CN110909420B - Iterative calculation method for alignment of ship propulsion shafting considering bearing factors - Google Patents

Abstract

The invention discloses a ship propulsion shafting alignment iterative calculation method considering bearing factors, which comprises the following steps: s1, discretizing the shaft section and giving an initial position value Z of the equivalent fulcrum of the tail bearing ⁽⁰⁾ (ii) a S2, centering and calculating a shaft system by using a three-bending moment method to obtain a journal corner at the tail bearing; s3, substituting a journal rotation angle into a calculation formula by using a tail bearing equivalent fulcrum calculation formula to obtain a new equivalent fulcrum position value; s4, when the new equivalent fulcrum position value does not meet the convergence condition, the Z is set ^(k) And Z ^(k‑1) The average value of the two is used as a new equivalent fulcrum position value, the basis of calculating the journal rotation angle at the tail bearing in the next time is used, and the step S2 is executed again; s5, when the new equivalent fulcrum position value meets the convergence condition, connecting Z ^(k) And substituting the three moments of bending method to calculate to obtain a final centering calculation result. The ship propulsion shafting alignment iterative calculation method provided by the invention can accurately determine the equivalent fulcrum position value of the tail bearing.

Description

Iterative calculation method for alignment of ship propulsion shafting considering bearing factors

technical field

The invention relates to the technical field of shaft alignment, in particular to an iterative calculation method for the alignment of ship propulsion shafts considering bearing factors.

Background technique

The alignment of the propulsion shafting is an important part of the shafting design and installation. The quality of the alignment of the shafting has an important impact on ensuring the normal operation of the shafting and the main engine, as well as reducing the vibration of the hull. Production practice has proved that shafting with poor alignment quality will cause rapid wear or even burn out of the stern tube bearing during operation, abnormal wear of the stern tube seal element and lead to leakage, resulting in the arm distance difference of the main engine crankshaft exceeding the allowable range. , destroy the normal meshing of the reduction gear and the normal operation of the bearing, and cause the hull to vibrate.

Due to the cantilever effect of the propeller, the stern tube bearing close to the propeller bears a larger load, so the stern tube bearing support model is the focus of attention. In the alignment calculation, the position of the equivalent fulcrum of the water-lubricated stern tube rear bearing is usually selected with reference to the regulations for the Tieli wood bearing, and the fulcrum position of the stern tube front bearing is usually taken as the midpoint. Whether this treatment method is reasonable is worth in-depth analysis. .

There are three commonly used methods for shaft alignment calculation: finite element method, transfer matrix method and three bending moment method. With the application of many new materials, the elastic modulus of the inner lining of the bearing has changed. At the same time, the trend of modern ships is developing towards large tonnage, which makes the aspect ratio of the bearing continue to increase, which makes the school environment more complicated. . However, the existing shaft alignment methods, such as the three-bending moment method, do not take into account the development and changes of ship bearings, while the ANSYS finite element method considers the changes of these factors, but its calculation process is complex, modeling and meshing. The other process relies on the experience of users, which makes the repeatability of this method relatively poor. Therefore, it is questionable whether the existing calibration results are accurate or not. Therefore, it is necessary to find a new fulcrum calculation method.

SUMMARY OF THE INVENTION

The main purpose of the present invention is to provide an iterative calculation method for the alignment of ship propulsion shafting considering bearing factors, aiming to accurately determine the position value of the equivalent fulcrum of the stern bearing.

In order to achieve the above purpose, the present invention provides an iterative calculation method for the alignment of ship propulsion shafting considering bearing factors, comprising the following steps:

S1, discretize the shaft segment and give the initial position value Z ⁽⁰⁾ of the equivalent fulcrum of the stern bearing;

S2, use the three-bending moment method to align and calculate the shafting to obtain the journal rotation angle at the stern bearing;

S3, use the calculation formula of the equivalent fulcrum of the stern bearing, substitute the journal rotation angle obtained in the previous step, and calculate the new equivalent fulcrum position value Z ^(k) , where k is the number of iterations;

S4, when the difference between the new equivalent fulcrum position value Z ^(k) and the equivalent fulcrum position value Z ^(k-1) before the iteration is greater than the preset difference, compare Z ^(k) and Z ^{( k-1)} The average value of the two is used as the new equivalent fulcrum position value, which is the basis for the next calculation of the journal rotation angle at the stern bearing, and returns to step S2;

S5, when the difference between the new equivalent fulcrum position value Z ^(k) and the equivalent fulcrum position value Z ^(k-1) before the iteration is less than or equal to the preset difference, that is, the iterative convergence satisfies the preset The final alignment calculation result is obtained by substituting Z ^(k) into the three-bending moment method.

