Nguyễn Quang Minh
0
0
/ 1 0 0 0
0
0 0
0 0 / 1 0
0 0 0 / 1
2 2 2
1 1 1 2
1
3
2
1
2
1
2
1
=
+
=
+
=
+
=
+
−
r
b a
r
b a
r
b a
r
b a
n n n n
n
n
K
K K
p
rr p
br
p
ar
p
br p
bb
p
ab
p
ar p
ab
p
aa
K
K K
r b a
r b a
r b a
p
p p
r
r
r
b
b
b
a
a
a
ω
ω ω
ω
ω ω
0
W
K
B
BP
0
W
NK
T
1
Trang 2
= +
+ +
+
= +
+ +
+
= +
+ +
+
= +
=
+
−
0
0
0
r r b
a
b r b
a
a r b
a
K p
rr K
p
br K
p
ar
K p
br K
p
bb K
p
ab
K p
ar K
p
ab K
p
aa
ω ω ω
0 W K
B
BP
0
W
NK
T
1
a
c c b
a
b c b
a
a c b
a
r r b
a
b r b
a
a r b
a
K tac K
tab taa
K
K tcc K tbc K
taa
K tbc K
tbb K
taa
K tac K
tab K
taa
K trr K
tbr K
taa
K tbr K
tbb K
taa
K tar K
tab K
taa
ω ω ω ω ω
ω ω
+ +
−
=
= + +
+
= + +
+
= + +
+
= + +
+ +
= + +
+ +
= + +
+ +
= +
= +
−
1
0 0 0
0
0
0
0 W K
B
BP
0 W
NK
T
1
Trang 3[ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
2 0
2
0 1 1 1
1
1
1
1 1
1
0 1
1
0 1
1
0 0
1
0 0 0
2 2
.
1 1
1
1
1
tcc K K
tcc
tbc tbb K
tbc tbb
tbc
tcc
K tbc tbb
K
K tcc
K
tbc
K tbc
K
tbb
tac taa K
tac taa
tab tcc K tac taa
tab
tbc
tab taa K
tab taa
tac tbc K tab taa
tab
tbb
K tac K tab
taa
K
K tcc K tbc
K
tac
K tbc K tbb
K
tab
K tac K tab
K
taa
c c c
c
b c c
b c b
c c b
b c b
a c c b
a b c b
a c b
a
c c b
a
b c b
a
a c b
a
ω ω
ω ω ω ω ω
ω ω
ω ω ω
ω ω ω
−
=
⇒
= +
=
+
+
−
=
= + +
= + +
=
+
+
=
+
+
+ +
−
=
= + +
+
= + +
+
= + +
+
Ký hiệu dòng a K a b K a c K c
a
b
E 1b ×a
b.1
c
E 1c ×a
E 2c ×b.1
c.2
Trang 4Ký hiệu dòng a
K a
b K a c K c
a
b
[ ] ( [ ] b [ ] c a)
taa
K =− 1 + +ω
Ký hiệu dòng a
K a
b Ka c Kc
a
b
E 1b ×a
b.1
[ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ] [ ]
[ ] ( [ ] [ ] ) [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ 1] [ 1] 0
0
1
0 0 0
1 = + +
=
− +
− +
−
+ +
−
=
= + + +
= + +
+
= + +
+
b c b
a b c b
a c b
a
c c b a
b c b
a
a c b
a
K tbc K tbb
tab taa K
tab taa
tac tbc K tab taa
tab tbb
K tac K tab taa K
K tcc K tbc K tac
K tbc K tbb K tab
K tac K tab K taa
ω
ω ω ω
ω ω ω
Trang 5Ký hiệu dòng a
K a
b K a c K c
a
b
E 1b ×a
b.1
c
E 1c ×a
E 2c ×b.1
c.2
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
2 0
2
0 1 1 1
1
1
1
1 1
1
0 1
1
0 1
1
0 0
1
0 0 0
2 2
.
