Method, system and device for calculating bevel gear pair transmission error and storage medium

Abstract

The application discloses a bevel gear pair transmission error calculation method, system, device and storage medium, including constructing a gear three-dimensional model, a pinion three-dimensional model and an eccentric shaft according to bevel gear pair parameters; rotating the pinion three-dimensional model by a preset step angle value according to the eccentric shaft, and extracting a first pinion working tooth surface set and a first gear working tooth surface set; obtaining a first normal vector of the first pinion working tooth surface set; calculating a first normal distance between the first normal vector and the first gear working tooth surface set; calculating a first optimal gear rotation angle value; and calculating a bevel gear pair transmission error set according to a first pinion angle value and a first gear angle value, the size wheel rotation angle under the eccentric condition is calculated by the preset step angle value, so that the transmission error is calculated, the accuracy of the calculation result is ensured, and the calculation speed is improved.

Description

Technical Field

[0001] This invention relates to the technical field of calculating transmission errors of bevel gear pairs, and in particular to methods, systems, devices, and storage media for calculating transmission errors of bevel gear pairs. Background Technology

[0002] Gearboxes have a wide range of applications in industry, such as aircraft gearboxes and marine gearboxes. With the deepening research into gear transmission systems, industry has placed increasingly stringent demands on gearboxes, requiring high reliability and high transmission accuracy. The parameters describing gear meshing performance are crucial indicators of the quality of gear transmissions. Among these, transmission error is a vital parameter describing the meshing performance of gear pairs. When the driving gear rotates uniformly, the deviation of the actual position of the driven gear from its theoretical position is the transmission error. Transmission error is particularly important because researchers have found a strong correlation with gear vibration and noise. Therefore, calculating the transmission error of gear pairs with eccentricity errors has always been a key research topic in the industry.

[0003] Currently, methods for calculating gear transmission errors under eccentric conditions include tooth surface contact analysis, finite element method, and experimental methods. However, the matrix equations for tooth surface contact analysis are complex to construct, and the computational difficulty increases after adding the eccentric matrix, requiring significant computational resources. The accuracy of the results from the finite element method depends on the mesh density, and a higher mesh density requires more computational resources. Experimental methods are labor-intensive and resource-intensive, and their accuracy depends on the sensitivity of the test bench sensors. Summary of the Invention

[0004] This invention aims to at least solve the technical problems existing in the prior art. To this end, this invention proposes a method, system, device, and storage medium for calculating the transmission error of bevel gear pairs, which can improve calculation efficiency and the accuracy of calculation results.

[0005] In a first aspect, the present invention provides a method for calculating the transmission error of a bevel gear pair, comprising the following steps:

[0006] Obtain the parameters of the bevel gear pair;

[0007] Based on the parameters of the bevel gear pair, construct the three-dimensional models of the large gear, the small gear, and the eccentric shaft respectively;

[0008] The eccentric shaft causes the pinion 3D model to rotate by a preset step angle value, and the first pinion working tooth surface set of the rotated pinion 3D model and the first large gear working tooth surface set of the large gear 3D model are extracted.

[0009] Obtain the first normal vector of the first set of working tooth surfaces of the first pinion;

[0010] Calculate the first normal distance between the first normal vector and the first normal distance between the working tooth surface set of the first large gear;

[0011] The first optimal large gear rotation angle value is calculated using the bisection method based on the first normal distance.

[0012] The large gear 3D model is rotated by the first optimal large gear rotation angle value according to the eccentric shaft, and the first small gear angle value of the rotated small gear 3D model and the first large gear angle value of the rotated large gear 3D model are obtained.

[0013] The transmission error set of the bevel gear pair is calculated based on the angle values ​​of the first pinion and the first gear.

[0014] The control method according to embodiments of the present invention has at least the following beneficial effects:

[0015] This method first constructs 3D models of the large gear, small gear, and eccentric shaft based on the parameters of the bevel gear pair. Then, the small gear 3D model is rotated by a preset step angle value using the eccentric shaft. The first set of working tooth surfaces of the small gear and the first set of working tooth surfaces of the large gear in the rotated small gear 3D model are extracted. These two sets are used as the objects for subsequent meshing simulation, instead of the 3D entities of the large and small gears, thus simplifying the calculation. Next, the first normal vector of the first small gear working tooth surface set is obtained. The first normal distance between the first normal vector and the first normal distance is calculated using a bisection method. The first optimal large gear rotation angle is calculated based on this first normal distance. Iterative calculation is used to achieve real-time meshing of the 3D model. Finally, the transmission error set of the bevel gear pair is calculated based on the first small gear angle value and the first large gear angle value. By calculating the angles rotated by the large and small gears under eccentric conditions step by step with preset step angle values, the transmission error is calculated, ensuring the accuracy of the calculation results while improving the calculation speed.

[0016] According to some embodiments of the present invention, calculating the transmission error set of the bevel gear pair based on the first pinion angle value and the first gear angle value includes:

[0017] Obtain the total rotation angle of the three-dimensional model of the small gear, and use the first small gear angle value as the initial small gear angle value and the first large gear angle value as the initial large gear angle value;

[0018] When the total rotation angle of the pinion 3D model is less than the preset total rotation angle of the pinion, the pinion 3D model is rotated again by the preset step angle value according to the eccentric shaft, and the second pinion working tooth surface set of the rotated pinion 3D model and the second large gear working tooth surface set of the large gear 3D model are extracted.

