CN104614161A - Method for recognizing falling weight and position of rotating part of rotating mechanism - Google Patents

Abstract

The invention discloses a method for recognizing falling weight and position of a rotating part of a rotating mechanism. The method is that sliding bearing oil film rigidity and damping coefficient are calculated by the ARMD software; a power equation is created for a bearing system of a rotor of the rotating mechanism by the finite element method; the mass unbalance force is respectively applied to the impeller at each level of the rotor so as to obtain the vibration variation of vibration measuring points of the bearings at two ends of the rotor; the unbalance response sensitivity of each vibration measuring point to the impeller at each level can be obtained by the vector calculation algorithm; the falling weight and position of the rotating part can be obtained according to the measured vibration variation of the rotor bearing vibration measuring points and an unbalance response sensitivity matrix.

Description

A kind of rotating machinery rotatable parts come off weight and location recognition method

Technical field

The present invention relates to a kind of rotating machinery rotatable parts to come off position and Weight identify method, the size of help technician to analyze position that rotatable parts on rotor come off and the weight that comes off.Main application comprises: the large rotating machinery such as power, metallurgy, petrochemical industry, aviation, as steam turbine, compressor, gas turbine, blower fan etc.

Background technology

Vibration is the key factor affecting the safe operations of large high-speed rotating machinery such as steam turbine, compressor, gas turbine, blower fan.In work process, moving vane rotates with High Rotation Speed rotor, its condition of work is very complicated, except bearing except higher static stress and dynamic stress because of high-speed rotation and steam flow effect, also working in high temperature super heated steam district, two-phase flow zone of transition and wet-steam region because it is in respectively and bears high temperature, corrosion and erosion effect.This just causes in operational process, the fragile fracture of moving vane.

Summary of the invention

Technical matters to be solved by this invention is to provide the operating rotatable parts of a kind of rotating machinery and comes off weight and location recognition method, and the present invention can analyze weight and the position of releasing part on rotor fast, accurately, easily, improves Fault Identification efficiency.

For solving the problems of the technologies described above, the invention provides a kind of rotating machinery rotatable parts and to come off weight and location recognition method, it is characterized in that, comprise the following steps:

1) according to rotating machinery sliding bearing geometric parameter and lubricating oil physical parameter, ARMD software is utilized to calculate stiffness coefficient and the ratio of damping of oil film bearings;

2) by discrete for rotary machine rotor be impeller units and shaft part unit, utilize Finite Element Method to set up the rotor-support-foundation system equation of motion as follows:

$\left\{\begin{array}{c}\left[M_1\right]\left\{{\stackrel{\·\·}{U}}_1\right\}+\mathrm{\Ω}\left[J_1\right]\left\{{\stackrel{\·}{U}}_2\right\}+\left[K_1\right]\left\{U_1\right\}=\left\{Q_1\right\}\\ \left[M_1\right]\left\{{\stackrel{\·\·}{U}}_2\right\}-\mathrm{\Ω}\left[J_1\right]\left\{{\stackrel{\·}{U}}_1\right\}+\left[K_1\right]\left\{U_2\right\}=\left\{Q_2\right\}\end{array}\right.$ Formula (1)

Wherein [M ₁], [J ₁], [K ₁] and Ω rotor lumped mass matrix, revolution matrix, stiffness matrix and angular velocity of rotation respectively, U ₁, U ₂for nodal displacement vector, Q ₁, Q ₂for broad sense Unbalanced force vector; for U ₁and U ₂second derivative, for U ₁and U ₂first order derivative;

3) using oil film rigidity coefficient and ratio of damping as the generalized force acting on axle journal Nodes, substitute into the rotor-support-foundation system equation of motion, obtain sliding bearing support rotor Equation of Motion:

$\left[M\right]\left\{\stackrel{\·\·}{U}\right\}+\left[C\right]\left\{\stackrel{\·}{U}\right\}+\left[K\right]\left\{U\right\}=\left\{Q\right\}$ Formula (2)

