A Method for Modifying the Spatial Tooth Profile of a Flexible Gear in Harmonic Drive

Abstract

The present invention discloses a method for modifying the spatial tooth profile of a flexible gear in harmonic drive. This method can make the tooth profile at the long-axis part of the front end of the flexible gear tend to be parallel to the rotation axis after deformation, eliminate the influence of the opening angle, eliminate the problems of tooth profile interference of the harmonic gear, and interference during meshing-in or meshing-out at the rear end, and improve the load-bearing capacity, transmission accuracy and transmission efficiency of the harmonic reducer. When the harmonic reducer operates overloaded, it effectively avoids the interference during meshing-in or meshing-out caused by the torsional deformation at the rear end of the flexible gear. A calculation model for modifying the tooth shape and tooth direction of the flexible gear in harmonic drive is established, solving the problem of spatial modification of the tooth profile of the harmonic gear.

Description

Technical Field

[0001] The present invention relates to a method for modifying the spatial tooth profile of a flexible gear in harmonic drive, belonging to the technical field of harmonic gear drive. Background Art

[0002] A harmonic reducer is a transmission device that relies on the controllable elastic deformation generated by a flexible gear to transmit motion and power, and has the characteristics of small volume, high load-bearing capacity, and high transmission accuracy. During the working process of harmonic drive, after the flexible gear is installed with a wave generator, the radial deformation of the flexible gear cylinder tilts. As shown in Figure 1 and Figure 2 , an outward tilting angle is generated near the long axis, and an inward shrinking angle is generated near the short axis. If the tooth directions of the rigid gear and the flexible gear are both processed according to spur gears, tooth profile interference will inevitably occur at the long axis position. In addition, when the flexible gear undergoes torsional deformation under load, meshing-in or meshing-out interference will occur at the rear end. Therefore, it is necessary to modify the tooth profile of the flexible gear to avoid meshing interference, which will cause a sharp decline in the load-bearing capacity, transmission accuracy, and transmission efficiency of the reducer. Summary of the Invention

[0003] The present invention provides a method for modifying the spatial tooth profile of a flexible gear in harmonic drive. This method establishes a deformation prediction model for the flexible gear in harmonic drive and a tooth shape and tooth direction modification calculation model, solves the problem of spatial modification of the harmonic gear tooth profile, and improves the load-bearing capacity, transmission accuracy, and transmission efficiency of the harmonic reducer.

[0004] The technical solution of the present invention: A method for modifying the spatial tooth profile of a flexible gear in harmonic drive includes the following steps:

[0005] Step 1: Take the length from the center of the ball of the flexible bearing to the bottom of the flexible gear cup as L1; the axial length of the starting point of the tooth direction of the flexible gear near the front end of the hole is L4, the ending length is L5, and the radial modification amount is T2; the axial length of the starting point of the modification of the tooth direction of the flexible gear near the bottom of the cup at the rear end is L3, the ending length is L2, and the radial modification amount is T3; the wall thickness of the tooth root of the flexible gear is T1; the inner hole radius of the flexible gear is R; the major semi-axis of the standard elliptical cam is a; the inner hole radius of the flexible bearing is r; the clearance of the flexible bearing is C, and the deformation inclination angle is θ. Then, the following relationships exist among the parameters:

[0006]

[0007]

[0008] The radial modification amount of any cross-section at the front end of the flexible gear (the straight-line distance from the L5 position to the L4 position):

[0009] Ty = tanθ * (L5 - Lx) (L4 ≤ Lx ≤ L5) (c)

[0010] Where: Ty represents the dimension of the Lx cross-section modified along the radial direction;

[0011] Lx represents the axial position of any cross-section at the front end of the flexspline.

[0012] The radial modification amount at the rear end of the flexspline (the straight-line distance from the L2 position to the L3 position):

[0013]

[0014] The radial modification amount of any cross-section at the rear end of the flexspline:

[0015]

[0016] Wherein: Tf represents the dimension of the Ln cross-section modified along the radial direction;

[0017] Ln represents the axial position of any cross-section at the rear end of the flexspline.

