A method for evaluating transmission smoothness of a cycloid pin gear planetary mechanism

Abstract

This invention belongs to the field of automotive technology, specifically a method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism. It includes: 1. Constructing an assembly finite element model of the cycloidal pinwheel planetary mechanism; 2. Defining the material properties of the finite element model; 3. Defining the stiffness of the spring unit used to simulate the rolling elements: the radial stiffness of the rolling elements in the bearing radial direction, the axial stiffness of the rolling elements in the bearing axial direction, and the warping stiffness of the rolling elements in a plane perpendicular to the bearing axial direction; 4. Defining the boundary conditions of the finite element model; 5. Defining the loads of the finite element model; 6. Defining the calculation conditions; 7. Performing finite element analysis; 8. Evaluating the transmission smoothness of the cycloidal pinwheel planetary mechanism; 9. Repeating steps 6 to 8 to evaluate the transmission smoothness of the cycloidal pinwheel based on manufacturing and assembly errors. This invention has strong versatility and effectively achieves accurate prediction of the meshing force between the cycloidal wheel and the pinwheel, as well as a reasonable evaluation of the transmission smoothness of the cycloidal pinwheel planetary mechanism.

Description

Technical Field

[0001] This invention belongs to the field of automotive technology, specifically a method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism. Background Technology

[0002] Cycloidal pinwheel planetary mechanisms possess advantages such as large transmission ratio, high transmission efficiency, strong load-bearing capacity, small size, and smooth transmission. They are widely used in various fields including petroleum, chemical, construction, metallurgy, mining, hoisting and transportation, textile printing and dyeing, engineering machinery, and food industry. In automobiles, they are frequently used for automatic gear shifting in transmission systems, automatic clutch engagement control, wheel steering, and parking brakes. When designing cycloidal pinwheel planetary mechanisms, to ensure the meshing teeth have certain top clearance, root clearance, and side clearance, the cycloidal gear is often machined using offset and equidistant shaping methods. However, the meshing of cycloidal teeth and pin teeth differs from that of involute teeth. Theoretically, a pin tooth of a specific diameter is only conjugate with a variable amplitude cycloid under specific conditions. When the pin tooth diameter, position, eccentricity, or the variable amplitude cycloid being machined changes, the two will no longer be conjugate, causing the transmission ratio to become inconsistent, resulting in changes in the meshing force, and consequently affecting the transmission smoothness of the cycloidal pinwheel planetary mechanism. Therefore, the transmission smoothness of the cycloidal pinwheel planetary mechanism should be effectively evaluated in the early stages of product development to determine the rationality of the structural design.

[0003] Currently, there are three main methods for evaluating the smoothness of gear transmissions:

[0004] One approach is to evaluate the transmission ratio. By considering the machining error of the cycloidal wheel or the meshing relationship between the modified tooth profile and the pin teeth of the pin wheel, a formula for calculating the instantaneous transmission ratio of the cycloidal pin wheel is established. The curve of the instantaneous transmission ratio changing with the rotation angle of the pin wheel is calculated, and the transmission smoothness of the cycloidal pin wheel is evaluated. This method is based on theoretical formulas and has the advantage of fast calculation speed. However, it does not consider the influence of the actual stiffness of the cycloidal wheel and the pin wheel, resulting in a less accurate curve of the transmission ratio changing with the rotation angle of the pin wheel.

[0005] The second method uses acceleration evaluation. An acceleration sensor is placed on the bearing housing closest to the meshing gear pair and convenient for testing. By measuring the acceleration of the driven gear shaft, the absolute average value, root mean square value, standard deviation, maximum value, and minimum value of the acceleration signal are analyzed to evaluate the smoothness of the gear pair transmission. Its advantage is that it takes into account the actual machining and installation errors of the gear pair, and the obtained acceleration signal is accurate. Its disadvantage is that this method can only be used when there is a test sample. It cannot be used when there is no test sample. In addition, there are many evaluation parameters, and there are conflicts between the parameters, which can easily cause problems in practical engineering applications.

[0006] Third, bandwidth evaluation is adopted. By changing the radial clearance and tooth flank clearance of the gear, the time history diagram of the gear meshing force under different clearance combinations is calculated. Then, spectrum analysis is performed to obtain the bandwidth near the meshing frequency, and the smoothness of the transmission is judged based on the bandwidth. Its advantages are that it considers the influence of the gear radial clearance and tooth flank clearance processing technology, calculates the gear meshing force based on theoretical formulas, and has a fast calculation speed. Its disadvantage is that it does not consider the influence of the actual stiffness of the cycloidal wheel and pin wheel, and the accuracy of the obtained gear meshing force is not high. Summary of the Invention

[0007] This invention provides a method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism. It can be used not only for comparative evaluation of the transmission smoothness of cycloidal pinwheel planetary mechanisms of the same model, but also for comparative analysis of the transmission smoothness of cycloidal pinwheel planetary mechanisms of different models. It has strong versatility and effectively realizes the correct prediction of the meshing force between the cycloidal wheel and the pinwheel, as well as the reasonable evaluation of the transmission smoothness of the cycloidal pinwheel planetary mechanism, thus solving the above-mentioned problems existing in the methods for evaluating the smoothness of gear transmission.

[0008] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0009] A method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism includes the following steps:

[0010] Step 1: Construct the assembly finite element model of the cycloidal pinwheel planetary mechanism;

[0011] Step 2: Define the material properties of the finite element model;

[0012] Step 3: Define the stiffness of the spring unit used to simulate the rolling element. The radial stiffness K of the rolling element in the radial direction of the bearing. r axial stiffness K of the rolling elements in the bearing axial direction a Warping stiffness of rolling elements in a plane perpendicular to the bearing axial direction

[0013] Step 4: Define the boundary conditions for the finite element model;

[0014] Step 5: Define the loads in the finite element model;

[0015] Step 6: Define the calculation conditions;

[0016] Step 7: Perform finite element analysis;

[0017] Step 8: Evaluate the transmission smoothness of the cycloidal pinwheel planetary mechanism;

[0018] Step 9: Based on manufacturing and assembly errors, repeat steps 6 to 8 to evaluate the transmission smoothness of the cycloidal pinwheel.

