Method for calculating shafting mode of hydraulic excavator

Abstract

The invention relates to the technical field of engineering machinery, in particular to a method for calculating a shafting mode of a hydraulic excavator, which is characterized in that an excavator shafting is calculated by applying MATLAB software based on a transfer matrix, specifically, firstly, a hydraulic excavator is selected to obtain related rotational inertia and torsional rigidity parameters, and equivalent rotational inertia conversion and equivalent torsional rigidity conversion are carried out; meanwhile, a calculation program is written in MATLAB according to the torsional vibration theory, the equivalent rotational inertia and the torsional rigidity are input into the calculation program, the inherent frequency and a vibration mode diagram of the excavator shaft system can be obtained, and hydraulic excavator shaft system modal calculation is completed. According to the method, shafting modeling and grid division do not need to be carried out, only relevant calculation parameters need to be known from manufacturers, the parameters are input through the listed calculation formulas, the shafting modality of the excavator can be obtained, the time for calculating the shafting modality of the excavator is greatly shortened, and operation becomes simple and clear.

Description

Technical Field

[0001] This invention relates to the field of engineering machinery technology, specifically to a method for calculating the shaft system modes of a hydraulic excavator. Background Technology

[0002] Excavators are indispensable construction machinery in earthmoving. During excavator operation, the shaft transmission system generates vibrations due to the transmission of engine torque. Among these vibrations, the torsional vibrations caused by the rotation of the excavator shafts have a particularly significant impact. If the shaft system's modes resonate with the excavator's operating speed, this can not only reduce the service life of the excavator shaft system but also, more seriously, lead to the breakage of the transmission shaft. Therefore, calculating the excavator shaft system modes and avoiding resonance at the "critical speed" is of paramount importance.

[0003] Currently, the most common method for calculating the shaft system of excavators is to model the excavator shaft system and then mesh it to calculate the modes of the excavator shaft system. This method can calculate the modes and vibration modes of the excavator shaft system, but it requires a lot of time to model and mesh the shaft system. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the shaft system modes of a hydraulic excavator, which aims to solve the problems of long time and complicated operation required by traditional methods for obtaining excavator shaft system information, which necessitates modeling, mesh generation, and finite element simulation.

[0005] To achieve the above objectives, the present invention provides a method for calculating the shaft system modes of a hydraulic excavator, comprising the following steps:

[0006] Step 1: Select a hydraulic excavator to simplify the structural degrees of freedom and obtain the relevant rotational inertia and torsional stiffness parameters;

[0007] Step 2: Perform parameter conversion on the moment of inertia and the torsional stiffness parameters;

[0008] Step 3: Based on torsional vibration theory, write a calculation program in MATLAB, input the data converted in Step 2 into the calculation program, and obtain the natural frequencies and mode shapes of the hydraulic excavator shaft system.

[0009] Optionally, in step 1, the model diagrams of the engine, coupling, and hydraulic pump of the hydraulic excavator are simplified and obtained according to the lumped mass method, and the degrees of freedom are divided; the rotational inertia and torsional stiffness parameters are directly provided by the manufacturer.

[0010] Optionally, in step 2, when performing the equivalent moment of inertia conversion:

[0011] For regularly shaped components, if they rotate about their center of gravity, the moment of inertia is calculated using the following formula:

[0012]

[0013] In the formula, d m The mass of an infinitesimal element on an object is represented by r; the radius from the infinitesimal element mass to the axis of rotation is represented by m; the mass of the part is represented by R; and the radius of rotation is represented by r.

[0014] If it does not rotate about its center of gravity, the moment of inertia is transformed using the translation axis theorem as follows:

[0015]

[0016] In the formula, J0 represents the moment of inertia of rotation about the center of gravity; m represents the mass of the part; and H represents the distance from the axis of rotation to the center of gravity.

[0017] For irregularly shaped parts, their moment of inertia can be obtained through experimental testing or by creating a 3D model of the part in 3D modeling software and then obtaining the inertia parameters.

[0018] Optionally, in step 2, when calculating the equivalent torsional stiffness of the lumped mass model, the torsional stiffness of the power transmission system components is first calculated according to the torsional stiffness calculation method of the variable cross-section stepped shaft; then, according to the allocation scheme of each degree of freedom in the lumped mass model, the torsional stiffness of the components obtained by each degree of freedom is equivalently converted in a series-parallel manner.

