A design method, system, equipment and medium for ultrasonic rolling horn of gear

Abstract

The present application discloses a design method, system, equipment and medium for a gear ultrasonic rolling horn. The method selects a modal order according to a vibration frequency that meets the design requirements; judges the vibration mode under the modal order according to the horn node data set and the gear node data set, and obtains the vibration mode judgment result; selects a target modal order that meets the design requirements according to the vibration frequency and vibration mode judgment result; uses harmonic response analysis to calculate the vibration amplitude and node position at each cross section of the gear ultrasonic rolling horn under the target modal order; uses the vibration amplitude and node position at each cross section of the gear ultrasonic rolling horn as fitness value indicators; adjusts the structural dimensions of the gear ultrasonic rolling horn, optimizes the adjusted structural dimensions based on the fitness value indicators, and obtains the target structural dimensions of the gear ultrasonic rolling horn. The present application can improve the efficiency and accuracy of the design of the gear ultrasonic rolling horn.

Description

Technical Field

[0001] The present application relates to the technical field of horn design, and in particular to a design method, system, equipment and medium for a gear ultrasonic rolling horn. Background Art

[0002] After preliminary theoretical calculations, the size of the amplitude transformer is analyzed and calculated using ANSYS software for modal and harmonic response. Currently, the modal calculation results are often used to select the vibration mode and corresponding frequency, and then a harmonic response analysis is performed. The vibration amplitude of each section of the amplitude transformer is calculated through the harmonic response analysis. Finally, the amplitude transformer size structure is analyzed and adjusted according to the calculation results of the harmonic response, and multiple simulation calculations are performed to finally select the optimal calculation result.

[0003] The above method requires repeated tedious processes of finite element setting and analysis, resulting in that the existing gear ultrasonic rolling amplitude rod design method reduces the efficiency of completing the amplitude rod optimization design, and the accuracy of the designed amplitude rod is not easy to control. Summary of the invention

[0004] The present application aims to propose a design method, system, equipment and medium for a gear ultrasonic rolling amplitude transformer, which can improve the efficiency of the gear ultrasonic rolling amplitude transformer design, and at the same time can better control the accuracy of the gear ultrasonic rolling amplitude transformer design, and can improve the accuracy of the gear ultrasonic rolling amplitude transformer design.

[0005] In a first aspect, an embodiment of the present application provides a method for designing a gear ultrasonic rolling horn, the method comprising:

[0006] Performing modal analysis on the structural dimensions of the gear ultrasonic rolling amplitude transformer system, and obtaining an amplitude transformer node data set and a gear node data set after the modal analysis, wherein the amplitude transformer node data set includes the relative vibration displacement of each node in the amplitude transformer node set at each vibration frequency, and the gear node data set includes the relative vibration displacement of each node in the gear node set at each vibration frequency;

[0007] Extracting vibration frequencies that meet design requirements during modal analysis, and selecting modal orders based on the vibration frequencies that meet the design requirements;

[0008] According to the amplitude transformer node data set and the gear node data set, determine the vibration mode under the modal order to obtain the vibration mode determination result;

[0009] According to the vibration frequency and the vibration mode judgment result, selecting the target modal order that meets the design requirements;

[0010] Invoke harmonic response analysis to calculate the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer at the target modal order;

[0011] The vibration amplitude and node position at each cross section of the gear ultrasonic rolling horn are used as fitness value indicators;

[0012] The structural dimensions of the gear ultrasonic rolling amplitude transformer are adjusted, and the adjusted structural dimensions are optimized based on the fitness value index to obtain the target structural dimensions of the gear ultrasonic rolling amplitude transformer.

[0013] Compared with the prior art, the first aspect of the present application has the following beneficial effects:

[0014] The method performs modal analysis on the structural dimensions of the gear ultrasonic rolling amplitude transformer system to obtain the amplitude transformer node data set and the gear node data set after modal analysis, wherein the amplitude transformer node data set includes the vibration relative displacement of each node in the amplitude transformer node set at each vibration frequency, and the gear node data set includes the vibration relative displacement of each node in the gear node set at each vibration frequency; extracts the vibration frequency that meets the design requirements during the modal analysis process, and selects the modal order according to the vibration frequency that meets the design requirements; judges the vibration shape under the modal order according to the amplitude transformer node data set and the gear node data set, and obtains the vibration shape judgment result; selects the target modal order that meets the design requirements according to the vibration frequency and the vibration shape judgment result; calls harmonic response analysis to calculate the vibration amplitude size and node position at each cross section of the gear ultrasonic rolling amplitude transformer under the target modal order; uses the vibration amplitude size and node position at each cross section of the gear ultrasonic rolling amplitude transformer as the fitness value index; adjusts the structural dimensions of the gear ultrasonic rolling amplitude transformer, optimizes the adjusted structural dimensions based on the fitness value index, and obtains the target structural dimensions of the gear ultrasonic rolling amplitude transformer. In this way, in order to avoid the tedious process of repeating the finite element setting and analysis, the vibration mode under the modal order is automatically determined, and then the target modal order that meets the design requirements is selected according to the vibration frequency and vibration mode judgment results, and then the vibration amplitude and node position at each cross section of the gear ultrasonic rolling transformer are calculated as the fitness value index, and finally the adjusted structural dimensions are optimized based on the fitness value index to obtain the target structural dimensions of the gear ultrasonic rolling transformer, which can improve the design efficiency of the gear ultrasonic rolling transformer, and at the same time can better control the design accuracy of the gear ultrasonic rolling transformer, and can improve the design accuracy of the gear ultrasonic rolling transformer.

[0015] In some implementations, judging the vibration mode under the modal order according to the amplitude transformer node data set and the gear node data set to obtain the vibration mode judgment result includes:

[0016] Obtaining the vibration relative displacement component of each node in the X direction, the vibration relative displacement component of each node in the Y direction, the vibration relative displacement component of each node in the Z direction and the coordinate vector of each node in the Z direction in the amplitude transformer node data set, and obtaining the vibration relative displacement component of each node in the gear node data set;

[0017] Calculate a first bending vibration ratio equation along the X direction, a second bending vibration ratio equation along the Y direction, and a third bending vibration ratio equation along any direction of the XY plane according to the vibration relative displacement component in the X direction, the vibration relative displacement component of each node in the Y direction, and the coordinate vector of each node in the Z direction;

[0018] Calculating the torsional vibration relative displacement by using the vibration relative displacement component of each node in the gear node data set;

[0019] Calculate the ratios of the vibration relative displacement components of each node in the X direction to the vibration relative displacement components of each node in the Z direction and the torsional vibration relative displacement to obtain a first displacement ratio and a second displacement ratio along the X direction; obtain a first displacement ratio and a second displacement ratio along the Y direction according to the ratios of the vibration relative displacement components of each node in the Y direction to the vibration relative displacement components of each node in the Z direction and the torsional vibration relative displacement; and calculate the sum of the vibration relative displacement components of each node in the X direction and the vibration relative displacement components of each node in the Y direction to obtain a displacement component sum; and calculate the ratios of the displacement component sum to the vibration relative displacement components of each node in the Z direction and the torsional vibration relative displacement to obtain a first displacement ratio and a second displacement ratio along any direction of the XY plane;

[0020] Calculating the ratio between the vibration relative displacement component of each node in the Z direction and the torsional vibration relative displacement to obtain a third displacement ratio;

[0021] According to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio along any direction of the XY plane, and the third displacement ratio, the vibration mode under the modal order is judged to obtain a vibration mode judgment result; wherein the vibration mode judgment result includes pure bending vibration, bending-torsion composite vibration, bending-longitudinal composite vibration, bending-torsion-longitudinal composite vibration, pure torsional vibration, pure longitudinal vibration and longitudinal-torsion composite vibration.