[0019] Furthermore, in step one,

[0020] The cycloidal pinwheel planetary mechanism includes a support, housing, pinwheel, screw, motor, bushing, cycloidal wheel, output shaft, input shaft, rotating arm, and bearing. The support, housing, pinwheel, screw, bushing, cycloidal wheel, output shaft, input shaft, rotating arm, bearing outer ring, and bearing inner ring are divided into solid meshes. The meshes of the contact parts are finely divided, and the meshes of other non-contact parts are coarsely divided.

[0021] The bearing inner ring and the swing arm are connected using RBE3 and RBE2 elements for a simplified connection. The slave point of the RBE3 element connecting the bearing inner ring is selected from the geometric center point of the inner diameter side surface of the bearing inner ring, and the master point is selected from a node on the inner diameter side surface of the bearing inner ring. The slave point of the RBE3 element connecting the swing arm is selected from a point along the bearing centerline that is offset from the slave point of the RBE3 element connecting the bearing inner ring, and the master point is selected from a node on the surface in contact with the bearing inner diameter. The slave points of the RBE3 element connecting the bearing inner ring and the slave point of the RBE3 element connecting the swing arm are connected using RBE2 elements. The two slave points connected by the RBE2 element are only uncoupled in the degree of freedom along the rotation direction of the bearing centerline, while all other degrees of freedom are coupled together.

[0022] The rolling elements of the bearing are simplified using spring elements. For bearings with outer and inner rings, the nodes at both ends of the spring element simulating the rolling elements are connected to the slave points of two RBE3 elements. The two slave points are located on the geometric center line of the bearing. The slave point of one RBE3 element is selected as the geometric center of the outer ring raceway, and the master point is selected as a node on the outer ring raceway. The slave point of the other RBE3 element is selected as the geometric center of the inner ring raceway, and the master point is selected as a node on the inner ring raceway. The number of spring elements is equal to the number of bearings.

[0023] Other contacting components are assembled together by defining contact relationships;

[0024] Adjust each component to its ideal assembly position.

[0025] Furthermore, in step two,

[0026] Define the elastic modulus E and Poisson's ratio μ of the materials in the finite element model of each component.

[0027] Furthermore, in step three,

[0028] 31) Establish the bearing finite element model: mesh the rolling elements, outer ring, and inner ring, with finer meshing at the contact positions; assume the outer and inner rings are rigid bodies to obtain the stiffness of the rolling elements alone; define the outer ring rigid body reference point at the geometric center of the outer ring raceway, and define the inner ring rigid body reference point at the geometric center of the inner ring raceway; assemble the contacting components together by defining the contact relationship, and define the position of the rolling element at this time as the first position;

[0029] 32) Define the material properties of the bearing finite element model: Define the elastic modulus E and Poisson's ratio μ of the rolling elements;

[0030] 33) Define the boundary conditions of the bearing finite element model: There are two types of boundary conditions. One is to fully constrain the inner ring rigid body reference point and fix the inner ring. The other is to constrain the rotational degree of freedom of the outer ring rigid body reference point about the bearing centerline.

[0031] 34) Define the loads in the bearing finite element model:

[0032] First load: The first load is the radial load F of the bearing. r Used to calculate the stiffness K of the rolling elements in the radial direction of the bearing. r The point of application is the outer rigid body reference point;

[0033] Second load: The second load is the axial load F of the bearing. a Used to calculate the stiffness K of the rolling elements in the axial direction of the bearing. a The point of application is the outer rigid body reference point;

[0034] Third load: The third load is the bearing's warping load. Used to calculate the stiffness of the rolling elements in a plane perpendicular to the bearing axial direction. The point of application is the outer rigid body reference point;

[0035] 35) Define the calculation conditions for rolling element stiffness:

[0036] First calculation case: includes all boundary conditions in step 33) and the first load in step 34);

[0037] The second calculation case includes all boundary conditions in step 33) and the second load in step 34);

[0038] The third calculation case includes all boundary conditions in step 33) and the third load in step 34);

[0039] 36) Perform finite element analysis of rolling element stiffness:

[0040] Based on the bearing finite element model in step 31), the radial deformation X of the rolling elements is calculated sequentially according to the calculation conditions defined in step 35). r1 Axial deformation X a Warp angle

[0041] 37) Calculate the radial stiffness K of the rolling element. r1 Axial stiffness K a and warpage stiffness Specifically as follows:

[0042]

[0043]

[0044]

[0045] 38) Perform finite element analysis of rolling element stiffness:

[0046] In step 31), all rolling elements in the bearing finite element model are kept in their relative positions. All rolling elements are rotated sequentially along the bearing centerline to the second position, the third position, ..., the nth position. Steps 33) to 35) are repeated at each position to calculate the radial stiffness K of the rolling element at the corresponding position. ri and warpage stiffness Specifically, i takes the values ​​2, 3, ..., n in sequence;

[0047]

[0048]

[0049] When all rolling elements rotate along the bearing centerline to the second position, third position...nth position, the angle between adjacent positions is the same, and the rotation angle is no greater than angle θ. k is the number of rolling elements; n is not less than 3;

[0050] 39) Based on the stiffness calculation values ​​in steps 37) and 38), calculate the average radial stiffness K of the rolling element using the following formula. r Average warpage stiffness

[0051]

[0052]

[0053] Furthermore, in step four,

[0054] First boundary condition: Constrain the end of the support furthest from the connecting screw;

[0055] Second boundary condition: constrain the axial rotational degree of freedom of the output shaft torque output end to simulate the support reaction force of the components driven by the output shaft on the output shaft;

[0056] The third boundary condition constrains the axial translational degree of freedom of the cycloidal wheel to ensure that the cycloidal wheel cannot move arbitrarily along the axial direction.

