Quick calculation method of meshing force of differential main reduction gear

Abstract

The present invention provides a rapid calculation method for the meshing force of the differential's main reduction gear. This method decomposes the force at the meshing point of the main reduction gear, defines the meshing point of the main reduction gear coaxial with the planetary shaft as the 0° meshing point, and obtains the force F at the 0° meshing point. z1 F x1 F y1 The value, according to F x1 F y1 Calculate F 合1 and F 合1 With F y1 The included angle α, based on the included angle α, the number of meshing points on the main reduction gear, and the F of each meshing point. 合n Based on the principle of equality, F at the nth meshing point is derived. xn and F yn The calculation formula is used to create the F at the nth engagement point. xn and F yn The interactive computing interface enables the F-value of the nth meshing point to be calculated. xn and F yn It features fast calculation, a simple and intuitive interactive interface, strong independent operation and compatibility, small memory footprint, and avoids miscalculations. It provides accurate load input values ​​for differential strength analysis, improving the efficiency, reliability and accuracy of differential strength analysis.

Description

Technical Field

[0001] This invention relates to a method for rapidly calculating the meshing force of the main reduction gear in a differential, belonging to the field of simulation analysis technology for new energy speed reducers. Background Technology

[0002] Strength analysis of the differential assembly in a new energy vehicle reducer is a crucial aspect of the entire reducer design and development. The load input for this strength analysis is the meshing force of the main reduction gear. New energy vehicle reducers typically employ two-stage gear transmissions, with the differential's main reduction gear being the driven gear of the second stage. The main reduction gear experiences a meshing force from the second-stage driving gear at the meshing point. The components of this meshing force in the three coordinate directions in the global coordinate system are F... x F y F z F z For axial force, F at different meshing points z The magnitude remains constant. The engagement point coaxial with the differential planetary shaft is defined as the 0° engagement point. The meshing force at the 0° engagement point can be obtained using MASTA software. As the gear rotates, the engagement point also moves, and the meshing force F at different engagement points varies. x and F y The magnitude of the axial force F also changes. z The load on the differential remains constant, meaning it will vary at different engagement points, resulting in different strength performance. Generally, to verify the differential strength at n engagement points, the meshing forces at these n points need to be obtained. Therefore, when performing strength analysis on the differential, the load input is given in a global coordinate system according to the magnitude and direction of the three component forces, requiring the F values ​​at different engagement points to be obtained. x and F y The value of the meshing force at different meshing points is obtained by coordinate conversion of the meshing force at the 0° meshing point. The conversion formula and process are cumbersome, have a high error rate, and take a long time, which affects the efficiency and reliability of differential strength analysis. Summary of the Invention

[0003] The present invention provides a method for rapid calculation of the meshing force of the differential main reduction gear, which realizes the F at the nth meshing point through an interactive calculation interface. xn and F yn The system performs rapid calculations by encapsulating complex conversion formulas within the executable code that forms the interactive calculation interface. Users only need to input known data into the interface to quickly calculate the meshing force value at any meshing point. The interactive calculation interface is simple and intuitive, operates independently with strong compatibility, has a small memory footprint, avoids miscalculations, and provides accurate load input values ​​for differential strength analysis, thereby improving the efficiency, reliability, and accuracy of differential strength analysis.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for rapidly calculating the meshing force of the differential's main reduction gear, characterized by comprising the following steps:

[0006] S1: Decompose the meshing force at the engagement point of the main reduction gear in the differential into an axial component F along the axis of the main reduction gear. z The radial component F along the radial direction of the main reduction gear x and the tangential component F in the radial direction of the main reduction gear y ;

[0007] S2: Define the meshing point of the main reduction gear, which is coaxial with the planetary axis, as the 0° meshing point. Based on the number N of meshing points on the main reduction gear, designate the 0° meshing point as the first meshing point, define the meshing point clockwise adjacent to the first meshing point as the second meshing point, and so on, defining each meshing point sequentially in a clockwise direction. Define the F of the nth meshing point... x Defined as F xn F y Defined as F yn F xn and F yn The resultant force is defined as F 合n Where n = 1, 2, ..., N;

[0008] S3: F to obtain the 0° engagement point z1 F x1 F y1 The F obtained at the 0° engagement point z1 F is set at each meshing point zn Calculate F x1 and F y1 The resultant force F 合1 and F 合1 With F y1 The included angle α;

[0009] S4: Based on the included angle α, the number of meshing points on the main reduction gear, and the F of each meshing point... 合n Based on the principle of equality, F at the nth meshing point is derived. xn and F yn The calculation formula;

[0010] S5: Based on the calculation formula derived in the previous step, create the F at the nth engagement point in the Python development environment. xn and F yn The interactive computing interface is packaged and encapsulated into an independent executable program, which quickly calculates F at the nth meshing point through the input and output of the interactive computing interface. xn and F yn .