[0019] Obtain the second normal vector of the second pinion working tooth surface set;

[0020] Calculate the second normal distance between the second normal vector and the second normal distance between the working tooth surface set of the second large gear;

[0021] The second optimal large gear rotation angle value is calculated using the bisection method based on the second normal distance.

[0022] The large gear 3D model is rotated by the second optimal large gear rotation angle value according to the eccentric shaft, and the second small gear angle value of the small gear 3D model after rotation and the second large gear angle value of the large gear 3D model after rotation are obtained.

[0023] The first transmission error of the bevel gear pair is calculated based on the initial pinion angle value, the initial gear angle value, the second pinion angle value, and the second gear angle value. This process is repeated until the total rotation angle of the three-dimensional model of the pinion is equal to the preset total rotation angle of the pinion, thus obtaining the transmission error set.

[0024] According to some embodiments of the present invention, the first transmission error of the bevel gear pair is calculated using the following formula based on the initial pinion angle value, the initial gear angle value, the second pinion angle value, and the second gear angle value:

[0025]

[0026] Where δ represents the first transmission error. This is the second largest gear angle value. This is the initial angle value of the large gear. This is the angle value of the second pinion. Z1 is the initial pinion angle value, Z2 is the number of teeth on the gear, and Z1 is the number of teeth on the pinion.

[0027] According to some embodiments of the present invention, the step of calculating the first optimal large gear rotation angle value based on the first normal distance using the bisection method includes:

[0028] When the minimum value of the first normal distance reaches the preset value, the first rotation angle of the three-dimensional model of the large gear at the current moment is obtained;

[0029] The first rotation angle of the large gear at the current moment is taken as the first optimal rotation angle value of the large gear.

[0030] According to some embodiments of the present invention, the step of calculating the first optimal large gear rotation angle value based on the first normal distance using the bisection method further includes:

[0031] When the minimum value of the first normal distance is greater than the preset value, the second rotation angle of the large gear 3D model at the current moment is obtained, and the second rotation angle is increased; until the large gear 3D model rotates to the third rotation angle, so that the minimum value of the third normal distance is less than the preset value. The third normal distance is obtained by extracting the third set of working tooth surfaces of the small gear 3D model after rotation and the third set of working tooth surfaces of the large gear 3D model, obtaining the third normal vector of the third set of working tooth surfaces of the small gear, and calculating the normal distance between the third normal vector and the third set of working tooth surfaces of the large gear.

[0032] The fourth rotation angle is calculated using the bisection method based on the second and third rotation angles, so that the minimum value of the fourth normal distance when the large gear rotates to the fourth rotation angle is equal to the preset value. The fourth normal distance is obtained by extracting the fourth set of working tooth surfaces of the small gear in the three-dimensional model of the rotated small gear and the fourth set of working tooth surfaces of the large gear in the three-dimensional model of the large gear, obtaining the fourth normal vector of the fourth set of working tooth surfaces of the small gear, and calculating the normal distance between the fourth normal vector and the fourth set of working tooth surfaces of the large gear.

[0033] The fourth rotation angle is taken as the first optimal large gear rotation angle value.

[0034] According to some embodiments of the present invention, the step of calculating the first optimal large gear rotation angle value based on the first normal distance using the bisection method further includes:

[0035] When the minimum value of the first normal distance is less than the preset value, the fifth rotation angle of the large gear 3D model at the current moment is obtained, and the fifth rotation angle is increased; until the large gear 3D model rotates to the sixth rotation angle, so that the minimum value of the sixth normal distance is greater than the preset value. The sixth normal distance is obtained by extracting the sixth set of working tooth surfaces of the small gear 3D model after rotation and the sixth set of working tooth surfaces of the large gear 3D model, obtaining the sixth normal vector of the sixth set of working tooth surfaces of the small gear, and calculating the normal distance between the sixth normal vector and the third set of working tooth surfaces of the large gear.

[0036] The seventh rotation angle is calculated using a bisection method based on the fifth and sixth rotation angles, so that the minimum value of the seventh normal distance when the large gear rotates to the seventh rotation angle is equal to the preset value. The seventh normal distance is obtained by extracting the seventh working tooth surface set of the small gear in the three-dimensional model of the rotated small gear and the seventh working tooth surface set of the large gear in the three-dimensional model of the large gear, obtaining the seventh normal vector of the seventh working tooth surface set of the small gear, and calculating the normal distance between the seventh normal vector and the seventh working tooth surface set of the large gear.

[0037] The seventh rotation angle is taken as the first optimal large gear rotation angle value.

[0038] According to some embodiments of the present invention, obtaining the parameters of the bevel gear pair includes:

[0039] Obtain the number of teeth of the large and small bevel gears, shaft intersection angle, offset distance, horizontal position error of the small gear, horizontal position error of the large gear, vertical position error of the large gear, shaft intersection angle error, position coordinates of the eccentric shaft of the large and small gears in their respective body coordinate systems, total angle rotated by the small gear, and angle step size of each rotation of the small gear.

[0040] A second aspect of the present invention provides a system for calculating the transmission error of a bevel gear pair, the system comprising:

[0041] The data acquisition module is used to acquire the parameters of the bevel gear pair.

[0042] The model building module is used to construct the three-dimensional models of the large gear, the small gear, and the eccentric shaft according to the parameters of the bevel gear pair.

[0043] The tooth surface set extraction module is used to rotate the three-dimensional model of the small gear by a preset step angle value according to the eccentric shaft, and extract the first working tooth surface set of the small gear and the first working tooth surface set of the large gear in the three-dimensional model of the large gear after rotation.