[0057] Fourth boundary condition: Apply an angular displacement at the torque output end of the output shaft along the rotation centerline of the output shaft;

[0058] The fourth boundary condition applies an angular displacement that causes the output shaft to rotate through at least one tooth relative to the pinion wheel to obtain an effective gear meshing force variation history; the angular displacement applied to the output shaft torque output end when the output shaft rotates by x teeth is calculated using the following formula:

[0059]

[0060] In the formula, z2 is the number of teeth on the pinwheel.

[0061] Furthermore, in step five,

[0062] First load: The first load is the screw preload, which acts on the screw in the direction of the screw axis;

[0063] Second load: The second load is the torque M transmitted by the input shaft, and its direction is along the centerline of the input shaft;

[0064] The torque M is equal to the rated torque of the motor;

[0065] The angular displacement of the fourth boundary condition is in the same direction as the torque M.

[0066] Furthermore, in step six,

[0067] The first calculation case includes the first boundary condition, the second boundary condition, the third boundary condition in step four, and the first load in step five, to simulate the assembly process of the cycloidal pinwheel planetary mechanism.

[0068] Second calculation condition: Based on the first calculation condition, the fourth boundary condition in step four and the second load in step five are applied to simulate the working process of the cycloidal pinwheel planetary mechanism and obtain the gear meshing force change history.

[0069] Furthermore, in step seven,

[0070] Following the calculation condition sequence defined in step six, the quasi-static finite element method is used to perform finite element analysis of the cycloidal pinwheel planetary mechanism, considering geometric nonlinearity. Both the first and second calculation conditions output the cycloidal wheel meshing force for transmission smoothness evaluation. The total calculation time for the first calculation condition is 1 second, and only the cycloidal wheel meshing force in the last step is output. The second calculation condition outputs the cycloidal wheel meshing force change history at an output frequency of no more than 0.01 seconds, and the total calculation time for the second calculation condition is 1 second.

[0071] Furthermore, in step eight,

[0072] Based on the variation history of the cycloidal gear meshing force output under the second calculated working condition, the coefficient of variation C is used. v Evaluate the transmission smoothness of the cycloidal pinwheel planetary mechanism when C vWhen the coefficient of variation is no greater than 5%, the cycloidal pinwheel planetary mechanism has good transmission stability; otherwise, the transmission stability of the cycloidal pinwheel planetary mechanism is poor and requires optimization design. The coefficient of variation is calculated as shown in the following formula.

[0073]

[0074]

[0075]

[0076] In the formula, C v The coefficient of variation is 1. S is the sample mean, S is the sample standard deviation, N is the sample size, and x is the sample size. k This is a sample of the meshing force of the cycloidal wheel.

[0077] Furthermore, in step nine,

[0078] Manufacturing error is equivalent to the positional error of the cycloidal wheel centerline along the tangent direction of the cycloidal wheel's revolution, i.e., the equivalent tangential positional error, as shown in the formula below; assembly error is equivalent to the positional error of the cycloidal wheel centerline along the radius direction of the cycloidal wheel's revolution, i.e., the equivalent radial positional error, as shown in the formula below; manufacturing error and assembly error are combined and applied to the cycloidal wheel using a comprehensive equivalent positional error. The calculation of the comprehensive equivalent positional error is shown in the formula below. Specifically, the cycloidal wheel is deviated from its ideal assembly position by a distance equal to a comprehensive equivalent positional error, to evaluate whether the design of the cycloidal pinwheel planetary mechanism meets the manufacturing process requirements;

[0079]

[0080]

[0081]

[0082] In the formula, △w1 is the equivalent tangential position error; p1 is the input shaft eccentricity error; p2 is the swing arm eccentricity error; p3 is the cycloidal wheel eccentricity error; p4 is the pin wheel eccentricity error; p5 is the output shaft eccentricity error; p6 is the pin hole eccentricity error; △w2 is the equivalent radial position error; a1 is the input shaft assembly error; a2 is the bearing assembly error at the swing arm; a3 is the cycloidal wheel assembly error; a4 is the pin wheel assembly error; a5 is the output shaft assembly error; and △w is the comprehensive equivalent position error.

[0083] The beneficial effects of this invention are as follows:

[0084] 1) This invention establishes a finite element model of the transmission stability of a fully flexible cycloidal pinwheel planetary mechanism, including a support, housing, pinwheel, screw, motor, bushing, cycloidal wheel, output shaft, input shaft, rotating arm, and bearing. It considers the actual stiffness of the components, making it closer to the physical prototype. Constraints are applied to the end of the support away from the screw fixing the support and housing, minimizing their impact on the meshing force between the cycloidal wheel and pinwheel. Loads are applied to the input shaft, ensuring the correct application of the motor torque. These measures effectively achieve accurate prediction of the meshing force between the cycloidal wheel and pinwheel, and a reasonable evaluation of the transmission stability of the cycloidal pinwheel planetary mechanism.

[0085] 2) This invention is based on the actual meshing force variation history between the cycloidal wheel and the pinwheel, calculates the sample mean, sample standard deviation and coefficient of variation of the meshing force variation history, and evaluates the transmission stability of the cycloidal pinwheel planetary mechanism through the coefficient of variation. Compared with dimensional parameters such as average value, root mean square, standard deviation, maximum value and minimum value, the coefficient of variation is a dimensionless parameter. It can be used not only for comparative evaluation of the transmission stability of the same type of cycloidal pinwheel planetary mechanism, but also for comparative analysis of the transmission stability of different types of cycloidal pinwheel planetary mechanisms, and has strong versatility.

[0086] 3) This invention uses spring elements to simulate the rolling elements of the bearing and gives them realistic support stiffness, which effectively reduces the size of the finite element model and improves the calculation speed.