[0022] In some embodiments, the vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane to obtain the vibration mode determination result, including:

[0023] If the ratio in the first bending vibration ratio equation is greater than or equal to a first threshold, and the first displacement ratio and the second displacement ratio along the X direction are both greater than or equal to a second threshold, then it is determined that the vibration mode is pure bending vibration along the X direction;

[0024] If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along the Y direction are both greater than or equal to the third threshold, then it is determined that the vibration mode is pure bending vibration along the Y direction;

[0025] If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along any direction of the XY plane are both greater than or equal to the fourth threshold, then the vibration mode is determined to be along Pure bending vibration in the direction.

[0026] In some embodiments, the vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane to obtain the vibration mode determination result, including:

[0027] If the ratio in the first bending vibration ratio equation is greater than or equal to a first threshold, and the first displacement ratio along the X direction is greater than or equal to a second threshold, and the second displacement ratio along the X direction is less than the second threshold, then the vibration mode is determined to be a bending-torsion composite vibration along the X direction;

[0028] If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along the Y direction is greater than or equal to the third threshold and the second displacement ratio along the Y direction is less than the third threshold, then the vibration mode is determined to be a bending-torsion composite vibration along the Y direction;

[0029] If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along any direction of the XY plane is greater than or equal to the fourth threshold, and the second displacement ratio along any direction of the XY plane is less than the fourth threshold, then the vibration mode is determined to be along Bending-torsion composite vibration in the direction.

[0030] In some embodiments, the vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane to obtain the vibration mode determination result, including:

[0031] If the ratio in the first bending vibration ratio equation is greater than or equal to a first threshold, and the first displacement ratio along the X direction is less than a second threshold and the second displacement ratio along the X direction is greater than or equal to the second threshold, then the vibration mode is determined to be a bending-longitudinal composite vibration along the X direction;

[0032] If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along the Y direction is less than the third threshold and the second displacement ratio along the Y direction is greater than or equal to the third threshold, then the vibration mode is determined to be a bending-longitudinal composite vibration along the Y direction;

[0033] If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along any direction of the XY plane is less than the fourth threshold and the second displacement ratio along any direction of the XY plane is greater than or equal to the fourth threshold, then the vibration mode is determined to be along Bending direction-longitudinal composite vibration.

[0034] In some embodiments, the vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane to obtain the vibration mode determination result, including:

[0035] If the ratio in the first bending vibration ratio equation is greater than or equal to a first threshold, and the first displacement ratio and the second displacement ratio along the X direction are both less than a second threshold, then the vibration mode is determined to be a bending-torsion-longitudinal composite vibration along the X direction;

[0036] If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along the Y direction are both less than the third threshold, then the vibration mode is determined to be a bending-torsion-longitudinal composite vibration along the Y direction;

[0037] If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along any direction of the XY plane are both less than the fourth threshold, then the vibration mode is determined to be along Bending-torsion-longitudinal composite vibration in the direction.

[0038] In some embodiments, the vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane to obtain the vibration mode determination result, including:

[0039] If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold value, and the third displacement ratio is greater than or equal to the fifth threshold value, then the vibration mode is determined to be pure torsional vibration;

[0040] If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold value, and the third displacement ratio is less than or equal to the inverse of the fifth threshold value, then the vibration mode is determined to be pure longitudinal vibration;

[0041] If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold, and the third displacement ratio is less than the fifth threshold, then the vibration mode is determined to be a longitudinal-torsional composite vibration.

[0042] In a second aspect, the embodiment of the present application further provides a design system for a gear ultrasonic rolling horn, the system comprising:

[0043] A data acquisition unit, used to perform modal analysis on the structural dimensions of the gear ultrasonic rolling horn system, and acquire a horn node data set and a gear node data set after the modal analysis, wherein the horn node data set includes the relative vibration displacement of each node in the horn node set at each vibration frequency, and the gear node data set includes the relative vibration displacement of each node in the gear node set at each vibration frequency;

[0044] A data extraction unit, used to extract vibration frequencies that meet design requirements during modal analysis, and select modal orders according to the vibration frequencies that meet the design requirements;

[0045] A vibration mode judgment unit, used to judge the vibration mode under the modal order according to the amplitude transformer node data set and the gear node data set, and obtain a vibration mode judgment result;

[0046] An order selection unit, used to select a target modal order that meets the design requirements according to the vibration frequency and the vibration mode judgment result;

[0047] A data calculation unit, used for invoking harmonic response analysis to calculate the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer under the target modal order;

[0048] An index determination unit, used to use the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer as fitness value indicators;

[0049] The size optimization unit is used to adjust the structural size of the gear ultrasonic rolling amplitude transformer, optimize the adjusted structural size based on the fitness value index, and obtain the target structural size of the gear ultrasonic rolling amplitude transformer.

[0050] In the third aspect, an embodiment of the present application also provides an electronic device, comprising at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor so that the at least one control processor can execute the design method of a gear ultrasonic rolling amplitude transformer as described above.

[0051] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the method for designing a gear ultrasonic rolling amplitude transformer as described above.

[0052] It can be understood that the beneficial effects of the second to fourth aspects compared with the related art are the same as the beneficial effects of the first aspect compared with the related art. Please refer to the relevant description in the first aspect, and no further details will be given here. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0054] Figure 1 It is a structural schematic diagram of the ultrasonic rolling horn vibration system for rolling gears provided in the present application;

[0055] Figure 2 It is a schematic flow chart of an embodiment of a design method for a gear ultrasonic rolling horn provided in the present application;

[0056] Figure 3 It is a flow chart of a method for optimizing a horn in a best embodiment of a method for designing a gear ultrasonic rolling horn provided in the present application;

[0057] Figure 4 It is a schematic diagram of node set extraction in the best embodiment of the design method of gear ultrasonic rolling horn provided by the present application;

[0058] Figure 5 It is a structural schematic diagram of an embodiment of a design system for a gear ultrasonic rolling horn provided by the present application;

[0059] Description of labels:

[0060] 101. gear; 102. amplitude transformer; 103. flange; 104. second support; 105. nut. DETAILED DESCRIPTION

[0061] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be understood as limiting the present application.

[0062] In the description of this application, if there is a description of first, second, etc., it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0063] In the description of the present application, it should be understood that the descriptions involving orientation, such as the orientation or positional relationship indicated as up, down, etc., are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0064] In the description of this application, it should be noted that, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meaning of the above terms in this application based on the specific content of the technical solution.

[0065] After preliminary theoretical calculations, the size of the amplitude transformer is analyzed and calculated using ANSYS software for modal and harmonic response. Currently, the modal calculation results are often used to select the vibration mode and corresponding frequency, and then a harmonic response analysis is performed. The vibration amplitude of each section of the amplitude transformer is calculated through the harmonic response analysis. Finally, the amplitude transformer size structure is analyzed and adjusted according to the calculation results of the harmonic response, and multiple simulation calculations are performed to finally select the optimal calculation result.

[0066] The above method requires repeated tedious processes of finite element setting and analysis, resulting in that the existing gear ultrasonic rolling amplitude rod design method reduces the efficiency of completing the amplitude rod optimization design, and the accuracy of the designed amplitude rod is not easy to control.

[0067] In order to solve the above-mentioned problems of low efficiency in the optimization design of the amplitude transformer and the difficulty in controlling the precision of the amplitude transformer design, the present application proposes a design method, system, equipment and medium for ultrasonic rolling amplitude transformer of gears.

