A 20° involute pinion with a pitch circle diameter of 192 mm is meshing gear. Calculate: The tangential force between the gears. The radial force between the gears. The normal force between the gears.

Here's how to calculate the forces between the gears: Given: Pressure angle, = 20^ Pitch circle diameter, D = 192 mm = 0.192 m Power transmitted, P = 18 kW = 18000 W Rotational speed, N = 200 rpm Step 1: Calculate the angular velocity and tangential velocity. First, convert the pitch circle diameter to radius: r = (D)/(2) = 0.192 m2 = 0.096 m Next, convert the rotational speed from rpm to angular velocity in rad/s: = (2 N)/(60) = 2 (200 rpm)60 s/min = (400 )/(60) rad/s = (20 )/(3) rad/s ≈ 20.944 rad/s Now, calculate the tangential velocity: v = r = ((20 )/(3) rad/s) (0.096 m) = 0.64 m/s ≈ 2.011 m/s Step 2: Calculate the tangential force (F_t). Power transmitted (P) is the product of tangential force (F_t) and tangential velocity (v): P = F_t · v Rearrange to solve for F_t: F_t = (P)/(v) = 18000 W0.64 m/s F_t ≈ (18000)/(2.0106) N ≈ 8952.55 N The tangential force between the gears is: 8950 N Step 3: Calculate the radial force (F_r). The radial force is related to the tangential force and the pressure angle by the formula: F_r = F_t () F_r = (8952.55 N) (20^) F_r ≈ 8952.55 N × 0.36397 F_r ≈ 3258.60 N The radial force between the gears is: 3260 N Step 4: Calculate the normal force (F_n). The normal force is the resultant force acting along the line of action and is related to the tangential force and pressure angle by: F_n = (F_t)/(()) F_n = 8952.55 N(20^) F_n ≈ 8952.55 N0.93969 F_n ≈ 9527.90 N The normal force between the gears is: 9530 N Send me the next one 📸