.234000.060240.3007.2Ymy0.1000.100 my0.4000.04my42000.080160.6009.6Couple Polygon:0.04my=73.62/10my=7.362/0.04mx = 184.05 kg θy =167.20+180°θx =347.20°Force Polygon:0.1mx=35.29my=35.29/0.1my = 352.9 kgθy =33.38+180°θy =213.38°TUTORIAL 3A shaft carries four rotating masses A, B, C and D which are completely balanced. The masses B, C and D are 50 kg, 80 kg and 70 kg respectively. The masses C and D make angles of 90° and 195° respectively with mass B in the same sense. The masses A, B, C and D are concentrated at radius 75 mm, 100 mm, 50 mm and 80 mm respectively. The plane of rotation of masses B and C are 250 mm apart. Determine The magnitude of mass A and its angular position andThe position planes A and D.Given Data:ma = - kgr1 = 75 mm θ1 = ?°mb = 50 kgr2 = 100 mmθ2 = 0°mc = 80 kgr3 = 50 mmθ3 = 90°md = 70 kgr4 = 80 mmθ4 = 195°To Find:Magnitude of A = ma Angular Position of A = θA Position of APosition of DSolution:Diagram:PlaneMass(kg)Radius(m)Force (mr) kg.mDistance From RP (m)Couple(kg.m2)A ma0.0750.075 ma-x-0.075 maxB(RP)500.100500C800.0504.251D700.0805.6y5.6yForce Polygon:0.075ma=25.83/10my=2.583/0.075ma= 34.44 kgθy=279.11°5.6y= 4.78/3y=1.59/5.6y= 28.39-0.075 max=29.13/3x=-376mm ................
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