[0087] 4) The present invention simplifies the connection between the bearing inner ring and the rotating arm by using RBE3 and RBE2 units. While ensuring the correct transmission of load, it reduces the torque loss caused by grid jamming, thereby improving the calculation accuracy of the meshing force between the cycloidal wheel and the pin wheel. Attached Figure Description

[0088] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0089] Figure 1 This is a schematic diagram of the overall structure of the cycloidal pinwheel planetary mechanism;

[0090] Figure 2 This is a first schematic diagram of the internal structure of a cycloidal pinwheel planetary mechanism;

[0091] Figure 3 for Figure 2 Enlarged view of local area A in the middle;

[0092] Figure 4This is a second schematic diagram of the internal structure of the cycloidal pinwheel planetary mechanism;

[0093] Figure 5 This is a third schematic diagram of the internal structure of the cycloidal pinwheel planetary mechanism;

[0094] Figure 6 This is a schematic diagram of the input shaft structure;

[0095] Figure 7 A schematic diagram of the RBE3 unit built on the inner ring of the bearing;

[0096] Figure 8 A schematic diagram of the RBE3 unit built on the rotating arm;

[0097] Figure 9 A schematic diagram of the bearing rolling element spring unit to be established;

[0098] Figure 10 A schematic diagram of the finite element model of bearing stiffness when the rolling element is in the first position;

[0099] Figure 11 This is a schematic diagram of the finite element model of the bearing stiffness when the rolling element is in the second position.

[0100] Figure 12 This is a schematic diagram of the finite element model of the bearing stiffness when the rolling element is in the third position.

[0101] Figure 13 A schematic diagram of the RBE3 unit built on the output shaft;

[0102] Figure 14 A schematic diagram of the RBE3 unit built on the cycloidal wheel;

[0103] Figure 15 This is a schematic diagram of the meshing force of the cycloidal wheel;

[0104] Figure 16 A schematic diagram illustrating the application of manufacturing and assembly errors;

[0105] Figure 17 A schematic diagram of the cycloidal wheel meshing force considering manufacturing and assembly errors;

[0106] Figure 18 This is a flowchart of the present invention. Detailed Implementation

[0107] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0108] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0109] like Figure 18 As shown, a method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism includes the following steps:

[0110] Step 1: Construct the assembly finite element model of the cycloidal pinwheel planetary mechanism;

[0111] like Figures 1-6 As shown, the cycloidal pinwheel planetary mechanism includes a support 1000, a first housing 2001, a second housing 2002, a pinwheel 2003, a screw 3000, a motor 4000, a first bushing 5001, a second bushing 5002, a first cycloidal wheel 6001, a second cycloidal wheel 6002, an output shaft 7000, an input shaft 8001, a first rotating arm 8002, a second rotating arm 8003, a first bearing 9001, a second bearing 9002, and a third bearing 9003, wherein the pinwheel 2003 is part of the first housing. The structural features on the body 2001 include the first rotating arm 8002 and the second rotating arm 8003, which are structural features on the input shaft 8001; the third bearing 9003 and bearing 9004 support the two ends of the input shaft 8001 on the second housing 2002 and the first housing 2001, respectively; the first rotating arm 8002 supports the first bearing 9001, and the first bearing 9001 supports the first cycloidal wheel 6001; the second rotating arm 8003 supports the second bearing 9002, and the second bearing 9002 supports the second cycloidal wheel 6002.

[0112] Solid meshing is performed on the support 1000, first housing 2001, second housing 2002, pinwheel 2003, screw 3001, first bushing 5001, bushing 5002, first cycloidal wheel 6001, second cycloidal wheel 6002, output shaft 7000, input shaft 8001, first rotating arm 8002, second rotating arm 8003, and the outer and inner rings of the first bearing 9001, second bearing 9002, and third bearing 9003 in the above structure. The mesh of the contact parts needs to be finely divided, while the mesh of other non-contact parts is coarsely divided, so as to reduce the calculation scale and improve the calculation speed of the model without affecting the force transmission accuracy. The mesh of the contact surface of the bushing 5001 and the housing 2001 is consistent, and the two are connected together through shared nodes. The mesh of the contact surface of the second bushing 5002 and the housing 2002 is consistent, and the two are connected together through shared nodes.

[0113] The bearing inner ring and the swing arm are connected using simplified RBE3 and RBE2 units to ensure correct load transfer while reducing torque loss caused by grid jamming. Taking the connection between bearing 9001 and swing arm 8002 as an example... Figure 7 As shown, the slave point of the inner ring RBE3 unit 90011 of the first bearing 9001 is selected as the first geometric center point 90013 of the inner diameter side surface 90012 of the inner ring of the first bearing 9001, and the master point is selected as the node on the inner diameter side surface 90012 of the bearing inner ring; as shown Figure 8 As shown, the surface 80021 of the first rotating arm 8002 that contacts the inner ring of the first bearing 9001 is shown separately. The RBE3 unit 90015 connecting the first rotating arm 8002 is selected from point 90016 along the bearing center line 90014, offset from point 90013 of the RBE3 unit 90011 connecting the inner ring of the first bearing 9001. The main point is selected from the node on the surface 80021 that contacts the inner diameter of the first bearing 9001.

[0114] The slave point of the RBE3 unit connecting the inner ring of the bearing and the slave point of the RBE3 unit connecting the swing arm are connected by an RBE2 unit. The two slave points connected by the RBE2 unit are only uncoupled in the degree of freedom along the rotational direction of the bearing centerline; all other degrees of freedom are coupled together. Taking the RBE2 unit 90017 connecting slave points 90013 and 90016 as an example, the points 90013 and 90016 connected by it are only uncoupled in the degree of freedom along the rotational direction of the bearing centerline 90014; all other degrees of freedom are coupled together. Figure 8 As shown;

[0115] The rolling elements of the bearing are simplified using spring elements to improve computational efficiency without affecting calculation accuracy. For bearings with outer and inner rings, taking the first bearing 9001 as an example, ... Figure 9 As shown, the two ends of the spring unit 90018 simulating the rolling element of the first bearing 9001 are connected to the slave points of two RBE3 units respectively. The two slave points are located on the bearing centerline 90014. The slave point of one RBE3 unit is selected from the second geometric center 900110 of the raceway of the outer ring 90019, and the master point is selected from the node on the raceway of the outer ring 90019. The slave point of the other RBE3 unit is selected from the third geometric center 900112 of the raceway of the inner ring 900111, and the master point is selected from the node on the raceway of the inner ring 900111. In fact, the geometric center 900110 and the third geometric center 900112 coincide. For the sake of explanation, the two points are shown separately. The total number of spring units simulating the rolling element of the bearing is 4, which is equal to the number of bearings.