[0044] The first normal vector acquisition module is used to acquire the first normal vector of the first pinion working tooth surface set;

[0045] The first normal distance calculation module is used to calculate the first normal distance between the first normal vector and the first set of working tooth surfaces of the first large gear.

[0046] The first optimal large gear rotation angle calculation module is used to calculate the first optimal large gear rotation angle value based on the first normal distance using the bisection method.

[0047] The gear angle value acquisition module is used to rotate the large gear three-dimensional model by the first optimal large gear rotation angle value according to the eccentric shaft, and to acquire the first small gear angle value of the rotated small gear three-dimensional model and the first large gear angle value of the rotated large gear three-dimensional model.

[0048] The transmission error calculation module is used to calculate the transmission error set of the bevel gear pair based on the angle values ​​of the first pinion and the first gear.

[0049] This system first constructs 3D models of the large gear, small gear, and eccentric shaft based on the parameters of the bevel gear pair. The small gear 3D model is rotated by a preset step angle value using the eccentric shaft, and the first set of working tooth surfaces of the small gear and the first set of working tooth surfaces of the large gear are extracted from the rotated small gear 3D model. These two sets are used as the objects for subsequent meshing simulation, instead of the 3D entities of the large and small gears, thus simplifying the calculation. The first normal vector of the first small gear working tooth surface set is then obtained. The first normal distance between the first normal vector and the first normal distance is calculated using a bisection method. The system utilizes iterative calculation to achieve real-time meshing of the 3D models. Finally, the transmission error set of the bevel gear pair is calculated based on the first small gear angle value and the first large gear angle value. By calculating the angles rotated by the large and small gears under eccentric conditions step by step angle value, the transmission error is calculated, ensuring the accuracy of the calculation results while improving the calculation speed.

[0050] A third aspect of the present invention provides an electronic device for calculating the transmission error of a bevel gear pair, comprising at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, the instructions being executed by the at least one control processor to enable the at least one control processor to perform the above-described method for calculating the transmission error of the bevel gear pair.

[0051] In a fourth aspect, the present invention provides a computer-readable storage medium storing computer-executable instructions for causing a computer to perform the above-described method for calculating the transmission error of a bevel gear pair.

[0052] It should be noted that the beneficial effects of the second to fourth aspects of the present invention compared with the prior art are the same as the beneficial effects of the above-described calculation system for the transmission error of a bevel gear pair compared with the prior art, and will not be described in detail here.

[0053] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0054] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0055] Figure 1 This is a flowchart of a method for calculating the transmission error of a bevel gear pair according to an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of the body coordinate system of the large and small gears in a method for calculating the transmission error of a bevel gear pair provided in an embodiment of the present invention.

[0057] Figure 3 This is an initial assembly drawing of a bevel gear pair, which is a method for calculating transmission error of a bevel gear pair provided in an embodiment of the present invention.

[0058] Figure 4 This invention provides a method for calculating the transmission error of a bevel gear pair, which establishes an eccentric shaft and a working tooth surface diagram.

[0059] Figure 5 This is a schematic diagram of the transmission error calculation results of a method for calculating the transmission error of a bevel gear pair provided in an embodiment of the present invention;

[0060] Figure 6 This is a schematic diagram of the structure of a bevel gear pair transmission error calculation system according to an embodiment of the present invention. Detailed Implementation

[0061] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0062] In the description of this invention, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance, or implicitly indicating the number of technical features indicated, or implicitly indicating the order of the technical features indicated.

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

[0064] In the description of this invention, it should be noted that, unless otherwise explicitly defined, terms such as "setting," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0065] Before introducing this application, let's first discuss eccentricity error:

[0066] Many types of errors can occur during gear manufacturing and assembly, one of which is geometric eccentricity error. The causes of geometric eccentricity error can be broadly categorized into three types: gear manufacturing errors, shaft manufacturing errors, and assembly errors. Gear manufacturing errors refer to errors present during gear machining, causing the inner hole of the gear to misalign with the pitch circle center. Shaft manufacturing errors refer to coaxiality errors caused by the misalignment of the centers of different shaft segments during machining. Assembly errors refer to the misalignment of the centers at the mating points of the shaft and gear during assembly. All three of these situations can cause geometric eccentricity error in gears.

[0067] Gearboxes have a wide range of applications in industry, such as aircraft gearboxes and marine gearboxes. With the deepening research into gear transmission systems, industry has placed increasingly stringent demands on gearboxes, requiring high reliability and high transmission accuracy. The parameters describing gear meshing performance are crucial indicators of the quality of gear transmissions. Among these, transmission error is a vital parameter describing the meshing performance of gear pairs. When the driving gear rotates uniformly, the deviation of the actual position of the driven gear from its theoretical position is the transmission error. Transmission error is particularly important because researchers have found a strong correlation with gear vibration and noise. Therefore, calculating the transmission error of gear pairs with eccentricity errors has always been a key research topic in the industry.

[0068] Currently, methods for calculating gear transmission errors under eccentric conditions include tooth surface contact analysis, finite element method, and experimental methods. However, the matrix equations for tooth surface contact analysis are complex to construct, and the computational difficulty increases after adding the eccentric matrix, requiring significant computational resources. The accuracy of the results from the finite element method depends on the mesh density, and a higher mesh density requires more computational resources. Experimental methods are labor-intensive and resource-intensive, and their accuracy depends on the sensitivity of the test bench sensors.

