makine dinamiği formüller
DESCRIPTION
Makine Dinamiği FormüllerTRANSCRIPT
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xx xy xz x xy yy yz y xz yz zz zH = I i - I j - I k + -I i + I j - I k + -I i - I j + I k
iG xx xy xz x xy yy yz y
xz yz zz z x y z
xx xy xz x xy yy yz y xz yz zz z
dHT = I i - I j - I k + -I i + I j - I k
dt
+ -I i - I j + I k + ( i + j + k)
I i - I j - I k + -I i + I j - I k + -I i - I j + I k
x y x y = = = = 0
i
2 2
G yz z xz z xz z yz z zz zT = (I - I )i - (I + I )j + (I )k
A G 2 2 A G 2 2 A G 2 2xx xx A A yy yy A A zz zz A AA G A G A G
xy xy A A xz xz A A, yz yz A A
I = I I = I I = I
I = I I = I I = I
M y + z M x + z , M x + y
Mx y , Mx z My z
, ,
-
G mil G
m(0.5Lj)r = = 0.5Lj k bileeni yok : r r
m
2 2 2
G mil mil
G A B B G A
a = k r - r k 0.5Lj - 0.5Lj = -0.5Li - 0.5L j
m a = F + F yazarak, F = m a - F ile
2 2
A B yz xz xz yz zz
2 2 2
xz yz zz
2
A G A
Tk + 2L kF - 2L kF = (I - I )i - (I + I )j + I k
m m mI = 0, I = 0, I = L + L L
12 4 3
mTk + 2L kF - 2L k m a - F = L k
3
2
2 2
2 2 2
2 2
4 -2 3
4 - -2 -0.5 - 0.53
4 - -3
- , - , 4 4 3
-
A G
A Ax Ay
Ax Ay
Ax Ay
Ax Ay
B G A
mTk L k F L k m a L k
F F i F j ile
mTk L F j F i L k m L i L j L k
mTk L F j F i mL j j i L k
mL mL mF F T L
F m a F ile
F
2
2 2 2 2
- , -4 4
,
Bx By
A Ax Ay B Bx By
mL mLF
F F F F F F
-
G mil
2 2
G mil mil
22 22
xz yz zz
2 2
A yz xz xz yz zz
2 2
Ax Ay
m(0.5Lj + 2Lk)r = = 0.5Lj + 2Lk r = 0.5Lj
m
a = k r - r -0.5L i - 0.5L j
mL L mLI = 0, I = mL , I = + m
12 4 3
Tk + 4L k F = (I - I ) i - (I + I )j + I k
Tk + 4L k F i + F j = mL
22
22 2 2
Ax Ay
2
Ax Ax
2 2 2
Ay Ay
2
mLi - mL j + k
3
mLTk + 4L F j - F i = mL i - mL j + k
3
mL4L F = -mL F
4
mL-4LF = mL F
4
mLT =
3
2
G A B B Ax Ay
2 2
B
2
2 2 2 2
A Ax Ay B Bx By
m a = F + F yazarak, F = -0.5mLi - 0.5mL j - F i - F j
mL mLF = -0.5mLi - 0.5mL j + i + j
4 4
mL mL = - i - j
4 4
F = F + F F = F + F ve
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A ve B deki tepki kuvvetlerini ve milin asal ivmesini herhangi bir T torku iin bulunuz? Ktle iin 1 kg/m kullannz.