[0068] In this embodiment, the vibration system of the rolling ultrasonic rolling equipment is optimized based on the gear 101. The method of this embodiment performs finite element calculation on the structural dimensions of the horn 102 based on theory, and optimizes the structural dimensions according to the finite element calculation results to improve the design efficiency and vibration effect of the horn 102. Figure 1 It is a structural schematic diagram of a vibration system of a rolling gear ultrasonic rolling horn, wherein the horn 102 is a conical transition section stepped double-node multi-section type.

[0069] Reference Figure 2 , is a flow chart of a design method for a gear ultrasonic rolling horn provided in an embodiment of the present application. The design method for a gear ultrasonic rolling horn is applied to an electronic device, which may be a server or a mobile terminal. Figure 2 As shown, the design method of the gear ultrasonic rolling horn may include the following steps:

[0070] Step S100, performing modal analysis on the structural dimensions of the gear ultrasonic rolling horn system, and obtaining a horn node data set and a gear node data set after the modal analysis, wherein the horn node data set includes the relative vibration displacement of each node in the horn node set at each vibration frequency, and the gear node data set includes the relative vibration displacement of each node in the gear node set at each vibration frequency;

[0071] Step S200, extracting the vibration frequency that meets the design requirements during the modal analysis process, and selecting the modal order according to the vibration frequency that meets the design requirements;

[0072] Step S300, judging the vibration mode under the modal order according to the amplitude transformer node data set and the gear node data set, and obtaining the vibration mode judgment result;

[0073] Step S400, selecting a target modal order that meets the design requirements according to the vibration frequency and vibration mode judgment results;

[0074] Step S500, calling harmonic response analysis to calculate the vibration amplitude and node position at each cross section of the gear ultrasonic rolling horn at the target modal order;

[0075] Step S600, taking the vibration amplitude and node position at each cross section of the gear ultrasonic rolling horn as fitness value indicators;

[0076] Step S700, adjusting the structural dimensions of the gear ultrasonic rolling amplitude transformer, optimizing the adjusted structural dimensions based on the fitness value index, and obtaining the target structural dimensions of the gear ultrasonic rolling amplitude transformer.

[0077] In this embodiment, by performing modal analysis on the structural dimensions of the gear ultrasonic rolling amplitude transformer system, the amplitude transformer node data set and the gear node data set after modal analysis are obtained, wherein the amplitude transformer node data set includes the relative vibration displacement of each node in the amplitude transformer node set at each vibration frequency, and the gear node data set includes the relative vibration displacement of each node in the gear node set at each vibration frequency; the vibration frequency that meets the design requirements is extracted during the modal analysis process, and the modal order is selected according to the vibration frequency that meets the design requirements; the modal order is determined according to the amplitude transformer node data set and the gear node data set. The vibration mode under the order is obtained to obtain the vibration mode judgment result; according to the vibration frequency and vibration mode judgment results, the target modal order that meets the design requirements is selected; the harmonic response analysis is called to calculate the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer 102 under the target modal order; the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer 102 are used as fitness value indicators; the structural dimensions of the gear ultrasonic rolling amplitude transformer 102 are adjusted, and the adjusted structural dimensions are optimized based on the fitness value indicators to obtain the target structural dimensions of the gear ultrasonic rolling amplitude transformer 102. In this way, in order to avoid the tedious process of repeating the finite element setting and analysis, the vibration mode under the modal order is automatically determined, and then the target modal order that meets the design requirements is selected according to the vibration frequency and vibration mode judgment results, and then the vibration amplitude and node position at each cross section of the gear ultrasonic rolling transformer 102 are calculated as the fitness value index, and finally the adjusted structural dimensions are optimized based on the fitness value index to obtain the target structural dimensions of the gear ultrasonic rolling transformer 102, which can improve the design efficiency of the gear ultrasonic rolling transformer 102, and at the same time can better control the design accuracy of the gear ultrasonic rolling transformer 102, and can improve the design accuracy of the gear ultrasonic rolling transformer 102.

[0078] The above-mentioned modal analysis of the structural dimensions of the gear ultrasonic rolling amplitude transformer system, and obtaining the amplitude transformer node data set and gear node data set after the modal analysis, can be a script written in Python language program for ANSYS parametric modeling and modal analysis, and then the script is used to perform modal analysis on the structural dimensions of the gear ultrasonic rolling amplitude transformer system, and obtain the amplitude transformer node data set and gear node data set after the modal analysis. The gear ultrasonic rolling amplitude transformer system includes a gear ultrasonic rolling amplitude transformer, a gear and a nut. Since the gear 101 and the nut 105 are standard parts, it is not convenient to modify the size structure. Therefore, this embodiment only optimizes the structural dimensions of the gear ultrasonic rolling amplitude transformer. It should be noted that in addition to being able to optimize the structural dimensions of the gear ultrasonic rolling amplitude transformer, this embodiment can also optimize the structural dimensions of the amplitude transformers in other ultrasonic processes, and this embodiment does not make specific restrictions.

[0079] The vibration frequency that meets the design requirements in the above-mentioned extraction of modal analysis process, because each modal analysis of the structural dimensions of the gear ultrasonic rolling horn system will obtain a horn modal analysis frequency calculation data set, and the modal analysis result (i.e., the horn modal analysis frequency calculation data set) will include the vibration frequency, so the Python program can be used to extract the vibration frequency that meets the design requirements in the modal analysis process. The Python program can be a Python program known to those skilled in the art, and this embodiment will not be described in detail.

[0080] The modal order is selected according to the vibration frequency that meets the design requirements. Since different modal orders correspond to different vibration frequencies in the modal analysis program, the modal order can be selected according to the vibration frequency that meets the design requirements.

[0081] The target modal order that meets the design requirements is selected based on the vibration frequency and mode shape judgment results. The modal order can be the modal order when the vibration frequency and mode shape in the mode shape judgment results all meet the design requirements. This modal order is used as the target modal order, that is, the vibration frequency and mode shape corresponding to the target modal order both meet the design requirements, and therefore the target modal order also meets the design requirements.

[0082] The above-mentioned use of the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer 102 as the fitness value index can be the use of the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer 102 as the fitness value index of the genetic algorithm, or the use of the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer 102 as the fitness value index of the particle swarm algorithm. This embodiment can also adopt some optimization algorithms involving fitness indexes known to those skilled in the art as the optimization algorithm of this embodiment, which is not specifically described or limited in this embodiment.

[0083] The above-mentioned adjustment of the structural dimensions of the gear ultrasonic rolling amplitude transformer 102, optimizing the adjusted structural dimensions based on the fitness value index, and obtaining the target structural dimensions of the gear ultrasonic rolling amplitude transformer 102, may be adjusting the structural dimensions of the gear ultrasonic rolling amplitude transformer 102, optimizing the adjusted structural dimensions based on the fitness value index using a genetic algorithm or a particle swarm algorithm, and obtaining the target structural dimensions of the gear ultrasonic rolling amplitude transformer 102.