[0018] Step 2: Substitute the inner hole radius R of the flexspline, the major semi-axis a of the standard elliptical cam, the inner hole radius r of the flexible bearing, the clearance C of the flexible bearing, the torsional stiffness K of the harmonic reducer under the maximum torque T, and the tooth profile pressure angle α of the flexible bearing into the formulas (a), (b), (c), (d), and (e), and the modification amounts of any cross-sections at the front and rear ends of the flexspline can be obtained.

[0019] In the above method, the dimension L1 from the center of the flexible bearing ball to the bottom of the cup is determined by the position of the wave generator after it is installed in the flexspline; the dimensions L2, L3, L4, and L5 are determined according to the design main cross-section of the flexspline tooth profile.

[0020] Due to the adoption of the above technical solution, the advantages of the present invention are as follows:

[0021] ① By adopting the modification method of the present invention, the tooth profile of the long-axis part at the front end of the flexspline after deformation can be in a parallel trend with the rotation axis, eliminating the influence of the included angle, eliminating the problems of tooth profile interference of the harmonic gear, and interference during meshing-in or meshing-out at the rear end, and improving the load-bearing capacity, transmission accuracy, and transmission efficiency of the harmonic reducer.

[0022] ② When the harmonic reducer operates overloaded, the interference during meshing-in or meshing-out caused by the torsional deformation at the rear end of the flexspline can be effectively avoided.

[0023] ③ A calculation model for tooth profile and tooth direction modification of the flexspline in harmonic drive is established, solving the problem of spatial modification of the harmonic gear tooth profile. Brief Description of the Drawings

[0024] Figure 1 is the deformation diagram near the long axis after the flexspline is assembled;

[0025] Figure 2 is the deformation diagram near the short axis after the flexspline is assembled

[0026] Figure 3It is the graph of the meshing deformation size of the flexspline;

[0027] Figure 4 It is the graph of the tooth profile modification of the flexspline;

[0028] Figure 5 It is Figure 4 the partial enlarged view of;

[0029] Figure 6 It is the graph of the size of the flexure bearing before deformation;

[0030] Figure 7 It is the meshing effect diagram after modification.

[0031] The marks in the attached drawings are: 1 - flexspline, 2 - rigid spline, 3 - wave generator, 4 - flexure bearing, 5 - standard elliptical cam. Specific implementation manners

[0032] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the attached drawings and embodiments.

[0033] Embodiment of the present invention: First, assume that the flexspline teeth of the flexspline 1 meshing with the rigid spline 2 in the harmonic reducer are rigid. During the transmission process, the flexspline teeth are rigid bodies relative to the flexspline tooth grooves, and the deformation occurs at the flexspline tooth groove part; when the flexspline 1 deforms, the neutral layer curve of it does not elongate before and after deformation, and after deformation, the flexspline 1 closely adheres to the wave generator 3, that is, the flexspline 1, the flexure bearing 4 and the standard elliptical cam 5 are closely adhered to each other. Under the action of the wave generator 3 and the load, the neutral layer of the flexspline 1 shows a linear deformation law along the tooth direction; the torsional stiffness of the harmonic reducer under the maximum torque T is K, and the tooth profile pressure angle of the flexspline 1 is α.

[0034] A method for modifying the spatial tooth profile of a flexspline in a harmonic drive of the present invention includes the following steps:

[0035] Step 1, referring to Figures 3 to 5 , take the length from the center of the ball of the flexure bearing 4 to the bottom of the cup of the flexspline 1 as L1; the axial length of the starting point at the front end of the flexspline tooth direction near the hole mouth is L4, the ending length is L5, and the radial modification amount is T2; the axial length of the starting point of the modification at the rear end of the flexspline tooth direction near the cup bottom is L3, the ending length is L2, and the radial modification amount is T3; the wall thickness of the flexspline tooth root is T1; the inner hole radius of the flexspline is R; the major semi - axis of the standard elliptical cam 5 is a; the inner hole radius of the flexure bearing 4 is r; the clearance of the flexure bearing 4 is C, and the deformation inclination angle is θ. Then, there are the following relationships between the parameters:

[0036]

[0037]

[0038] Radial modification amount of any cross-section at the front end of the flexspline (linear distance from position L5 to position L4):

[0039] Ty = tanθ * (L5 - Lx) (L4 ≤ Lx ≤ L5) (c)