[0069] To address the aforementioned technical deficiencies, referring to... Figure 1 This invention provides a method for calculating the transmission error of a bevel gear pair, including:

[0070] Step S101: Obtain the parameters of the bevel gear pair;

[0071] Step S102: Construct the three-dimensional model of the large gear, the three-dimensional model of the small gear, and the eccentric shaft according to the parameters of the bevel gear pair;

[0072] Step S103: Rotate the three-dimensional model of the small gear by a preset step angle value according to the eccentric shaft, and extract the first set of working tooth surfaces of the small gear and the first set of working tooth surfaces of the large gear in the three-dimensional model of the large gear after rotation.

[0073] Step S104: Obtain the first normal vector of the first pinion working tooth surface set;

[0074] Step S105: Calculate the first normal distance between the first normal vector and the first normal distance between the working tooth surfaces of the first large gear;

[0075] Step S106: Calculate the first optimal large gear rotation angle value using the bisection method based on the first normal distance;

[0076] Step S107: Rotate the large gear 3D model by the first optimal large gear rotation angle value according to the eccentric shaft, and obtain the first small gear angle value of the small gear 3D model after rotation and the first large gear angle value of the large gear 3D model after rotation.

[0077] Step S108: Calculate the transmission error set of the bevel gear pair based on the angle values ​​of the first pinion and the first gear.

[0078] Specifically, refer to Figure 2 First, it's essential to define the basic parameters of the gear pair, including: the number of teeth on the large and small gears, the shaft intersection angle, the offset distance, the horizontal position error of the small gear, the horizontal position error of the large gear, the vertical position error, the shaft intersection angle error, the position coordinates of the eccentric shafts of the large and small gears in their respective body coordinate systems, the total angle rotated by the small gear, and the angular step size of each rotation of the small gear. Based on some of these parameters, a 3D model of the large and small gears can be constructed using commercial software. After importing the 3D model of the large and small gears, the algorithm will, based on the previously input parameters and using the position of the large gear as a reference, rotate and translate the small gear model. To complete the initial meshing assembly of the gear pair; establishing a tooth surface set means that after determining the direction of rotation, the working tooth surfaces of the large and small gears are extracted and integrated into two sets. In subsequent meshing simulations, these two sets are used as the objects, instead of the three-dimensional solids of the large and small gears, thus greatly simplifying the calculations; the eccentric shaft is constructed using the previously input "position coordinates of the eccentric shaft of the large and small gears in their respective body coordinate systems." The position of the eccentric shaft is determined in the body coordinate system of each gear, and the position of the shaft is determined by the coordinates of the eccentric shaft. The body coordinate systems of the large and small gears are as follows: Figure 2 As shown.

[0079] Specifically, refer to Figure 3 and Figure 4 Import the 3D model of the large and small gears to complete the initial assembly, as shown below. Figure 3 As shown, the working tooth surfaces and eccentric rotating shaft of both are constructed simultaneously. Figure 4 As shown.

[0080] This method first constructs 3D models of the large gear, small gear, and eccentric shaft based on the parameters of the bevel gear pair. Then, the small gear 3D model is rotated by a preset step angle value using the eccentric shaft. The first set of working tooth surfaces of the small gear and the first set of working tooth surfaces of the large gear in the rotated small gear 3D model are extracted. These two sets are used as the objects for subsequent meshing simulation, instead of the 3D entities of the large and small gears, thus simplifying the calculation. Next, the first normal vector of the first small gear working tooth surface set is obtained. The first normal distance between the first normal vector and the first normal distance is calculated using a bisection method. The first optimal large gear rotation angle is calculated based on this first normal distance. Iterative calculation is used to achieve real-time meshing of the 3D model. Finally, the transmission error set of the bevel gear pair is calculated based on the first small gear angle value and the first large gear angle value. By calculating the angles rotated by the large and small gears under eccentric conditions step by step with preset step angle values, the transmission error is calculated, ensuring the accuracy of the calculation results while improving the calculation speed.

[0081] In some embodiments, calculating the transmission error set of the bevel gear pair based on the first pinion angle value and the first gear angle value includes:

[0082] Step S201: Obtain the total rotation angle of the 3D model of the small gear, and use the first small gear angle value as the initial small gear angle value and the first large gear angle value as the initial large gear angle value.

[0083] Step S202: When the total rotation angle of the pinion 3D model is less than the preset total rotation angle of the pinion, the pinion 3D model is rotated again by a preset step angle value according to the eccentric shaft, and the second pinion working tooth surface set of the rotated pinion 3D model and the second large gear working tooth surface set of the large gear 3D model are extracted.

[0084] Step S203: Obtain the second normal vector of the second pinion working tooth surface set;

[0085] Step S204: Calculate the second normal distance between the second normal vector and the second normal distance between the working tooth surfaces of the second large gear;

[0086] Step S205: Calculate the second optimal large gear rotation angle value using the bisection method based on the second normal distance;

[0087] Step S206: Rotate the large gear 3D model by the eccentric shaft to the second optimal large gear rotation angle value, and obtain the second small gear angle value of the small gear 3D model after rotation and the second large gear angle value of the large gear 3D model after rotation;

[0088] Step S207: Calculate the first transmission error of the bevel gear pair based on the initial pinion angle value, the initial large gear angle value, the second pinion angle value, and the second large gear angle value. Repeat this process until the total rotation angle of the three-dimensional model of the pinion is equal to the preset total rotation angle of the pinion, thus obtaining the transmission error set.