[0011] Preferably, a simulation model of a two-stage gear transmission new energy reducer is established in MASTA software. In the simulation model, the meshing force at the meshing point of the main reduction gear is decomposed into F. z F x F y And the F at the 0° engagement point was obtained through simulation analysis. z1 F x1 F y1 .

[0012] Preferably, step S3 specifically refers to: taking the 0° engagement point as the origin of the global coordinate system, F x The direction is defined as the x-axis, F y The direction is defined as the y-axis, according to F x1 F y1 F is calculated using the following formula (1). 合1 ;

[0013]

[0014] According to the inverse cosine law, F is calculated by using the following formula (2). 合1 Angle α with the y-axis;

[0015]

[0016] Preferably, step S4 specifically refers to: based on the number N of meshing points on the main reduction gear, determining the central angle θ corresponding to the arc between the nth meshing point and the 0° meshing point as (n-1)×360° / N, F 合n The angle between F and the y-axis of the global coordinate system is α+θ. 合n Orthogonally decomposed into F along the global coordinate system xn and F yn F is calculated using the following formula (3). xn :

[0017] F xn =F 合1 ×sin(α+θ) (3)

[0018] F is calculated using the following formula (4). yn :

[0019] F yn =F 合1 ×cos(α+θ) (4).

[0020] Preferably, the interactive computing interface includes an interactive window, which has an input field F. x1 Input label, input F y1The input labels are: the input label for the nth engagement point and the input label for the number N engagement points. Each input label has a corresponding input box to its right. The interactive window displays the output F. 合1 Output label, output label of included angle α, output label of central angle θ, output F xn Output label, output F yn The output labels have corresponding output boxes, and the interactive window has a Calculate button to trigger the output box to output the calculation result.

[0021] Preferably, the title of the interactive window is "Conversion of Force at Different Meshing Points in Main Reduction," and the input F... x1 Name the input label "Force in the X direction at 0° engagement point:", and input F y1 The input label is named: "Force in the Y direction at 0° engagement point:", the input label for the nth engagement point is named: "Number of engagement points / k:", the input label for the number of engagement points N is named: "Number of engagement points / n:", and the output F 合1 Name the output label "Resultant force F of X and Y:", name the output label for the included angle α "Angle α between the resultant force F at the 0° meshing point and the Y-axis (in radians):", name the output label for the central angle θ "Meshing point interval angle θ (in radians):", and name the output F... xn The output label is named "Force in the X Direction at the Meshing Point after Rotation Angle kθ", and the output F yn The output label is named "Force in the Y direction at the meshing point after rotation angle kθ:".

[0022] Preferably, the input labels are displayed in green, and the interactive window displays the message "Green parameters are required input, other parameters are calculated".

[0023] Preferably, F is created at the nth engagement point in the Python development environment. xn and F yn The interactive computing interface is packaged and encapsulated into a standalone executable program, including the following steps:

[0024] S51: Import the following modules in sequence: tkinter for creating the GUI interface, math for numerical computation, filedialog for using the file dialog, and win32com.client for interacting with COM components of the Windows operating system.

[0025] S52: Create a root window, set the window title to "Conversion of Force at Different Meshing Points of Main Subtraction", set the window size to 600x370, disable window resizing, and define the text on the window;

[0026] S53: Define a function `file_open()` to open a file dialog box and select a file. The `file_open()` function opens a file dialog box, allows the user to select a file, and returns the path of the selected file. Create an object that interacts with the COM component of Kingsoft WPS word processing software and assign it to the `wps` variable. Use the `Documents.open()` method of the `wps` object to open the document corresponding to the file path stored in the `file_path` variable.