A B B A Ax Ay
2 2
A B yz xz xz yz zz
xz
yz
F + F = 0 F = -F = -(F i + F j)
a aTk + 3(b + )kF -3(b + )kF = (I - I ) i - (I + I )j + I k
2 2
a a a + b a a a 3a 3 a 3aI = -a + b - ba - a - a + b - ba a + b - a + 2b
2 2 2 2 2 2 2 2 2 2
a 3aI = -a + 2b
2 2
2 2
2
zz
2
zz Ax xz yz
2
Ay yz xz
2 2
A B Ax Ay
3 a 3a a a 1 a a- ba a + b - a + b - a - ba a + b - a + b
2 2 2 2 2 2 2 2
aa aI = 8 +8a 0 + + 4b 0 + a
12 4
= T / I = dt, F = -(I + I ) / (6b + 3a),
F = (I - I ) / (6b + 3a)
F = F = F + F
G mil2
G mil mil
G A B B G A
2 2
A yz xz xz yz zz
2
xz yz zz
m(r i + rk) + m(rj + 4rk) r i + rj + 5rk rr = = r = i + rj
2m 2 2
a = k r - r
2m a = F + F , F = 2m a - F
Tk + 6rkF = (I - I ) i - (I + I )j + I k
I = m(r)(r), I = m(r)(4r), I = mr + mr
,
2
A Ax Ay
ve
F = F i + F j,
-
2
G A B A Ax Ay B Bx By
2 2
1 A 2 B yz xz xz yz zz
2 2
xz yz zz
2 2 2 2
A Ax Ay B Bx By
ma -m(ei + ej) = F + F ve F = F i + F j, F = F i + F j
Tk + L k F - L k F = (I - I ) i - (I + I )j + I k
I = 0, I = 0, I = 0.5mR + me
F = F + F F = F + F ve
G mil
2
G mil mil
2 2 2 2
xz yz zz
A Ax Ay
m(0.5aj + 3.5ak) + 2m(ai + 3.5ak) 2 1 7 2 1r = = a( i + j + k), r = a( i + j)
3m 3 6 2 3 6
a = k r - r
m mI = 2m(a)(3.5a), I = m(0.5a)(3.5a), I = a + (2a) + ma m(0.5a)
12 12
ve F = F i + F j ile
Tk + 3.5a
2 2
A B yz xz xz yz zzkF -3.5a kF = (I - I ) i - (I + I )j + I k
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Aada verilen sistemde A ve B yataklarna gelen kuvvetleri ve milin asal hzn t=3s iin bulunuz?
1 2 1 2
2 2
yz xz xz yz zz
T(t)=20sin(3t),m 2m 4 kg, r 0.1 m, 45 , 270
T = (I I )i (I + I )j + I k
1 2
mil
1 2
xz yz
zz A Ax Ay
2
G mil mil
m 3r 0.7071 i+j +m 3r jr = 0.1414i+0.0414j
m m
I = 4(0.2121)(0.8) = 0.6788, I = 4(0.2121)(0.8) + 2( 0.3)(0.1) = 0.6188,
I = 4(0.09) 2(0.09) = 0.54 ve F = F i + F j
a =k r r 0.0414+
2 2
2 2
A yz xz xz yz zz
2 2
Ax Ay
Ax
0.1414 i+ 0.1414 0.0414 j
Tk + 0.7kF = (I I )i (I + I )j + I k
Tk + 0.7 F j F i = (0.6188 0.6788)i (0.6788 + 0.6188)j + 0.54k
20 20T 0.54=20sin(3t) sin(3t) cos(3t)
0.54 1.62
F
2
2
Ay
G A B B G A
(0.9697 + 0.884) = 230.93
F (0.884 0.9697) = 174.8
6 a = F + F F = 6 a F
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Dnm Eksen Takm
11 12 13
21 22 23
31 32 33
2 2 2
x'x' xx 11 yy 21 yy 31
2 2 2
y'y' xx 12 yy 22 zz 32
2 2 2
z'z' xx 13 yy 23 zz 33
x'y' xx 11 12 yy 21 22 zz 31 32
y
I = I + I + I
I = I + I + I
I = I + I + I
I = -(I + I + I )
I
i i
j j
k k
'z' xx 12 13 yy 22 23 zz 32 33
x'z' xx 13 11 yy 23 21 zz 33 31
= -(I + I + I )
I = -(I + I + I )
Disk iin asal eksende
2zz
2 2xx yy
A B B A Ax Ay Az
2 2A y'z' x'z' x'z' y'z' z'z'
I = MR / 2
I = I = M(3R + h ) /12
F + F = 0 F = -F = -(F i' + F j' + F k')
Tk + Lk'F = (I - I )i' - (I + I )j' + I k'
2 2
z'z' yy 23 zz 33
y'z' yy 22 23 zz 32 33
x'z'
i i I = I + I 1 0 0
j = 0 cos -sin j I = -(I + I )
0 sin cos I = 0k k