[0040] Where: Ty represents the dimension of the radial modification of the Lx cross-section;

[0041] Lx represents the axial position of any cross-section at the front end of the flexspline;

[0042] Therefore, the radial modification amount T2 can be calculated according to the company (c);

[0043] Radial modification amount at L2 of the rear end of the flexspline (linear distance from position L2 to position L3):

[0044]

[0045] Radial modification amount of any cross-section at the rear end of the flexspline:

[0046]

[0047] Where: Tf represents the dimension of the radial modification of the Ln cross-section;

[0048] Ln represents the axial position of any cross-section at the rear end of the flexspline;

[0049] Step 2: Determine the dimension L1 from the center of the ball of the flexible bearing 4 to the bottom of the cup through the position after the wave generator 3 is inserted into the flexspline 1; Determine the dimensions L2, L3, L4, and L5 according to the designed main cross-section of the tooth profile of the flexspline 1; Refer to Figures 3 to 6 , substitute the inner hole radius R of the flexspline 1, the major semi-axis a of the standard elliptical cam 5, the inner hole radius r of the flexible bearing 4, the clearance C of the flexible bearing 4, the torsional stiffness K of the harmonic reducer under the maximum torque T, and the tooth profile pressure angle α of the flexible bearing 4 into the formulas (a), (b), (c), (d), (e), and the modification amounts of any cross-sections at the front and rear ends of the flexspline 1 can be obtained.

[0050] Refer to Figure 7 , by adopting the modification method of the present invention, it is possible to make the tooth profile at the long axis part of the front end of the flexspline parallel to the rotation axis after deformation, eliminate the influence of the included angle, eliminate the interference of the harmonic gear tooth profile, and the interference of meshing in or out at the rear end, and improve the load-bearing capacity, transmission accuracy, and transmission efficiency of the harmonic reducer. When the harmonic reducer operates overloaded, the interference of meshing in or out caused by the torsional deformation at the rear end of the flexspline is effectively avoided.

Claims

1. A method for modifying the spatial tooth profile of a flexible gear in a harmonic drive, characterized in that It includes the following steps: Step 1: Take the length from the center of the ball of the flexible bearing (4) to the bottom of the cup of the flexspline (1) as L1; the axial length of the starting point of the flexspline tooth profile at the front end near the orifice is L4, the ending length is L5, and the radial modification amount is T2; the axial length of the starting point of the modification of the flexspline tooth profile at the rear end near the bottom of the cup is L3, the ending length is L2, and the radial modification amount is T3; the wall thickness of the flexspline tooth root is T1; the inner hole radius of the flexspline is R; the major semi-axis of the standard elliptical cam (5) is a; the inner hole radius of the flexible bearing (4) is r; the clearance of the flexible bearing (4) is C, and the deformation inclination angle is θ. Then, there are the following relationships among the parameters: The radial modification amount of any cross-section at the front end of the flexspline: Ty = tanθ * (L5 - Lx) L4 ≤ Lx ≤ L5 (c) Where: Ty represents the dimension of the radial modification of the Lx cross-section; Lx represents the axial position of any cross-section at the front end of the flexspline; The radial modification amount at L2 at the rear end of the flexspline: The radial modification amount of any cross-section at the rear end of the flexspline: Where: Tf represents the dimension of the radial modification of the Ln cross-section; Ln represents the axial position of any cross-section at the rear end of the flexspline; Step 2: Substitute the inner hole radius R of the flexspline (1), the major semi-axis a of the standard elliptical cam (5), the inner hole radius r of the flexible bearing (4), the clearance C of the flexible bearing (4), the torsional stiffness K of the harmonic reducer under the maximum torque T, and the tooth profile pressure angle α of the flexible bearing (4) into the formulas (a), (b), (c), (d), and (e), and the modification amounts of any cross-sections at the front and rear ends of the flexspline (1) can be obtained.

2. The harmonic drive flexible gear spatial tooth profile modification method according to claim 1, characterized in that: Determine the dimension L1 from the center of the ball of the flexible bearing (4) to the bottom of the cup through the position after the wave generator (3) is installed in the flexspline (1); determine the dimensions L2, L3, L4, and L5 according to the design main cross-section of the flexspline (1) tooth profile.

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