[0089] It should be noted that in subsequent iterations, the initial pinion angle value for calculating the second or third transmission error remains the same as the first pinion angle value, and the initial gear angle value remains the same as the first gear angle value. That is, in subsequent calculations of the transmission error, the initial gear angle value and the initial pinion angle value remain the same.

[0090] Specifically, refer to Figure 5 The output gears are post-processed to obtain the gear pair transmission error under the condition of eccentricity, and a chart is constructed for display.

[0091] Specifically, this embodiment achieves the real-time meshing function of the three-dimensional model in the finite element method by using the multiple iteration calculation idea in the TCA method. Then, the loop will enter the transmission error calculation, output the rotation angle of each of the working tooth surfaces of the large and small gears in this loop, and enter the next loop with the position of the large and small gears after this loop as the initial position, thereby obtaining the transmission error set.

[0092] In some embodiments, the first transmission error of the bevel gear pair is calculated using the following formula based on the initial pinion angle value, the initial gear angle value, the second pinion angle value, and the second gear angle value:

[0093]

[0094] Where δ represents the first transmission error. This is the second largest gear angle value. This is the initial angle value of the large gear. This is the angle value of the second pinion. Z1 is the initial pinion angle value, Z2 is the number of teeth on the gear, and Z1 is the number of teeth on the pinion.

[0095] In some embodiments, step S106 calculates the first optimal large gear rotation angle value based on the first normal distance using the bisection method, including:

[0096] Step S301: When the minimum value of the first normal distance reaches the preset value, the first rotation angle of the large gear 3D model at the current moment is obtained.

[0097] Step S302: Take the first rotation angle of the large gear at the current moment as the first optimal rotation angle value of the large gear.

[0098] It should be noted that the preset value in this embodiment is 10 to the power of -4.

[0099] Specifically, this application ensures that the gear pairs are correctly meshed at every moment under a specified rotation angle and rotation step size when the large and small gears rotate around their respective eccentric axes through a cyclic iteration of "rotation of the large and small gears around the eccentric shaft" and "contact judgment of the working tooth surfaces of the large and small gears". It also ensures that the rotation angle of the large and small gears at the correct meshing time can be obtained when the large and small gears are correctly meshed.

[0100] In some embodiments, step S106, which calculates the first optimal large gear rotation angle value based on the first normal distance using the bisection method, further includes:

[0101] Step S401: When the minimum value of the first normal distance is greater than the preset value, the second rotation angle of the large gear 3D model at the current moment is obtained, and the second rotation angle is increased; until the large gear 3D model rotates to the third rotation angle so that the minimum value of the third normal distance is less than the preset value. The third normal distance is obtained by extracting the third small gear working tooth surface set of the rotated small gear 3D model and the third large gear working tooth surface set of the large gear 3D model, obtaining the third normal vector of the third small gear working tooth surface set, and calculating the normal distance between the third normal vector and the third large gear working tooth surface set.

[0102] Step S402: Calculate the fourth rotation angle using the bisection method based on the second and third rotation angles, so that the minimum value of the fourth normal distance when the large gear 3D model rotates to the fourth rotation angle is equal to the preset value. The fourth normal distance is obtained by extracting the fourth small gear working tooth surface set of the rotated small gear 3D model and the fourth large gear working tooth surface set of the large gear 3D model, obtaining the fourth normal vector of the fourth small gear working tooth surface set, and calculating the normal distance between the fourth normal vector and the fourth large gear working tooth surface set.

[0103] Step S403: Take the fourth rotation angle as the first optimal large gear rotation angle value.

[0104] Specifically, this application achieves the goal of reducing the iteration time spent in each cycle to reach the required high precision level while ensuring calculation accuracy by setting preset values. Through the iterative process of "rotation of large and small gears around the eccentric axis" and "contact judgment of working tooth surfaces of large and small gears", it ensures that the gear pairs are correctly meshed at every moment under the specified rotation angle and rotation step size when the large and small gears rotate around their respective eccentric axes. Moreover, it ensures that the rotation angle of the large and small gears when they are correctly meshed can be obtained even before the large and small gears have made contact.

[0105] In some embodiments, step S106, which calculates the first optimal large gear rotation angle value based on the first normal distance using the bisection method, further includes:

[0106] Step S501: When the minimum value of the first normal distance is less than the preset value, the fifth rotation angle of the current large gear 3D model is obtained, and the fifth rotation angle is increased; until the large gear 3D model rotates to the sixth rotation angle, so that the minimum value of the sixth normal distance is greater than the preset value. The sixth normal distance is obtained by extracting the sixth small gear working tooth surface set of the rotated small gear 3D model and the sixth large gear working tooth surface set of the large gear 3D model, obtaining the sixth normal vector of the sixth small gear working tooth surface set, and calculating the normal distance between the sixth normal vector and the third large gear working tooth surface set.

[0107] Step S502: Calculate the seventh rotation angle using the bisection method based on the fifth and sixth rotation angles, so that the minimum value of the seventh normal distance when the large gear 3D model rotates to the seventh rotation angle is equal to the preset value. The seventh normal distance is obtained by extracting the seventh small gear working tooth surface set of the rotated small gear 3D model and the seventh large gear working tooth surface set of the large gear 3D model, obtaining the seventh normal vector of the seventh small gear working tooth surface set, and calculating the normal distance between the seventh normal vector and the seventh large gear working tooth surface set.