[0084] In some implementations, judging the vibration mode under the modal order according to the amplitude transformer node data set and the gear node data set to obtain the vibration mode judgment result includes:

[0085] Obtain the vibration relative displacement component of each node in the X direction, the vibration relative displacement component of each node in the Y direction, the vibration relative displacement component of each node in the Z direction and the coordinate vector of each node in the Z direction in the amplitude transformer node data set, and obtain the vibration relative displacement component of each node in the gear node data set;

[0086] According to the vibration relative displacement component in the X direction, the vibration relative displacement component of each node in the Y direction and the coordinate vector of each node in the Z direction, the first bending vibration ratio equation along the X direction, the second bending vibration ratio equation along the Y direction and the third bending vibration ratio equation along any direction of the XY plane are calculated;

[0087] The relative displacement of torsional vibration is calculated by using the relative displacement component of each node in the gear node data set;

[0088] Calculate the ratios of the vibration relative displacement components of each node in the X direction to the vibration relative displacement components and torsional vibration relative displacement of each node in the Z direction, and obtain a first displacement ratio and a second displacement ratio along the X direction; obtain a first displacement ratio and a second displacement ratio along the Y direction according to the ratios of the vibration relative displacement components of each node in the Y direction to the vibration relative displacement components and torsional vibration relative displacement of each node in the Z direction; and calculate the sum of the vibration relative displacement components of each node in the X direction and the vibration relative displacement components of each node in the Y direction to obtain the sum of displacement components; and calculate the ratios of the displacement components and the vibration relative displacement components and torsional vibration relative displacement of each node in the Z direction to obtain the first displacement ratio and the second displacement ratio along any direction of the XY plane;

[0089] Calculate the ratio between the vibration relative displacement component and the torsional vibration relative displacement of each node in the Z direction to obtain a third displacement ratio;

[0090] According to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio along any direction of the XY plane, and the third displacement ratio, the vibration mode under the modal order is judged to obtain the vibration mode judgment result; wherein the vibration mode judgment result includes pure bending vibration, bending-torsion composite vibration, bending-longitudinal composite vibration, bending-torsion-longitudinal composite vibration, pure torsional vibration, pure longitudinal vibration and longitudinal-torsion composite vibration.

[0091] In this embodiment, it is only necessary to judge the vibration mode under the modal order according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio along any direction of the XY plane, and the third displacement ratio, and it is possible to judge the vibration mode under the modal order and obtain the vibration mode judgment result, and it can be judged for multiple vibration modes, including pure bending vibration, bending-torsion composite vibration, bending-longitudinal composite vibration, bending-torsion-longitudinal composite vibration, pure torsional vibration, pure longitudinal vibration and longitudinal-torsion composite vibration, etc. In this way, by automatically judging the vibration mode under the modal order, the efficiency of vibration mode judgment can be improved, thereby improving the efficiency of the design of the gear ultrasonic rolling horn 102.

[0092] In some embodiments, according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio along any direction of the XY plane, and the third displacement ratio, the vibration mode under the modal order is determined to obtain the vibration mode determination result, including:

[0093] If the ratio in the first bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along the X direction are both greater than or equal to the second threshold, then the vibration mode is determined to be pure bending vibration along the X direction;

[0094] If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along the Y direction are both greater than or equal to the third threshold, then the vibration mode is determined to be pure bending vibration along the Y direction;

[0095] If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along any direction of the XY plane are both greater than or equal to the fourth threshold, then the vibration mode is determined to be along Pure bending vibration in the direction.

[0096] In this embodiment, by comprehensively considering the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, and the first displacement ratio and the second displacement ratio along any direction of the XY plane, the pure bending vibration in each direction can be more accurately judged, the accuracy of the vibration mode judgment is improved, and thus the design accuracy of the gear ultrasonic rolling amplitude transformer 102 can be improved.

[0097] In some embodiments, according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio along any direction of the XY plane, and the third displacement ratio, the vibration mode under the modal order is determined to obtain the vibration mode determination result, including:

[0098] If the ratio in the first bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along the X direction is greater than or equal to the second threshold and the second displacement ratio along the X direction is less than the second threshold, then the vibration mode is determined to be a bending-torsion composite vibration along the X direction;

[0099] If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along the Y direction is greater than or equal to the third threshold and the second displacement ratio along the Y direction is less than the third threshold, then the vibration mode is judged to be a bending-torsion composite vibration along the Y direction;

[0100] If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio in any direction along the XY plane is greater than or equal to the fourth threshold and the second displacement ratio in any direction along the XY plane is less than the fourth threshold, then the vibration mode is determined to be along Bending-torsion composite vibration in the direction.

[0101] In this embodiment, by comprehensively considering the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, and the first displacement ratio and the second displacement ratio along any direction of the XY plane, the bending-torsion composite vibration in each direction can be more accurately judged, the accuracy of vibration mode judgment is improved, and thus the accuracy of the design of the gear ultrasonic rolling amplitude transformer 102 can be improved.

[0102] In some embodiments, according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio along any direction of the XY plane, and the third displacement ratio, the vibration mode under the modal order is determined to obtain the vibration mode determination result, including:

[0103] If the ratio in the first bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along the X direction is less than the second threshold and the second displacement ratio along the X direction is greater than or equal to the second threshold, then the vibration mode is determined to be a bending-longitudinal composite vibration along the X direction;

[0104] If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along the Y direction is less than the third threshold and the second displacement ratio along the Y direction is greater than or equal to the third threshold, then the vibration mode is judged to be a bending-longitudinal composite vibration along the Y direction;

[0105] If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio in any direction along the XY plane is less than the fourth threshold and the second displacement ratio in any direction along the XY plane is greater than or equal to the fourth threshold, then the vibration mode is determined to be along Bending direction-longitudinal composite vibration.

[0106] In this embodiment, by comprehensively considering the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, and the first displacement ratio and the second displacement ratio along any direction of the XY plane, the bending-longitudinal composite vibration in each direction can be more accurately judged, the accuracy of vibration type judgment is improved, and thus the design accuracy of the gear ultrasonic rolling amplitude transformer 102 can be improved.

[0107] In some embodiments, according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio along any direction of the XY plane, and the third displacement ratio, the vibration mode under the modal order is determined to obtain the vibration mode determination result, including:

[0108] If the ratio in the first bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along the X direction are both less than the second threshold, then the vibration mode is determined to be a bending-torsion-longitudinal composite vibration along the X direction;

[0109] If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along the Y direction are both less than the third threshold, then the vibration mode is judged to be a bending-torsion-longitudinal composite vibration along the Y direction;

[0110] If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along any direction of the XY plane are both less than the fourth threshold, then the vibration mode is determined to be along Bending-torsion-longitudinal composite vibration in the direction.

[0111] In this embodiment, by comprehensively considering the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, and the first displacement ratio and the second displacement ratio along any direction of the XY plane, the bending-torsion-longitudinal composite vibration in each direction can be more accurately judged, the accuracy of vibration mode judgment is improved, and thus the design accuracy of the gear ultrasonic rolling amplitude transformer 102 can be improved.

[0112] In some embodiments, according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio along any direction of the XY plane, and the third displacement ratio, the vibration mode under the modal order is determined to obtain the vibration mode determination result, including:

[0113] If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold value, and the third displacement ratio is greater than or equal to the fifth threshold value, then the vibration mode is determined to be pure torsional vibration;

[0114] If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold value, and the third displacement ratio is less than or equal to the reciprocal of the fifth threshold value, then the vibration mode is determined to be pure longitudinal vibration;

[0115] If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold, and the third displacement ratio is less than the fifth threshold, then the vibration mode is judged to be a longitudinal-torsional composite vibration.

[0116] In this embodiment, by comprehensively considering the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation and the third displacement ratio, pure torsional vibration, pure longitudinal vibration and longitudinal-torsional composite vibration can be more accurately judged, thereby improving the accuracy of vibration type judgment, thereby improving the design accuracy of the gear ultrasonic rolling amplitude transformer 102.

[0117] To facilitate understanding by those skilled in the art, a set of best embodiments is provided below:

[0118] In this embodiment, the vibration system of the rolling ultrasonic rolling equipment is optimized based on the gear 101. The method of this embodiment performs finite element calculation on the structural dimensions of the horn 102 based on theory, and optimizes the structural dimensions according to the finite element calculation results to improve the design efficiency and vibration effect of the horn 102. Figure 1 It is a structural schematic diagram of a vibration system of a rolling gear ultrasonic rolling horn, wherein the horn 102 is a conical transition section stepped double-node multi-section type.

