24 table of motions revolutions of elements step no

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Unformatted text preview: 130 × 103 W First of all, let us find the number of teeth on the sunwheel D (T D). Let dA , dB , dC and dD be the pitch circle diameters of wheels A , B , C and D respectively. From Fig. 13.29, dD d d d or dD + dC + dB = dA + C+ B= A 2 2 2 2 Since the module is same for all teeth and the number of teeth are proportional to their pitch circle diameters, therefore TD + T C + T B = T A or T D = T A – (T C + T B) = 60 – (20 + 15) = 25 The table of motions is given below : Table 13.24. Table of motions. Revolutions of elements Step No. Conditions of motion Arm (or shaft X) Wheel D Compound wheel C-B TD TC 1. Arm fixed-wheel D rotated through + 1 revolution (anticlockwise) 0 +1 – 2. Arm fixed-wheel D rotated through + x revolutions 0 +x – x× 3. Add + y revolutions to all elements +y +y +y 4. Total motion +y x+y y –x× Wheel A (or shaft Y) – TD TC TD TB × TC TA –x × TD TB × TC TA +y TD TC y –x× TD TB × TC TA Since the shaft Y or wheel A rotates at 740 rad/s, therefore y –x × TD TB × = 740 TC TA y – 0.3125 x = 740 or y –x× 25 15 × = 740 20 60 ...(i) Chapter 13 : Gear Trains l 469 Also the wheel D is fixed, therefore x +y=0 or y=–x ...(ii) From equations (i) and (ii), x = – 563.8 and y = 563.8 Speed of shaft X Since the shaft X will make the same number of revolutions as the arm, therefore Speed of shaft X , ωX = Speed of arm = y = 563.8 rad/s Ans. Holding torque on wheel D We know that torque on A = P/ωA = 130 × 103 / 740 = 175.7 N-m and Torque on X = P/ωX = 130 × 103/563.8 = 230.6 N-m ∴ Holding torque on wheel D = 230.6 – 175.7 = 54.9 N-m Ans. Example 13.23. Fig. 13.30 shows some details of a compound epicyclic gear drive where I is the driving or input shaft and O is the driven or output shaft which carries two arms A and B rigidly fixed to it. The arms carry planet wheels which mesh with annular wheels P and Q and the sunwheels X and Y. The sun wheel X is a part of Q. Wheels Y and Z are fixed to the shaft I. Z engages with a planet wheel carried on Q and this planet wheel engages the fixed annular whe...
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