1 1
1
1
1
tcc K K
tcc
tbc tbb K
tbc tbb
tbc
tcc
K tbc tbb
K
K tcc
K
tbc
K tbc
K
tbb
tac taa K
tac taa
tab tcc K tac taa
tab
tbc
tab taa K
tab taa
tac tbc K tab taa
tab
tbb
K tac K tab
taa
K
K tcc K tbc
K
tac
K tbc K tbb
K
tab
K tac K tab
K
taa
c c c
c
b c c
b c b
c c b
b c b
a c c b
a b c b
a c b
a
c c b
a
b c b
a
a c b
a
ω ω
ω ω ω ω ω
ω ω
ω ω ω
ω ω ω
−
=
⇒
= +
=
− +
−
+
−
=
= + +
= + +
=
+
+
=
+
+
+ +
−
=
= + +
+
= + +
+
= + +
+
Trang 6[ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
2 0
2
0 1 1 1
1
1
1
1 1
1
0 1
1
0 1
1
0 0
1
0 0 0
2 2
.
1 1
1
1
1
tcc K K
tcc
tbc tbb K
tbc
tbb
tbc
tcc
K tbc
tbb
K
K tcc
K
tbc
K tbc
K
tbb
tac taa K
tac taa
tab tcc K tac
taa
tab
tbc
tab taa K
tab taa
tac tbc K tab
taa
tab
tbb
K tac K
tab
taa
K
K tcc K
tbc
K
tac
K tbc K
tbb
K
tab
K tac K
tab
K
taa
c c c
c
b c c
b c b
c c b
b c b
a c c b
a b c b
a c b
a
c c b
a
b c b
a
a c b
a
ω ω
ω ω ω ω ω
ω ω
ω ω ω
ω ω ω
−
=
⇒
=
+
=
+
+
−
=
= + +
= + +
=
+
+
=
+
+
+ +
−
=
= + +
+
= + +
+
= + +
+
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
2 0
2
0 1 1 1
1
1
1
1 1
1
0 1
1
0 1
1
0 0
1
0 0 0
2 2
.
1 1
1
1
1
tcc K K
tcc
tbc tbb K
tbc
tbb
tbc
tcc
K tbc
tbb
K
K tcc
K
tbc
K tbc
K
tbb
tac taa K
tac taa
tab tcc K tac
taa
tab
tbc
tab taa K
tab taa
tac tbc K tab
taa
tab
tbb
K tac K
tab
taa
K
K tcc K
tbc
K
tac
K tbc K
tbb
K
tab
K tac K
tab
K
taa
c c c
c
b c c
b c b
c c b
b c b
a c c b
a b c b
a c b
a
c c b
a
b c b
a
a c b
a
ω ω
ω ω ω ω ω
ω ω
ω ω ω
ω ω ω
−
=
⇒
=
+
=
− +
−
+
−
=
= + +
= + +
=
+
+
=
+
+
+ +
−
=
= + +
+
= + +
+
= + +
+
Trang 7[ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
2 0
2
0 1 1 1
1
1
1
1 1
1
0 1
1
0 1
1
0 0
1
0 0 0
2 2
.
1 1
1
1
1
tcc K K
tcc
tbc tbb K
tbc
tbb
tbc
tcc
K tbc
tbb
K
K tcc
K
tbc
K tbc
K
tbb
tac taa K
tac taa
tab tcc K tac
taa
tab
tbc
tab taa K
tab taa
tac tbc K tab
taa
tab
tbb
K tac K
tab
taa
K
K tcc K
tbc
K
tac
K tbc K
tbb
K
tab
K tac K
tab
K
taa
c c c
c
b c c
b c b
c c b
b c b
a c c b
a b c b
a c b
a
c c b
a
b c b
a
a c b
a
ω ω
ω ω ω ω ω
ω ω
ω ω ω
ω ω ω
−
=
⇒
=
+
=
+
+
−
=
= + +
= + +
=
+
+
=
+
+
+ +
−
=
= + +
+
= + +
+
= + +
+
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
2 0
2
0 1 1 1
1
1
1
1 1
1
0 1
1
0 1
1
0 0
1
0 0 0
2 2
.
