Spline meshing characteristic calculation method based on time-varying meshing position

Abstract

The invention discloses a spline meshing characteristic calculation method based on a time-varying meshing position. The spline meshing characteristic calculation method comprises the following steps: establishing a spline meshing state characterization model of a spline; the spline tooth backlash and the pressure angle containing parallel misalignment of the spline are obtained through the spline meshing state characterization model; establishing a spline single-tooth meshing stiffness calculation model through a potential energy method, the spline tooth backlash and the pressure angle; spline tooth meshing deformation coordination conditions are obtained according to the spline single-tooth meshing rigidity calculation model; a spline meshing deformation calculation method of the spline is obtained according to the spline tooth meshing deformation coordination condition; establishing a spline meshing force model containing parallel misalignment according to a spline meshing deformation calculation method; and acquiring spline meshing characteristics of the spline according to the spline meshing force model. According to the method, a spline meshing force model containing parallel misalignment is established; the spline meshing characteristics can be described more accurately, and the design of a high-speed, high-reliability and low-vibration mechanical transmission system is facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of gear design, and in particular to a method for calculating spline meshing characteristics based on time-varying meshing positions. Background Art

[0002] Involute splines are widely used in various transmission systems for power transmission between the main engine and actuators. Due to installation space limitations and the uneven mass of the shafting structure, parallel misalignment is unavoidable in the shafting system, causing changes in the spline meshing position and affecting the spline meshing characteristics. Existing studies have mostly assumed that parallel misalignment does not significantly affect the meshing position of the spline teeth, resulting in inaccurate calculations of the spline meshing characteristics. As mechanical transmission mechanisms develop towards higher speeds, higher reliability, and lower vibration, existing spline meshing characteristic calculation methods have difficulty providing theoretical support for spline structure design. Summary of the Invention

[0003] An embodiment of the present invention provides a method for calculating spline meshing characteristics based on time-varying meshing position, which is used to solve the problem in the prior art of assuming that parallel misalignment does not significantly affect the meshing position of the spline teeth, resulting in inaccurate calculation of the spline meshing characteristics.

[0004] In one aspect, an embodiment of the present invention provides a method for calculating spline meshing characteristics based on time-varying meshing position, comprising: Establish a spline meshing state characterization model for the spline; Obtaining the spline tooth backlash and pressure angle of the spline including parallel misalignment by using the spline meshing state characterization model; A calculation model for the meshing stiffness of a single spline tooth with parallel misalignment is established by using a potential energy method, the spline tooth backlash, and the pressure angle; Obtaining a spline tooth meshing deformation coordination condition of the spline according to the spline single tooth meshing stiffness calculation model; A method for calculating the spline meshing deformation of the spline is obtained according to the spline tooth meshing deformation coordination condition; Establishing a spline meshing force model with parallel misalignment according to the spline meshing deformation calculation method; The spline meshing characteristics of the spline are obtained according to the spline meshing force model.

[0005] In a possible implementation, establishing a spline meshing state characterization model of the spline includes: The spline meshing state characterization model is established based on the pitch circle, pitch circle and meshing point of the standard spline.

[0006] In a possible implementation, obtaining the spline tooth backlash and pressure angle of the spline including parallel misalignment by using the spline meshing state characterization model includes: Obtaining displacement data of the external spline in a parallel misalignment state by moving the actual tooth position of the external spline of the spline on the spline meshing state representation model; Obtaining a time-varying backlash variation and a pressure angle of the spline containing parallel misalignment according to the displacement data of the external spline in the parallel misalignment state; The spline tooth side clearance including parallel misalignment of the spline is obtained according to the variation of the time-varying side clearance of the spline.

[0007] In one possible implementation, establishing a calculation model for the meshing stiffness of a single spline tooth with parallel misalignment by using a potential energy method, the spline tooth backlash, and the pressure angle includes: Calculating the single tooth bending stiffness, shear stiffness, and axial compression stiffness of the external spline and the internal spline of the spline; According to the single tooth bending stiffness, shear stiffness, axial compression stiffness and the spline single tooth meshing stiffness calculation model containing parallel misalignment is established.

[0008] In one possible implementation, establishing a calculation model for the meshing stiffness of a single spline tooth with parallel misalignment by using a potential energy method, the spline tooth backlash, and the pressure angle includes: Calculating the single tooth bending stiffness, shear stiffness, and axial compression stiffness of the external spline and the internal spline of the spline; According to the single tooth bending stiffness, shear stiffness, axial compression stiffness and the spline single tooth meshing stiffness calculation model containing parallel misalignment is established.