[0027] S54: Define a `create_menu()` function to create a parent menu `menu` and associate it with the window root; create a submenu `file_menu` and associate it with the parent menu `menu`; add a command option labeled "Open" to the submenu `file_menu` and specify that clicking this option will call the `file_open()` function; add the submenu `file_menu` to the parent menu `menu` and name it "File"; configure the parent menu `menu` as the menu bar of the root window. S55: Create nine string variables `StringVar()` to store user input values ​​and calculation result output values;

[0028] S56: Input labels and corresponding input boxes, as well as output labels and corresponding output boxes, were created, and the input labels and output labels were named respectively;

[0029] S57: Defines a calcu() function that performs coordinate transformation and updates the results based on input information;

[0030] S58: Created a Calculate button to trigger the calcu() function.

[0031] S59: Call the create_menu() function to create the menu bar and enter the main event loop to display the root window;

[0032] S510: Package the main program into an independent executable program using a custom method and icon.

[0033] The beneficial effects of the invention are:

[0034] The present invention provides a rapid calculation method for the meshing force of the differential's main reduction gear. This method decomposes the force at the meshing point of the main reduction gear, defines the meshing point of the main reduction gear coaxial with the planetary shaft as the 0° meshing point, and obtains the force F at the 0° meshing point. z1 F x1 F y1 The value, according to F x1 F y1 Calculate F 合1and F 合1 With F y1 The included angle α, based on the included angle α, the number of meshing points on the main reduction gear, and the F of each meshing point. 合n Based on the principle of equality, F at the nth meshing point is derived. xn and F yn The calculation formula is used to create the F at the nth engagement point. xn and F yn The interactive computing interface enables the F-value of the nth meshing point to be calculated. xn and F yn The system performs rapid calculations by encapsulating complex conversion formulas within the executable code that forms the interactive calculation interface. Users only need to input known data into the interface to quickly calculate the meshing force value at any meshing point. The interactive calculation interface is simple and intuitive, operates independently with strong compatibility, has a small memory footprint, avoids miscalculations, and provides accurate load input values ​​for differential strength analysis, thereby improving the efficiency, reliability, and accuracy of differential strength analysis. Attached Figure Description

[0035] Figure 1 Force analysis diagram of the 0° meshing point and the second meshing point on the main reduction gear.

[0036] Figure 2 This is a schematic diagram of an interactive computing interface.

[0037] Figure 3 This is a diagram of the icon for the executable program. Detailed Implementation

[0038] The following is combined Figures 1-3 The embodiments of the present invention will be described in detail below.

[0039] A method for rapidly calculating the meshing force of the differential's main reduction gear, characterized by comprising the following steps:

[0040] S1: Decompose the meshing force at the engagement point of the main reduction gear in the differential into an axial component F along the axis of the main reduction gear. z The radial component F along the radial direction of the main reduction gear x and the tangential component F in the radial direction of the main reduction gear y ;

[0041] S2: Define the meshing point of the main reduction gear, which is coaxial with the planetary axis, as the 0° meshing point. Based on the number N of meshing points on the main reduction gear, the 0° meshing point is taken as the first meshing point. The meshing point clockwise adjacent to the first meshing point is defined as the second meshing point, and so on. Define each meshing point sequentially in a clockwise direction. The F of the nth meshing point... x Defined as F xn ,F y Defined as Fyn ,F xn and F yn The resultant force is defined as F 合n , where n = 1, 2, ..., N;

[0042] S3: F obtains the 0° engagement point z1 F x1 F y1 The F obtained at the 0° engagement point z1 F is set at each meshing point zn Calculate F x1 and F y1 The resultant force F 合1 and F 合1 With F y1 The included angle α;

[0043] S4: Based on the included angle α, the number of meshing points on the main reduction gear, and the F of each meshing point... 合n Based on the principle of equality, F at the nth meshing point is derived. xn and F yn The calculation formula;

[0044] S5: Based on the calculation formula derived in the previous step, create the F at the nth engagement point in the Python development environment. xn and F yn The interactive computing interface is packaged and encapsulated into an independent executable program, which quickly calculates F at the nth meshing point through the input and output of the interactive computing interface. xn and F yn .

[0045] The above-described method for quickly calculating the meshing force of the differential's main reduction gear decomposes the force at the meshing point on the main reduction gear, defines the meshing point of the main reduction gear coaxial with the planetary shaft as the 0° meshing point, and obtains the F at the 0° meshing point. x1 F y1 The value, according to F z1 F x1 F y1 Calculate F 合1 and F 合1 With F y1 The included angle α, based on the included angle α, the number of meshing points on the main reduction gear, and the F of each meshing point. 合n Based on the principle of equality, F at the nth meshing point is derived. xn and F yn The calculation formula is used to create the F at the nth engagement point. xn and F yn The interactive computing interface enables the F-value of the nth meshing point to be calculated. xn and F ynThe system performs rapid calculations by encapsulating complex conversion formulas within the executable code that forms the interactive calculation interface. Users only need to input known data into the interface to quickly calculate the meshing force value at any meshing point. The interactive calculation interface is simple and intuitive, operates independently with strong compatibility, has a small memory footprint, avoids miscalculations, and provides accurate load input values ​​for differential strength analysis, thereby improving the efficiency, reliability, and accuracy of differential strength analysis.