[0119] After the size of the horn 102 is preliminarily calculated according to the theory, the modal analysis and harmonic response analysis are performed using ANSYS software. The current related methods often use the modal calculation results to screen out the vibration mode and corresponding frequency to be used, and then perform harmonic response analysis. The vibration amplitude of each section of the horn 102 is obtained through harmonic response analysis and calculation. Finally, the size structure of the horn 102 is analyzed and adjusted according to the calculation results of the harmonic response, and then multiple simulation calculations are performed to finally select the optimal calculation result, which will lead to repeated finite element settings and analysis, making the design efficiency of the horn 102 low. The method of this embodiment uses MATLAB and Python to jointly develop ANSYS for secondary development, extract the finite element calculation results and process and judge the results (i.e., including frequency judgment and vibration mode judgment), and finally uses genetic algorithms to optimize the structural size of the horn 102 according to the simulation results, avoiding the cumbersome process of repeated finite element settings and analysis, and thus efficiently completing the optimization design of the horn 102.

[0120] Figure 3 The flowchart of the method for optimizing the amplitude transformer 102 is shown in FIG. 1. The method of this embodiment firstly uses the Python language program to write the script for ANSYS parametric modeling and modal analysis. The dimension structure of the amplitude transformer 102 (i.e., the structural dimension of the gear ultrasonic rolling amplitude transformer 102) determined initially is used as the input parameter to the ANSYS parametric modeling and modal analysis program. After the finite element calculation, the Python language program is used to extract the vibration relative displacement of each node of the node set of the amplitude transformer 102 and the gear 101 components in the modal analysis results at each natural frequency. The node set extraction is as follows: Figure 4 As shown, Figure 4(a) is a schematic diagram of extracting the node set on the horn 102. Figure 4 (b) is a schematic diagram of extracting the node set on the gear 101, and then the Python program is used to extract the vibration frequency that meets the design requirements and determine the vibration mode of the amplitude rod 102 to obtain the target vibration order (i.e., the target modal order), and then the Python program is used to perform harmonic response analysis and calculation under the target vibration order, that is, the Python program is used to obtain the vibration amplitude and node position of each end face of the amplitude rod 102 and the gear 101 under the excitation (i.e., the target modal order), and the node position and output vibration amplitude are used as fitness value indicators of the genetic algorithm. The calculation results are input into the genetic algorithm, and then a new population is generated, and the new population parameters are written into a txt file through the MATLAB program, and the Python program is called to calculate and extract the results until the maximum number of iterations is reached to output the optimal solution, i.e., the size structure of the amplitude rod 102 (i.e., the target structural size of the gear ultrasonic rolling amplitude rod 102). The method of this embodiment includes:

[0121] 1. Extract the frequency, that is, extract the resonant frequency (i.e., vibration frequency) in the modal analysis results after ANSYS modal analysis calculation through the Python program, and select the modal order that meets the design requirements according to the design requirements of the gear ultrasonic rolling horn 102, wherein the design requirements of the gear ultrasonic rolling horn 102 can be set according to actual conditions, and this embodiment does not impose specific restrictions.

[0122] Second, vibration type judgment, that is, after the ANSYA modal analysis calculation, the vibration relative displacement of each node in the node set at each natural frequency is processed, and the vibration form of the amplitude rod 102 at each order mode is realized quickly and accurately. The vibration form can be judged as: pure bending vibration, bending-torsion composite vibration, bending-longitudinal composite vibration, bending-torsion-longitudinal composite vibration, pure torsional vibration, pure longitudinal vibration and longitudinal-torsion composite vibration. The specific process of vibration type judgment includes:

[0123] Taking the axial direction of the amplitude rod 102 as the Z axis as an example, the Python program is called to extract the corresponding one-dimensional vectors along each vibration relative displacement of each node in node set 1 (i.e., the amplitude rod node data set) and node set 2 (i.e., the gear node data set) at each frequency. The one-dimensional vector corresponding to each vibration relative displacement includes the vibration relative displacement component along the X direction. , the relative displacement component of vibration along the Y direction , the relative displacement component of vibration along the Z direction and relative displacement components under torsional vibration The coordinates of each node in the Z-axis direction in the node set 1 are extracted to form a vector Z, and the vibration mode judgment calculation method is as follows.

[0124] If the slope between the nodes after the vibration deformation of the node set 1 and the slope between the maximum node and the minimum node along the radial deformation of the horn 102 are greater than the set requirements, it is judged that bending vibration is involved, that is, at least one of formula (1) or formula (2) or formula (3) is established. Formula (1) indicates bending vibration along the X direction, formula (2) indicates bending vibration along the Y direction, and formula (3) indicates bending vibration along a certain direction of the XY plane. The mathematical expression is:

[0125] (1);

[0126] (2);

[0127] (3);

[0128] in, Indicates The relative displacement component of the vibration of the node along the X direction, Indicates The relative displacement component of the vibration of the node along the X direction, Represents the first nodes, , represents the total number of nodes in node set 1, represents the maximum value of the relative displacement component of the vibration along the X direction, represents the minimum value of the relative displacement component of the vibration along the X direction, express , and The corresponding index number, the index number is one of the, express , and The corresponding index number, Indicates The Z-axis coordinate of each node, Indicates The Z-axis coordinate of each node, Indicates The Z-axis coordinate of each node, Indicates The Z-axis coordinate of each node, Indicates The relative displacement component of the vibration of the node along the Y direction, Indicates The relative displacement component of the vibration of the node along the Y direction, represents a constant (ie, the first threshold), which is generally set between 0 and 0.1 and can be set according to the design requirements of the amplitude transformer 102. This embodiment does not impose any specific limitation.

[0129] The longitudinal vibration at different cross sections along the axial direction of the horn 102 can be judged by the relative displacement component of the vibration along the Z axis of each node in the node set 1 at each natural frequency (i.e., vibration frequency). Generally, the end mounting tool of the horn 102 (gear 101 in this embodiment) is generally designed to use the relative displacement component at the minimum end as the longitudinal vibration judgment index, that is, .

[0130] This embodiment uses the gear 101 as a tool to extract the vibration relative displacement component of the torsional vibration at each natural frequency near the pitch circle of the gear 101. To judge, the method of this embodiment uses the average value of the relative displacement of torsional vibration of each node of node set 2 at each natural frequency as the relative displacement of torsional vibration of gear 101 at the natural frequency. , as shown in formula (4).

[0131] (4);

[0132] in, Indicates the number of nodes in node set 2.

[0133] For the composite vibration among bending vibration, torsional vibration and longitudinal vibration, the relative displacement component ratio between the two components is used for evaluation and judgment, that is, formula (5) to formula (7):

[0134] and (5);

[0135] and (6);

[0136] and (7);

[0137] Among them, the constant (i.e., the second threshold), (i.e., the third threshold) and (i.e., the fourth threshold) represents the threshold of the ratio of the magnitude of the relative displacement components of the bending vibration, the longitudinal vibration, and the torsional vibration. It can be greater than a certain commonly used ratio and is set according to the design requirements of the horn 102. This embodiment does not impose any specific restrictions. Representation Node The relative displacement component of vibration along the X direction, Representation Node The relative displacement component of vibration along the Y direction, Representation Node The relative displacement component of vibration along the Z direction.

[0138] Therefore, the relevant data corresponding to the extracted node set 1 and node set 2 are processed, and the specific analysis is as follows:

[0139] 1. Pure bending vibration.

[0140] If the data corresponding to the node set 1 and the node set 2 satisfy both formula (1) and formula (5), it means that the amplitude transformer 102 is in pure bending vibration along the x direction;

[0141] If the data corresponding to the node set 1 and the node set 2 satisfy both formula (2) and formula (6), it means that the amplitude transformer 102 is in pure bending vibration along the y direction;

[0142] If the data corresponding to node set 1 and node set 2 satisfy both formula (3) and formula (7), it means that the amplitude rod 102 is along Direction pure bending vibration;

[0143] 2. Bending-torsion composite vibration.