[0116] Other contacting components are assembled together by defining contact relationships;

[0117] Without considering manufacturing and assembly errors of the components, adjust each component to the ideal assembly position;

[0118] Step 2: Define the material properties of the finite element model;

[0119] Define the elastic modulus E and Poisson's ratio μ of the materials in the finite element model of each component.

[0120] Among them, the material of support 1000 is aluminum alloy AlSi9Cu3, E=71000MPa, μ=0.33; the material of shell 2001 and shell 2002 is composite material PA66+30%GF, E=10100MPa, μ=0.35; the others are iron alloys, E=210000MPa, μ=0.3;

[0121] Step 3: Define the stiffness of the spring unit used to simulate the rolling element. The radial stiffness K of the rolling element in the radial direction of the bearing. r axial stiffness K of the rolling elements in the bearing axial direction a Warping stiffness of rolling elements in a plane perpendicular to the bearing axial direction Specifically as follows:

[0122] 31) Establish the finite element model of the bearing: Taking the second bearing 9002 as an example, such as... Figure 10 As shown, the rolling element 900213, outer ring 90029, and inner ring 900211 of the second bearing 9002 are meshed. The mesh at the contact points needs to be finely divided to improve load transfer accuracy and deformation calculation accuracy. The outer ring 90029 and inner ring 900211 are assumed to be rigid bodies to obtain the stiffness of the rolling element 900213 alone. The reference point for the outer ring rigid body is defined at the fourth geometric center 900210 of the raceway of the outer ring 90029, and the reference point for the inner ring rigid body is defined at the fifth geometric center 900212 of the raceway of the inner ring 900211. In reality, the fourth geometric center 900210 and the fifth geometric center 900212 coincide; however, for ease of explanation... Figure 9 The two points are displayed separately; the contacting parts are assembled together by defining the contact relationship; Figure 10 The position of the rolling element shown is defined as the first position;

[0123] 32) Define the material properties of the bearing finite element model: Define the elastic modulus of the rolling element as E = 210000 MPa and the Poisson's ratio as μ = 0.3;

[0124] 33) Define the boundary conditions of the bearing finite element model: The boundary conditions include two types. One is to fully constrain the inner ring rigid body reference point 900212 and fix the inner ring 900211. The other is to constrain the rotational degree of freedom of the outer ring rigid body reference point 900210 around the bearing center line 90024, so as to ensure that the outer ring 900211 cannot rotate freely around the bearing center line and improve the convergence speed of the simulation calculation.

[0125] 34) Define the loads in the bearing finite element model:

[0126] First load: The first load is the radial load F of the bearing. r F r =10000N, which is used to calculate the stiffness K of the rolling element in the radial direction of the bearing. r The point of application is the outer rigid body reference point 900210;

[0127] Second load: The second load is the axial load F of the bearing. a F a =10000N, which is used to calculate the stiffness K of the rolling element in the axial direction of the bearing. a The point of application is the outer rigid body reference point 900210;

[0128] Third load: The third load is the bearing's warping load. It is used to calculate the stiffness of the rolling elements in a plane perpendicular to the bearing axial direction. The point of application is the outer rigid body reference point 900210;

[0129] 35) Define the calculation conditions for rolling element stiffness:

[0130] First calculation case: includes all boundary conditions in step 33) and the first load in step 34);

[0131] The second calculation case includes all boundary conditions in step 33) and the second load in step 34);

[0132] The third calculation case includes all boundary conditions in step 33) and the third load in step 34);

[0133] 36) Perform finite element analysis of rolling element stiffness:

[0134] Based on the bearing finite element model in step 31), the radial deformation X of the rolling elements is calculated sequentially according to the calculation conditions defined in step 35). r1 Axial deformation X a Warp angle The calculated value is as follows: X r1 =0.03692mm, X a =0.02782mm,

[0135] 37) Calculate the radial stiffness K of the rolling element. r1 Axial stiffness K a and warpage stiffness See calculation formulas (1) to (3) for details;

[0136]

[0137]

[0138]

[0139] The calculated value is as follows: K r1 =270856 N / mm, K a =359456 N / mm

[0140] 38) Perform finite element analysis of rolling element stiffness:

[0141] Step 31) Keeping the relative positions of all rolling elements in the bearing finite element model unchanged, rotate all rolling elements sequentially along the bearing centerline to the second position 2, the third position, as follows: Figure 11 As shown, at this time n=3, the angle between two adjacent positions is 20°, which is less than the angle θ, thus meeting the requirements; according to Since k equals the number of rolling elements (6), we know that θ = 30°.

[0142] Repeat steps 33) to 35) at each position, and calculate the radial stiffness K of the rolling element corresponding to the second and third positions using formulas (4) to (5). ri and warpage stiffness i takes the values ​​2 and 3 in sequence;

[0143]

[0144]

[0145] Second position: K r2 =268673 N / mm

[0146] Third position: K r3 =268025 N / mm

[0147] 39) Based on the stiffness calculation values ​​in steps 37) and 38), calculate the average radial stiffness K of the rolling element using formulas (6) to (7). r Average warpage stiffness

[0148]

[0149]

[0150] Mean radial stiffness K r =269184 N / mm, average warping stiffness

[0151] Step 4: Define the boundary conditions for the finite element model;

[0152] First boundary condition: Constrain the end 1001 of support 1000 away from connecting screw 3000, such as Figure 1 As shown;

[0153] Second boundary condition: Constrain the axial rotational degree of freedom of the 7000 torque output end of the output shaft to simulate the support reaction force of the components driven by the output shaft on the output shaft; the specific application method is as follows: Figure 13 As shown, an RBE3 element 7004 is established with a point 7002 on the center line 7001 of the output shaft 7000 as the slave point and a node on the torque output end face 7003 of the output shaft as the master point, and the rotational degree of freedom of the slave point 7002 about the center line 7001 is constrained.