[0108] Step S503: Take the seventh rotation angle as the first optimal large gear rotation angle value.

[0109] Specifically, this application ensures that the gear pairs are correctly meshed at every moment under a specified rotation angle and rotation step size when the large and small gears rotate around their respective eccentric axes through a cyclic iteration of "rotation of the large and small gears around the eccentric shaft" and "contact judgment of the working tooth surfaces of the large and small gears". It also ensures that the rotation angle of the large and small gears when they are correctly meshed can be obtained when there is interference between the large and small gears.

[0110] Specifically, in some embodiments, in the "rotation function of the large and small gears around the eccentric axis", based on the input parameters of the total rotation angle θ of the small gear and the rotation angle (step size θ1) of each step, at the beginning of each cycle, the small gear is first rotated by θ1 degrees, and simultaneously according to the transmission ratio... This allows the large wheel to rotate at an angle θ2 under ideal conditions. At this point, the large and small gears are transmitting under ideal conditions, meaning the transmission error δ = 0. Then, the algorithm loops through the "contact state judgment function for the working tooth surfaces of the large and small gears." Here, the algorithm determines the normal distance from each point on the small gear's working tooth surface set 1 to the large gear's working tooth surface set 2. If the normal distance at any point is negative, it indicates interference between the two sets. If the normal distance at each point is positive, it means they are not yet in contact. If the normal distance at a point has both positive and zero values, it indicates correct meshing, meaning the tooth surfaces are exactly tangent. In practice, the algorithm sets this "zero value" to 10 to the power of -4. This ensures computational accuracy while reducing the iteration time spent in each loop to achieve the required high precision.

[0111] Specifically, when the two sets are not yet in contact, the algorithm gradually increases the rotation angle of the large gear in the current loop to θ3, until the normal distance between the two sets of working tooth surfaces of the large and small gears is negative. This indicates that the correct rotation angle θ4 of the large gear is between θ2 and θ3. At this point, the algorithm continuously divides between θ2 and θ3 using a bisection method until the judgment function determines that the two are exactly tangent, thus obtaining the correct rotation angle θ4 of the large gear in this loop. Similarly, when the two sets interfere with each other, the algorithm gradually decreases the rotation angle of the large gear in the current loop to θ3, until the two sets of working tooth surfaces of the large and small gears are not yet in contact. This indicates that the correct rotation angle θ4 of the large gear is between θ2 and θ3. At this point, the algorithm continuously divides between θ2 and θ3 using a bisection method to obtain θ4, thus obtaining the correct rotation angle θ4 of the large gear in this loop. In the above process, the algorithm utilizes the multiple iteration calculation idea in the TCA method to achieve the real-time meshing function of the three-dimensional model in the finite element method. Then the loop enters the "result output function", which outputs the rotation angle of each set of working tooth surfaces of the large and small gears in this loop. and Starting from the position of the large and small gears after this cycle, the next cycle begins, continuing until the set total rotation angle θ of the small gear is reached. The result is the rotation angle of the set of working tooth surfaces of the large and small gears in each cycle. and

[0112] In some embodiments, step S101, obtaining the parameters of the bevel gear pair, includes:

[0113] Step S601: Obtain the number of teeth of the large and small bevel gears, shaft intersection angle, offset distance, horizontal gear position error of the small gear, horizontal gear position error of the large gear, vertical gear position error, shaft intersection angle error, position coordinates of the eccentric shaft of the large and small gears in their respective body coordinate systems, total angle rotated by the small gear, and angle step size of the small gear's rotation per step.

[0114] Specifically, this embodiment takes a pair of bevel gears with 47 teeth on the large gear and 10 teeth on the small gear as an example to illustrate the calculation process of this application. In the preprocessing stage, various parameters are input in Table 1, where Table 1 is the bevel gear pair parameters that need to be set.

[0115] Table 1

[0116]

[0117] This embodiment provides a data foundation for subsequent calculations of transmission errors by setting the parameters of the bevel gear pair, thus ensuring the accuracy of the data.

[0118] Additionally, refer to Figure 6 An embodiment of the present invention provides a system for calculating the transmission error of a bevel gear pair, comprising a data acquisition module 1100, a model construction module 1200, a tooth surface set extraction module 1300, a first normal vector acquisition module 1400, a first normal distance calculation module 1500, a first optimal large gear rotation angle value calculation module 1600, a gear angle value acquisition module 1700, and a transmission error calculation module 1800, wherein:

[0119] The data acquisition module 1100 is used to acquire the parameters of the bevel gear pair;

[0120] The model building module 1200 is used to build the three-dimensional models of the large gear, the small gear, and the eccentric shaft according to the parameters of the bevel gear pair.

[0121] The tooth surface set extraction module 1300 is used to rotate the three-dimensional model of the small gear by a preset step angle value according to the eccentric shaft, and extract the first working tooth surface set of the small gear and the first working tooth surface set of the large gear in the three-dimensional model of the large gear after rotation.

[0122] The first normal vector acquisition module 1400 is used to acquire the first normal vector of the first pinion working tooth surface set;

[0123] The first normal distance calculation module 1500 is used to calculate the first normal distance between the first normal vector and the first normal distance between the first working tooth surface set of the first large gear.

[0124] The first optimal large gear rotation angle calculation module 1600 is used to calculate the first optimal large gear rotation angle value based on the first normal distance using the bisection method.