[0144] and (8);

[0145] and (9);

[0146] and (10);

[0147] If the data corresponding to the node set 1 and the node set 2 satisfy both formula (1) and formula (8), it means that the horn 102 is in bending-torsion composite vibration along the x direction;

[0148] If the data corresponding to the node set 1 and the node set 2 satisfy both formula (2) and formula (9), it means that the horn 102 is in bending-torsion composite vibration along the y direction;

[0149] If the data corresponding to node set 1 and node set 2 satisfy both formula (3) and formula (10), it means that the amplitude rod 102 is along Directional bending-torsion composite vibration;

[0150] 3. Bending-longitudinal composite vibration.

[0151] and (11);

[0152] and (12);

[0153] and (13);

[0154] If the data corresponding to the node set 1 and the node set 2 satisfy both formula (1) and formula (11), it means that the horn 102 is in a bending-longitudinal composite vibration along the x direction;

[0155] If the data corresponding to the node set 1 and the node set 2 satisfy both formula (2) and formula (12), it means that the amplitude rod 102 is subjected to a bending-longitudinal composite vibration along the y direction;

[0156] If the data corresponding to node set 1 and node set 2 satisfy both formula (3) and formula (13), it means that the amplitude rod 102 is along Directional bending - longitudinal composite vibration;

[0157] 4. Bending-torsion-longitudinal composite vibration.

[0158] and (14);

[0159] and (15);

[0160] and (16);

[0161] If the data corresponding to the node set 1 and the node set 2 satisfy both formula (1) and formula (14), it means that the horn 102 is in a bending-torsion-longitudinal composite vibration along the x direction;

[0162] If the data corresponding to the node set 1 and the node set 2 satisfy both formula (2) and formula (15), it means that the horn 102 is in a bending-torsion-longitudinal composite vibration along the y direction;

[0163] If the data corresponding to node set 1 and node set 2 satisfy both formula (3) and formula (16), it means that the amplitude rod 102 is along Directional bending-torsion-longitudinal composite vibration;

[0164] According to the above data processing, the vibration forms of each mode including bending vibration can be identified. Therefore, various vibration forms excluding bending vibration are subsequently identified by processing the extracted data, that is, satisfying formulas (17) to (19).

[0165] (17);

[0166] (18); (19);

[0167] For the composite vibration between torsional vibration and longitudinal vibration, the relative displacement component ratio between the two is used for evaluation and judgment, that is, formula (20) to formula (22):

[0168] (20);

[0169] (twenty one);

[0170] (twenty two);

[0171] in, represents a constant (ie, the fifth threshold value), which may be changed according to actual conditions and is not specifically limited in this embodiment.

[0172] 5. Pure torsional vibration.

[0173] If the data corresponding to the node set 1 and the node set 2 are extracted and satisfy the formulas (17) to (19) and (20) at the same time, it means that the amplitude transformer 102 is in pure torsional vibration;

[0174] 6. Pure longitudinal vibration.

[0175] If the data corresponding to the node set 1 and the node set 2 are extracted and satisfy the formulas (17) to (19) and (21) at the same time, it means that the amplitude transformer 102 performs pure longitudinal vibration;

[0176] 7. Longitudinal-torsional composite vibration.

[0177] If the data corresponding to the node set 1 and the node set 2 are extracted and satisfy Formula (17) to Formula (19) and Formula (22) at the same time, it means that the amplitude transformer 102 is subject to longitudinal-torsional composite vibration.

[0178] After the vibration mode is judged, the appropriate modal order is selected according to the vibration mode, frequency and design requirements of the amplitude rod 102 corresponding to each order mode, and the Python program is called to perform ANSYS harmonic response analysis to calculate the vibration amplitude and node position at each section of the amplitude rod 102 under excitation, and the calculation results are input into the data.txt file, and then the MATLAB function is called to read the data information (including vibration amplitude and node position) in the data.txt file as the fitness index of the genetic algorithm to screen the population of the adjusted structural size. After screening, a new population is generated through crossover, mutation and inheritance, and then the ANSYS parametric modeling program is called to calculate the new population, and the structural size of the amplitude rod 102 is optimized according to the calculation results. After the iteration, the optimal size solution (i.e., the target structural size) is output. This solves the problem of cumbersome process of selecting the optimal solution due to repeated design operations every time and the problem of insufficient accuracy of the solution. Among them, the selection of the modal order and the detailed description of the genetic algorithm are as follows:

[0179] (1) Description of genetic algorithm.

[0180] The calculation process of the genetic algorithm of this embodiment is basically the same as the steps of the genetic algorithm in the prior art. The genetic algorithm optimization of this embodiment belongs to a simple multi-objective optimization, that is, the fitness calculation is slightly different, specifically:

[0181] The fitness value of the genetic algorithm of this embodiment is a two-dimensional vector, the first value of which indicates the node position (i.e., whether they coincide), and the second value indicates the output vibration amplitude. By extracting the data after the harmonic response analysis and calculation, it is determined whether the positions of the amplitude rod 102, the second support 104, and the flange 103 coincide with the node positions of the amplitude rod 102 calculated by the harmonic response analysis. If they coincide, the first value of the fitness vector is recorded as 1, otherwise it is 0. When comparing different populations, first ensure that the first value of the fitness vector is 1, and then compare the second value of the fitness. The second value is optimized and calculated according to the principle that the closer the output vibration amplitude is to the vibration amplitude required by the design, the better, that is, the closer the vibration amplitude output by the genetic algorithm after each iteration is to the vibration amplitude required by the design, the better.

[0182] (2) Selection of modal order.

[0183] This embodiment optimizes the size of the horn 102 after preliminary theoretical calculations to meet the processing requirements. Assume that the design requirements are: the vibration frequency of the ultrasonic horn 102 is 20KHz±2KHz, and the vibration mode (ie vibration mode) is longitudinal-torsion composite vibration.

[0184] According to the initial structure size of the horn 102, the Python language ANSYS parametric modeling and modal analysis program are input to obtain preliminary calculation results. The order mode in the frequency range of 18KHz-22KHz that meets the design requirements is extracted from the preliminary calculation results, and the vibration type is determined. Specifically, the preliminary calculation results are (within the selected frequency range): the frequency corresponding to the 8th-order mode is 18035 Hz, the vibration mode corresponding to the 8th-order mode is longitudinal vibration, the frequency corresponding to the 9th-order mode is 19058 Hz, the vibration mode corresponding to the 9th-order mode is torsional vibration, the frequency corresponding to the 10th-order mode is 19551 Hz, the vibration mode corresponding to the 10th-order mode is bending vibration in the y direction, the frequency corresponding to the 11th-order mode is 19554 Hz, the vibration mode corresponding to the 11th-order mode is bending vibration in the x direction, and the frequency corresponding to the 12th-order mode is 21771 Hz, the vibration mode corresponding to the 12th-order mode is longitudinal-torsional composite vibration, and the harmonic response calculation of the frequency corresponding to the 12th-order mode shows that the longitudinal vibration amplitude is 19.495 μm, and the torsional vibration amplitude is 5.16 μm.

[0185] From the calculation results before optimization, it can be found that the 12th-order mode is more in line with the design requirements, but there is a problem that the vibration node of the amplitude transformer 102 and the second support 104 do not overlap. In actual engineering applications, there may be leakage waves. The reason for this phenomenon is that in the current theoretical calculation, the consideration of material properties, the interaction between the tool and the amplitude transformer 102 is relatively simple. According to the actual vibration mode and vibration amplitude of the structural size, there is a big difference from the theory, which leads to problems such as system instability and poor vibration effect. Therefore, the structural size must be optimized to address this phenomenon.

