A three-point contact non-circular gear pair

Abstract

The present invention discloses a three-point contact non-circular gear pair, belonging to the field of gear transmission technology. The non-circular gear A and the non-circular gear B are provided. The tooth profile curve of the non-circular gear A includes a transition arc curve segment A1 and a working arc curve segment A2. The tooth profile curve of the non-circular gear B includes a tooth top chamfered straight line segment B1, a convex arc curve segment B2, a spline curve segment B3, a parabola curve segment B4, a convex arc curve segment B5, and a tooth root chamfered arc segment B6, which are connected in sequence. During the meshing process of the non-circular gears A and B, the working arc curve segment A2 forms a three-point contact with the convex arc curve segment B2, the spline curve segment B3, the parabola curve segment B4, and the convex arc curve segment B5. The non-circular gear pair of the present invention forms a three-point contact during the meshing process and has the characteristics of high load-bearing capacity, low vibration and noise, and long service life.

Description

Technical Field

[0001] The invention belongs to the technical field of gear transmission, and in particular relates to a three-point contact non-circular gear pair. Background Art

[0002] Gears, as the primary components in mechanical transmissions, are used to transmit motion between two shafts and are the most widely used transmission elements in machines and instruments. Common types of gear transmissions, such as involute, circular arc, and cycloid, are often used to achieve constant-speed, linear transmission between the driving and driven gears. Non-circular gear transmissions, a key branch of gear transmission, are primarily used in variable-speed transmissions and offer the potential for nonlinear transmission between the driving and driven gears.

[0003] Existing noncircular gear pairs are mostly constructed with straight teeth, and the meshing process is a line contact method. During meshing, there is relative sliding between the tooth profiles, causing adverse factors such as tooth surface wear and deformation, resulting in reduced transmission efficiency and vibration. In addition, the tooth surface load capacity is also somewhat lower than that of other transmission methods. Domestic and foreign scholars have conducted relevant research on pitch curve design, tooth surface modification, dynamic analysis, and manufacturing processes to further improve the transmission performance of noncircular gears. However, it still fails to meet the current social production requirements for high-load, high-efficiency, and low-wear gear transmission.

[0004] Therefore, starting from the basic tooth profile of the non-circular gear, a three-point contact non-circular gear pair is constructed, which has the characteristics of high load-bearing capacity, low vibration and noise, and long service life. Summary of the Invention

[0005] In view of this, the object of the present invention is to provide a three-point contact non-circular gear pair, which is in three-point contact during the meshing process and has the characteristics of high load-bearing capacity, low vibration and noise, and long service life.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention provides a three-point contact non-circular gear pair, comprising: a non-circular gear A and a non-circular gear B meshing with the non-circular gear A, the tooth profile curve of the non-circular gear A comprising a transition arc curve segment A1 and a working arc curve segment A2 connected to the transition arc curve segment A1, the tooth profile curve of the non-circular gear B comprising a tooth top chamfered straight line segment B1, a convex arc curve segment B2, a spline curve segment B3, a parabola curve segment B4, a convex arc curve segment B5 and a tooth root chamfered arc segment B6 connected in sequence, and during the meshing process of the non-circular gears A and B, the working arc curve segment A2 forms a three-point contact with the convex arc curve segment B2, the spline curve segment B3, the parabola curve segment B4 and the convex arc curve segment B5.

[0008] Furthermore, the general expression of the transition arc curve segment A1 in the tooth profile curve of the non-circular gear A is:

[0009]

[0010] Among them, ρ a is the arc radius of the working arc curve segment A2, ρ b is the arc radius of the working arc curve segment A2, θ b is the design parameter that determines the position of the point on the arc; min is the minimum value of the design parameter, α min =sin -1 ((ρ b -h f1 ) / (ρ a +ρ b ));h f1 is the tooth root height.

[0011] The general expression of the working arc curve segment A2 in the tooth profile curve of the non-circular gear A is:

[0012]

[0013] where α a is the meshing parameter angle, satisfying α min ≤α a ≤α max , α max =sin -1 (h a1 / ρ a ), h a1 is the tooth top height; l a Indicates point O a to x n Axis distance; " symbols represent the left and right tooth surfaces respectively.