[0019] If the parts are connected in series, the equivalent torsional stiffness is equal to the reciprocal of the sum of the reciprocals of the torsional stiffnesses of the individual parts, calculated as follows:

[0020]

[0021] If the parts are connected in parallel, the equivalent torsional stiffness is equal to the sum of the torsional stiffnesses of the parallel parts, and the calculation formula is as follows:

[0022] .

[0023] Optionally, in step 3, the hydraulic excavator shaft system can be considered as an undamped free torsional vibration system. The differential equation of motion for the undamped free torsional vibration system is:

[0024]

[0025] in, Let n be the rotational inertia matrix; Let n be the stiffness matrix; It is an n×1 shifted column vector; It is an n×1 column vector of angular accelerations.

[0026] Optionally, step 3, the process of writing the calculation program in MATLAB, includes the following steps:

[0027] Step 3.1: Define the input parameter format and input the parameters;

[0028] Step 3.2: Write a program to check the format of the input parameters to ensure their correctness;

[0029] Step 3.3: The procedure for constructing the rotational inertia matrix and torsional stiffness matrix;

[0030] Step 3.4: Solve for eigenvalues ​​and extract intrinsic frequencies;

[0031] Step 3.5: Write the program for displaying the results and the program for calculating the mode shape;

[0032] Step 3.6: Run the program to obtain the calculation results.

[0033] This invention provides a method for calculating the modal characteristics of a hydraulic excavator's shaft system. Based on the transfer matrix, it utilizes MATLAB software to calculate the excavator's shaft system. Specifically, it first selects a hydraulic excavator and obtains relevant rotational inertia and torsional stiffness parameters, then performs equivalent rotational inertia and torsional stiffness conversions. Simultaneously, based on torsional vibration theory, a calculation program is written in MATLAB. By inputting the equivalent rotational inertia and torsional stiffness into the program, the natural frequencies and mode shapes of the excavator's shaft system are obtained, completing the modal calculation of the hydraulic excavator's shaft system. This method eliminates the need for shaft system modeling and mesh generation; it only requires obtaining relevant calculation parameters from the manufacturer and inputting these parameters using the listed calculation formulas to obtain the excavator's shaft system modes. This significantly reduces the time required for calculating the excavator's modes, making the operation simple and straightforward. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a schematic diagram illustrating the detailed implementation steps of a method for calculating the shaft system modes of a hydraulic excavator according to the present invention.

[0036] Figure 2 This is a schematic diagram of the undamped free torsional vibration system structure used in this invention.

[0037] Figure 3 This is a schematic diagram of the vibration modes of each degree of freedom of the excavator shaft system in a specific embodiment of the present invention. Detailed Implementation

[0038] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0039] This invention provides a method for calculating the shaft system modes of a hydraulic excavator, comprising the following steps:

[0040] Step 1: Select a hydraulic excavator to simplify the structural degrees of freedom and obtain the relevant rotational inertia and torsional stiffness parameters;

[0041] Step 2: Perform parameter conversion on the moment of inertia and the torsional stiffness parameters;

[0042] Step 3: Based on torsional vibration theory, write a calculation program in MATLAB, input the data converted in Step 2 into the calculation program, and obtain the natural frequencies and mode shapes of the hydraulic excavator shaft system.

[0043] Detailed process steps are as follows Figure 1 As shown, the following provides further explanation in conjunction with the execution steps and specific implementation process:

[0044] Step 1: Simplify the shaft system structure of the hydraulic excavator. Specifically, this involves simplifying the degrees of freedom based on the structure of the hydraulic excavator. The specific structure of the engine, coupling, and hydraulic pump, as well as the relevant rotational inertia and torsional stiffness parameters, need to be obtained from the manufacturer. Basically, the degrees of freedom for the above three components are determined based on the simplified model diagram provided by the manufacturer using the lumped mass method.

[0045] Step 2: Based on the moment of inertia and torsional stiffness obtained from the manufacturer above, perform parameter conversion. The parameter conversion should follow these principles:

[0046] (1) Equivalent moment of inertia conversion method

[0047] Moment of inertia characterizes the amount of inertia (remaining stationary or rotating at a constant speed) of an object when it rotates around an axis. For regularly shaped parts, if they rotate around the axis of gravity, their moment of inertia can be calculated according to equation (1); if they do not rotate around the axis of gravity, their moment of inertia can be transformed according to the translation axis theorem in equation (2); for irregularly shaped parts, their moment of inertia can be obtained by experimental testing or by creating a three-dimensional model of the part in three-dimensional modeling software and then obtaining its inertia parameters.