[0125] The gear angle value acquisition module 1700 is used to rotate the three-dimensional model of the large gear by the eccentric shaft to the first optimal large gear rotation angle value, and to acquire the first small gear angle value of the three-dimensional model of the small gear after rotation and the first large gear angle value of the three-dimensional model of the large gear after rotation.

[0126] The transmission error calculation module 1800 is used to calculate the transmission error set of the bevel gear pair based on the angle values ​​of the first pinion and the first gear.

[0127] This system first constructs 3D models of the large gear, small gear, and eccentric shaft based on the parameters of the bevel gear pair. The small gear 3D model is rotated by a preset step angle value using the eccentric shaft, and the first set of working tooth surfaces of the small gear and the first set of working tooth surfaces of the large gear are extracted from the rotated small gear 3D model. These two sets are used as the objects for subsequent meshing simulation, instead of the 3D entities of the large and small gears, thus simplifying the calculation. The first normal vector of the first small gear working tooth surface set is then obtained. The first normal distance between the first normal vector and the first normal distance is calculated using a bisection method. The system utilizes iterative calculation to achieve real-time meshing of the 3D models. Finally, the transmission error set of the bevel gear pair is calculated based on the first small gear angle value and the first large gear angle value. By calculating the angles rotated by the large and small gears under eccentric conditions step by step angle value, the transmission error is calculated, ensuring the accuracy of the calculation results while improving the calculation speed.

[0128] It should be noted that this system embodiment is based on the same inventive concept as the above system embodiment. Therefore, the relevant content of the above method embodiment is also applicable to this system embodiment, and will not be repeated here.

[0129] This application also provides an electronic device for calculating the transmission error of a bevel gear pair, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method for calculating the transmission error of the bevel gear pair as described above.

[0130] The processor and memory can be connected via a bus or other means.

[0131] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0132] The non-transient software program and instructions required to implement the bevel gear pair transmission error calculation method of the above embodiments are stored in memory. When executed by the processor, the bevel gear pair transmission error calculation method of the above embodiments is executed, for example, the method described above is executed. Figure 1 The method steps S101 to S108.

[0133] This application also provides a computer-readable storage medium storing computer-executable instructions for performing, as described above, the method for calculating the transmission error of a bevel gear pair.

[0134] The computer-readable storage medium stores computer-executable instructions that are executed by a processor or controller, for example, by a processor in the above-described electronic device embodiment, causing the processor to perform the method for calculating the transmission error of the bevel gear pair in the above-described embodiment, for example, performing the above-described... Figure 1 The method steps S101 to S108.

[0135] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media 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 units, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program units, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0136] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for calculating the transmission error of a bevel gear pair, characterized in that, The calculation method for the transmission error of the bevel gear pair includes: Obtain the parameters of the bevel gear pair; Based on the parameters of the bevel gear pair, construct the three-dimensional models of the large gear, the small gear, and the eccentric shaft respectively; The eccentric shaft causes the pinion 3D model to rotate by a preset step angle value, and the first pinion working tooth surface set of the rotated pinion 3D model and the first large gear working tooth surface set of the large gear 3D model are extracted. Obtain the first normal vector of the first set of working tooth surfaces of the first pinion; Calculate the first normal distance between the first normal vector and the first normal distance between the working tooth surface set of the first large gear; The first optimal large gear rotation angle value is calculated using the bisection method based on the first normal distance. The large gear 3D model is rotated by the first optimal large gear rotation angle value according to the eccentric shaft, and the first small gear angle value of the rotated small gear 3D model and the first large gear angle value of the rotated large gear 3D model are obtained. The transmission error set of the bevel gear pair is calculated based on the angle values ​​of the first pinion and the first gear.

2. The method for calculating the transmission error of a bevel gear pair according to claim 1, characterized in that, The step of calculating the transmission error set of the bevel gear pair based on the angle values ​​of the first pinion and the first gear includes: Obtain the total rotation angle of the three-dimensional model of the small gear, and use the first small gear angle value as the initial small gear angle value and the first large gear angle value as the initial large gear angle value; When the total rotation angle of the pinion 3D model is less than the preset total rotation angle of the pinion, the pinion 3D model is rotated again by the preset step angle value according to the eccentric shaft, and the second pinion working tooth surface set of the rotated pinion 3D model and the second large gear working tooth surface set of the large gear 3D model are extracted. Obtain the second normal vector of the second pinion working tooth surface set; Calculate the second normal distance between the second normal vector and the second normal distance between the working tooth surface set of the second large gear; The second optimal large gear rotation angle value is calculated using the bisection method based on the second normal distance. The large gear 3D model is rotated by the second optimal large gear rotation angle value according to the eccentric shaft, and the second small gear angle value of the small gear 3D model after rotation and the second large gear angle value of the large gear 3D model after rotation are obtained. The first transmission error of the bevel gear pair is calculated based on the initial pinion angle value, the initial gear angle value, the second pinion angle value, and the second gear angle value. This process is repeated until the total rotation angle of the three-dimensional model of the pinion is equal to the preset total rotation angle of the pinion, thus obtaining the transmission error set.

3. The method for calculating the transmission error of a bevel gear pair according to claim 2, characterized in that, The first transmission error of the bevel gear pair is calculated using the following formula based on the initial pinion angle value, the initial gear angle value, the second pinion angle value, and the second gear angle value: Where δ represents the first transmission error. This is the second largest gear angle value. This is the initial angle value of the large gear. This is the angle value of the second pinion. Z1 is the initial pinion angle value, Z2 is the number of teeth on the gear, and Z1 is the number of teeth on the pinion.

