Design method of non-circular gear planetary gear train based on motion envelope

Abstract

The invention relates to the technical field of gear design, and discloses a design method of a non-circular gear planetary gear train based on motion envelope, comprising the following steps: step 1, solving pitch curves of the non-circular gear planetary gear train, including a pitch curve equation of a sun gear and a pitch curve equation of an inner gear ring; step 2, establishing a non-circular gear blank and assembling the non-circular gear blank with a slotting cutter; 3, performing motion enveloping to obtain a non-circular gear tooth profile; and step 4, optimizing the precision of the tooth profile of the non-circular gear. According to the design method of the non-circular gear planetary gear train based on the motion envelope, the model of the non-circular gear planetary gear train is established based on the UG motion envelope and generating principle, the surface precision of the non-circular gear planetary gear train is optimized, and the design method has the advantages of being high in calculation precision, high in efficiency, high in flexibility and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of gear design, and in particular to a design method of a non-circular gear planetary gear train based on a motion envelope. Background Art

[0002] Non-circular gear hydraulic motor is a new type of low-speed high-torque motor. It is widely used because of its compact structure, strong impact resistance, high volumetric efficiency and other advantages, and has high industrial value. Non-circular gear planetary mechanism is the core component of non-circular gear hydraulic motor. Due to the difficulty of designing and processing non-circular gears, it is subject to certain limitations in structural design and practical application. Extensive research has been conducted on the design of non-circular gear planetary gear trains at home and abroad. At present, the methods for tooth profile design of non-circular gear planetary gear trains are divided into numerical calculation method and Fancheng simulation method. The numerical calculation method uses the principle of gear meshing to calculate the tooth profile coordinates. Its design accuracy is high, but the design difficulty is relatively large; the Fancheng simulation method uses the processing principle of non-circular gears to simulate the Fancheng motion between the tool and the gear blank to obtain the non-circular gear tooth profile entity. Generally, it needs to be combined with secondary development of three-dimensional software. The design is not easy and it is easy to produce cutting marks, so that the accuracy of the tooth profile cannot meet the production requirements. Summary of the invention

[0003] In order to solve the technical problems raised in the background technology, the present invention provides a design method for a non-circular gear planetary gear train based on motion envelope.

[0004] The present invention is implemented by the following technical solution: a design method of a non-circular gear planetary gear train based on motion envelope, comprising the following steps:

[0005] Step 1, solving the pitch curve of the non-circular gear planetary gear train, including the pitch curve equation of the sun gear and the pitch curve equation of the inner gear ring;

[0006] Step 2: Create a non-circular gear blank and assemble it with a gear shaping cutter;

[0007] Step 3: Get the non-circular gear tooth profile by motion envelope;

[0008] Step 4: Optimize the accuracy of the non-circular gear tooth profile.

[0009] Preferably, the step 1 is specifically as follows:

[0010] Establish a coordinate system, take the center of the sun gear as the origin, and establish a fixed coordinate system S0-O0x0y0 in space; set the center of the gear shaping cutter as the origin, and establish a coordinate system S fixed at the center of the gear shaping cutter f -O f x f y f and the coordinate system S describing the movement of the gear shaping cutter m-O m x m y m ;

[0011] In the initial position, S f -O f x f y f , S p -O p x p y p The directions of the coordinate axes are consistent. When the gear cutter rotates by an angle When S m -O m x m y m Relative to S f -O f x f y f Rotate angle accordingly S m -O m x m y m To S f -O f x f y f The coordinate transformation matrix is:

[0012]

[0013] Let S f -O f x f y f Origin O f The coordinates in S-Oxy are (x f ,y f ),S f -O f x f y f The coordinate transformation matrix to S-Oxy is:

[0014]

[0015] Then the gear cutter tooth profile (x0, y0) can be obtained by S m -O m x m y m After the coordinate transformation, the coordinates under S0-O0x0y0 are:

[0016]

[0017] From formula (3), we can only obtain the coordinates (xf, yf) of point Of in S0-O0x0y0 and the tooth profile of the gear shaping cutter in S m -O m x m y m The coordinates (x m ,y m ) to get the envelope graph.