[0048] (1)

[0049] In the formula, d m The mass of an infinitesimal element on an object is represented by r; the radius from the infinitesimal element mass to the axis of rotation is represented by m; the mass of the part is represented by R; and the radius of rotation is represented by r.

[0050] (2)

[0051] In the formula, J0 represents the moment of inertia of rotation about the center of gravity; m represents the mass of the part; and H represents the distance from the axis of rotation to the center of gravity.

[0052] When establishing a lumped mass model, the power transmission system is discretized into a finite number of degrees of freedom according to its arrangement. Each degree of freedom contains several power transmission system components. Due to speed ratios, the rotational speeds of different components differ. Therefore, when calculating the equivalent inertia of each degree of freedom in the model, the first component represented by that degree of freedom is used as a reference. Based on the principle of conservation of kinetic energy, the inertia of the other components in the group is equivalent to the rotational inertia under the condition of rotating at the same speed as the first component. Finally, the equivalent inertia of all components in the group are added together to obtain the equivalent resultant inertia of that degree of freedom.

[0053] The formula for calculating the kinetic energy of a part rotating about a fixed axis is shown in equation (3):

[0054] (3)

[0055] According to the principle of conservation of kinetic energy, the inertia of the i-th rotating part is equivalent to the same kinetic energy before and after, that is:

[0056] (4)

[0057] In the formula, J i J represents the actual moment of inertia of the i-th part; i The equivalent moment of inertia of the i-th part is represented by ω. i ω represents the actual angular velocity of the i-th part; i The equivalent representation is the angular velocity of the equivalent axis (the axis where the first part of this degree of freedom is located).

[0058] Due to ω i Equivalent to ω i There exists a transmission ratio, as shown in equation (5):

[0059] (5)

[0060] In the formula, r i Let represent the cumulative transmission ratio from the i-th part to the first part in the equivalent degree of freedom. Substituting equation (5) into equation (4), we get:

[0061] (6)

[0062] In the formula ri This represents the cumulative transmission ratio from the i-th part to the first part in the equivalent degree of freedom.

[0063] (2) Equivalent torsional stiffness conversion method

[0064] When calculating the equivalent torsional stiffness of the lumped mass model, the torsional stiffness of the power transmission system components is first calculated according to the torsional stiffness calculation method of the variable cross-section stepped shaft. Then, according to the allocation scheme of each degree of freedom in the lumped mass model, the torsional stiffness of the components included in each degree of freedom is equivalently converted in a series-parallel manner.

[0065] If the parts are connected in series, the equivalent torsional stiffness is equal to the reciprocal of the sum of the reciprocals of the torsional stiffnesses of the individual parts, calculated as follows:

[0066] (7)

[0067] If the parts are connected in parallel, the equivalent torsional stiffness is equal to the sum of the torsional stiffnesses of the parallel parts, and the calculation formula is as follows:

[0068] (8)

[0069] Because the hydraulic excavator's shafting connection involves the engine crankshaft to the flywheel, then a coupling, and finally the hydraulic pump input shaft, with a transmission ratio of 1:1, the excavator's shafting moment of inertia does not require parameter conversion and can be determined based on the manufacturer's provided parameters. Furthermore, to clearly analyze the excavator's shafting's inherent modes, no structural simplification or equivalence of the engine and coupling is performed; therefore, the torsional stiffness of the engine and coupling components is also based on the manufacturer's parameters.

[0070] Step 3: Write a calculation program in MATLAB based on the theory of torsional vibration. The theory of torsional vibration is as follows:

[0071] Free vibration refers to a system that, after being subjected to an initial disturbance, vibrates independently without external forces. Undamped vibration refers to vibration in which there is no energy loss due to friction or other forms of resistance. Studies have shown that the damping of power transmission shaft systems is relatively small, and damping has virtually no impact on the calculation of free vibration of power transmission systems. Therefore, damping and excitation torque are generally not considered when calculating free vibration. A diagram of an undamped free torsional vibration system is shown below. Figure 2 As shown.

[0072] The differential equation of motion for an undamped free torsional vibration system is:

[0073]

[0074] in, Let n be the rotational inertia matrix; Let n be the stiffness matrix; It is an n×1 shifted column vector; It is an n×1 column vector of angular accelerations.

[0075] The solution is set as follows in the calculated results: (3.4) Substituting the set solution into the above differential equation of motion for the undamped free torsional vibration system, and after a series of calculations and transformations, the generalized characteristic equation can finally be obtained:

[0076] Where λ is the eigenvalue (i.e., the natural frequency) (the square value) This is the eigenvector (i.e., the principal mode) corresponding to the eigenvalue.