[0046] In this study, a simulation model of a two-stage gear transmission new energy reducer was established in MASTA software. In the simulation model, the meshing force at the meshing point of the main reduction gear was decomposed into F. z F x F y And the F at the 0° engagement point was obtained through simulation analysis. z1 F x1 F y1 New energy speed reducers are generally two-stage gear drives. The differential's main reduction gear is the driven gear of the second stage. At the meshing point, the main reduction gear experiences a meshing force from the second-stage driving gear. The components of this meshing force in the three coordinate directions in the global coordinate system are F... z F x F y Among them, F z As the axial force, based on the force characteristics of gear meshing transmission, it can be derived that F varies for different meshing points. z The magnitude remains constant. The engagement point coaxial with the differential planetary shaft is defined as the 0° engagement point. The meshing force at the 0° engagement point can be obtained using MASTA software. As the gear rotates, the engagement point also moves, and the meshing force F at different engagement points varies. x and F y The magnitude of the force also changes, while the axial force Fz remains constant.

[0047] Specifically, step S3 refers to: taking the 0° engagement point as the origin of the global coordinate system, F x The direction is defined as the x-axis, F y The direction is defined as the y-axis, according to F x1 F y1 F is calculated using the following formula (1). 合1 ;

[0048]

[0049] According to the inverse cosine law, F is calculated by using the following formula (2). 合1 Angle α with the y-axis;

[0050]

[0051] like Figure 1As shown, with the 0° meshing point as the origin, the radial direction of the main reduction gear is defined as the x-axis, and the perpendicular radial direction is defined as the y-axis. This coordinate system is the global coordinate system, i.e., F at the 0° meshing point. x1 For radial force, F y1 For tangential force, according to the Pythagorean theorem, F can be obtained from... x1 and F y1 Derive F 合1 The calculation formula: In the triangle formed by the resultant force and the two component forces, the formula for calculating the included angle α can be derived using the inverse cosine function:

[0052] Specifically, step S4 refers to: based on the number N of meshing points on the main reduction gear, determining the central angle θ corresponding to the arc between the nth meshing point and the 0° meshing point as (n-1)×360° / N, F 合n The angle between F and the y-axis of the global coordinate system is α+θ. 合n Orthogonally decomposed into F along the global coordinate system xn and F yn F is calculated using the following formula (3). xn :

[0053] F xn =F 合1 ×sin(α+θ) (3)

[0054] F is calculated using the following formula (4). yn :

[0055] F yn =F 合1 ×cos(α+θ) (4).

[0056] like Figure 1 As shown, assuming there are 8 meshing points on the main reduction gear, that is, N = 8, the central angle θ corresponding to the arc between the second meshing point and the 0° meshing point is 45°, F x2 and F y2 The resultant force is F 合2 Because the torque transmitted by the second-stage driving gear remains constant, therefore F 合2 =F 合1 At this time, F 合2 The angle between F and the y-axis of the global coordinate system is α+θ. 合2 Orthogonal decomposition along the global coordinate system yields F x2 and F y2 The formula for calculating F is: x2 =F 合1 ×sin(α+θ) and F y2 =F 合1 ×cos(α+θ).

[0057] The interactive computing interface includes an interactive window, which has an input field F. x1 Input label, input F y1 The input labels are: the input label for the nth engagement point and the input label for the number N engagement points. Each input label has a corresponding input box to its right. The interactive window displays the output F. 合1 Output label, output label of included angle α, output label of central angle θ, output F xn Output label, output F yn The interface has output labels, each with a corresponding output box. The interactive window includes a "Calculate" button to trigger the output of the calculation results. Users manually enter known values ​​in the input boxes corresponding to the input labels, and then click the "Calculate" button to display the output values ​​in the output boxes corresponding to the output labels. By simply inputting known data, the meshing force at any meshing point can be quickly calculated. The interactive calculation interface is simple and intuitive, effectively avoiding miscalculations.

