UNIT 5 Balancing of Reciprocating Masses 1.Obtain an expression for primary forces for V engine having two identical cylinders lying in a plane. The included angle between the cylinder centre line is 22. (06 Marks) (June 2015) Balancing of V - engines Consider a symmetrical two cylinder V-engine as shown in Fig. The common crank OC is driven by two connecting rods PC and QC: The lines of stroke OP and OQ are inclined to the vertical OY, at an angle a as shown in Fig. Let m = Mass of reciprocating parts per cylinder,, = Length of connecting rod, r = Radius of crank, n = Ratio of length of connecting rod to crank radius = 1/ r () = Inclination of crank to the vertical at any instant, w = Angular velocity of crank. Dept of Mechanical Engineering, SJBIT Page 52
Fp2 = m.co2.rcos(0. - 8) Component of F 2 along the vertical line OY = F, cos" a. = m.co2.rcos(0. - 8) cos a.... (iii) pz and component of Fp2 along the horizontal line OX = Fp2 sin a. = m.co2.rcos(0. -'8) sin a.... (iv) Total component of primary force along the vertical line OY Fpv = (0 + (iii) = m.co2.rcos a [cos (a - 8) + cos (a + 8)] = m.co2.rcos a x 2 cos a cos b. Dept of Mechanical Engineering, SJBIT Page 53
2.A four crank engine has two outer cranks set at 1200 to each other, and their reciprocating masses are each 400 kg. The distance between the planes of rotation of adjacent cranks are 450 mm, 750 mm and 600 mm. If the engine is to be in complete primary balance, find the reciprocating mass and the relative angular position for each of the inner cranks. If the length of each crank is 300 mm, length of each connecting rod id 1.2 m and the speed of rotation is 240 rpm, what is maximum secondary unbalanced force? (14 Marks) (June 2014) Dept of Mechanical Engineering, SJBIT Page 54
Dept of Mechanical Engineering, SJBIT Page 55
Dept of Mechanical Engineering, SJBIT Page 56
4.A single cylinder reciprocating engine has the following data: Speed the engine = 120rpm: Stroke = 320 mm; Mass of reciprpcating parts = 45 kg; Mass of revolving parts = 35 kg at crank radius. If 60% of the reciprocating parts and all revolving parts are to balanced, find i) Balance mass required at radius of 300 mm and ii) unbalanced force when the crank has turned 60 from the TDC. (10 Marks) (Dec 2014) 5.A 90 V engine has 2 cylinders, placed symmetrically. The two connecting rods operate a common crank. The length of connecting rods are 320 mm each and crank radius is 80mm. The reciprocating mass per cylinder is 12kg. If the engine runs at 600 rpm, determine the resultant primary and secondary forces. Also, find the maximum resultant secondary force. (10 Marks) (Dec 2014) Dept of Mechanical Engineering, SJBIT Page 57
ii) Secondary reverse crank position: Reverse crank for cylinder I rotates 20 = 2 x 45 = 900 counter clock wise from the line of stroke of cylinder 1 for cylinder 2 it rotates 20 = 2 x 315 = 6300 counter clockwise from the line of stroke of cylinder 2 thus the positions of secondary reverse cranks are as shown in fig.... max unbalanced secondary for = 820.543N Dept of Mechanical Engineering, SJBIT Page 58
6.Check the condition of primary and secondary balancing of 2 - cylinder and 3 - Cylinder in line engine. (06 Marks) (June 2015) A multi - cylinder engine with the cylinder centre 'lines in the same plane and on the centre line of the crank shaft are known as In - line engines. The following two conditions must be satisfied in order to give complete primary balance of an engine. 1. The algebraic sum of the primary forces = O. In other words the primary force polygon must close. 2. The algebraic sum of the couples about any point in the plane of the primary forces equal to zero. The algebraic sum of the couples about any point in the plane must be equal to zero. In other words th! secondary couple polygon must close. 7.In an in line six cylir der engine working on two stroke cycle, the cylinder centre lines are spaced at 650 mm. In the end view, the cranks are 60 apart and. in the order 1-4-5-2-3-6. The stroke of each piston is 400mm and the connecting rod length is 1m. The rotating part is 100 Kg per crank and reciprocating mass is 250 kg/cylinder and operating speed is 240 rpm. Examine the engine for the balance for primary and secondary forces and couples. (14 marks) (June 2015) Dept of Mechanical Engineering, SJBIT Page 59
Dept of Mechanical Engineering, SJBIT Page 60
Dept of Mechanical Engineering, SJBIT Page 61
Explain the terms primary balancing and secondary balancing as used in balancing of reciprocating masses. (5 marks) (June 2013) Primary balancing means the resultant primary forces and couple is zero. i.e., I: Primary forces = 0 I: Primary couples= 0 Primary forces gi yes by rnrw'cosa which acts along the line of stroke and varies through a cycle which coincides with the shaft rotation. Secondary balancing means the resultant secondary forces and couples is zero. i.e., I: Secondary forces = 0 L Secondary couples = 0 Secondary force is given by which acts along the line of stroke but undergoes a cyclic variation at twice the speed of shaft. Dept of Mechanical Engineering, SJBIT Page 62
The pistons of a 4-cylinder vertical inline engine reach their uppermost position at 90 interval in order of their axial position. Pitch of the cylinder = 0.35m, crank radius =0.12m, length of CR = 0.42m. The engine runs at 600 rpm. If the reciprocating parts of each engine have a mass of 2.5kg, find the unbalanced primary and secondary forces and couples. Take the central plane of the engine as reference plane. (15 marks) (June 2013) Dept of Mechanical Engineering, SJBIT Page 63
The firing order in a six cylinder four stroke jnline engine is 1-4-2-6-3-5. The piston stroke is 100 mm and length of each connecting rod is 200 mm. The pitch distance between cylinder centre lines are 100 mm, 100 mm, 150 mm, 100 mm and 100 mm respectively. The reciprocating mass per cylinder is 1 kg and engine runs at 300 rpm. Determine the output primary and secondary forces and couples on the engine, taking a plane midway between the cylinders 3 and 4 as reference plane. (16 Marks) (Dec 2014) Dept of Mechanical Engineering, SJBIT Page 64
Dept of Mechanical Engineering, SJBIT Page 65
A five cylinder inline engine running at 500 rpm has successive cranks at 1440 apart. The distance between the cylinder line is 300 mm. Piston stroke is 240 mm, length of connecting rod is 480 mm. Examine the engine for balance of primary and secondary forces and couples. Find the maximum value of these and position of central crank at which these maximum 'values occur. The reciprocating' mass for each cylinder is 150 N (15Marks) (June 2014) N=500rpm stroke=240mm d=480mm=0.48m m=-kg1=5015.3kg 9.81 W = 27tN = 27tx 500 = 52.36rad I s 60 60 n = stroke = 240 = 120mm = 0.12m Dept of Mechanical Engineering, SJBIT Page 66
Dept of Mechanical Engineering, SJBIT Page 67