In formula, $\left[M\right]=\left[\begin{array}{cc}{M}_1& 0\\ 0& M_1\end{array}\right];\left\{U\right\}=\left\{\begin{array}{c}{U}_1\\ U_2\end{array}\right\};\left[C\right]=\left[\begin{array}{cc}{c}_{\mathrm{xx}}& c_{\mathrm{xy}}+\mathrm{\Ω}{J}_1\\ c_{\mathrm{yx}}-\mathrm{\Ω}{J}_1& c_{\mathrm{yy}}\end{array}\right];$ $\left[K\right]=\left[\begin{array}{cc}{k}_{\mathrm{xx}}+K_1& k_{\mathrm{xy}}\\ k_{\mathrm{yx}}& k_{\mathrm{yy}}+K_1\end{array}\right];\left\{Q\right\}=\left\{\begin{array}{c}{Q}_1\\ Q_2\end{array}\right\}$

K _xx, k _yyoil film bearings For Horizontal Stiffness Coefficient and oil film bearings vertical stiffness coefficient, k _xyrepresent the horizontal direction oil-film force increment that axle journal vertical direction unit displacement causes, k _yxrepresent the vertical direction oil-film force increment that axle journal horizontal direction unit displacement causes., c _xx, c _yyoil film bearings horizontal damping coefficient and oil film bearings vertical damping coefficient, c _xyrepresent the horizontal direction oil-film force increment that axle journal vertical direction unit speed causes, c _yxrepresent the vertical direction oil-film force increment that axle journal horizontal direction unit speed causes;

4) suppose total n vibration measuring point in rotating shaft, first apply out-of-balance force at the 1st grade of impeller place solve formula (2) rotor Equation of Motion, draw rotor vibrates measuring point 1, measuring point 2 ..., measuring point n place unbalance response be respectively then on rotor, the unbalance response sensitivity vector of n measuring point to first order impeller place out-of-balance force is:

In like manner, out-of-balance force is applied at i-th grade of impeller place i represents any one-level, solves formula (2) rotor Equation of Motion, draw rotor vibrates measuring point 1, measuring point 2 ..., measuring point n place unbalance response be respectively then the unbalance response sensitivity vector of two ends n measuring point to i-th grade of impeller place out-of-balance force is:

Suppose total m level impeller, the unbalance response sensitivity coefficient of n measuring point to each impeller place out-of-balance force be combined as following matrix form,

formula (3)

(5) after rotating machinery rotatable parts come off, the vibration variable quantity of two ends of rotor n measuring point is respectively: Δ vib ₁, Δ vib ₂..., Δ vib _n, according to the matrix form (3) of the unbalance response sensitivity that step (4) is obtained, then the vector expression of releasing part weight and position is:

formula (4).

Δ m is a vector, has direction and size, and namely the absolute value of Δ m comes off the size of quality, and the direction of vector is exactly the position come off.

The beneficial effect that the present invention reaches:

Compared with prior art, the beneficial effect that the present invention reaches is:

1) utilize existing rotator model, use finite element method to draw equation of rotor motion, thus obtain the unbalance response sensitivity matrix of each vibration measuring point to impeller at different levels, save as data file, call at any time to facilitate.

2) according to vibration measuring point vibration amplitude and SPA sudden phase anomalies amount, utilize sensitivity matrix conveniently can obtain rotatable parts and fly off weight and position, improve fault diagnosis efficiency.

3) fixing algorithm can be formed, convenient and swiftly judge that rotating machinery rotatable parts fly off weight and position accurately.

Accompanying drawing explanation

Fig. 1 is model schematic of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further.

Rotating machinery rotatable parts of the present invention come off weight and location recognition method, it is characterized in that, comprise the following steps:

1) according to rotating machinery sliding bearing geometric parameter and lubricating oil physical parameter, ARMD software is utilized to calculate stiffness coefficient and the ratio of damping of oil film bearings;

2) by discrete for rotary machine rotor be impeller units and shaft part unit, utilize Finite Element Method to set up the rotor-support-foundation system equation of motion as follows:

