Question

ch20Engg-1 pdf (c) The total sleeve movement in a spring controlled Hartnell governor is 30 mm. The mass of rotating balls is 1.4 kg each. At the mid-position of the sleeve, the sleeve arm, which is 65 mm long, is horizontal. The ball! arm is 75 mm long. The balls rotate at a radius of 100 mm when the sleeve is at mid-position. Due to the wrong adjustment of spring, the top speed of the governor is 422 rpm and that corresponding to the lower position is 435 rpm. Determine 6) the stiffness of the spring, and (i) the required initial compression of the spring to give an equilibrium speed at the topmost position which is 12 rpm more than at the lowest position, if the sleeve mass is neglected. Neglect the effect of obliquity of arms.

Answer 1

Solutions Given data: Total sleeve movement (5,-2) = 30 mm. Mass of rotating balls (m) = 1.4kg Sleeve arm (6) = 65 mm, Ball arm (a) = 75 mm Radius of rotation at mid-position () = joo mm. Top speed of Governor (Mg) = 422 8pm, At lower position, speed (N₂) = 435 8pm. – we know that, (x2-x) = b (de-la) > By- og = 65-X)Xq - 30% This = 34.6) Also, t= litry » Atky = 24 = 2x 150 - 200 mm - (2) from egn (1) & (2), (2= 82.6925 mm and l= 117.3075 mm ! Now, fiz mog op? = 4X82-6125615% * (250X435) [F, = 240: 231 Fy mly.co2 = 1:48 117.3645 x16?x (271X42212 1F, = 320.727 N 60 Stifte, (is given by, s=2048) (H)? Se * 1.- 2 (320-727- 240-231) (117.3075 - 82.6925) x 16 → S = 6192.068 W/W) Als

(s. Let N = N. 8pm then, H₂ = (N+12) spm. As the stiffness of spring Se 2(f-) (912 remains constant, = 6-192 = 20 2.89.6020 KPH - (4) → (F4-Fi) = 80.495 Ml G = 4,2 = 148 12-3-45 x15 x C +11) F = 1-801 X 1003 (12+ 24N+144). — (3) fiz mody w 2 = 1-4X82-6925 X163 x x N2] F = 1.269 X 163 M2 Subtracting egh (4) from eqn (3). 1.Sol X10-3 (N2+24 N +144) - 1.269 X 16-3 N2 = (fs-F) = 80.495 Solving the equation, N= 349.849. 8pm] Now, f = 1.269x103N2 = 1.269816-3x(3.49.849)2 [E = 155-318 N/ Also, spring force (Fs.) = 29 h = 2X (75) x 155.318. F = 358.427N Dritial Compeetsion, x = fsi x = 358-427 124 = 57.88 mm Aus. 358-427 6-192