Question

For the bevel gear set shown below, shaft AB is rotating at 700 rpm and transmits 8.5kw, with a 25° pressure angle. 75 mm -165 mm 100 mm 20 mm dia. 75 mm 33 mm 100 mm 28 mm dia. a) Determine the bevel angle y for the pinion on shaft AB and bevel angler for the gear on shaft CD. (8 marks) b) Determine the pitch-line velocity. (4 marks) c) Determine the tangential, radial, and axial forces transmitted through the gears (pinion and gear). (8 marks)

Answer 1

Given Data

Diameter of pinion Dp = 66mm

Diameter of Gear Dg = 200mm

Diameter of pinion shaft D1=.20mm

Diameter of Gear shaft D2 = 28mm

Power developed P= 8.5kW

Pressure angle of the gear ϕ=25o

Speed in rpm, N =700 Rpm

(a) (i) the bevel angle for pinion on shaft AB is :

tan $\gamma$ = (Np/NG)

tan $\gamma$ =(Dp/Dg)

$\gamma$ = tan-1(Dp/Dg) =   tan-1(66/200) = 18.27o

(a) (ii) the bevel angle for the gear of shaft CD is :

tan $\Gamma$ = (NG/Np)

tan $\Gamma$ =(Dg/Dp)

$\Gamma$ = tan-1(Dg/Dp) = tan-1( 200/66) = 71.74o

(b)The pitch line velocity is given as :

V 1 x Dp XN 60

2 7 X 0.066 x 700 60

V = 2.4178m/s

(c)(i) Calculation for tangential force :

$F_{_{_{T}}} = \frac{P}{v}$

$F_{_{_{T}}} = \frac{8.5}{2.4178}$

(c)(ii) Calculation for radial force :

$F_{_{_{r}}} = F_{t} \times tan \phi \times cos\gamma$

$F_{_{_{r}}} = 3.5156 \times 0.4663 \times 0.9496$

(c)(iii) Calculation for axial force :

$F_{_{_{a}}} = F_{T} \times tan\phi \times sin\gamma$

$F_{_{_{a}}} = 3.5156 \times 0.4663 \times 0.454$