[0018] The pitch curve of the sun gear is a high-order elliptical gear, and its pitch curve equation is:

[0019]

[0020] Where k, θ1, and A are eccentricity, polar angle, and major axis radius, respectively.

[0021] The closing condition of the pitch curve between the sun gear and the inner ring gear is:

[0022]

[0023] In the formula, μ1 is the angle between the tangent and the radial direction of the driving wheel, which can be determined by the following formula:

[0024]

[0025] In order to ensure that all gear teeth are evenly spaced along the pitch curve and that each gear has the same module, the number of teeth z and the module m should satisfy the following equation:

[0026]

[0027] Where L is the arc length of the pitch curve.

[0028] According to the basic motion relationship of non-circular planetary gears, the pitch curve equation of the inner gear ring is:

[0029]

[0030] The conditions for a non-circular gear planetary gear train to not produce motion interference during operation are:

[0031] r 3min ≥r 1max +2h a (9)

[0032] Finally, the sun gear pitch curve data is calculated by combining formula (4)-formula (7), and then the inner gear ring pitch curve data is obtained by formula (8) and substituted into formula (9) for verification.

[0033] Preferably, the step 2 is specifically as follows:

[0034] Step 2.1, according to the pitch curve equation calculated in step 1, obtain the pitch curve point data of the non-circular gear planetary gear train through MATLAB, export the point data as a TXT file, and then import it into the three-dimensional software UG and perform curve fitting to obtain the pitch curves of the sun gear and the inner ring gear;

[0035] Step 2.2, offset the pitch curve of the sun gear by the distance of the tooth top height to obtain the tooth top curve;

[0036] Step 2.3, using curve stretching to obtain the sun gear blank entity;

[0037] Step 2.4, perform the same operation on the inner gear ring to obtain the inner gear ring entity;

[0038] Step 2.5: Use CAXA CAD electronic drawing board to input the planetary gear parameters and obtain the planetary gear entity.

[0039] Step 2.6: Assemble the sun gear blank entity and the gear shaping cutter entity properly.

[0040] Preferably, the step 2.6 is specifically as follows:

[0041] The sun gear and the gear shaping cutter, the inner gear ring and the gear shaping cutter are assembled at the same place, and the pitch circle of the gear shaping cutter is set to be tangent to the pitch curve of the sun gear to ensure the accuracy of subsequent motion simulation;

[0042] In order to ensure that the pitch circle of the gear shaping cutter is always in a tangent relationship with the sun gear pitch curve, the gear shaping cutter pitch circle component is called to perform contact constraint at the tangent position;

[0043] Create an auxiliary link through sketching to control the movement of the gear shaping cutter during the molding process.

[0044] Preferably, the step of obtaining the tooth profile of the sun gear in step 3 is the same as the step of obtaining the tooth profile of the inner ring gear, and the step of obtaining the tooth profile of the sun gear is as follows:

[0045] Carry out the steps of "Define the kinematic body - Establish kinematic pairs - Create constraints - Calculate and solve - Motion envelope" for the model assembled in step 2;

[0046] The purpose of applying a revolute pair to the auxiliary connecting rod is to give a certain initial velocity to the gear shaping cutter;

[0047] Constraints are set between the pitch circle of the gear shaping cutter and the pitch curve of the sun gear. The purpose is to ensure that the gear shaping cutter is always tangent to the pitch curve of the sun gear and performs pure rolling during its rotation.

[0048] A constraint is set between the center of the pitch circle of the gear shaping cutter and the auxiliary connecting rod, the purpose of which is to drive the gear shaping cutter to move together;

[0049] In the solution, the tooth profile accuracy and the computing power of the computer are comprehensively considered, the calculation step is set at a reasonable value, and a certain motion time is defined for motion simulation;

[0050] After the solution is successful, the motion envelope is set, the gear shaping cutter is selected as the envelope object, and the envelope generated by the planetary gear is obtained; after the envelope is converted into a convergent body, the projection curve of the envelope is obtained through the projection command;

[0051] The tooth profile curve is trimmed to obtain the tooth profile curve of the sun gear.

