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# Verify Results2

## Verify Results

(OP)
Hi All,

Could you please check my calculations to see if I have this correct, it's been a while & need to check.

Stress in Flywheel
4140 Steel
Tensile strength 655 MPa 95000 psi
Yield strength 415 MPa 60200 psi

σt-max = d/4 * w^2 * ( 3+ v * R2^2 + (1-v) * R1^2

σt-max is the maximum internal stress in the flywheel N/m^2

d is the density of the flywheel material Kg/m^3

ω is the angular velocity of the flywheel rad/sec

v is the Poisson ratio of the flywheel material-Steel

The Factor of safety FOS can be calculated as

FOS = σ-yield / σt-max

Where

(σ yield) is the possible angular velocity when the maximum internal stress equals the yield stress of the material.

Flwheel Diam R2 = 0.15 radius mtrs

Flywheel inner dia R1 = 0.025 radius mtrs

Density of steel = 7850 Kg/m^3

Tensile strength = 655 Mpa

Pa = 655000000 Pascals

Poisson's ratio (v) = 0.3

Velocity = 235.65 m/s

rpm max = 15000

σt-max = d/4 * w^2 * ( 3+ v * R2^2 + (1-v) * R1^2

d/4 = 1962.5

ω^2 = 2468041

3+v = 3.3

R2^2 = 0.0225

1-v = 0.7

R1^2 = 0.000625

σt-max = 2343814.663 N/m^2

= 2.343814663 Mpa

FOS = σ yield / σt-max

= 415 Mpa / 2.343814663 Mpa

FOS = 177.0618 ??

The FOS appears to be very high do I have this correct?

### RE: Verify Results

your brackets don't balance. I suspect you're missing three ... ( (3+ v) * R2^2 + (1-v) * R1^2 )

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

### RE: Verify Results

(OP)
Thanks rb1957, that works!

### RE: Verify Results

stilkikin (Mechanical)(OP),

The units are not consistent .Apparently you are following SI units , the unit of density SHALL BE ( WT=Newton / 9.8) That is , 78500/9.81=
The answer should be in the range of 180 mPa.
Will you post the excerpt showing the formula?

Use it up, wear it out;
Make it do, or do without.

NEW ENGLAND MAXIM

### RE: Verify Results

(OP)
HTURKAK,
The formula was from memory, which is fading obviously & why I need correction.
Not sure I follow what you are suggesting?
The SI units for solids-density are Kg/m^3 or g/cm^3 which would be 7850Kg/m^3 or 7.85g/cm^3

Could you give me an example to have a look at?

### RE: Verify Results

The following is excerpt from STANDARD HANDBOOK OF MACHINE DESIGN ( By E. Shigley , R. Mischke )

If we put your data to the expression (18.58)
σ0 = 78500*(0.15**2)*(1571**2)*(3+0.3)/(8*9.81) =183298744 N/m2 =183 MPa.

and the max. tangential stress would be around double of σ0. I think there are some typo mistake at your expression. If you post the original formula we can see the mistake. Regarding the density , i have used one more zero with typing mistake and corrected .

Use it up, wear it out;
Make it do, or do without.

NEW ENGLAND MAXIM

### RE: Verify Results

weight density (N/m3) divided by "g" is just mass density (kg/m3). dividing things by "g" is a sign of the imperial system. Maybe that equation assumes imperial units (ie weight density in lbf/in3) ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

### RE: Verify Results

(OP)
Rearranging my missing brackets as kindly suggested, I get the following.

4140 Steel
Tensile strength 655 MPa 95000 psi
Yield strength 415 MPa 60200 psi

Stress in Flywheel
σt-max = d/4 * w^2 *((3 + v) * R2^2 + (1-v) * R1)
σt-max = the maximum internal stress in the flywheel N/m^2
d = the density of the flywheel material Kg/m^3

ω = the angular velocity of the flywheel rad/sec
v = the Poisson ratio of the flywheel material 0.3
The Factor of safety FOS can be calculated as
FOS = σ yield / σt-max
Where
σ yield is the maximum possible angular velocity when the maximum internal stress equals the yield stress of the material.

Flwheel Diam R2 = 0.15 radius mtrs
Flywheel inner dia R1 = 0.025 radius mtrs
Density of steel = 7850 Kg/m^3
Tensile strength = 655 Mpa
Yield strength = 415 MPa
Poisson's ratio v = 0.3
Velocity- Peripheral = 235.65 m/s
kph = 848
rpm max = 15000

σt-max = d/4 * ω^2 * ((3 + v) * R2^2 + (1-v) * R1)

= 1962.5 * 2468041 *(( 3.3 ) * 0.0225 + (0.7) * 0.025)

= 4,843,530,462.5 * 0.07425 + 0.0175

= 4,843,530,462.5 * 0.09175
= 444,393,919.9 N/m^2
= 444.4 MPa

FOS = σ yield / σt-max
415 MPa / 444.5 MPa
= 0.933 = DANGER ?

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