[0058] The interactive window is titled "Conversion of Force at Different Meshing Points in Main Reduction," and you will input F. x1 Name the input label "Force in the X direction at 0° engagement point:", and input F y1 The input label is named: "Force in the Y direction at 0° engagement point:", the input label for the nth engagement point is named: "Number of engagement points / k:", the input label for the number of engagement points N is named: "Number of engagement points / n:", and the output F 合1 Name the output label "Resultant force F of X and Y:", name the output label for the included angle α "Angle α between the resultant force F at the 0° meshing point and the Y-axis (in radians):", name the output label for the central angle θ "Meshing point interval angle θ (in radians):", and name the output F... xn The output label is named "Force in the X Direction at the Meshing Point after Rotation Angle kθ", and the output F yn The output label is named "Force in the Y direction at the meshing point after rotation angle kθ:". The naming of the interactive window's title, input labels, and output labels is easy for first-time users to understand. Even first-time users can correctly input relevant known data based on the label naming prompts, ensuring the accuracy of the output data. The input and output label naming of the interactive calculation interface is easy to understand, effectively improving the user experience.

[0059] The input labels are displayed in green, and the interactive window displays the message "Green parameters are required input; other parameters are calculated." This guides first-time users to input relevant known data, further enhancing the user experience.

[0060] In the Python development environment, F is used to create the nth engagement point. xnand F yn The interactive computing interface is packaged and encapsulated into a standalone executable program, including the following steps:

[0061] S51: Import the following modules in sequence: tkinter for creating the GUI interface, math for numerical computation, filedialog for using the file dialog, and win32com.client for interacting with COM components of the Windows operating system.

[0062] S52: Create a root window, set the window title to "Conversion of Force at Different Meshing Points of Main Subtraction", set the window size to 600x370, disable window resizing, and define the text on the window;

[0063] S53: Define a function `file_open()` to open a file dialog box and select a file. The `file_open()` function opens a file dialog box, allows the user to select a file, and returns the path of the selected file. Create an object that interacts with the COM component of Kingsoft WPS word processing software and assign it to the `wps` variable. Use the `Documents.open()` method of the `wps` object to open the document corresponding to the file path stored in the `file_path` variable.

[0064] S54: Define a create_menu() function to create a parent menu and associate it with the root window; create a submenu file_menu and associate it with the parent menu; add a command option labeled "Open" to the submenu file_menu and specify that the file_open() function should be called when this option is clicked; add the submenu file_menu to the parent menu and name it "File"; configure the parent menu as the menu bar of the root window.

[0065] S55: Nine string variables StringVar() were created to store user input values ​​and calculation result output values;

[0066] S56: Input labels and corresponding input boxes, as well as output labels and corresponding output boxes, were created, and the input labels and output labels were named respectively;

[0067] S57: Defines a calcu() function that performs coordinate transformation and updates the results based on input information;

[0068] S58: Created a Calculate button to trigger the calcu() function.

[0069] S59: Call the create_menu() function to create the menu bar and enter the main event loop to display the root window;

[0070] S510: Package the main program into an independent executable program using a custom method and icon.

[0071] The icon of the executable program is as follows Figure 3 As shown, packaging the main program into an independent executable program with a customizable method and icon eliminates the pop-up command window, improving execution efficiency. When using it, double-clicking the executable program's icon opens the interactive calculation interface. Input the known data according to the input label prompts, and click the Calculate button to display the output value in the output box.

[0072] The technical solutions of the embodiments of the present invention have been fully described above with reference to the accompanying drawings. It should be noted that the described embodiments are only a part of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