[0077] Based on the above theory, the specific steps for writing a program in MATLAB are as follows: First, open a new script in MATLAB and open the editor to write the program. The specific steps are as follows:

[0078] Step 3.1 involves inputting parameters to define the input format. In MATLAB, calculations require setting the input parameters to a specified format. This is done in the MATLAB script editor by defining the moment of inertia and torsional stiffness in the following format:

[0079] Set the moment of inertia to J = [,] where the equivalent moment of inertia of the shaft system is separated by commas; similarly, set the torsional stiffness to k = [,] where the torsional stiffness of the shaft system is separated by commas; this completes the definition of the parameter format. Subsequent parameter inputs can be entered directly within this format.

[0080] Step 3.2 involves writing a program to check the format of the input parameters to ensure their correctness and prevent errors during calculation. The specific steps are as follows: Use the `if length` function to check the format of the set moment of inertia J and torsional stiffness k.

[0081] Step 3.2.1 Use the if length function mentioned above to check the number of rotational inertia parameters. The specific format is defined as follows: if length(J) ~= number of rotational inertia parameters. Make the above settings to ensure that the number and format of the input rotational inertia are correct.

[0082] Similarly, in step 3.2.2, the if length function is used to check the number of torsional stiffness parameters. The specific format is defined as follows: if length(k) ~= the number of torsional stiffness parameters, perform the above settings to ensure the correct number and format of the input torsional stiffness.

[0083] Step 3.3 is to write a program to construct the moment of inertia matrix and the torsional stiffness matrix. In this step, we need to use the diag function to define the moment of inertia J as a diagonal matrix. Perform the following operations in the MATLAB script editor:

[0084] Step 3.3.1 Define the moment of inertia J as a diagonal matrix. The specific format is defined as follows: J_matrix = diag(J);

[0085] Step 3.3.2 At the same time, in this step, we also need to use the for loop statement and the if else statement to define the torsional stiffness k as a band matrix. The specific steps are as follows: First, initialize by creating a zero matrix with n rows and n columns, called kt, to store the total stiffness information of the system. The format is as follows: kt = zeros(the number of moments of inertia); Second, construct the main diagonal elements. The element in the i-th row and i-th column of the matrix represents the total stiffness contribution received by the i-th degree of freedom. Specifically:

[0086] When i = 1 (the first degree of freedom): It is only connected to the first spring, so its main diagonal value is equal to the stiffness of the first spring, k(1).

[0087] When i = the last degree of freedom: It is only connected to the last spring (i.e., the n-th spring), so its main diagonal value is equal to the stiffness of the last spring, k(=n - 1).

[0088] When i is an intermediate degree of freedom (from the 2nd to the n - 1th): It is connected to the two adjacent springs in front and behind (the i - 1th and the i-th springs respectively), so its main diagonal value is equal to the sum of the stiffnesses of these two springs, that is, k(i - 1) + k(i).

[0089] Finally, define the off-diagonal elements (coupling stiffness): The adjacent degrees of freedom interact with each other through springs, and this coupling effect is reflected in the sub-diagonal of the matrix:

[0090] For any degree of freedom i, as long as it is not the last one (i.e., i < n - 1), there is a spring k(i) between it and the next degree of freedom i + 1.

[0091] Therefore, in matrix kt: the value of the i-th row and the (i+1)-th column is set to -k(i), and the value of the (i+1)-th row and the i-th column is also set to -k(i) (to ensure matrix symmetry).

[0092] These negative values ​​represent the mutual tension between the two degrees of freedom.

[0093] Since there is no direct connection between non-adjacent degrees of freedom, their corresponding positions in the stiffness matrix remain 0.

[0094] All of the above definitions require the use of for loops and if-else statements for implementation.

[0095] Step 3.4 involves solving for eigenvalues ​​and extracting intrinsic frequencies. This step primarily involves calculating the desired eigenvalues ​​and extracting intrinsic frequencies from the input parameters and constructed matrix. In this step, we need to use the `eig` function to solve for the matrix's eigenvalues. Enter the following program in the MATLAB text editor to write the eigenvalue solving program:

[0096] Step 3.4.1 is for solving the generalized eigenvalue problem. The specific format is defined as follows:

[0097] [K]{X} = w^2[M]{X}

[0098] [V, D] = eig(kt, J_matrix);

[0099] Step 3.4.2 involves extracting the natural frequency. This requires using the sqrt function to calculate the square root of the natural angular frequency, and then converting the natural angular frequency to obtain the natural frequency. The following code needs to be written in the MATLAB script editor:

[0100] The specific definition format is as follows: wn = sqrt(diag(D)); fn = wn / (2 * pi);

[0101] Step 3.5 involves writing the program to display the results and the program to calculate the mode shape. In this step, the `fprintf` command will be used to display the calculated natural frequencies as images. Specifically, the following program will be written in the MATLAB script editor:

[0102] Step 3.5.1 Initialize the figure window: First, the program creates a new figure window to begin drawing charts. The `figure;` command is used for this purpose.