[0052] Preferably, the step 4 is specifically as follows:

[0053] Use SOLIDWORKS to open the IGS file of the tooth profile model obtained in step 3, insert a certain number of points evenly on each line of the tooth profile curve, and output it as an SLDPRT file;

[0054] Use UG to export the file as a PRT file, and then export it as a DWG file. At this time, the point components become points on the sketch;

[0055] After the curve fitting operation, the single tooth profile curve is obtained;

[0056] The curve is further smoothed, and the angle threshold and distance threshold are controlled to make the NURBS curve second-order continuous. After the tooth profile curve is smoothed, the optimized tooth profile curve is finally obtained.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] The design method of the non-circular gear planetary gear train based on motion envelope proposed in the present invention establishes a model of the non-circular gear planetary gear train based on UG motion envelope and Fan Cheng principle, optimizes its surface accuracy, and has the advantages of high calculation accuracy, high efficiency, strong flexibility, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 The schematic diagram of the arrangement of the gear shaping cutter and the non-circular gear blank;

[0060] Figure 2 A schematic diagram of the gear shaping cutter provided in the present invention performing gear shaping motion on the outside of a non-circular gear;

[0061] Figure 3 The pitch curve diagram of the sun gear and the inner gear ring obtained by fitting the curve in UG according to the design method proposed in the present invention;

[0062] Figure 4 It is a model assembly diagram of the sun gear model and the gear shaping cutter in the design method proposed by the present invention;

[0063] Figure 5 The design method proposed in the present invention selects the gear shaping cutter as the envelope object to obtain the envelope body generated by the planetary gear;

[0064] Figure 6 A tooth profile curve diagram of the sun gear obtained in the design method proposed by the present invention;

[0065] Figure 7 A tooth profile curve diagram of the inner gear ring obtained in the design method proposed by the present invention;

[0066] Figure 8 A single tooth profile model diagram obtained by the design method proposed in the present invention;

[0067] Fig. 9 A single tooth profile curve diagram after smoothing optimization obtained in the design method proposed in the present invention;

[0068] Fig.10 The optimized sun gear tooth profile curve diagram obtained after the tooth profile curve is smoothed in the design method proposed by the present invention;

[0069] Fig.11 It is a graph of the optimized tooth profile curve of the inner gear ring obtained after the tooth profile curve is smoothed in the design method proposed by the present invention;

[0070] Fig.12 This is a solid model assembly drawing of the sun gear, planetary gears and inner ring gear of the non-circular gear planetary gear train obtained by the design method proposed in the present invention. DETAILED DESCRIPTION

[0071] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods. It should be noted that, under the premise of no conflict, the various embodiments or technical features described below can be arbitrarily combined to form a new embodiment.

[0072] Example: Refer to Figure 1-Figure 12 This scheme takes a non-circular gear planetary gear train with known basic parameters as an example, and designs a non-circular gear planetary gear mechanism according to the design method proposed by the present invention. The design parameters of the non-circular gear planetary gear train are shown in Table 1.

[0073] Table 1- Basic parameters of non-circular gear planetary gear train

[0074]

[0075] like Figure 1As shown in the figure, the gear shaping cutter performs linear reciprocating motion in the axial direction of the non-circular gear, assisting the cutter movement to perform the main cutting motion; during the main cutting motion, the gear shaping cutter performs feed motion in the radial direction; when the non-circular gear rotates an angle, the gear shaping cutter also rotates a corresponding angle to perform the tooth splitting and developing motion. The gear profile of the non-circular gear is obtained through multiple cutting motions of the gear shaping cutter. In the analysis process, the gear shaping process is equivalent to the pure rolling of the gear shaping cutter pitch circle and the non-circular gear pitch curve. In the pure rolling process, the gear shaping cutter shapes the required tooth profile on the non-circular gear blank.