1 1
1
1
1
tcc K K
tcc
tbc tbb K
tbc
tbb
tbc
tcc
K tbc
tbb
K
K tcc
K
tbc
K tbc
K
tbb
tac taa K
tac taa
tab tcc K tac
taa
tab
tbc
tab taa K
tab taa
tac tbc K tab
taa
tab
tbb
K tac K
tab
taa
K
K tcc K
tbc
K
tac
K tbc K
tbb
K
tab
K tac K
tab
K
taa
c c c
c
b c c
b c b
c c b
b c b
a c c b
a b c b
a c b
a
c c b
a
b c b
a
a c b
a
ω ω
ω ω ω ω ω
ω ω
ω ω ω
ω ω ω
−
=
⇒
=
+
=
− +
−
+
−
=
= + +
= + +
=
+
+
=
+
+
+ +
−
=
= + +
+
= + +
+
= + +
+
Trang 8[ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
2 0
2
0 1 1 1
1
1
1
1 1
1
0 1
1
0 1
1
0 0
1
0 0 0
2 2
.
1 1
1
1
1
tcc K K
tcc
tbc tbb K
tbc tbb
tbc
tcc
K tbc
tbb
K
K tcc
K
tbc
K tbc
K
tbb
tac taa K
tac taa
tab tcc K tac
taa
tab
tbc
tab taa K
tab taa
tac tbc K tab
taa
tab
tbb
K tac K tab
taa
K
K tcc K
tbc
K
tac
K tbc K
tbb
K
tab
K tac K
tab
K
taa
c c c
c
b c c
b c b
c c b
b c b
a c c b
a b c b
a c b
a
c c b
a
b c b
a
a c b
a
ω ω
ω ω ω ω ω
ω ω
ω ω ω
ω ω ω
−
=
⇒
=
+
=
+
+
−
=
= + +
= + +
=
+
+
=
+
+
+ +
−
=
= + +
+
= + +
+
= + +
+
=
− +
+
= + +
+
= +
+ +
0 1 4
2 2
0 0
2 3
0 5
0 2
3
c b
a
c b
a
c b
a
K K
K
K K
K
K K
K
Giải hệ phương trình chuẩn số liên hệ như sau
Trang 9Ký hiệu dòng a K a b K a c K c
E1 ( -1 -0.33333 -0.66667 -0.16667 Ka
E1b×a -0.33333 -0.66667 -0.16667
K a =-0.5 K b =-0.25 K c =0.625
phương
ñộ chính xác
x x
x x
P m m m
m P
1
0
2
2 0
=
=
0
m
Trang 10đánh giá ựộ chắnh xác: - Xác ựịnh sai số trung
phương
2
3 1
A
C
E B
D α
α 12
α
S
?
m
?
=
S
m
phương
ựộ chắnh xác
x x
x x
P m m m
m P
1
0
2
2 0
=
=
0
m
Trang 11Sai số trung phương trọng số ñơn vị xác ñịnh
bằng công thức
[ ]
t n
pvv m
−
=
0
[ ]pvv =∑n p i v i v i
1
[ ]
[ ]
∑
−
=
−
=
=
=
⇒
=
=
−
=
⇒
= +
=
−
=
−
−
−
−
−
r i i
r
i i
k pvv
pvv
k
pvv
1 1
1 1 1
1
1
0
;
ω
ω
W K K B BP K K B PP BP K
K
B
P
V
BP
K
V
W NK W
NK PV
V
T T
T T T
T
T
T
T
[ ]
2 1 2
2 2 1
1
−
−
−
−
−
=
−
r
r
trr tbb
taa
pvv ω ω ω
F
P
1
[ ] [ ] [ ] [ [ ] ] [ [ ] ]
[ ] [ ] [ ][ ] [ ] [ [ ][ ] ] [ [ ][ ] ]