Preferably, in step S1, the value range of Z ⁽⁰⁾ is (1/4～1/3)L, where L is the length of the stern bearing.

Preferably, in step S3, when the new equivalent fulcrum position value Z ^(k) is calculated, it is calculated according to the journal rotation angle, elastic modulus and aspect ratio.

Preferably, in the calculation formula of the equivalent fulcrum of the stern bearing, the finite element method is used to calculate the position of the equivalent fulcrum of the stern bearing under different bearing length-diameter ratios, journal rotation angles and elastic modulus of the inner lining, and then the fulcrum is obtained by fitting the linear regression analysis method. coefficient.

Preferably, in step S3, the relationship between the elastic modulus, the aspect ratio and the rotation angle of the stern bearing and the position of the equivalent fulcrum is:

Z ^(k) = a(L/D) ^b (θ ^(k) ) ^c E ^d ;

Where: Z ^(k) is the equivalent fulcrum position of the stern bearing calculated at the k-th iteration; L/D is the length-diameter ratio of the stern bearing; θ ^(k) is the journal rotation angle calculated at the k-th iteration; E is the elastic modulus of the stern bearing lining; a, b, c, and d are the fulcrum coefficients, which are calculated by the linear regression analysis method combined with the simulation data.

Preferably, in step S5, the criterion for iterative convergence is:

where b is the iterative convergence coefficient.

Preferably, in step S5, the final alignment calculation result includes: rotation angle, deflection, bending moment, bending stress, rotation angle and support reaction force.

Compared with the prior art, the iterative calculation method for the alignment of the ship propulsion shafting proposed by the present invention has the following advantages:

1. The cyclic iterative alignment method is adopted to solve the problem that the position of the fulcrum of the stern bearing that is subjectively assumed in the alignment calculation does not match the actual shafting state by means of iterative calculation;

2. The equivalent fulcrum model and its calculation method considering bearing factors are proposed. On the basis of the traditional equivalent fulcrum model, bearing factors are taken into account, and the bearing length-diameter ratio, lining elastic modulus and bearing axis are analyzed. The relationship between the rotation angle and the position of the equivalent fulcrum, and the derivation process of its calculation formula is given;

3. Using this cycle iterative alignment method, considering the shortcomings of the finite element method and the traditional three-bending moment method in calculating the shaft alignment, the position value of the fulcrum of the stern bearing can be accurately obtained, which solves the subjective assumption in alignment calculation. The problem that the position of the fulcrum of the stern bearing does not match the actual state of the shaft system, and then the calculation result of the alignment can be accurately obtained.

Description of drawings

FIG. 1 is a schematic flowchart of the iterative calculation method for the alignment of the ship propulsion shafting system according to the present invention considering bearing factors.

The realization, functional characteristics and advantages of the present invention will be further described with reference to the accompanying drawings in conjunction with the embodiments.

Detailed ways

It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

Referring to Figure 1, an iterative calculation method for the alignment of ship propulsion shafting considering bearing factors, including the following steps:

S1, discretize the shaft segment and give the initial position value Z ⁽⁰⁾ of the equivalent fulcrum of the stern bearing;

S2, use the three-bending moment method to align and calculate the shafting to obtain the journal rotation angle at the stern bearing;

S3, use the calculation formula of the equivalent fulcrum of the stern bearing, substitute the journal rotation angle obtained in the previous step, and calculate the new equivalent fulcrum position value Z ^(k) , where k is the number of iterations;

S4, when the difference between the new equivalent fulcrum position value Z ^(k) and the equivalent fulcrum position value Z ^(k-1) before the iteration is greater than the preset difference (that is, the new equivalent fulcrum position value does not meet the convergence conditions), take the average value of Z ^(k) and Z ^(k-1) as the new equivalent fulcrum position value, and calculate the basis for the journal rotation angle at the stern bearing next time, and return to step S2;

S5, when the difference between the new equivalent fulcrum position value Z ^(k) and the equivalent fulcrum position value Z ^(k-1) before the iteration is less than or equal to the preset difference, that is, the iterative convergence satisfies the preset The final alignment calculation result is obtained by substituting Z ^(k) into the three-bending moment method.