[0076] like Figure 2 As shown, the analytical expression of the envelope process is obtained by coordinate transformation. Establish a coordinate system, take the center of the sun gear as the origin, and establish a spatial fixed coordinate system S0-O0x0y0; set the center of the gear shaping cutter as the origin, and establish a coordinate system S fixed at the center of the gear shaping cutter f -O f x f y f and the coordinate system S describing the movement of the gear shaping cutter m -O m x m y m . In the initial position, S f -O f x f y f , S p -O p x p y p The directions of the coordinate axes are consistent. When the gear cutter rotates by an angle When S m -O m x m y m Relative to S f -O f x f y f Rotate angle accordingly S m -O m x m y m To S f -O f x f y f The coordinate transformation matrix is:

[0077]

[0078] Let S f -O f x f y f Origin O f The coordinates in S-Oxy are (xf ,y f ),S f -O f x f y f The coordinate transformation matrix to S-Oxy is:

[0079]

[0080] Then the gear cutter tooth profile (x0, y0) can be obtained by S m -O m x m y m After the coordinate transformation, the coordinates under S0-O0x0y0 are:

[0081]

[0082] From formula (3), we can only obtain the coordinates (xf, yf) of point Of in S0-O0x0y0 and the tooth profile of the gear shaping cutter in S m -O m x m y m The coordinates (x m ,y m ) to get the envelope graph. The method of establishing the envelope graph of the inner gear ring is the same as that of the sun gear, so it will not be repeated.

[0083] The pitch curve of the sun gear is a high-order elliptical gear, and its pitch curve equation is:

[0084]

[0085] Where k, θ1, and A are eccentricity, polar angle, and major axis radius, respectively.

[0086] The closing condition of the pitch curve between the sun gear and the inner ring gear is:

[0087]

[0088] In the formula, μ1 is the angle between the tangent and the radial direction of the driving wheel, which can be determined by the following formula:

[0089]

[0090] In order to ensure that all gear teeth are evenly spaced along the pitch curve and that each gear has the same module, the number of teeth z and the module m should satisfy the following equation:

[0091]

[0092] Where L is the arc length of the pitch curve.

[0093] According to the basic motion relationship of non-circular planetary gears, the pitch curve equation of the inner gear ring is:

[0094]

[0095] The conditions for a non-circular gear planetary gear train to not produce motion interference during operation are:

[0096] r 3min ≥r 1max +2h a (9)

[0097] The sun gear pitch curve data is calculated by using equations (4) to (7) simultaneously, and then the inner gear ring pitch curve data is obtained by equation (8) and substituted into equation (9) for verification.

[0098] like Figure 3 As shown, according to the pitch curve equation, the non-circular gear planetary gear train pitch curve point data is obtained through MATLAB, the point data is exported as a TXT file, imported into the three-dimensional software UG and fitted to obtain the pitch curves of the sun gear and the inner ring gear. The pitch curve of the sun gear is offset by the distance of the tooth top height to obtain the tooth top curve. The sun gear blank entity is obtained by curve stretching. The same operation is performed on the inner ring gear to obtain the inner ring gear entity. Using the CAXA CAD electronic drawing board, the planetary gear parameters are input to obtain the planetary gear entity.

[0099] Assemble the sun gear blank entity and the gear shaping cutter entity reasonably. Set the assembly positions of the sun gear and the gear shaping cutter, the inner gear ring and the gear shaping cutter at the same place, and set the gear shaping cutter pitch circle to be tangent to the sun gear pitch curve to ensure the accuracy of subsequent motion simulation. In order to ensure that the gear shaping cutter pitch circle and the sun gear pitch curve are always in a tangent relationship, call the gear shaping cutter pitch circle component to perform contact constraints at the tangent position. Create an auxiliary connecting rod through sketching to facilitate the control of the gear shaping cutter movement during the modeling process.

[0100] like Figure 4 As shown in the figure, the assembled model is carried out according to the steps of "defining the moving body - establishing the kinematic pair - creating constraints - calculating and solving - motion envelope". The purpose of applying a revolute pair on the auxiliary connecting rod is to give a certain initial velocity to the gear cutter; the purpose of setting constraints between the pitch circle of the gear cutter and the pitch curve of the sun gear is to ensure that the gear cutter is always tangent to the pitch curve of the sun gear and performs pure rolling during the rotation process; the purpose of setting constraints between the center of the pitch circle of the gear cutter and the auxiliary connecting rod is to drive the gear cutter to move together. In the solution, the tooth profile accuracy and the computing power of the computer are comprehensively considered, the calculation step is set at a reasonable value, and a certain movement time is defined for motion simulation.