[0103] Step 3.5.2 Keep the current graph: Use the hold on; command to allow multiple graphs or images to be plotted in the same figure window. However, in this particular case, since each mode shape is plotted in a separate subplot, this command is not actually necessary.

[0104] Step 3.5.3 Traverse each mode shape: The program will process each mode shape in turn using a for loop. Assume V is a matrix where each column represents a different mode shape, and the loop variable i ranges from 1 to size(V, 2), which is the number of columns in V, indicating the total number of mode shapes.

[0105] Step 3.5.4 Normalize Mode Shapes: For each mode shape, the program normalizes it. This is done by dividing the mode shape vector by the maximum absolute value to ensure that the values ​​of all data points are between -1 and 1. This step is accomplished using V_normalized = V(:,i) / max(abs(V(:,i)));

[0106] Step 3.5.5 Create subgraph layout and draw mode shapes:

[0107] The `subplot` function dynamically creates the layout of subplots based on the number of mode shapes. It determines the number of rows and columns based on the length of the natural frequency vector `fn` to ensure that all subplots are arranged logically.

[0108] On each subplot, the normalized mode shape is plotted using the bar function. Here, the bar chart color is specified as 'flat', and the color data (CData) is directly associated with the absolute magnitude of the mode shape value, so that the amplitude change of the mode shape can be visually observed through color changes.

[0109] Set a title for each subgraph to display which mode shape is being observed.

[0110] Add labels for the x-axis and y-axis, labeled "Degrees of Freedom" and "Normalized Displacement" respectively.

[0111] Enable gridlines and use axis tight; to optimize the axis range and make the chart display the data as compactly as possible.

[0112] The program is written by following the steps described above.

[0113] Step 3.6 Run the program to obtain the calculation results. At this point, the MATLAB program for calculating the natural frequencies of the shaft system is complete. You only need to input the equivalent moment of inertia and torsional stiffness and then click to run the script to obtain the natural frequencies and mode shapes of the excavator shaft system. Thus, the MATLAB program can be used to quickly calculate the modes of the hydraulic excavator shaft system.

[0114] Furthermore, this invention also proposes a specific embodiment, taking a certain excavator equipped with a six-cylinder diesel engine as an example to perform the above operations. The diesel engine parameters include structural parameters provided by the manufacturer and obtained using the "lumped mass method," including rotational inertia and torsional stiffness parameters. In the entire calculation, the transmission shaft system includes the engine, coupling, and hydraulic pump. The parameter conversion of each structure follows the parameter conversion principles mentioned above. The parameters are input into the program, and the calculation results in MATLAB are as follows:

[0115] Natural frequency:

[0116] First natural frequency: 0.0000Hz

[0117] Second natural frequency: 18.6470Hz

[0118] Third natural frequency: 94.7807Hz

[0119] Fourth natural frequency: 195.9303Hz

[0120] 5th natural frequency: 475.9328Hz

[0121] The 6th natural frequency is 777.2559 Hz.

[0122] 7th natural frequency: 1005.7248Hz

[0123] 8th natural frequency: 1223.3200Hz

[0124] 9th natural frequency: 1335.1987Hz

[0125] 10th natural frequency: 1488.4173Hz

[0126] The calculation results yielded the first 10 natural frequencies of the excavator's shaft system and the mode shapes for each degree of freedom, as follows: Figure 3 As shown.

[0127] These 10 natural frequencies are the natural modes of the transmission system shaft of this hydraulic excavator. By analyzing the natural frequencies, the commonly used speeds and main engine excitations of this hydraulic excavator, the resonant speeds can be effectively avoided, torsional vibrations can be reduced, and the stability of the transmission shaft can be improved.