[0009] In a possible implementation, obtaining the spline tooth meshing deformation coordination condition of the spline according to the spline single tooth meshing stiffness calculation model includes: The front side meshing deformation and the back side meshing deformation of the spline are calculated by using a spline single tooth meshing stiffness calculation model in the parallel misalignment state of the spline.

[0010] In a possible implementation, a method for calculating the spline meshing deformation of the spline according to the spline tooth meshing deformation coordination condition includes: Calculating the spline meshing force of the spline by using the spline meshing deformation calculation method of the spline; A calculation method for obtaining the spline meshing deformation of the spline is obtained through the spline meshing force.

[0011] The method for calculating spline meshing characteristics based on time-varying meshing position in the present invention has the following advantages: Establishing a spline meshing force model with parallel misalignment can more accurately describe the spline meshing characteristics, which is of great significance to the design of high-speed, high-reliability and low-vibration mechanical transmission systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0013] Figure 1 A flow chart of a method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 2 A schematic diagram of spline tooth meshing with parallel misalignment according to a method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 3 A schematic diagram of a spline single tooth meshing state with parallel misalignment according to a method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 4 A schematic diagram of an external spline meshing state according to a method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 5 A schematic diagram of an internal spline meshing state according to a method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 6 A schematic diagram of the coordinate transformation of K1' and K2' in the method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 7 A schematic diagram of an external spline cantilever beam model for a method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 8 Schematic diagram of an internal spline cantilever beam model for a method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 9 A schematic diagram of the external spline tooth root circle geometry of a method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 10 A schematic diagram of the internal spline tooth root circle geometry for the method for calculating spline meshing characteristics based on time-varying meshing position provided in an embodiment of the present application; Figure 11 A comparison diagram of the spline meshing forces with and without considering the time-varying meshing position when the parallel misalignment amount is 50 μm in the spline meshing characteristics calculation method based on the time-varying meshing position provided in an embodiment of the present application. DETAILED DESCRIPTION

[0014] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0015] Figure 1 A flow chart of a method for calculating spline meshing characteristics based on time-varying meshing positions provided in an embodiment of the present invention; an embodiment of the present invention provides a method for calculating spline meshing characteristics based on time-varying meshing positions, comprising: Establish a spline meshing state characterization model for the spline; Obtaining the spline tooth backlash and pressure angle of the spline including parallel misalignment by using the spline meshing state characterization model; A calculation model for the meshing stiffness of a single spline tooth with parallel misalignment is established by using a potential energy method, the spline tooth backlash, and the pressure angle; Obtaining a spline tooth meshing deformation coordination condition of the spline according to the spline single tooth meshing stiffness calculation model; A method for calculating the spline meshing deformation of the spline is obtained according to the spline tooth meshing deformation coordination condition; Establishing a spline meshing force model with parallel misalignment according to the spline meshing deformation calculation method; The spline meshing characteristics of the spline are obtained according to the spline meshing force model.

[0016] The establishment of a spline meshing state characterization model of the spline comprises: The spline meshing state characterization model is established based on the pitch circle, pitch circle and meshing point of the standard spline.

[0017] The obtaining of the spline tooth backlash and pressure angle of the spline including parallel misalignment by the spline meshing state characterization model includes: Obtaining displacement data of the external spline in a parallel misalignment state by moving the actual tooth position of the external spline of the spline on the spline meshing state representation model; Obtaining a time-varying backlash variation and a pressure angle of the spline containing parallel misalignment according to the displacement data of the external spline in the parallel misalignment state; The spline tooth side clearance including parallel misalignment of the spline is obtained according to the variation of the time-varying side clearance of the spline.

[0018] The calculation model of the spline single tooth meshing stiffness with parallel misalignment is established by using the potential energy method, the spline tooth backlash, and the pressure angle, including: Calculating the single tooth bending stiffness, shear stiffness, and axial compression stiffness of the external spline and the internal spline of the spline; According to the single tooth bending stiffness, shear stiffness, axial compression stiffness and the spline single tooth meshing stiffness calculation model containing parallel misalignment is established.

[0019] The spline tooth meshing deformation coordination condition of the spline obtained according to the spline single tooth meshing stiffness calculation model includes: The front side meshing deformation and the back side meshing deformation of the spline are calculated by using a spline single tooth meshing stiffness calculation model in a parallel misalignment state of the spline.

[0020] The method for calculating the spline meshing deformation of the spline according to the spline tooth meshing deformation coordination condition includes: Calculating the spline meshing force of the spline by using the spline meshing deformation calculation method of the spline; A calculation method for obtaining the spline meshing deformation of the spline is obtained through the spline meshing force.