[0101] like Figure 5 As shown, the motion envelope is set, the gear shaping cutter is selected as the envelope object, and the envelope generated by the planetary gear is obtained.

[0102] like Figure 6 As shown in the figure, after the envelope is converted into a convergent body, the projection curve of the envelope is obtained by the projection command. The tooth profile curve is trimmed to obtain the tooth profile curve of the sun gear.

[0103] like Figure 7 As shown, the forming process of the inner ring gear is the same as that of the sun gear, and the tooth profile curve of the inner ring gear is obtained.

[0104] like Figure 8 As shown, taking a single tooth profile as an example, use SOLIDWORKS to open the tooth profile model IGS file, evenly insert a certain number of points on each line of the tooth profile curve, and output it as an SLDPRT file.

[0105] like Fig. 9 As shown in the figure, UG is used to export the file as a PRT file, and then as a DWG file. At this time, the point components become points on the sketch. After the curve fitting operation, the single tooth profile curve is obtained. The curve is further smoothed, and the NURBS curve is made second-order continuous by controlling the angle threshold and distance threshold. After the tooth profile curve is smoothed, the optimized tooth profile curve is obtained.

[0106] like Fig.10 As shown, the above method is used to obtain a high-precision sun gear tooth profile curve in a non-circular gear planetary gear train.

[0107] like Fig.11 As shown, the above method is used to obtain a high-precision tooth profile curve of the inner ring gear in a non-circular gear planetary gear train.

[0108] like Fig.12 As shown, by using Boolean operations, the solid models of the sun gear, planetary gear, and inner ring gear of the non-circular gear planetary gear train are obtained, and the non-circular gear planetary gear train model is obtained after assembly.

[0109] The above-mentioned embodiments are only preferred embodiments of the present invention and cannot be used to limit the scope of protection of the present invention. Any non-substantial changes and substitutions made by technicians in this field on the basis of the present invention shall fall within the scope of protection required by the present invention.

Claims

1. A design method for a non-circular gear planetary gear train based on motion envelope, characterized in that: The steps include: Step 1, solving the pitch curve of the non-circular gear planetary gear train, including the pitch curve equation of the sun gear and the pitch curve equation of the inner gear ring; Step 2: Create a non-circular gear blank and assemble it with a gear shaping cutter; Step 3: Get the non-circular gear tooth profile by motion envelope; Step 4: Optimize the accuracy of the non-circular gear tooth profile.

2. The design method of a non-circular gear planetary gear train based on motion envelope according to claim 1, characterized in that: The step 1 is specifically as follows: Establish a coordinate system, take the center of the sun gear as the origin, and establish a fixed coordinate system S0-O0x0y0 in space; set the center of the gear shaping cutter as the origin, and establish a coordinate system S fixed at the center of the gear shaping cutter f -O f x f y f and the coordinate system S describing the movement of the gear shaping cutter m -O m x m y m ; In the initial position, S f -O f x f y f , S m -O m x m y m The directions of the coordinate axes are consistent. When S m -O m x m y m Relative to S f -O f x f y f Rotate angle accordingly S m -O m x m y m To S f -O f x f y f The coordinate transformation matrix is: Let S f -O f x f y f Origin O f The coordinates in S-Oxy are (x f ,y f ),S f -O f x f y f The coordinate transformation matrix to S-Oxy is: Then the gear cutter tooth profile (x0, y0) can be obtained by S m -O m x m y m After the coordinate transformation, the coordinates under S0-O0x0y0 are: From formula (3), we can only obtain the coordinates (xf, yf) of point Of in S0-O0x0y0 and the tooth profile of the gear shaping cutter in S m -O m x m y m The coordinates (x m ,y m ) to get the envelope graph; The pitch curve of the sun gear is a high-order elliptical gear, and its pitch curve equation is: Where k, θ1, and A are eccentricity, polar angle, and major axis radius, respectively. The closing condition of the pitch curve between the sun gear and the inner ring gear is: In the formula, μ1 is the angle between the tangent and the radial direction of the driving wheel, which can be determined by the following formula: In order to ensure that all gear teeth are evenly spaced along the pitch curve and that each gear has the same module, the number of teeth z and the module m should satisfy the following equation: Where L is the arc length of the pitch curve. According to the basic motion relationship of non-circular planetary gears, the pitch curve equation of the inner gear ring is: The conditions for a non-circular gear planetary gear train to not produce motion interference during operation are: r 3min ≥r 1max +2h a (9) Finally, the sun gear pitch curve data is calculated by combining formula (4)-formula (7), and then the inner gear ring pitch curve data is obtained by formula (8) and substituted into formula (9) for verification.

