Question

Horizontal true centrifugal casting is used to make aluminum rings with length = 5 cm, outside diameter = 65 cm, and inside diameter = 60 cm. (a) Determine the rotational speed that will provide a G-factor = 60. (b) Suppose that the ring were made out of steel instead of aluminum. If the rotational speed computed in part (a) were used in the steel casting operation, determine the G-factor and (c) centrifugal force per square meter (Pa) on the mold wall. (d) Would this rotational speed result in a successful operation? The density of steel = 7.87 g/cm3

Answer 1

a) 423 rpm

b) G-factor = 60

c)
`P= 231634.882 Pa`

d) Yes, it would result in a successful operation

Step-by-step explanation:

Given that:

length of aluminium ring = 5 cm

outside diameter
`d_1` = 65 cm

inside diameter
`d_2` = 60 cm

rotational G - factor = 60

G- factor =
`(centrifugal force)/(gravitational force )`

G- factor =
`(mv^2)/(r.mg)`

G- factor =
`(v^2)/(rg)`

where v = r ω and ω =
`(2 \pi N)/(60)`

`\omega = (2*3.14N)/(60)`

G- factor =
`( r ((2(3.14)/(60)N)^2 )/(g)`

G- factor =
`(2r (0.005477)*N^2)/(9.81)`

`N^2 = (60)/(2r*0.000558)`

`N = \sqrt{(107526.882)/(60*10^(-2)) }`

N = 423 rpm

b) However, the material is steel and N = 423 rpm

∴ 423 ⇒
`42.3\sqrt{(G-factor)/(60*10^(-2)) }`

`10 = \sqrt{(G-factor)/(6.0*10^(-2)) }`

G-factor = 60

Thus, the G-factor is independent of the material

c) Centrifugal force per square meter is expressed as:

`P = (F)/(A)`

where; F =
`(mv^2)/(r)`

`P= (mv^2)/(r.A)`

Also; m = ρ. V

and V = A. l

∴

`P = (\rho (A.l)V^2)/(r.A)`

`P = (\rho lV^2)/(r)`

where;

ρ = 7.87 g/cm ³

ρ = 7870 kg/m³

`P = (7870(5*10^(-2))(r.\omega)^2)/(r)`

`P = {7870(5*10^(-2))r.\omega^2}`

`P = {7870(5*10^(-2))*30*10^(-2).((2 \pi 423)/(60) )^2`

`P= 231634.882 Pa`

d)

The rotational speed will possibly result into a successful operation. This is so because the range of speed of operation of centrifugal casting is between (300- 3000) rpm and N = 423 rpm which tells us that; it is still in range and will definitely result into a successful operation.