[0154] The third boundary condition constrains the axial translational degrees of freedom of the first cycloidal wheel 6001 and the second cycloidal wheel 6002 to ensure that the cycloidal wheels cannot move arbitrarily along the axial direction, thereby improving the convergence of the simulation calculation. The method of applying the axial translational degrees of freedom is illustrated using the first cycloidal wheel 6001 as an example. Figure 14 As shown, an RBE3 element 60014 is established with a point 60012 on the center line 60011 of the first cycloidal wheel 6001 as the slave point and a node on the end face 60013 of the cycloidal wheel 6001 away from the first bearing 9001 as the master point, and the translational degree of freedom of the slave point 60012 along the center line 60011 is constrained.

[0155] Fourth boundary condition: such as Figure 13 As shown, along the rotation center line 7001 of the output shaft 7000, an angular displacement θ is applied from point 7002 at the torque output end RBE3 unit 7004 of the output shaft. Specifically, an angular displacement θ is applied along the positive direction of the Z-axis of the coordinate system 7005, and the Z-axis coincides with the center line 7001. In order to obtain an effective gear meshing force change history and save computing resources, the applied angular displacement should be able to make the output shaft 7000 rotate by one tooth relative to the pin wheel 2003, that is, x = 1. The angular displacement θ calculated according to formula (8) is 0.105 rad.

[0156] The angular displacement applied to the torque output end of the output shaft is calculated using formula (8) when the output shaft rotates by x teeth:

[0157]

[0158] In the formula, z2 is the number of teeth on the pinwheel.

[0159] Step 5: Define the loads in the finite element model;

[0160] First load: The first load is the screw preload, which acts on screw 3000 in the direction of the screw axis;

[0161] Second load: The second load is the torque M transmitted by the input shaft 8001, which is equal to the rated torque of the motor 4000, 0.3 Nm, and is directed along the center line of the input shaft. The direction is consistent with the direction of the angular displacement θ of the boundary condition 4 in step four.

[0162] Step 6: Define the calculation conditions;

[0163] The first calculation condition includes the first boundary condition, the second boundary condition, the boundary condition 3 in step four, and the first load in step five, to simulate the assembly process of the cycloidal pinwheel planetary mechanism.

[0164] Second calculation condition: Based on the first calculation condition, the fourth boundary condition in step four and the second load in step five are applied to simulate the working process of the cycloidal pinwheel planetary mechanism and obtain the gear meshing force change history.

[0165] Step 7: Perform finite element analysis;

[0166] Following the calculation condition sequence defined in step six, the quasi-static finite element method is used to perform finite element analysis of the cycloidal pinwheel planetary mechanism, considering geometric nonlinearity. Both the first and second calculation conditions output the meshing force of the first cycloidal wheel 6001 and the second cycloidal wheel 6002 for transmission smoothness evaluation. The calculated meshing forces of the first cycloidal wheel 6001 and the second cycloidal wheel 6002 are as follows: Figure 15 As shown; the total calculation time for the first calculation condition is 1 second, and only the cycloidal wheel meshing force in the last step is output to save disk space; the second calculation condition outputs the cycloidal wheel meshing force change process at an output frequency of no more than 0.01 seconds to accurately capture the change of the cycloidal wheel meshing force, and the total calculation time for the second calculation condition is 1 second.

[0167] Step 8: Evaluate the transmission smoothness of the cycloidal pinwheel planetary mechanism;

[0168] Based on the variation history of the cycloidal gear meshing force output under the second calculated working condition, the coefficient of variation C is used. v Evaluate the transmission smoothness of the cycloidal pinwheel planetary mechanism when C v When the transmission smoothness of the cycloidal pinwheel planetary mechanism is not greater than 5%, the transmission smoothness is good; otherwise, the transmission smoothness of the cycloidal pinwheel planetary mechanism is poor and the design needs to be optimized.

[0169] Depend on Figure 15 According to the data and the formulas (9) to (11) for calculating the coefficient of variation, the sample mean of cycloidal wheel 6001 is 454.7N, the sample standard deviation is 2.02N, and the coefficient of variation is 0.44%; the sample mean of cycloidal wheel 6002 is 250.5N, the sample standard deviation is 1.57N, and the coefficient of variation is 0.63%. The coefficients of variation of both cycloidal wheels are less than 5%. Without considering manufacturing errors and assembly errors, the cycloidal pinwheel planetary mechanism has good transmission stability.

[0170]

[0171]

[0172]

[0173] In the formula, C v The coefficient of variation is 1. S is the sample mean, S is the sample standard deviation, N is the sample size, and x is the sample size. k This is a sample of the meshing force of the cycloidal wheel.

[0174] Step 9: Based on manufacturing and assembly errors, repeat steps S6 to S8 to evaluate the transmission smoothness of the cycloidal pinwheel.

[0175] Manufacturing error is equivalent to the position error of the cycloidal wheel centerline along the tangent of the cycloidal wheel's revolution, i.e., the equivalent tangential position error, as shown in calculation formula (12); assembly error is equivalent to the position error of the cycloidal wheel centerline along the radius of the cycloidal wheel's revolution, i.e., the equivalent radial position error, as shown in calculation formula (13); manufacturing error and assembly error are applied to the cycloidal wheel using a comprehensive equivalent position error, and the comprehensive equivalent position error is calculated using formula (14). Specifically, the cycloidal wheel is deviated from the ideal assembly position by a distance equal to a comprehensive equivalent position error, in order to evaluate whether the design of the cycloidal pinwheel planetary mechanism meets the manufacturing process requirements;

[0176]

[0177]

[0178]

[0179] In the formula, △w1 is the equivalent tangential position error; p1 is the input shaft eccentricity error; p2 is the swing arm eccentricity error; p3 is the cycloidal wheel eccentricity error; p4 is the pin wheel eccentricity error; p5 is the output shaft eccentricity error; p6 is the pin hole eccentricity error; △w2 is the equivalent radial position error; a1 is the input shaft assembly error; a2 is the bearing assembly error at the swing arm; a3 is the cycloidal wheel assembly error; a4 is the pin wheel assembly error; a5 is the output shaft assembly error; and △w is the comprehensive equivalent position error.