$\left\{\begin{array}{c}\left[M_1\right]\left\{{\stackrel{\·\·}{U}}_1\right\}+\mathrm{\Ω}\left[J_1\right]\left\{{\stackrel{\·}{U}}_2\right\}+\left[K_1\right]\left\{U_1\right\}=\left\{Q_1\right\}\\ \left[M_1\right]\left\{{\stackrel{\·\·}{U}}_2\right\}-\mathrm{\Ω}\left[J_1\right]\left\{{\stackrel{\·}{U}}_1\right\}+\left[K_1\right]\left\{U_2\right\}=\left\{Q_2\right\}\end{array}\right.$ Formula (1)

Wherein [M ₁], [J ₁], [K ₁] and Ω rotor lumped mass matrix, revolution matrix, stiffness matrix and angular velocity of rotation respectively, U ₁, U ₂for nodal displacement vector, Q ₁, Q ₂for broad sense Unbalanced force vector; for U ₁and U ₂second derivative, for U ₁and U ₂first order derivative;

3) using oil film rigidity coefficient and ratio of damping as the generalized force acting on axle journal Nodes, substitute into the rotor-support-foundation system equation of motion, obtain sliding bearing support rotor Equation of Motion:

$\left[M\right]\left\{\stackrel{\·\·}{U}\right\}+\left[C\right]\left\{\stackrel{\·}{U}\right\}+\left[K\right]\left\{U\right\}=\left\{Q\right\}$ Formula (2)

In formula, $\left[M\right]=\left[\begin{array}{cc}{M}_1& 0\\ 0& M_1\end{array}\right];\left\{U\right\}=\left\{\begin{array}{c}{U}_1\\ U_2\end{array}\right\};\left[C\right]=\left[\begin{array}{cc}{c}_{\mathrm{xx}}& c_{\mathrm{xy}}+\mathrm{\Ω}{J}_1\\ c_{\mathrm{yx}}-\mathrm{\Ω}{J}_1& c_{\mathrm{yy}}\end{array}\right];$ $\left[K\right]=\left[\begin{array}{cc}{k}_{\mathrm{xx}}+K_1& k_{\mathrm{xy}}\\ k_{\mathrm{yx}}& k_{\mathrm{yy}}+K_1\end{array}\right];\left\{Q\right\}=\left\{\begin{array}{c}{Q}_1\\ Q_2\end{array}\right\}$

K _xx, k _yyoil film bearings For Horizontal Stiffness Coefficient and oil film bearings vertical stiffness coefficient, k _xy, k _yxoil film intersection stiffness coefficient, c _xx, c _yyoil film bearings horizontal damping coefficient and oil film bearings vertical damping coefficient, c _xy, c _yxit is oil film cross damping coefficient;

4) suppose total n vibration measuring point in rotating shaft, first apply out-of-balance force at the 1st grade of impeller place solve formula (2) rotor Equation of Motion, draw rotor vibrates measuring point 1, measuring point 2 ..., measuring point n place unbalance response be respectively then on rotor, the unbalance response sensitivity vector of n measuring point to first order impeller place out-of-balance force is:

In like manner, out-of-balance force is applied at i-th grade of impeller place i represents any one-level, solves formula (2) rotor Equation of Motion, draw rotor vibrates measuring point 1, measuring point 2 ..., measuring point n place unbalance response be respectively then the unbalance response sensitivity vector of two ends n measuring point to i-th grade of impeller place out-of-balance force is:

Suppose total m level impeller, the unbalance response sensitivity coefficient of n measuring point to each impeller place out-of-balance force be combined as following matrix form,

formula (3)

(5) after rotating machinery rotatable parts come off, the vibration variable quantity of two ends of rotor n measuring point is respectively: Δ vib ₁, Δ vib ₂..., Δ vib _n, according to the matrix form (3) of the unbalance response sensitivity that step (4) is obtained, then the vector expression of releasing part weight and position is:

formula (4).

Δ m is a vector, has direction and size, and namely the absolute value of Δ m comes off the size of quality, and the direction of vector is exactly the position come off.

Model is example as shown in Figure 1, and this rotor includes level Four impeller.