3. The design method of a non-circular gear planetary gear train based on motion envelope according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1, according to the pitch curve equation calculated in step 1, obtain the pitch curve point data of the non-circular gear planetary gear train through MATLAB, export the point data as a TXT file, and then import it into the three-dimensional software UG and perform curve fitting to obtain the pitch curves of the sun gear and the inner ring gear; Step 2.2, offset the pitch curve of the sun gear by the distance of the tooth top height to obtain the tooth top curve; Step 2.3, using curve stretching to obtain the sun gear blank entity; Step 2.4, perform the same operation on the inner gear ring to obtain the inner gear ring entity; Step 2.5: Use CAXA CAD electronic drawing board to input the planetary gear parameters and obtain the planetary gear entity. Step 2.6: Assemble the sun gear blank entity and the gear shaping cutter entity properly.

4. The design method of a non-circular gear planetary gear train based on motion envelope according to claim 1, characterized in that: The step 2.6 is as follows: The sun gear and the gear shaping cutter, the inner gear ring and the gear shaping cutter are assembled at the same place, and the pitch circle of the gear shaping cutter is set to be tangent to the pitch curve of the sun gear to ensure the accuracy of subsequent motion simulation; In order to ensure that the pitch circle of the gear shaping cutter is always in a tangent relationship with the sun gear pitch curve, the gear shaping cutter pitch circle component is called to perform contact constraint at the tangent position; Create an auxiliary link through sketching to control the movement of the gear shaping cutter during the molding process.

5. The design method of a non-circular gear planetary gear train based on motion envelope according to claim 1, characterized in that: The step of obtaining the tooth profile of the sun gear in step 3 is the same as the step of obtaining the tooth profile of the inner ring gear. The step of obtaining the tooth profile of the sun gear is as follows: Carry out the model assembled in step 2 according to the steps of "define motion body - establish motion pair - create constraints - calculate and solve - motion envelope"; Apply a revolute joint to the auxiliary link; Constraints are set between the pitch circle of the gear shaping cutter and the pitch curve of the sun gear. The purpose is to ensure that the gear shaping cutter is always tangent to the pitch curve of the sun gear and performs pure rolling during its rotation. A constraint is set between the center of the pitch circle of the gear shaping cutter and the auxiliary connecting rod, the purpose of which is to drive the gear shaping cutter to move together; In the solution, the tooth profile accuracy and the computing power of the computer are comprehensively considered, the calculation step is set at a reasonable value, and a certain motion time is defined for motion simulation; After the solution is successful, the motion envelope is set, the gear shaping cutter is selected as the envelope object, and the envelope generated by the planetary gear is obtained; after the envelope is converted into a convergent body, the projection curve of the envelope is obtained through the projection command; The tooth profile curve is trimmed to obtain the tooth profile curve of the sun gear.

6. A design method for a non-circular gear planetary gear train based on motion envelope as claimed in claim 1, characterized in that: The step 4 is specifically as follows: Use SOLIDWORKS to open the IGS file of the tooth profile model obtained in step 3, insert a certain number of points evenly on each line of the tooth profile curve, and output it as an SLDPRT file; Use UG to export the file as a PRT file, and then export it as a DWG file. At this time, the point components become points on the sketch; After the curve fitting operation, the single tooth profile curve is obtained; The curve is further smoothed, and the angle threshold and distance threshold are controlled to make the NURBS curve second-order continuous. After the tooth profile curve is smoothed, the optimized tooth profile curve is finally obtained.

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