[0180] In the embodiment, the manufacturing error and assembly error of the parts are shown in Table 1. Substituting the specific values ​​into formulas (12) to (14) yields Δw1 = 0.056 mm, Δw2 = 0.031 mm, and Δw = 0.064 mm. The corresponding application process is as follows: Figure 16 As shown, based on step one, the first cycloidal wheel 6001, RBE3 unit 60014, outer ring 90019, inner ring 900111, spring unit 90018, and the RBE3 unit connected to both ends of spring unit 90018 are first moved △w1 in the opposite direction of the revolution of the first cycloidal wheel 6001, and then moved △w2 in the direction of the line connecting the center line 60011 and the center line 7001;

[0181] Table 1 Component Error Values

[0182]

[0183]

[0184] Repeat steps six through eight to calculate the meshing force of the first cycloidal wheel 6001 and the meshing force of the second cycloidal wheel 6002 as follows: Figure 17 As shown, by Figure 17 According to the data and the formulas (9) to (11) for calculating the coefficient of variation, the sample mean of the first cycloidal wheel 6001 is 558.5N, the sample standard deviation is 169.3N, and the coefficient of variation is 30.31%; the sample mean of the second cycloidal wheel 6002 is 298.5N, the sample standard deviation is 131.7N, and the coefficient of variation is 44.13%. The coefficients of variation of both cycloidal wheels are greater than 5%. Therefore, after considering the manufacturing error and assembly error, the coefficient of variation of the meshing force between the cycloidal wheel and the pinwheel is relatively large. In the future, the manufacturing error and assembly error of the cycloidal pinwheel planetary mechanism should be strictly controlled to reduce the coefficient of variation of the meshing force and improve the transmission stability of the cycloidal pinwheel planetary mechanism.

[0185] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the invention. Further modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method of evaluating transmission smoothness of a cycloidal pin wheel planetary mechanism, characterized by, Includes the following steps: Step 1: Construct the assembly finite element model of the cycloidal pinwheel planetary mechanism; Step 2: Define the material properties of the finite element model; Step three, defining the stiffness of the spring unit simulating the rolling element in the radial direction of the bearing, the radial stiffness of the rolling element in the radial direction of the bearing , the axial stiffness of the rolling element in the axial direction of the bearing and the warping stiffness of the rolling element in the plane perpendicular to the axial direction of the bearing ; Step 4: Define the boundary conditions for the finite element model; Step 5: Define the loads in the finite element model; Step 6: Define the calculation conditions; Step 7: Perform finite element analysis; Step 8: Evaluate the transmission smoothness of the cycloidal pinwheel planetary mechanism; Step 9: Based on manufacturing and assembly errors, repeat steps 6 to 8 to evaluate the transmission smoothness of the cycloidal pinwheel. Among them, step one, The cycloidal pinwheel planetary mechanism includes a support, housing, pinwheel, screw, motor, bushing, cycloidal wheel, output shaft, input shaft, rotating arm, and bearing. The support, housing, pinwheel, screw, bushing, cycloidal wheel, output shaft, input shaft, rotating arm, bearing outer ring, and bearing inner ring are divided into solid meshes. The meshes of the contact parts are finely divided, and the meshes of other non-contact parts are coarsely divided. The bearing inner ring and the swing arm are connected using RBE3 and RBE2 elements for a simplified connection. The slave point of the RBE3 element connecting the bearing inner ring is selected from the geometric center point of the inner diameter side surface of the bearing inner ring, and the master point is selected from a node on the inner diameter side surface of the bearing inner ring. The slave point of the RBE3 element connecting the swing arm is selected from a point along the bearing centerline that is offset from the slave point of the RBE3 element connecting the bearing inner ring, and the master point is selected from a node on the surface in contact with the bearing inner diameter. The slave points of the RBE3 element connecting the bearing inner ring and the slave point of the RBE3 element connecting the swing arm are connected using RBE2 elements. The two slave points connected by the RBE2 element are only uncoupled in the degree of freedom along the rotation direction of the bearing centerline, while all other degrees of freedom are coupled together. The rolling elements of the bearing are simplified using spring elements. For bearings with outer and inner rings, the nodes at both ends of the spring element simulating the rolling elements are connected to the slave points of two RBE3 elements. The two slave points are located on the geometric center line of the bearing. The slave point of one RBE3 element is selected as the geometric center of the outer ring raceway, and the master point is selected as a node on the outer ring raceway. The slave point of the other RBE3 element is selected as the geometric center of the inner ring raceway, and the master point is selected as a node on the inner ring raceway. The number of spring elements is equal to the number of bearings. Other contacting components are assembled together by defining contact relationships; Adjust each component to its ideal assembly position; Step four, First boundary condition: Constrain the end of the support furthest from the connecting screw; Second boundary condition: constrain the axial rotational degree of freedom of the output shaft torque output end to simulate the support reaction force of the components driven by the output shaft on the output shaft; The third boundary condition constrains the axial translational degree of freedom of the cycloidal wheel to ensure that the cycloidal wheel cannot move arbitrarily along the axial direction. Fourth boundary condition: Apply an angular displacement at the torque output end of the output shaft along the rotation centerline of the output shaft; The fourth boundary condition applies an angular displacement that causes the output shaft to rotate through at least one tooth relative to the pinwheel to obtain an effective gear meshing force variation history; the output shaft rotates. The angular displacement applied to the output shaft torque output end is calculated using the following formula: （8） In the formula, This refers to the number of teeth on the pinwheel. Step five, First load: The first load is the screw preload, which acts on the screw in the direction of the screw axis; Second load: The second load is the torque transmitted by the input shaft. The direction is along the centerline of the input shaft; The torque Its size is equal to the rated torque of the motor; The angular displacement and torque of the fourth boundary condition Same direction; Step six, The first calculation case includes the first boundary condition, the second boundary condition, the third boundary condition in step four, and the first load in step five, to simulate the assembly process of the cycloidal pinwheel planetary mechanism. Second calculation condition: Based on the first calculation condition, the fourth boundary condition in step four and the second load in step five are applied to simulate the working process of the cycloidal pinwheel planetary mechanism and obtain the gear meshing force change history. Step eight, Based on the variation history of the cycloidal gear meshing force output under the second calculated operating condition, the coefficient of variation is used. Evaluate the transmission smoothness of the cycloidal pinwheel planetary mechanism when When the coefficient of variation is no greater than 5%, the cycloidal pinwheel planetary mechanism has good transmission stability; otherwise, the cycloidal pinwheel planetary mechanism has poor transmission stability and requires optimized design. The coefficient of variation is calculated as shown in the following formula. （9） （10） （11） In the formula, The coefficient of variation is 1. The sample mean. The standard deviation of the sample. For the sample size, This is a sample of the meshing force of the cycloidal wheel.