Rotating machinery rotatable parts of the present invention come off weight and location recognition method, comprise the following steps:

(1) bearing diameter 300mm, long 250mm, bearing clearance 0.33mm, utilize ARMD software to calculate the oil film rigidity of this bearing when 3000 revs/min and damping parameter;

(2) be 25 shaft parts and impeller pattern by this rotor modelling;

(3) rotor-bearing system motion finite element equation is set up;

(4) according to a large amount of engineering experience, in actual motion, rotary part comes off and mostly occurs on blade, shroud, so only demand goes out the sensitivity that impeller section unit mass comes off to bearings at both ends level and vertical measuring point vibratory response.

(5), when each impeller place amount of unbalance is 1kg ∠ 0 °, the unbalance response sensitivity matrix α at this unit bearings at both ends level and vertical measuring point place is:

$\mathrm{\α}=1\×{10}^{-4}\left[\begin{array}{cccc}-0.6911+0.4203i& -0.5276+0.3297i& -0.3521+0.2286i& -0.1613+0.1152i\\ 0.0349-0.0900i& -0.2110+0.0369i& -0.4418+0.1599i& -0.6567+0.2795i\\ -0.7566-0.1956i& -0.6700-0.2563i& -0.5602-0.3108i& -0.4241-0.3577i\\ -0.1123-0.4889i& -0.2704-04767i& -0.4154-0.4445i& -0.5469-0.3893i\end{array}\right]$

(6) suppose that this unit third level impeller to come off quality 2.7kg in circumference 190 degree positions, the bearings at both ends horizontal and vertical direction now caused vibrates variable quantity and is respectively:

Table 1 bearing measuring point vibration variable quantity (amplitude μm ∠ angle °)

Measuring point	1 level	1 is vertical	2 levels	2 is vertical
					Fundamental vibration variation delta vib	113.4∠337	126.9∠350	173∠39	164.3∠57

Each measuring point vibration values variable quantity is expressed as plural form:

$\mathrm{\Δvib}=\left[\begin{array}{c}{\mathrm{\Δ}}_{1x}\\ {\mathrm{\Δ}}_{1y}\\ {\mathrm{\Δ}}_{2x}\\ {\mathrm{\Δ}}_{2y}\end{array}\right]=1\×{10}^{-3}\×\left[\begin{array}{c}0.1043-0.0443i\\ 0.1250-0.0218i\\ 0.1344+0.1089i\\ 0.0896+0.1377i\end{array}\right]$

Then, the come off complex expression Δ m of quality and position of this unit is:

$\mathrm{\Δm}=\mathrm{\α}\backslash \mathrm{\Δvib}=\left[\begin{array}{c}5.2480e-007+2.5259e-007i\\ -1.5550e-006-7.8501e-007i\\ -2.6590-0.4688i\\ -5.0159e-007-2.7775e-007i\end{array}\right]$

The form by above-mentioned complex representation being amplitude and angle is as follows:

$\mathrm{\Δm}=\left[\begin{array}{c}5.2480e-007+2.5259e-007i\\ -1.5550e-006-7.8501e-007i\\ -2.6590-0.4688i\\ -5.0159e-007-2.7775e-007i\end{array}\right]=\left[\begin{array}{c}5.8\×{10}^{-7}\∠26\\ 1.7\×{10}^{-6}\∠207\\ 2.7\∠190\\ 5.7\×{10}^{-7}\∠209\end{array}\right]$

Can find out, utilize sensitivity matrix to identify third level impeller and to come off 190 degree of positions 2.7kg, with come off weight and circumferential position consistent.Below disclose the present invention with preferred embodiment, so it is not intended to limiting the invention, and all employings are equal to replacement or the technical scheme that obtains of equivalent transformation mode, all drop within protection scope of the present invention.