[0021] For example, a spline meshing state characterization model is first established to obtain the spline tooth side clearance and pressure angle with parallel misalignment; then, based on the potential energy method, a spline single tooth meshing stiffness calculation model with parallel misalignment is established according to the spline tooth pressure angle; finally, based on the spline tooth meshing deformation coordination condition, a spline meshing deformation calculation method is proposed, and then a spline meshing force model with parallel misalignment is established. The overall calculation process is as follows: Figure 1 shown.

[0022] First, a spline meshing state characterization model is established, including the parallel misaligned spline single tooth meshing state as follows: Figure 3 As shown. For a normal spline, the pitch circle and the pitch circle coincide, and the meshing point is K1 (K2) (K1 is located on the external spline teeth, and K2 is located on the internal spline teeth). When the spline has a parallel misalignment error, assuming that the internal spline is fixed, the actual tooth position of the external spline moves along the tooth profile symmetry line. At this time, the external spline engagement point becomes K 1' , the internal spline engagement point becomes K 2' Assume that the moving distance from K2 to K2 along the tooth symmetry line is 0.5 , then the pitch radius of any tooth of the spline with parallel misalignment is: (1) Where, and is the spline pitch circle radius and number of teeth; Internal spline engagement point The vertical distance to the symmetry line of the external spline tooth profile is calculated according to formula (8); The equivalent misalignment of any spline tooth is calculated as follows: (2) Where, and For inner / outer spline edge x and y Directional displacement; E mis and is the parallel misalignment and phase angle; is the position angle of any tooth, and its calculation formula is: (3) Where, j is the tooth number; θ e is the external spline angular displacement.

[0023] The schematic diagram of the external spline engagement state is as follows Figure 4 As shown in the figure, there are two sets of coordinate systems: one is the global coordinate system ( X G , Y G ), the other is the local coordinate system used to determine the coordinates of the external spline meshing line ( X Le , Y Le In the local coordinate system ( X Le , Y Le ), K 1' The coordinates can be expressed as: (4) Where r b is the base circle radius; Is the external spline in K 1' The pressure angle of a point is expressed as: (5) The schematic diagram of the internal spline engagement state is as follows Figure 5 As shown in the figure, the local coordinate system ( X Li , Y Li ) is used to determine the involute coordinates of the external spline. In the local coordinate system ( X Li , Y Li ), the coordinates of K2' can be expressed as: (6) Where, Internal spline K 2' The pressure angle of a point is expressed as: (7) based on Figure 5According to the geometric relationship in , the vertical distance from the internal spline tooth meshing point K2' to the external spline tooth profile symmetry line is: (8) Where, is the angle between the meshing line of the meshing point K1' and the tooth thickness direction; α 2 is the half tooth angle. Their calculation formula is: (9) (10) In the above formula is the pressure angle at the spline pitch circle. When the external spline rotates a certain angle to mesh with the internal spline, K1' and K2' coincide. By solving the rotation angle, the time-varying backlash of the spline with parallel misalignment can be calculated. This angle can be calculated based on the coordinates of K1' and K2' in the global coordinate system, as follows Figure 6 As shown. The coordinates of K1' in the global coordinate system are: (11) The coordinates of K2' in the global coordinate system are: (12) Therefore, the rotation angle is: (13) The change in spline tooth backlash caused by parallel misalignment is: (14) The variable backlash of the spline teeth is: (15) Where, b s0 is the initial side clearance.

[0024] Secondly, the spline single tooth meshing stiffness model with parallel misalignment is constructed as follows: Considering the influence of the time-varying meshing position of the spline teeth caused by parallel misalignment, the equivalent cantilever beam models of the internal and external spline teeth are as follows: Figure 7 、 8 As shown in Figures 9 and 10, the single tooth bending stiffness, shear stiffness and axial compression stiffness are: (16) (17) (18) (19) (20) (twenty one) Where, K be / i 、 K se / i and K ae / i are the bending stiffness, shear stiffness and axial compression stiffness of a single tooth of the external / internal spline; E , G and v are Young's modulus, shear modulus and Poisson's ratio respectively; β The distance from the starting point of the involute tooth profile on the tooth root fillet x The angle between the root radius at point 1 and the perpendicular line of the tooth profile symmetry line passing through the center of the root fillet; β 0 is the angle between the tooth root fillet radius at the starting point of the external spline involute tooth profile and the perpendicular line of the tooth profile symmetry line passing through the center of the tooth root fillet circle; β 1 is the angle between the root fillet radius at the end point of the external spline tooth root fillet and the perpendicular line of the tooth profile symmetry line passing through the center of the root fillet circle; β i0 It is the angle between the tooth root fillet radius at the starting point of the internal spline involute tooth profile and the perpendicular line of the tooth profile symmetry line passing through the center of the tooth root fillet circle; β i1 It is the angle between the root fillet radius at the end point of the internal spline tooth root fillet and the perpendicular line of the tooth profile symmetry line passing through the center of the root fillet circle; γ 1', d 1', h e '、 d i 'and h i ' is the angle between the perpendicular line of the meshing line at point K2' and the tooth profile symmetry line, the distance from the intersection of the external spline tooth root circle and the involute tooth profile to the meshing point along the tooth profile symmetry line, the vertical distance from the external spline meshing point to the tooth profile symmetry line, the distance from the intersection of the internal spline tooth root circle and the involute tooth profile to the meshing point along the tooth profile symmetry line, and the vertical distance from the internal spline meshing point to the tooth profile symmetry line. Their expressions are: (twenty two) (twenty three) (twenty four) (25) (26) The meshing stiffness of a single spline tooth is: (27) Where, K fe 、 K fi and Kh are the outer spline matrix stiffness, inner spline matrix stiffness and Hertz contact stiffness.

