Question

12. A truck carrying a load of 9 kN has a mass of 450 kg. The driving wheels are 1.066 m in diameter. The total coefficient of air and road resistance is 0.22. The gear ratio and efficiencies are e = 8:1, 1-92% for the transmission and e = 5:1, n=95% for the differential, respectively. T e-8:1, 7-92% I Engine e-5:1, n=95% Differential Transmission Address the following: a) compute the total tracking force (N) b) compute the wheel rotational speed and speed of the transmission and engines shafts at a truck speed of 15 km/hr. c) calculate the power necessary to move the vehicle at a speed of V = 15 km/hr d) estimate the service factor for the four-cylinder engine e) determine power, torque, rotational speed for engine, transmission, and rear end wheel shaft at a truck speed of 15 km/hr, thus fill out the following table (fill out both Sl and ENG values): Power (kW)/(HP) Speed (rad/sec) / (rpm) Torque (N-m) / (in-lb) Component Engine Transmission Wheel Shaft 1 /

Answer 1

The detailed step by step calculations for the sub-parts of the question are described in the images below:

Page 1 e=8:1, n = 92% e= 5:1, n=95% Engine C . 'Differential Transmission > * Criven Data: Load carried by the truck, Wy = 9 KN - goooN Mass of the truck, me = 450 kg. Diameter of the driving wheels, dw = 1.066 m - Total coefficient of air and road resistance, K = 0.22 For transmission : Greas ratio, e, = 8:1 'R Efficiency, nt= = 927. - For differential: Crear ratio, e₂=5:1 Efficiency, no = 95 y. Now, Total weight of the truck (W) is given by, W = Wit (m. g) 9000 + ( 450 * 9.81) = 13,414.5 N 13.415 KN Now, Total Resistance to the motion of the truck (including air and road resistances) is given by, KRXW = 0.22 x 13.415 = 2.9513 KN R Total

Page - 2 Now, the velocity of the truck, v = 15 km/hr 15 X 100 3600 4.17 m/s Overall Efficiency ชา = ne xn O D -0.92 x 0.95 0.874 col 87.4.) - Hence, Power required to move the vehicle at a speed of v=4.17 m/s (15 km/he) is given by, Pengine = R Total XV mo 2.9513 x 103 x 4.17 0.874 14,081.15 Pengine 14.081 kW Ans is given by, Now, total tracking force F Torque at driving wheel (Tw) trucking Radius of driving wheel (rw) e,. e. no. Tengine (dw/2) . F 11 tracking 2e,. e2.no. Tengine dw

Page 3 Now, the peripheral velocity of the driving wheel, V = Tdw. No 60 Nw - V x 60 T X dw 4.17 X 60 T X 1.066 .. Nw 74.71 rpm Ans - Now, differential gear ratio of e2= 5:1 is between the transmission and driving wheels, we can write, Cread Ratio , ez speed of transmission shaft speed of driving wheel 5 11 T کی لم .: NT 5X Nw Ans - NT 373.55 rpm Now, transmission gear ratio of e, = 8:1 is between the transmission shaft and the engine shaft, .. we can write, creaus Ratio, = speed of the engine shaft Speed of the transmission shaft e -

NE Page-4 NT e, xNT 8 X 373.55 NE - 2988. 4 1 rpm Ans - Now, Pengine = 2INETE 60 X1000 TE 44.995 Nim .: From equation tracking 2.e,. ez.no. Te dw こ 2 X 8 X 5 X 0.874 X 44.995 1.066 - 2951.27 N Ans 4 tracking Now, Power available at the transmission shaft, P. = na pengine transmission 0.92 X 14.08! P transmission 12.95 KW we also know that, - P transmission ZINITT 60 X1000 Т. transmission mission Ppx60x1000 2т хJт

Page - 5 T 12.95 x 60 X 1000 T 2x X 373.55 331.16 N.m T Power available at wheel shaft, Now, Puheed nox transmission 0.95 X 12.95 wheel 12.30 25 kw wh - we also know that wheel = 27 Nw Tw 60 x 1000 Tw Pw xboxlovo 2X TXNw 12.3025 X 60 X1000 2XT x 74,71 Tw = 1572.48 Nom Answers → Component Power (KW) Engine 14.081 Transmission 12.95 wheel shaft 12.3025 speed CRPM) 2988.41 Torque Nim) 44.995 373.55 331.16 74.71 1572.48