GEARS AND GEAR TRAIN EXAMPLES

In all cases, assume a pressure angle of 200.

Q1. A pinion gear, having 24 teeth, has a module of 2 mm/tooth and rotates at 1200 rpm. It drives a gear at 400 rpm. Determine the number of teeth on the gear, the pitch circle diameter of the pinion and gear and the centre distance of the gears.

Q2. For the spur gear configuration shown in Figure Q2 and assuming a 100% gear efficiency, m = 2, NA = 20, NB = 40 and NC = 30, calculate:-

i) the pitch circle diameter (in mm) and angular velocity (in rad/s) for each gear;ii) the torque transmitted to Gear C (in Nm);iii) the force exerted by Gear C on its shaft (in kN);iv) the force exerted on the lay shaft bearings (in kN).

Figure Q2Q3. Repeat Q2, with a gear-pair efficiency of 95%.

Q4. A double-reduction gear train, based on the configuration previously used in the notes, has the following parameters:-

mA = mB = 4; mC = mD = 3; NA = 10; NB = 15; NC = 12; ND = 20

The motor (attached to Gear A) produces 20 kW @ 1200 rpm and the bearing configuration on the countershaft is a = 25 mm, b = 100 mm, c = 50 mm. Assuming no power loss in the gears, calculate:-

i) the speed (in rpm) of each gear;ii) the overall speed reduction ratio;iii) the input and output torques (in Nm);iv) the radial force on each bearing (in kN).

Q5. Repeat Q4, with a gear-pair efficiency of 90%.

Q6. If the speed reduction ratio in Q4 is to be increased by 50%, suggest an alternative gear-pair arrangement and comment on the resulting effect on the countershaft bearings.