Claims

1. A method for rapid calculation of the meshing force of the differential's main reduction gear, characterized in that, Includes the following steps: S1: Decompose the meshing force at the engagement point of the main reduction gear in the differential into an axial component along the axis of the main reduction gear. Radial component of force along the radial direction of the main reduction gear and the tangential component of the radial force of the vertical main reduction gear ; S2: Define the meshing point of the main reduction gear, which is coaxial with the planetary axis, as the 0° meshing point. Based on the number N of meshing points on the main reduction gear, the 0° meshing point is taken as the first meshing point. The meshing point clockwise adjacent to the first meshing point is defined as the second meshing point, and so on. Define each meshing point sequentially in a clockwise direction. , where n = 1, 2, ..., N; S3: Obtain the 0° engagement point The obtained 0° engagement point Set as each meshing point ,calculate ; S4: Based on the included angle The number of meshing points on the main reduction gear, combined with the number of meshing points The principle of equality leads to the derivation of the nth meshing point. The calculation formula; S5: Based on the calculation formula derived in the previous step, create the nth engagement point in the Python development environment. The interactive computing interface is packaged and encapsulated into an independent executable program, which can quickly calculate the nth engagement point through the input and output of the interactive computing interface. ; A simulation model of a two-stage gear transmission new energy reducer was established in MASTA software. In the simulation model, the meshing force at the meshing point of the main reduction gear was decomposed into... And the 0° engagement point was obtained through simulation analysis. ; Step S3 specifically refers to: taking the 0° engagement point as the origin of the global coordinate system. The direction is defined as the x-axis. The direction is defined as the y-axis, according to Calculate using the following formula (1) ; ； According to the inverse cosine law, the following formula (2) can be used to calculate... Angle with the y-axis ; ； Step S4 specifically refers to: based on the number N of meshing points on the main reduction gear, determining the central angle corresponding to the arc between the nth meshing point and the 0° meshing point. It is (n-1)×360° / N. ,Will Orthogonal decomposition along the global coordinate system Calculated using the following formula (3) : ； Calculate using the following formula (4) : ； The interactive computing interface includes an interactive window, which has input... Input labels, input The input labels include the label for the nth engagement point and the label for the number N engagement points. Each input label has a corresponding input box to its right. The interactive window displays the output. Output label, output angle Output label, output center angle Output tags, output Output tags, output The output labels have corresponding output boxes, and the interactive window has a Calculate button to trigger the output box to output the calculation result. The interactive window is titled "Conversion of Force at Different Meshing Points in Main Reducer," where you will input... Name the input label "Force in the X direction at the 0° engagement point:" and input The input label is named: "Force in the Y direction at 0° engagement point:", the input label for the nth engagement point is named: "Number of engagement points / k:", the input label for the number of engagement points N is named: "Number of engagement points / n:", and the output... Name the output label "Resultant force of X and Y F:", and output the included angle. The output label is named "0° Angle between the resultant force F at the meshing point and the Y-axis α / radians:", and the output central angle is... Name the output label "Meshing point interval angle θ / radians:", and the output Name the output label "Force in the X Direction at the Meshing Point After Rotation Angle kθ" and output The output label is named "Force in the Y direction at the meshing point after rotation angle kθ:".

2. The method for rapid calculation of the meshing force of the differential main reduction gear according to claim 1, characterized in that: Input labels are displayed in green, and the interactive window displays the message "Green parameters are required input, other parameters are calculated".

3. The method for rapid calculation of the meshing force of the differential main reduction gear according to claim 2, characterized in that: Create the nth engagement point in the Python development environment. The interactive computing interface is packaged and encapsulated into a standalone executable program, including the following steps: S51: Import the following modules in sequence: tkinter for creating the GUI interface, math for numerical computation, filedialog for using the file dialog, and win32com.client for interacting with COM components of the Windows operating system. S52: Create a root window, set the window title to "Conversion of Force at Different Meshing Points of Main and Subtractive Control", set the window size to 600x370, disable window resizing, and define the text on the window; S53: Define a function `file_open()` to open a file dialog box and select a file. The `file_open()` function opens the file dialog box, allows the user to select a file, and returns the path of the selected file. Create an object that interacts with the COM component of Kingsoft WPS word processing software and assign it to the `wps` variable. Use the `Documents.open()` method of the `wps` object to open the document corresponding to the file path stored in the `file_path` variable. S54: Define a `create_menu()` function to create a parent menu `menu` and associate it with the window root; create a submenu `file_menu` and associate it with the parent menu `menu`; add a command option labeled "Open" to the submenu `file_menu` and specify that clicking this option will call the `file_open()` function; add the submenu `file_menu` to the parent menu `menu` and name it "File"; configure the parent menu `menu` as the menu bar of the root window. S55: Nine string variables StringVar() were created to store user input values ​​and calculation result output values; S56: Input labels and corresponding input boxes, as well as output labels and corresponding output boxes, were created, and the input labels and output labels were named respectively; S57: Defines a calcu() function that performs coordinate transformation and updates the results based on input information; S58: Created a Calculate button to trigger the calcu() function; S59: Call the create_menu() function to create the menu bar and enter the main event loop to display the root window; S510: Package the main program into an independent executable program using a custom method and icon.

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