运动方程式求解方程
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Fig.2.1 OECD vertical vibration model diagram
2
38/I m =117/r I m =
3.2Model parameters of winding 2:1, SMR
3.3 elevator rope length of winding 2:1, SMR
Fig.2.2 Diagram of rope length
3.3 Equation of motion
----- Quality is car + frame, CWT, hitch, Rope and rubber are spring -----
2111l l T T x m += Car + frame 5422l l T T x m += CWT 16363333333l T x k x c x k x c x m -++--= Car hitch 56464444444l T x k x c x k x c x m -++--= CWT hitch 426565555555l l T T x k x c x k x c x
m ++++--= Traction machine(up rubber-up) 51444433336654355665435566)()(l l T T x k x c x k x
c x k k k k x k x c c c c x c x
m --+++++++-++++-= Traction
machine(down rubber-up)
---------- Sheave rotate ----------
217777l l T T x c x m +--= Car sheave 328888l l T T x c x
m +--= Traction sheave
439999l l T T x c x m +--= Guide sheave 5410101010l l T T x c x
m +--= CWT sheave ---------- Tension of rope extension ----------
176********/)(/)(l c x x x x
l k x x x x T r r l ++-+++-= Car sheave —car hitch 25178217852/)(/)(l c x x x x
l k x x x x T r r l ---+--+-=Car sheave —traction sheave 3893893/)(/)(l c x x
l k x x T r r l -+-=Traction sheave —guide sheave 4291054291054/)(/)(l c x x x x
l k x x x x T r r l --+-+--+-= Guide sheave —CWT sheave
5102465106245/)(/)(l c x x x x
l k x x x x T r r l --++-+-= CWT sheave —CWT hitch
---------- Rope length ----------
711x L L l -+= ; 8722x x L L l -++=;9833x x L l -+=; 10944x x L l -+=; 1055x L l +=
3.4 Equation of motion converts to state equation
The length of each rope when position of car is Z
z L L l -+=11; L z L l +-=22; 33L l =; z L l +=44; z L l +=55
Stiffness coefficient of rope is )(/)(z l k z k i r ri = )(/)(z l c z c i r ri = i=1, (5)
Tension equation based on rope extension 。
176********)()(r r l c x x x x
k x x x x T ++-+++-= Car sheave--hitch 25178251782)()(r r l c x x x x
k x x x x T ---+---= Car sheave —traction sheave 3893893)()(r r l c x x
k x x T -+-= Traction sheave —guide sheave 4291054291054)()(r r l c x x x x
k x x x x T --+-+--+-= Guide —CWT sheave 5106245106245)()(r r l c x x x x
k x x x x T -+-+-+-= CWT —CWT hitch
Rope tension and weight of trailing cable substitute into equation of motion
8
27216152311218272161523112111)()()()(x k x k k x k x k x k x k k x c x c c x c x c x c x c c x
m r r r r r r r r r r r r r r r r +-++-++-+-++-++-= Car +Frame
10
549465544525410549465544525422)()()()(x k k x k x k x k x k x k k x c c x c x c x c x c x c c x
m r r r r r r r r r r r r r r r r -+-+-++--+-+-++-=
CWT
7
161331311716133131133)()()()(x k x k k x k k x k x c x c c x c c x c x
m r r r r r r r r --++-+--++-= Car hitch
10
5654454251056544542544)()()()(x k x k k x k k x k x c x c c x c c x c x
m r r r r r r r r +-++-+-++-= CWT hitch
10
49482726554252412104948272655425241255)()(x k x k x k x k x k x k k k x k x k x c x c x c x c x c x c c c x c x c x
m r r r r r r r r r r r r r r r r +-+-+++---+-+-+++---=
Traction machine （up rubber-up ）
10
571651654355454313251110571651654355454313251166)()()()()()(x k x k x k k k k k k x k x k k x k k x k x k x c x c x c c c c c c x c x c c x c c x c x c x
m r r r r r r r r r r r r r r r r +-+++++-+-+-++++-+++++-+-+-++= Traction machine （down rubber-up ）
8
272161523112182721761523112177)()()()(x k x k k x k x k x k x k k x c x c c c x c x c x c x c c x
m r r r r r r r r r r r r r r r r ++-----+++-----= Car sheave
9
383272521293832872521288)()(x k x k k x k x k x k x c x c c c x c x c x c x m r r r r r r r r r r r r ++-++++++-++= Traction sheave
10
4943835424104943983542499)()(x k x k k x k x k x k x c x c c c x c x c x c x
m r r r r r r r r r r r r ++-+--+++-+--= Guide sheave
10
5494655445254105410946554452541010)()()()(x k k x k x k x k x k x k k x c c c x c x c x c x c x c c x
m r r r r r r r r r r r r r r r r +-++++-+++-++++-= CWT sheave
So, state equation is T B M x x I K M C M x x
dt d ⎥⎦
⎤⎢⎣⎡+⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡---00111 Where ，[]T
x x x x x x x x x x x 109
87654321
=
[]T
t
m m m m m m m m m m m diag M 109
8765432
1+=
[]0000010000
=B