[0186] According to the results, it can be found that after the modal calculation, the 8th to 12th order modes all meet the frequency design requirements, and then the method of this embodiment is used for optimization according to the vibration type design requirements; since the gear 101 and the nut 105 are both standard parts in the engineering application process, it is not convenient to modify the structural dimensions of the parts, so only the size of the horn 102 is optimized using the genetic algorithm. The calculation results after optimization using the method of this embodiment are as follows:

[0187] The frequency obtained after optimization is 21910 Hz, the vibration mode is longitudinal-torsion composite vibration, the longitudinal vibration amplitude is 45.36 μm, and the torsional vibration amplitude is 11.105 μm. The calculation results after optimization show that the vibration frequency and vibration mode of the amplitude transformer 102 meet the design requirements. In addition, the node position coincides well with the second support 104 and the flange 103, and the vibration amplitude is more than double that before optimization.

[0188] Compared with the prior art, the technical solution of this embodiment has the following advantages:

[0189] 1. Taking the gear ultrasonic rolling vibration system as an example, a new idea for optimizing the design of the amplitude transformer 102 is developed, which can improve the efficiency and accuracy of the design of the amplitude transformer 102, and can solve the problems of cumbersome operation and difficult control of accuracy in the past.

[0190] 2. The method for determining the modal vibration form of different horn 102 can automatically and accurately determine the modal vibration form, thereby improving the efficiency and accuracy of the design of the horn 102 .

[0191] Reference Figure 5 The embodiment of the present application also provides a gear ultrasonic rolling horn design system, which includes a data acquisition unit 100, a data extraction unit 200, a vibration type judgment unit 300, an order selection unit 400, a data calculation unit 500, an index determination unit 600 and a size optimization unit 700, wherein:

[0192] A data acquisition unit 100 is used to perform modal analysis on the structural dimensions of the gear ultrasonic rolling horn system, and obtain a horn node data set and a gear node data set after the modal analysis, wherein the horn node data set includes the relative vibration displacement of each node in the horn node set at each vibration frequency, and the gear node data set includes the relative vibration displacement of each node in the gear node set at each vibration frequency;

[0193] The data extraction unit 200 is used to extract the vibration frequency that meets the design requirements during the modal analysis process, and select the modal order according to the vibration frequency that meets the design requirements;

[0194] A vibration mode determination unit 300 is used to determine the vibration mode under the modal order according to the amplitude transformer node data set and the gear node data set, and obtain the vibration mode determination result;

[0195] The order selection unit 400 is used to select the target modal order that meets the design requirements according to the vibration frequency and vibration mode judgment results;

[0196] The data calculation unit 500 is used to call the harmonic response analysis to calculate the vibration amplitude and node position at each cross section of the gear ultrasonic rolling horn 102 at the target modal order;

[0197] An index determination unit 600 is used to use the vibration amplitude and node position at each cross section of the gear ultrasonic rolling horn 102 as a fitness value index;

[0198] The size optimization unit 700 is used to adjust the structural size of the gear ultrasonic rolling horn 102, optimize the adjusted structural size based on the fitness value index, and obtain the target structural size of the gear ultrasonic rolling horn 102.

[0199] It should be noted that since the design system of a gear ultrasonic rolling amplitude transformer in this embodiment and the design method of a gear ultrasonic rolling amplitude transformer mentioned above are based on the same inventive concept, the corresponding contents in the method embodiment are also applicable to the system embodiment and will not be described in detail here.

[0200] An embodiment of the present application also provides an electronic device, comprising: at least one control processor and a memory for communicating with the at least one control processor.

[0201] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely disposed relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0202] The non-transient software program and instructions required to implement the above-mentioned method for designing a gear ultrasonic rolling horn are stored in the memory. When executed by the processor, the above-mentioned method for designing a gear ultrasonic rolling horn is executed, for example, the above-mentioned method is executed. Figure 2 The method comprises steps S100 to S700.

[0203] The system embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separated, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0204] The present application also provides a computer-readable storage medium, which stores computer-executable instructions. The computer-executable instructions are executed by one or more control processors, which can enable the one or more control processors to execute a design method for a gear ultrasonic rolling horn in the above method embodiment, for example, to execute the above described Figure 2 The functions of method steps S100 to S700 in the method.

[0205] It will be appreciated by those skilled in the art that all or some of the steps and systems in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software may be distributed on a computer-readable medium, which may include a computer storage medium (or non-transitory medium) and a communication medium (or transient medium). As known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically embodies computer readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0206] The above is a specific description of the preferred implementation of the embodiments of the present application, but the embodiments of the present application are not limited to the above-mentioned implementation methods. Technical personnel familiar with the field can also make various equivalent modifications or substitutions without violating the spirit of the embodiments of the present application. These equivalent modifications or substitutions are all included in the scope defined by the claims of the embodiments of the present application.

Claims

1. A design method for a gear ultrasonic rolling horn, characterized in that: The method comprises: Performing modal analysis on the structural dimensions of the gear ultrasonic rolling amplitude transformer system, and obtaining an amplitude transformer node data set and a gear node data set after the modal analysis, wherein the amplitude transformer node data set includes the relative vibration displacement of each node in the amplitude transformer node set at each vibration frequency, and the gear node data set includes the relative vibration displacement of each node in the gear node set at each vibration frequency; Extracting vibration frequencies that meet design requirements during modal analysis, and selecting modal orders based on the vibration frequencies that meet the design requirements; According to the amplitude transformer node data set and the gear node data set, the vibration mode under the modal order is judged to obtain the vibration mode judgment result, including: According to the vibration relative displacement components of each node in the X direction, the vibration relative displacement components of each node in the Y direction and the coordinate vectors of each node in the Z direction, the first bending vibration ratio equation along the X direction, the second bending vibration ratio equation along the Y direction and the third bending vibration ratio equation along any direction of the XY plane are calculated; Calculating the torsional vibration relative displacement by using the vibration relative displacement component of each node in the gear node data set; Calculate the ratios of the vibration relative displacement components of each node in the X direction and the Y direction to the vibration relative displacement components of each node in the Z direction and the torsional vibration relative displacement, and obtain a first displacement ratio and a second displacement ratio along the X direction, and a first displacement ratio and a second displacement ratio along the Y direction, and calculate the sum of the vibration relative displacement components of each node in the X direction and the vibration relative displacement components of each node in the Y direction to obtain a displacement component sum, and calculate the ratios of the displacement component sum to the vibration relative displacement components of each node in the Z direction and the torsional vibration relative displacement, and obtain a first displacement ratio and a second displacement ratio along any direction of the XY plane; Calculating the ratio between the vibration relative displacement component of each node in the Z direction and the torsional vibration relative displacement to obtain a third displacement ratio; According to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane, the vibration mode under the modal order is judged to obtain a vibration mode judgment result; wherein the vibration mode judgment result includes pure bending vibration, bending-torsion composite vibration, bending-longitudinal composite vibration, bending-torsion-longitudinal composite vibration, pure torsional vibration, pure longitudinal vibration and longitudinal-torsion composite vibration; According to the vibration frequency and the vibration mode judgment result, selecting the target modal order that meets the design requirements; Invoke harmonic response analysis to calculate the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer at the target modal order; The vibration amplitude and node position at each cross section of the gear ultrasonic rolling horn are used as fitness value indicators; The structural dimensions of the gear ultrasonic rolling amplitude transformer are adjusted, and the adjusted structural dimensions are optimized based on the fitness value index to obtain the target structural dimensions of the gear ultrasonic rolling amplitude transformer.