[0128] The normalized mode shape diagram corresponds to the first 10 natural frequencies and mode shapes. Figure 1 =0, mode shape Figure 2 Corresponding to the second natural frequency, the torsional vibration in this mode manifests as vibration of the coupling and hydraulic pump components, with the following mode shape. Figure 3 Corresponding to the third natural frequency, the torsional vibration in this mode is manifested as the vibration of the coupling part. Similarly, the mode shapes 4, 5, 6, 7, 8, 9, and 10 are manifested as the vibration of the engine part. In practice, this invention mainly focuses on the natural frequencies and mode shapes of the first three modes. The subsequent modes and mode shapes are usually not considered because they deviate from the commonly used operating speed and the vibration energy is too small.

[0129] In summary, the present invention has the following beneficial effects:

[0130] The technical problem solved by this invention is that traditional methods for calculating the shaft system of excavators require modeling, mesh generation, finite element simulation, and actual measurement, which takes a long time and cannot quickly produce results. This invention provides a method for parametric calculation of the shaft system modes using MATLAB software, which can effectively improve the calculation efficiency of shaft system modes and also provide some guidance for the selection of excavator shaft system parameters.

[0131] The above description discloses only one or more preferred embodiments of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A method of calculating a hydraulic excavator shafting mode, characterized by, The method comprises the following steps: Step 1: selecting a hydraulic excavator to simplify the structural degrees of freedom, and obtaining relevant moment of inertia and torsional stiffness parameters; Step 2: performing parameter conversion on the moment of inertia and the torsional stiffness parameters; Step 3: writing a calculation program in MATLAB based on torsional vibration theory, inputting the data converted in step 2 into the calculation program, and obtaining the natural frequency and mode shape diagram of the hydraulic excavator shaft system.

2. The method for calculating the mode of the hydraulic excavator shaft system according to claim 1, wherein In step 1, the model diagram of the engine, the shaft coupling and the hydraulic pump of the hydraulic excavator is obtained by simplification according to the lumped mass method, and the degrees of freedom are divided; the moment of inertia and the torsional stiffness parameters are directly provided by the manufacturer.

3. The method for calculating the mode of the hydraulic excavator shaft system according to claim 2, wherein In step 2, when the equivalent moment of inertia is converted: For a regular-shaped part, if it rotates around the center of gravity axis, the moment of inertia is calculated according to the following formula: ； where d m represents the mass of the microelement on the object; r represents the microelement mass to the radius of the shaft; m represents the mass of the part; R represents the radius of rotation; If it does not rotate around the center of gravity axis, the moment of inertia is converted according to the parallel axis theorem: ； In the formula, J0 represents the moment of inertia around the center of gravity axis; m represents the mass of the part; H represents the distance from the rotation axis to the center of gravity axis; For irregular-shaped parts, the moment of inertia is obtained by testing or establishing a three-dimensional model of the part in three-dimensional modeling software, and then obtaining the inertia parameters.

4. The method for calculating the mode of the hydraulic excavator shaft system according to claim 3, wherein In step 2, when the equivalent torsional stiffness of the lumped mass model is calculated, first, the torsional stiffness of the power transmission system parts is calculated according to the variable cross-section stepped shaft torsional stiffness calculation method; then, according to the distribution scheme of each degree of freedom in the lumped mass model, the torsional stiffness of each degree of freedom containing the parts is equivalent to the equivalent conversion in series-parallel mode; If the parts are in series, the equivalent torsional stiffness is equal to the reciprocal of the sum of the reciprocals of the torsional stiffness of the parts, and the calculation formula is as follows: ； If the parts are in parallel, the equivalent torsional stiffness is equal to the sum of the torsional stiffness of the parallel parts, and the calculation formula is as follows: 。 5. The method for calculating the mode of the hydraulic excavator shaft system according to claim 4, wherein In step 3, the hydraulic excavator shaft system is regarded as a free torsional vibration system without damping, and the motion differential equation of the free torsional vibration system without damping is as follows: ； wherein, is an n x n matrix of rotational inertia moments; is an n x n matrix of stiffness; is an n x 1 displacement column vector; is an n x 1 angular acceleration column vector.

6. The method for calculating the mode of the hydraulic excavator shaft system according to claim 5, wherein In step 3, the process of writing a calculation program in MATLAB includes the following steps: Step 3.1: defining the input parameter format and inputting the parameters; Step 3.2: writing a program to check the input parameter format to ensure the correctness of the input parameters; Step 3.3: constructing the program for the moment of inertia matrix and the torsional stiffness matrix; Step 3.4: solving the eigenvalues and extracting the natural frequency; Step 3.5: writing a program to display the result diagram and calculate the mode shape diagram; Step 3.6: running the program to obtain the calculation result.

Images