[0025] Finally, the meshing force model of a single spline tooth with parallel misalignment is constructed as follows: Considering the time-varying meshing position of the spline caused by parallel misalignment, the meshing deformation of the front side of the spline is: (28) The back side meshing deformation is: (29) The spline engagement force can be expressed as: (30) Where, F sj f / b is the front and back engagement force; C sj For meshing damping.

[0026] The comparison of spline meshing force when considering the time-varying meshing position and not considering the time-varying meshing position when the parallel misalignment is 50μm is as follows Figure 11 As shown in the figure, the results show that when the parallel misalignment is 50 μm, the peak-to-peak values ​​of the spline meshing force with and without considering the time-varying meshing position are 1035.06 N and 275.49 N, respectively, with a difference of 759.57 N. The results show that not considering the time-varying meshing position of the spline will lead to a large error in the spline meshing force, proving the importance of considering the time-varying meshing position of the spline.

[0027] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including all changes and modifications that fall within the scope of the present invention and the preferred embodiments.

[0028] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A method for calculating spline meshing characteristics based on time-varying meshing position, characterized in that: include: Establish a spline meshing state characterization model for the spline; Obtaining the spline tooth backlash and pressure angle of the spline including parallel misalignment by using the spline meshing state characterization model; A calculation model for the meshing stiffness of a single spline tooth with parallel misalignment is established by using a potential energy method, the spline tooth backlash, and the pressure angle; Obtaining a spline tooth meshing deformation coordination condition of the spline according to the spline single tooth meshing stiffness calculation model; A method for calculating the spline meshing deformation of the spline is obtained according to the spline tooth meshing deformation coordination condition; Establishing a spline meshing force model with parallel misalignment according to the spline meshing deformation calculation method; The spline meshing characteristics of the spline are obtained according to the spline meshing force model.

2. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that: The establishment of a spline meshing state characterization model of the spline comprises: The spline meshing state characterization model is established based on the pitch circle, pitch circle and meshing point of the standard spline.

3. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that: The obtaining of the spline tooth backlash and pressure angle of the spline including parallel misalignment by the spline meshing state characterization model includes: Obtaining displacement data of the external spline in a parallel misalignment state by moving the actual tooth position of the external spline of the spline on the spline meshing state representation model; Obtaining a time-varying backlash variation and a pressure angle of the spline containing parallel misalignment according to the displacement data of the external spline in the parallel misalignment state; The spline tooth side clearance including parallel misalignment of the spline is obtained according to the variation of the time-varying side clearance of the spline.

4. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that: The calculation model of the spline single tooth meshing stiffness with parallel misalignment is established by using the potential energy method, the spline tooth backlash, and the pressure angle, including: Calculating the single tooth bending stiffness, shear stiffness, and axial compression stiffness of the external spline and the internal spline of the spline; A calculation model for the spline single tooth meshing stiffness with parallel misalignment is established based on the single tooth bending stiffness, shear stiffness, axial compression stiffness, the spline tooth side clearance, and the pressure angle.

5. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that: The spline tooth meshing deformation coordination condition of the spline obtained according to the spline single tooth meshing stiffness calculation model includes: The front side meshing deformation and the back side meshing deformation of the spline are calculated by using a spline single tooth meshing stiffness calculation model in a parallel misalignment state of the spline.

6. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that: The method for calculating the spline meshing deformation of the spline according to the spline tooth meshing deformation coordination condition includes: Calculating the spline meshing force of the spline by using the spline meshing deformation calculation method of the spline; A calculation method for obtaining the spline meshing deformation of the spline is obtained through the spline meshing force.

Images