2. The design method of the gear ultrasonic rolling horn according to claim 1 is characterized in that: The vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane, to obtain a vibration mode determination result, including: If the ratio in the first bending vibration ratio equation is greater than or equal to a first threshold, and the first displacement ratio and the second displacement ratio along the X direction are both greater than or equal to a second threshold, then the vibration mode is determined to be pure bending vibration along the X direction; If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along the Y direction are both greater than or equal to the third threshold, then it is determined that the vibration mode is pure bending vibration along the Y direction; If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along any direction of the XY plane are both greater than or equal to the fourth threshold, then the vibration mode is determined to be along Pure bending vibration in the direction, where It represents the relative displacement component of the vibration at the end of the horn along the Y direction, It represents the relative displacement component of the vibration at the end of the transformer rod along the X direction.

3. The design method of the gear ultrasonic rolling horn according to claim 1 is characterized in that: The vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane, to obtain a vibration mode determination result, including: If the ratio in the first bending vibration ratio equation is greater than or equal to a first threshold, and the first displacement ratio along the X direction is greater than or equal to a second threshold, and the second displacement ratio along the X direction is less than the second threshold, then the vibration mode is determined to be a bending-torsion composite vibration along the X direction; If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along the Y direction is greater than or equal to the third threshold and the second displacement ratio along the Y direction is less than the third threshold, then the vibration mode is determined to be a bending-torsion composite vibration along the Y direction; If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along any direction of the XY plane is greater than or equal to the fourth threshold, and the second displacement ratio along any direction of the XY plane is less than the fourth threshold, then the vibration mode is determined to be along The bending-torsion composite vibration in the direction of It represents the relative displacement component of the vibration at the end of the horn along the Y direction, It represents the relative displacement component of the vibration at the end of the transformer rod along the X direction.

4. The design method of the gear ultrasonic rolling horn according to claim 1 is characterized in that: The vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane, to obtain a vibration mode determination result, including: If the ratio in the first bending vibration ratio equation is greater than or equal to a first threshold, and the first displacement ratio along the X direction is less than a second threshold and the second displacement ratio along the X direction is greater than or equal to the second threshold, then the vibration mode is determined to be a bending-longitudinal composite vibration along the X direction; If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along the Y direction is less than the third threshold and the second displacement ratio along the Y direction is greater than or equal to the third threshold, then the vibration mode is determined to be a bending-longitudinal composite vibration along the Y direction; If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio along any direction of the XY plane is less than the fourth threshold and the second displacement ratio along any direction of the XY plane is greater than or equal to the fourth threshold, then the vibration mode is determined to be along Bending-longitudinal composite vibration, in which: It represents the relative displacement component of the vibration at the end of the horn along the Y direction, It represents the relative displacement component of the vibration at the end of the transformer rod along the X direction.

5. The design method of the gear ultrasonic rolling horn according to claim 1 is characterized in that: The vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane, to obtain a vibration mode determination result, including: If the ratio in the first bending vibration ratio equation is greater than or equal to a first threshold, and the first displacement ratio and the second displacement ratio along the X direction are both less than a second threshold, then the vibration mode is determined to be a bending-torsion-longitudinal composite vibration along the X direction; If the ratio in the second bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along the Y direction are both less than the third threshold, then the vibration mode is determined to be a bending-torsion-longitudinal composite vibration along the Y direction; If the ratio in the third bending vibration ratio equation is greater than or equal to the first threshold, and the first displacement ratio and the second displacement ratio along any direction of the XY plane are both less than the fourth threshold, then the vibration mode is determined to be along The bending-torsion-longitudinal composite vibration in the direction of It represents the relative displacement component of the vibration at the end of the horn along the Y direction, It represents the relative displacement component of the vibration at the end of the transformer rod along the X direction.

6. The design method of the gear ultrasonic rolling horn according to claim 1 is characterized in that: The vibration mode under the modal order is determined according to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane, to obtain a vibration mode determination result, including: If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold value, and the third displacement ratio is greater than or equal to the fifth threshold value, then the vibration mode is determined to be pure torsional vibration; If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold value, and the third displacement ratio is less than or equal to the inverse of the fifth threshold value, then the vibration mode is determined to be pure longitudinal vibration; If the ratio in the first bending vibration ratio equation, the ratio in the second bending vibration ratio equation and the ratio in the third bending vibration ratio equation are all less than the first threshold, and the third displacement ratio is less than the fifth threshold, then the vibration mode is determined to be a longitudinal-torsional composite vibration.

7. A design system for gear ultrasonic rolling horn, characterized in that: The system comprises: A data acquisition unit, used to perform modal analysis on the structural dimensions of the gear ultrasonic rolling horn system, and acquire a horn node data set and a gear node data set after the modal analysis, wherein the horn node data set includes the relative vibration displacement of each node in the horn node set at each vibration frequency, and the gear node data set includes the relative vibration displacement of each node in the gear node set at each vibration frequency; A data extraction unit, used to extract vibration frequencies that meet design requirements during modal analysis, and select modal orders according to the vibration frequencies that meet the design requirements; A vibration mode judgment unit is used to judge the vibration mode under the modal order according to the amplitude transformer node data set and the gear node data set to obtain a vibration mode judgment result, including: According to the vibration relative displacement components of each node in the X direction, the vibration relative displacement components of each node in the Y direction and the coordinate vectors of each node in the Z direction, the first bending vibration ratio equation along the X direction, the second bending vibration ratio equation along the Y direction and the third bending vibration ratio equation along any direction of the XY plane are calculated; Calculating the torsional vibration relative displacement by using the vibration relative displacement component of each node in the gear node data set; Calculate the ratios of the vibration relative displacement components of each node in the X direction and the Y direction to the vibration relative displacement components of each node in the Z direction and the torsional vibration relative displacement, and obtain a first displacement ratio and a second displacement ratio along the X direction, and a first displacement ratio and a second displacement ratio along the Y direction, and calculate the sum of the vibration relative displacement components of each node in the X direction and the vibration relative displacement components of each node in the Y direction to obtain a displacement component sum, and calculate the ratios of the displacement component sum to the vibration relative displacement components of each node in the Z direction and the torsional vibration relative displacement, and obtain a first displacement ratio and a second displacement ratio along any direction of the XY plane; Calculating the ratio between the vibration relative displacement component of each node in the Z direction and the torsional vibration relative displacement to obtain a third displacement ratio; According to the first bending vibration ratio equation, the second bending vibration ratio equation, the third bending vibration ratio equation, the first displacement ratio and the second displacement ratio along the X direction, the first displacement ratio and the second displacement ratio along the Y direction, the first displacement ratio and the second displacement ratio and the third displacement ratio along any direction of the XY plane, the vibration mode under the modal order is judged to obtain a vibration mode judgment result; wherein the vibration mode judgment result includes pure bending vibration, bending-torsion composite vibration, bending-longitudinal composite vibration, bending-torsion-longitudinal composite vibration, pure torsional vibration, pure longitudinal vibration and longitudinal-torsion composite vibration; An order selection unit, used to select a target modal order that meets the design requirements according to the vibration frequency and the vibration mode judgment result; A data calculation unit, used for invoking harmonic response analysis to calculate the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer under the target modal order; An index determination unit, used to use the vibration amplitude and node position at each cross section of the gear ultrasonic rolling amplitude transformer as fitness value indicators; The size optimization unit is used to adjust the structural size of the gear ultrasonic rolling amplitude transformer, optimize the adjusted structural size based on the fitness value index, and obtain the target structural size of the gear ultrasonic rolling amplitude transformer.

8. An electronic device, characterized in that: It includes at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor so that the at least one control processor can execute the design method of the gear ultrasonic rolling amplitude transformer as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the method for designing a gear ultrasonic rolling horn as described in any one of claims 1 to 6.

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