Specifically, in step S1, the value range of Z ⁽⁰⁾ is (1/4～1/3)L, where L is the length of the stern bearing. The value range of Z ⁽⁰⁾ is selected with reference to the regulations for iron pear wood bearings. Referring to the CB/Z 388-2005 standard, for the iron pear wood bearing lining, the distance between the equivalent fulcrum and the rear end face of the bearing lining is taken within the range of (1/4 ~ 1/3) L, where L is the length of the tail bearing.

In step S2, the alignment calculation is performed under the MATLAB program using the three-bending moment method. Input parameters such as the length-diameter ratio of the stern bearing and the elastic modulus of the inner lining are given, together with the initial equivalent fulcrum position Z ⁽⁰⁾ . Substitute into the three-bending moment method for alignment calculation, and obtain the journal rotation angle at the stern bearing.

In step S3, when the new equivalent fulcrum position value Z ^(k) is calculated, it is calculated according to the journal rotation angle, elastic modulus and aspect ratio.

In the calculation formula of the equivalent fulcrum of the stern bearing, the finite element method is used to calculate the position of the equivalent fulcrum of the stern bearing under different bearing length-diameter ratios, journal rotation angles and elastic modulus of the lining, and then the fulcrum coefficient is obtained by fitting the linear regression analysis method.

In step S3, the relationship between the elastic modulus, aspect ratio and rotation angle of the stern bearing and the position of the equivalent fulcrum is:

Z ^(k) = a(L/D) ^b (θ ^(k) ) ^c E ^d ; (1)

where Z ^(k) is the equivalent fulcrum position of the stern bearing calculated at the k-th iteration; L/D is the length-diameter ratio of the stern bearing; θ ^(k) is the journal rotation angle calculated at the k-th iteration; E is the elastic modulus of the stern bearing lining; a, b, c, and d are the fulcrum coefficients, which are calculated by the linear regression analysis method combined with the simulation data.

In step S5, the criterion for iterative convergence is:

where b is the iterative convergence coefficient. B can be taken as 0.001.

In step S5, the final alignment calculation result includes: rotation angle, deflection, bending moment, bending stress, rotation angle and support reaction force.

The equivalent fulcrum calculation formula in step S3 can be derived by regression analysis, and its specific derivation method is as follows:

Z=a(L/D) ^b θ ^c E ^d ; (3)

Linearize formula (3) and take the logarithm on both sides of the equal sign, we get

ln(Z)=ln(a)+b ln(L/D)+c ln(θ)+d ln(E) (4)

Then the linear regression equation is

y=m+bx ₁ +cx ₂ +dx ₃ (5)

y=ln(Z), m=ln(a), x ₁ =ln(L/D), x ₂ =ln(θ), x ₃ =ln(E) (6)

Using the regression analysis method to formula (5), the squared sum of the deviations of the positions of each fulcrum is obtained as:

为第i点的支点位置理论值。In the formula: n is the sample size; d _i is the fulcrum position deviation of the ith point; y _i is the measured value of the fulcrum position of the ith point;

is the theoretical value of the fulcrum position of the i-th point.

越小，支点位置理论值与测量值越接近，取最小值的必要条件是

The smaller the value, the closer the theoretical value of the fulcrum position is to the measured value. The necessary condition for taking the minimum value is

The system of linear equations is sorted as

The matrix form of the above system of equations is Ab=B

The coefficient matrix to be determined is b=A ^-1 B.

The coefficient matrix to be determined in the above formula is obtained by fitting and calculating the simulation data. Input the values of L/D, θ and E in the simulation software to obtain the corresponding Z value, and change different input parameter values to obtain different Z values, thus obtaining a large amount of simulation data, which can be calculated by Obtain the undetermined coefficients a, b, c, and d.

Compared with the prior art, the iterative calculation method for the alignment of the ship propulsion shafting proposed by the present invention has the following advantages:

1. The cyclic iterative alignment method is adopted to solve the problem that the position of the fulcrum of the stern bearing that is subjectively assumed in the alignment calculation does not match the actual shafting state by means of iterative calculation;

2. The equivalent fulcrum model and its calculation method considering bearing factors are proposed. On the basis of the traditional equivalent fulcrum model, bearing factors are taken into account, and the bearing length-diameter ratio, lining elastic modulus and bearing axis are analyzed. The relationship between the rotation angle and the position of the equivalent fulcrum, and the derivation process of its calculation formula is given;

3. Using this cycle iterative alignment method, considering the shortcomings of the finite element method and the traditional three-bending moment method in calculating the shaft alignment, the position value of the fulcrum of the stern bearing can be accurately obtained, which solves the subjective assumption in alignment calculation. The problem that the position of the fulcrum of the stern bearing does not match the actual state of the shaft system, and then the calculation result of the alignment can be accurately obtained.