Claims (1)

1. rotating machinery rotatable parts come off weight and a location recognition method, it is characterized in that, comprise the following steps:

1) according to rotating machinery sliding bearing geometric parameter and lubricating oil physical parameter, ARMD software is utilized to calculate stiffness coefficient and the ratio of damping of oil film bearings;

2) by discrete for rotary machine rotor be impeller units and shaft part unit, utilize Finite Element Method to set up the rotor-support-foundation system equation of motion as follows:

$\left\{\begin{array}{c}\left[M_1\right]\left\{{\stackrel{..}{U}}_1\right\}+\mathrm{\Ω}\left[J_1\right]\left\{{\stackrel{.}{U}}_2\right\}+\left[K_1\right]\left\{U_1\right\}=\left\{Q_1\right\}\\ \left[M_1\right]\left\{{\stackrel{..}{U}}_2\right\}-\mathrm{\Ω}\left[J_1\right]\left\{{\stackrel{.}{U}}_1\right\}+\left[K_1\right]\left\{U_2\right\}=\left\{Q_2\right\}\end{array}\right.$ Formula (1)

Wherein [M ₁], [J ₁], [K ₁] and Ω rotor lumped mass matrix, revolution matrix, stiffness matrix and angular velocity of rotation respectively, U ₁, U ₂for nodal displacement vector, Q ₁, Q ₂for broad sense Unbalanced force vector; for U ₁and U ₂second derivative, for U ₁and U ₂first order derivative;

3) using oil film rigidity coefficient and ratio of damping as the generalized force acting on axle journal Nodes, substitute into the rotor-support-foundation system equation of motion, obtain sliding bearing support rotor Equation of Motion:

$\left[M\right]\left\{\stackrel{..}{U}\right\}+\left[C\right]\left\{\stackrel{.}{U}\right\}+\left[K\right]\left\{U\right\}=\left\{Q\right\}$ Formula (2)

In formula, $\left[M\right]=\left[\begin{array}{cc}{M}_1& 0\\ 0& M_1\end{array}\right];$ $\left\{U\right\}=\left\{\begin{array}{c}{U}_1\\ U_2\end{array}\right\};$ $\left[C\right]=\left[\begin{array}{cc}{c}_{\mathrm{xx}}& c_{\mathrm{xy}}+\mathrm{\Ω}{J}_1\\ c_{\mathrm{yx}}-\mathrm{\Ω}{J}_1& c_{\mathrm{yy}}\end{array}\right];$

$\left[K\right]=\left[\begin{array}{cc}{k}_{\mathrm{xx}}+K_1& k_{\mathrm{xy}}\\ k_{\mathrm{yx}}& k_{\mathrm{yy}}+K_1\end{array}\right];$ $\left\{Q\right\}=\left\{\begin{array}{c}{Q}_1\\ Q_2\end{array}\right\}$

K _xx, k _yyoil film bearings For Horizontal Stiffness Coefficient and oil film bearings vertical stiffness coefficient, k _xyrepresent the horizontal direction oil-film force increment that axle journal vertical direction unit displacement causes, k _yxrepresent the vertical direction oil-film force increment that axle journal horizontal direction unit displacement causes; , c _xx, c _yyoil film bearings horizontal damping coefficient and oil film bearings vertical damping coefficient, c _xyrepresent the horizontal direction oil-film force increment that axle journal vertical direction unit speed causes, c _yxrepresent the vertical direction oil-film force increment that axle journal horizontal direction unit speed causes;

4) suppose total n vibration measuring point in rotating shaft, first apply out-of-balance force at the 1st grade of impeller place solve formula (2) rotor Equation of Motion, draw rotor vibrates measuring point 1, measuring point 2 ..., measuring point n place unbalance response be respectively then on rotor, the unbalance response sensitivity vector of n measuring point to first order impeller place out-of-balance force is:

In like manner, out-of-balance force is applied at i-th grade of impeller place i represents any one-level, solves formula (2) rotor Equation of Motion, draw rotor vibrates measuring point 1, measuring point 2 ..., measuring point n place unbalance response be respectively then the unbalance response sensitivity vector of two ends n measuring point to i-th grade of impeller place out-of-balance force is:

Suppose total m level impeller, the unbalance response sensitivity coefficient of n measuring point to each impeller place out-of-balance force be combined as following matrix form,

formula (3)

(5) after rotating machinery rotatable parts come off, the vibration variable quantity of two ends of rotor n measuring point is respectively: Δ vib ₁, Δ vib ₂..., Δ vib _n, according to the matrix form (3) of the unbalance response sensitivity that step (4) is obtained, then the vector expression of releasing part weight and position is:

formula (4).