Spur gear pair dimensions numerical

Standard 20 degree full-depth system: addendum $= m$, dedendum $= 1.25m$, clearance $= 0.25m$, tooth thickness $= p_c/2$ (no backlash).

(a) Pitch circle diameters

$$d_1 = mz_1 = 5 \times 24 = 120\ \text{mm}, \qquad d_2 = mz_2 = 5 \times 60 = 300\ \text{mm}$$

(b) Centre distance

$$C = \frac{d_1 + d_2}{2} = \frac{120 + 300}{2} = 210\ \text{mm}$$

(c) Speed of gear

$$N_2 = N_1\frac{z_1}{z_2} = 1200 \times \frac{24}{60} = 480\ \text{rpm}$$

Velocity ratio $= z_2/z_1 = 2.5$.

(d) Circular pitch and tooth thickness

$$p_c = \pi m = \pi \times 5 = 15.708\ \text{mm}, \qquad t = \frac{p_c}{2} = 7.854\ \text{mm}$$

(e) Tooth proportions

(f) Outside and root diameters

(g) Base circle diameters ($d_b = d\cos\phi$, $\cos 20^\circ = 0.9397$)

$$d_{b1} = 120\cos 20^\circ = 112.76\ \text{mm}, \quad d_{b2} = 300\cos 20^\circ = 281.91\ \text{mm}$$

(Base circle radii: 56.38 mm and 140.95 mm.)

Answer: $d_1 = 120$ mm, $d_2 = 300$ mm, $C = 210$ mm, $N_2 = 480$ rpm, $p_c = 15.708$ mm, $t = 7.854$ mm; addendum 5 mm, dedendum 6.25 mm, clearance 1.25 mm, whole depth 11.25 mm; outside diameters 130 and 310 mm, root diameters 107.5 and 287.5 mm; base circle diameters 112.76 and 281.91 mm.