2. The method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism according to claim 1, characterized in that, Step two, Define the elastic modulus of the materials in the finite element model of each component. Poisson's ratio .

3. The method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism according to claim 1, characterized in that, Step three 31) Establish the bearing finite element model: mesh the rolling elements, outer ring, and inner ring, with finer meshing at the contact positions; assume the outer and inner rings are rigid bodies to obtain the stiffness of the rolling elements alone; define the outer ring rigid body reference point at the geometric center of the outer ring raceway, and define the inner ring rigid body reference point at the geometric center of the inner ring raceway; assemble the contacting components together by defining the contact relationship, and define the position of the rolling element at this time as the first position; 32) Define the material properties of the bearing finite element model: Define the elastic modulus of the rolling elements. Poisson's ratio ; 33) Define the boundary conditions of the bearing finite element model: There are two types of boundary conditions. One is to fully constrain the inner ring rigid body reference point and fix the inner ring. The other is to constrain the rotational degree of freedom of the outer ring rigid body reference point about the bearing center line. 34) Define the loads in the bearing finite element model: First load: The first load is the radial load of the bearing. Used to calculate the stiffness of the rolling elements in the radial direction of the bearing. The point of application is the outer rigid body reference point; Second load: The second load is the axial load of the bearing. Used to calculate the stiffness of the rolling elements in the axial direction of the bearing. The point of application is the outer rigid body reference point; Third load: The third load is the bearing's warping load. Used to calculate the stiffness of the rolling elements in a plane perpendicular to the bearing axial direction. The point of application is the outer rigid body reference point; 35) Define the calculation conditions for rolling element stiffness: First calculation case: includes all boundary conditions in step 33) and the first load in step 34); The second calculation case includes all boundary conditions in step 33) and the second load in step 34); The third calculation case includes all boundary conditions in step 33) and the third load in step 34); 36) Perform finite element analysis of the rolling element stiffness: Based on the bearing finite element model in step 31), the radial deformation of the rolling elements is calculated sequentially according to the calculation conditions defined in step 35). Axial deformation Warp angle ; 37) Calculate the radial stiffness of the rolling element. axial stiffness and warpage stiffness The details are as follows: （1） （2） （3）； 38) Perform finite element analysis of rolling element stiffness: In step 31), all rolling elements in the bearing finite element model remain in their relative positions, and all rolling elements are rotated sequentially along the bearing centerline to the second position, the third position, and so on. The position is determined, and steps 33) through 35) are repeated at each position to calculate the radial stiffness of the rolling element at the corresponding position. and warpage stiffness The details are as follows: Take 2, 3... in sequence ; （4） （5） All rolling elements rotate along the bearing centerline to the second position, the third position, and so on. When positioning, the angles between adjacent positions are the same, and the rotation angle is no greater than the angle. , , The number of rolling elements; Not less than 3; 39) Based on the stiffness calculation values ​​in steps 37) and 38), calculate the average radial stiffness of the rolling element using the following formula. Average warpage stiffness ; （6） （7）。 4. The method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism according to claim 1, characterized in that, Step seven, Following the calculation condition sequence defined in step six, the quasi-static finite element method is used to perform finite element analysis of the cycloidal pinwheel planetary mechanism in sequence, considering geometric nonlinearity. Both the first calculation condition 1 and the second calculation condition output the cycloidal wheel meshing force for the purpose of evaluating transmission smoothness. The total calculation time for the first calculation condition is 1 second, and only the cycloidal wheel meshing force in the last step is output. The second calculation condition outputs the cycloidal wheel meshing force change history at an output frequency of no more than 0.01 seconds, and the total calculation time for the second calculation condition is 1 second.

5. The method for evaluating the transmission smoothness of a cycloidal pinwheel planetary mechanism according to claim 1, characterized in that, Step nine, Manufacturing error is equivalent to the positional error of the cycloidal wheel centerline along the tangent direction of the cycloidal wheel's revolution, i.e., the equivalent tangential positional error, as shown in the formula below; assembly error is equivalent to the positional error of the cycloidal wheel centerline along the radius direction of the cycloidal wheel's revolution, i.e., the equivalent radial positional error, as shown in the formula below; manufacturing error and assembly error are combined and applied to the cycloidal wheel using a comprehensive equivalent positional error. The calculation of the comprehensive equivalent positional error is shown in the formula below. Specifically, the cycloidal wheel is deviated from its ideal assembly position by a distance equal to a comprehensive equivalent positional error, to evaluate whether the design of the cycloidal pinwheel planetary mechanism meets the manufacturing process requirements; （12） （13） （14） In the formula, This is the equivalent tangential position error; This refers to the input shaft eccentricity error; This refers to the eccentricity error of the swing arm; This refers to the eccentricity error of the cycloidal wheel; This refers to the error caused by the eccentricity of the needle wheel. This refers to the output shaft eccentricity error. This is due to the eccentricity error of the pin hole; This is the equivalent radial position error; This refers to the assembly error of the input shaft. This is due to the bearing assembly error at the swing arm. This is due to assembly error of the cycloidal wheel; This is due to assembly error of the pinwheel; This refers to the assembly error of the output shaft. This is to comprehensively assess the equivalent positional error.

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