4. The method for calculating the transmission error of a bevel gear pair according to claim 1, characterized in that, The step of calculating the first optimal large gear rotation angle value based on the first normal distance using the bisection method includes: When the minimum value of the first normal distance reaches the preset value, the first rotation angle of the three-dimensional model of the large gear at the current moment is obtained; The first rotation angle of the large gear at the current moment is taken as the first optimal rotation angle value of the large gear.

5. The method for calculating the transmission error of a bevel gear pair according to claim 4, characterized in that, The step of calculating the first optimal large gear rotation angle value based on the first normal distance using the bisection method further includes: When the minimum value of the first normal distance is greater than the preset value, the second rotation angle of the large gear 3D model at the current moment is obtained, and the second rotation angle is increased; until the large gear 3D model rotates to the third rotation angle, so that the minimum value of the third normal distance is less than the preset value. The third normal distance is obtained by extracting the third set of working tooth surfaces of the small gear 3D model after rotation and the third set of working tooth surfaces of the large gear 3D model, obtaining the third normal vector of the third set of working tooth surfaces of the small gear, and calculating the normal distance between the third normal vector and the third set of working tooth surfaces of the large gear. The fourth rotation angle is calculated using the bisection method based on the second and third rotation angles, so that the minimum value of the fourth normal distance when the large gear rotates to the fourth rotation angle is equal to the preset value. The fourth normal distance is obtained by extracting the fourth set of working tooth surfaces of the small gear in the three-dimensional model of the rotated small gear and the fourth set of working tooth surfaces of the large gear in the three-dimensional model of the large gear, obtaining the fourth normal vector of the fourth set of working tooth surfaces of the small gear, and calculating the normal distance between the fourth normal vector and the fourth set of working tooth surfaces of the large gear. The fourth rotation angle is taken as the first optimal large gear rotation angle value.

6. The method for calculating the transmission error of a bevel gear pair according to claim 5, characterized in that, The step of calculating the first optimal large gear rotation angle value based on the first normal distance using the bisection method further includes: When the minimum value of the first normal distance is less than the preset value, the fifth rotation angle of the large gear 3D model at the current moment is obtained, and the fifth rotation angle is increased; until the large gear 3D model rotates to the sixth rotation angle, so that the minimum value of the sixth normal distance is greater than the preset value. The sixth normal distance is obtained by extracting the sixth set of working tooth surfaces of the small gear 3D model after rotation and the sixth set of working tooth surfaces of the large gear 3D model, obtaining the sixth normal vector of the sixth set of working tooth surfaces of the small gear, and calculating the normal distance between the sixth normal vector and the third set of working tooth surfaces of the large gear. The seventh rotation angle is calculated using a bisection method based on the fifth and sixth rotation angles, so that the minimum value of the seventh normal distance when the large gear rotates to the seventh rotation angle is equal to the preset value. The seventh normal distance is obtained by extracting the seventh working tooth surface set of the small gear in the three-dimensional model of the rotated small gear and the seventh working tooth surface set of the large gear in the three-dimensional model of the large gear, obtaining the seventh normal vector of the seventh working tooth surface set of the small gear, and calculating the normal distance between the seventh normal vector and the seventh working tooth surface set of the large gear. The seventh rotation angle is taken as the first optimal large gear rotation angle value.

7. The method for calculating the transmission error of a bevel gear pair according to claim 1, characterized in that, The acquisition of bevel gear pair parameters includes: Obtain the number of teeth of the large and small bevel gears, shaft intersection angle, offset distance, horizontal position error of the small gear, horizontal position error of the large gear, vertical position error of the large gear, shaft intersection angle error, position coordinates of the eccentric shaft of the large and small gears in their respective body coordinate systems, total angle rotated by the small gear, and angle step size of each rotation of the small gear.

8. A system for calculating the transmission error of a bevel gear pair, characterized in that, The system for calculating the transmission error of the bevel gear pair includes: The data acquisition module is used to acquire the parameters of the bevel gear pair. The model building module is used to construct the three-dimensional models of the large gear, the small gear, and the eccentric shaft according to the parameters of the bevel gear pair. The tooth surface set extraction module is used to rotate the three-dimensional model of the small gear by a preset step angle value according to the eccentric shaft, and extract the first working tooth surface set of the small gear and the first working tooth surface set of the large gear in the three-dimensional model of the large gear after rotation. The first normal vector acquisition module is used to acquire the first normal vector of the first pinion working tooth surface set; The first normal distance calculation module is used to calculate the first normal distance between the first normal vector and the first set of working tooth surfaces of the first large gear. The first optimal large gear rotation angle calculation module is used to calculate the first optimal large gear rotation angle value based on the first normal distance using the bisection method. The gear angle value acquisition module is used to rotate the large gear three-dimensional model by the first optimal large gear rotation angle value according to the eccentric shaft, and to acquire the first small gear angle value of the rotated small gear three-dimensional model and the first large gear angle value of the rotated large gear three-dimensional model. The transmission error calculation module is used to calculate the transmission error set of the bevel gear pair based on the angle values ​​of the first pinion and the first gear.

9. A device for calculating the transmission error of a bevel gear pair, characterized in that, It includes at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enable the at least one control processor to perform a method for calculating the transmission error of a bevel gear pair as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions for causing a computer to perform a method for calculating the transmission error of a bevel gear pair as described in any one of claims 1 to 7.

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