In the actual alignment of the propulsion shaft system, the selection of the stern bearing fulcrum position is usually based on empirical data, but the stern bearing fulcrum position obtained in this way is not necessarily consistent with the actual situation. The alignment method can solve this problem very well, and get a more realistic fulcrum position of the stern bearing. In addition, with the development of modern ships, the change of the bearing aspect ratio and other factors makes the alignment environment more complicated. For this problem, the present invention comprehensively considers the bearing aspect ratio, the journal rotation angle and the bearing lining elastic modulus to the bearing. The influence of the fulcrum position makes the selection of the bearing fulcrum position more convenient and accurate under different factors.

The above are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any equivalent structural transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly applied in other related technical fields, are the same. Included in the scope of patent protection of the present invention.

Claims (6)

1. an iterative calculation method for the alignment of ship propulsion shafting, is characterized in that, comprises the following steps: S1, discretize the shaft segment and give the initial position value Z ⁽⁰⁾ of the equivalent fulcrum of the stern bearing; S2, use the three-bending moment method to align and calculate the shafting to obtain the journal rotation angle at the stern bearing; S3, use the calculation formula of the equivalent fulcrum of the stern bearing, substitute the journal rotation angle obtained in the previous step, and calculate the new equivalent fulcrum position value Z ^(k) , where k is the number of iterations; S4, when the difference between the new equivalent fulcrum position value Z ^(k) and the equivalent fulcrum position value Z ^(k-1) before the iteration is greater than the preset difference, compare Z ^(k) and Z ^{( k-1)} The average value of the two is used as the new equivalent fulcrum position value, which is the basis for the next calculation of the journal rotation angle at the stern bearing, and returns to step S2; S5, when the difference between the new equivalent fulcrum position value Z ^(k) and the equivalent fulcrum position value Z ^(k-1) before the iteration is less than or equal to the preset difference, that is, the iterative convergence satisfies the preset Conditions, substitute Z ^(k) into the three bending moment method to obtain the final alignment calculation result; In the calculation formula of the equivalent fulcrum of the stern bearing, the finite element method is used to calculate the position of the equivalent fulcrum of the stern bearing under different bearing length-diameter ratios, journal rotation angles and elastic modulus of the lining, and then the fulcrum coefficient is obtained by fitting the linear regression analysis method. 2. The iterative calculation method for alignment of ship propulsion shafting according to claim 1, wherein in step S1, the value range of Z ⁽⁰⁾ is (1/4～1/3)L, wherein L is Stern bearing length. 3. The iterative calculation method for alignment of ship propulsion shafting as claimed in claim 1, characterized in that, in step S3, when the new equivalent fulcrum position value Z ^(k) is obtained by calculation, according to the journal rotation angle, elastic modulus and the aspect ratio is calculated. 4. The iterative calculation method for alignment of ship propulsion shafting as claimed in claim 1, characterized in that, in step S3, the relationship between the elastic modulus, aspect ratio and rotation angle of the stern bearing and the equivalent pivot position is: Z ^(k) = a(L/D) ^b (θ ^(k) ) ^c E ^d ; Where: Z ^(k) is the equivalent fulcrum position of the stern bearing calculated at the k-th iteration; L/D is the length-diameter ratio of the stern bearing; θ ^(k) is the journal rotation angle calculated at the k-th iteration; E is the elastic modulus of the stern bearing lining; a, b, c, and d are the fulcrum coefficients, which are calculated by the linear regression analysis method combined with the simulation data. 5. The iterative calculation method for the alignment of ship propulsion shafting as claimed in claim 1, wherein in step S5, the criterion of iterative convergence is:

where b is the iterative convergence coefficient. 6. The iterative calculation method for the alignment of ship propulsion shafting according to any one of claims 1 to 5, wherein in step S5, the final alignment calculation result comprises: rotation angle, deflection, bending moment, bending stress , corners, and support forces.

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