i i i
i
i
r r r r
F
r r F
n
i
i
n n n
n
f r b
a
s
trr trs trf tbb
tbs tbf taa
tas taf tfs tfs
P
trr
trf tbb
tbf taa
taf
tff
P
f
f
f
L
F
f
v L
F v
L
F v L
F L L L F L L
L
F
F
+ + +
+
=
−
−
−
−
=
=
−
−
−
−
=
=
∂
∂
=
∂
∂ + +
∂
∂ +
∂
∂ +
=
=
−
−
−
−
−
1 1 1
1
1 1 1
) , , , ( ) , , ,
(
1 1 1 1
2 1 2
2
2
1
2 2 1 1 2
1 0 2
1
f
Trang 12Ký hiệu dòng a K a b K b c K c [tff]
a
E 1 ( -1
b
E 1b ×a
b.1
c
E 1c ×a
E 2c ×b.1
c.2
Trang 13Cho lưới khống chế ñộ cao
A
D
B
C
004 10
=
A
H
105 10
=
D
H
1
2
m
h1=1.02
m
h2=0.92
m
h3=5.32
m
h4=−0.15
m
h5=3.85
190 16
=
B
H
185 20
=
C
H
A
D
B
C
004 10
=
A
H
105 10
=
D
H
1
2
m
h1=1.02
m
h2=0.92
m
h3=5.32
m
h4=−0.15
m
h5=3.85
190 16
=
B
H
185 20
=
C
H
2
5
=
=
−
=
t n
t n r
Trang 14mm H
H h
h
h
v
v
v
H h
h
h
H
v
v
mm H
H
h
h
v
v
H
h
h
H
v
v
mm H
H
h
h
v
v
H
h
h
H
B A ựo
ựo
ựo
c
c
B A
C B ựo
ựo
b
b
C
B
D A
ựo
ựo
a
a
D
A
4 190 16 004 10 15 0 32 5 02 1
; 0
0
0
5
5 185 20 190 16 85 3 15 0
;
0
0
0
1
1 105 10 004 10 92 0 02 1
;
0
0
4
3
1
4
3
1
4
3
1
5
4
5
4
5
4
5
4
2
1
2
1
2
1
2
1
=
− +
− +
=
− + +
+
=
=
+
+
+
=
−
+
+
+
=
+
+
−
+
=
− + +
=
− +
+
−
=
=
+
+
−
=
−
+
−
=
−
−
−
=
− +
−
=
− +
−
=
=
+
−
=
−
−
+
ω
ω
ω
ω
ω
ω
đánh giá ựộ chắnh xác ựộ cao H1
Trang 15Ka Kb Kc ω [f.] [.s]
Ký hiệu dòng a
K a
b
K a
c K c [t.f] [t.s]
E 1 ( -1 0 -0.5 0.5 -0.5 -2
E 2 ( -1 0.5 -2.5 0 -0.5
2.25 -4.25 -3.5
Trang 16STT v 1 v 2 v 3 v 4 v 5 ω K
a 1 -1 0 0 0 -1 2.25
b 0 0 0 -1 1 5 -4.25
c 1 0 1 1 0 4 -3.5
f 1 0 0 0 0
v -1.25 -2.25 -3.5 0.75 -4.25 [pvv]=37.5 [pvv]=37.5
Sai số trung phương
đánh giá ựộ chắnh xác ựộ cao H 1
[ ] [ ]
.016mm 2
ổ 57 0
ổ3.535mm 0.325
ổ3.535mm
325 0 625 0 0 2 3 5 2 25 0 0
4
5
.
0
3
.
.
1
1 1
1
325 0 125 0 0 5 0 1 25 0 5 0 0 0 1
5
.
0
1
1
.
.
1
1 1
1
1
1 1
1
2 1 2
2
=
ừ
=
ừ
=
=
−
−
−
=
ừ
−
−
ừ
−
=
−
−
−
−
=
=
=
−
−
−
=
ừ
−
ừ
−
ừ
−
=
−
−
−
−
=
−
−
−
−
−
H
r
r r r
F
F
r r
F
m
trr
trs trf tbb
tbs tbf taa
tas taf tfs
tfs
P
P
trr
trf tbb
tbf taa
taf
tff
P