EQUATIONS AND CONSTANTS

[Pages:6]EQUATIONS AND CONSTANTS

CONSTANTS

gc = 32.2 lbm-ft/lbf-sec2 Kair = 1.395

R = 53.34 lbf-ft/lbm- ?R Cp air = 0.240 BTU/lbm- ?R

Cp water at 70EF = 0.998 BTU/lbm-?F

Cp water at 160EF = 1.000 BTU/lbm-?F

1 HP = 42.4 BTU/min = 0.746 Kwatts = 550 ft-lbf/sec

1 Watt = 1 J/sec = 0.05688 BTU/min

1 BTU = 778 ft-lbf 1 in. H20 = 0.03611 lbf/in2 = 5.199840 lbf/ft2 1 in.hg. = 0.491 lbf/in2 1 gal = 0.1337 ft3

1 ton ref. = 200 BTU/min

1 BTU/lbm-EF = 1 cal/g-?C

1 slug = 32.2 1bm

T(?C) = 5/9(?F-32)

g H2O = 62.4 lbf/ft3 air at STP = 0.07654 lbm/ft3

T(?R) = T(?F) + 460 T(?K) = T(?C) + 273

?F = degrees Fahrenheit

?C = degrees Celsius

?K = degrees Kelvin

?R = degrees Rankine

DYNAMIC BALANCING EQUATIONS

A1 =

( A10 )2 + ( A1180 )2 - 2 A2 = 2

( A190 )2 + ( A1270 )2 - 2 A2 2

A2 =

( A20 ) + ( A2180 )2 - 2 A2 = 2

( A290 )2 + ( A2270 )2 - 2 A2 2

B1 =

(B10 )2 + (B1180 )2 - 2B 2 = 2

(B190 )2 + (B1270 )2 - 2B 2 2

B2 =

(B20 )2 + (B2180 )2 - 2B 2 = 2

(B290 )2 + (B2270 )2 - 2B 2 2

= The angle of original unbalance

=

Tan

-1

A190 ( A10

) )

2 2

- (A1 )2 - (A1 )2

- A2

-

A2

B

=

Tan

-1

(B190 ) 2 (B10 ) 2

- (B1 )2 - (B1 )2

- -

B2 B2

M A = RA M trial

RAA1 + RB A2 = - A

R Ax

=

B(A2 ) cos B - A(B2 ) cos (A2 )(B2 ) - (A2 )(B1 )

A

R Ay

=

B(A2 ) sin B - A(B2 ) sin A (A1 )(B2 ) - (A2 )(B1 )

M B = RB M trial

RAB1 + RB B2 = -B

RBx

=

-

A cos A - RAx A1 A2

RBy

=

-

Asin A - RAy A1 A2

VIBRATIONS/MECHATRONICS EXPERIMENT

Beam Data:

E = 69GPa

b

=

2700

kg m3

Lb = 30cm

b = 0.0127m (Width of the beam)

hb = 0.00317m (Thickness of the beam in the bending direction)

n Lb = 1.875

Equations:

fn

=

( n Lb )2 2Lb 2

EI l

,

I

= bhb3 12

,

l

=

bbhb

U

n

(x)

=

cosh(

n

x)

-

cos(

n

x)

+

B2 B1

n

(sinh( n

x)

-

sin( n

x))

B2 B1

n

=

sin( n Lb ) cos( n Lb )

- sinh( n Lb ) + cosh( n Lb )

f mass-added

fn 1+ MU n (x*)2

Mb

k

= ln

x1 xk

,

=

k k 2 + 4(k -1)2 2

fd = fn 1- 2

1-D TRIANGULAR FIN

1-D Fin Equation

d 2 dx 2

+

1 x

d dx

- x

p2

=

0

where

= T - T ,

x' L'

= x,

L=

L' , Bi = h l and p =

l

k

BiL2 f

x = 0,

= finite

x = 1,

= 0 = Tw - T

= I 0 (2 Bx ) where B = hl L2 1 + 1

0 I0 (2 B )

k

L2

Least Squares Methodology General Fi = A fi i = Fi - ( A fi )

S = 2 = fi2 - 2 A Fi fi + A2 fi2

S = 0 results in A

A = Fi fi fi2

2 = (i - )2 n

= i

n

Specific

i = D I 0 (2 Bxi ) = D Ii i = i - D Ii

S =2

=

2 i

-

2D

iIi + D2

I

2 i

S = 0 results in D

D = i Ii = i I0 (2 Bxi )

I

2 i

I

2 0

(2

Bxi )

2 = (i - )2 n = i n

ACOUSTICS

=1

-

SP L

; c = f ; S W R = 10 20

, c2

T H E O R Y = K T Rgc , U =

p c

pt = pi

+

pr = A s i n t

+

B s i n ( t

-

2

c

x -

)

| pt | =

A 2

+

B2 + 2 AB

c o s (2 x

+ )

c

n

=

A2 - B2 A2

= 1

-

B 2 A2

| pt |MAX = A2 + B2 + 2 AB = A + B

| pt |MIN = A2 + B2 - 2 AB = A - B

n

=

4 | pt |MAX | pt |MIN (| pt |MAX + | pt |MIN )2

Lp,max

?

Lp,min

=

20

log

10

|

|

Pt Pt

|max |min

dB

SWR

=

p MAX

=

A

+

B

=

1 +

B/A

SP L

= 10 20

pMIN A - B 1 - B/A

n

=

(1

4 SWR + SWR

) 2

m& = V A

1 H = g ( Po u t - Pi n )

Pw = g Q H Ps = 2 N T

= Pw Ps

v =

Q

Q + QL

ud =

u

2 o

+

u c2

uy =

f x1

u

x1

2

+

f x2

u

x2

2

PUMP EXPERIMENT

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