[0014] Furthermore, the formed tooth surface of the non-circular gear A includes a transition arc tooth surface W1 and a working arc tooth surface W2 corresponding to the transition arc curve segment A1 and the working arc curve segment A2 respectively;

[0015] The equation of the transition arc tooth surface W1 is:

[0016]

[0017] The equation of the working arc tooth surface W2 is:

[0018]

[0019] Among them, r1 is the base circle radius of the non-circular gear A at the gear tooth position, is the angle that the non-circular gear A rotates after the preset time, and β is the gear helix angle.

[0020] Furthermore, the general expression of the tooth top chamfer straight line segment B1 in the tooth profile curve of the non-circular gear B is:

[0021]

[0022] in, The normal line representing the intersection of the tooth top chamfer straight line segment B1 and the convex arc curve segment B2 and y n The angle between the axes; δ e The tooth top chamfer straight line segment B1 and x n The angle between the tooth top chamfered straight line segment B1 and the convex arc curve segment B2 is l. The normal and y of the intersection of convex arc curve segment B2 and spline curve segment B3 n The angle between the axes; l f Indicates point O f to x n Axis distance.

[0023] The general expression of the convex arc curve segment B2 in the tooth profile curve of the non-circular gear B is:

[0024]

[0025] in is the arc radius of the convex arc curve segment B2, α f (Ι) is the design parameter that determines the position of the point on the arc;

[0026] The general expression of the spline curve segment B3 in the tooth profile curve of the non-circular gear B is:

[0027]

[0028] where t o is a parameter, t o ∈[0,1], are the x-coordinate and y-coordinate of the control point respectively;

[0029] The general expression of the parabolic curve segment B4 in the tooth profile curve of the non-circular gear B is:

[0030]

[0031] Where t1 is the independent variable of the parabola, t1∈[-ρ a sinθ1,ρ a sinθ1], P1 is the parabola coefficient, P1 = ρa cosθ1; L1 is the distance from the vertex of the parabola to the origin O n distance, The normal and y of the intersection of spline curve segment B3 and parabola curve segment B4 are n The angle between the axes; The normal line of the intersection of parabola curve segment B4 and convex arc curve segment B5 and y n The angle between the axes.

[0032] The general expression of the convex arc curve segment B5 in the tooth profile curve of the non-circular gear B is:

[0033]

[0034] in is the arc radius of the convex arc curve segment B5, α f (V) is the design parameter that determines the location of the point;

[0035] The general expression of the tooth root chamfer arc segment B6 in the tooth profile curve of the non-circular gear B is:

[0036]

[0037] where ρ f3 is the arc radius of the tooth root chamfer arc segment B6, is the design parameter that determines the position of the point on the arc, is the tooth root height.

[0038] Furthermore, the formed tooth surface of the non-circular gear B includes a tooth top chamfered straight line segment tooth surface M1, a convex arc curve segment tooth surface M2, a spline curve segment tooth surface M3, a parabola segment tooth surface M4, a convex arc curve segment tooth surface M5 and a tooth root chamfered arc segment tooth surface M6 corresponding to the tooth top chamfered straight line segment B1, the convex arc curve segment B2, the spline curve segment B3, the parabola curve segment B4, the convex arc curve segment B5 and the tooth root chamfered arc segment B6 respectively;

[0039] The equation of the tooth surface M1 of the tooth top chamfer straight line segment is:

[0040]

[0041] The equation of the convex arc curve segment tooth surface M2 is:

[0042]

[0043] The equation of the spline curve segment tooth surface M3 is:

[0044]

[0045] The equation of the parabolic segment tooth surface M4 is:

[0046]

[0047] The equation of the convex arc curve segment tooth surface M5 is:

[0048]

[0049] The equation of the tooth surface M6 of the tooth root chamfered arc segment is:

[0050]

[0051] Where r2 is the base circle radius of the non-circular gear B at the preset tooth position, It is the angle that the non-circular gear B rotates after the preset time.

[0052] The beneficial effects of the present invention are:

[0053] The present invention proposes a three-point contact non-circular gear pair, which has the advantages of high load-bearing capacity, high transmission efficiency, and low friction and wear during the meshing process, and solves the problems of existing non-circular gear pairs such as single tooth profile form, large relative sliding wear, and high transmission noise.

[0054] Other advantages, objectives and features of the present invention will be described in the following description and will be apparent to those skilled in the art to some extent, or those skilled in the art can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0056] Figure 1 Schematic diagram of the basic tooth profile of the non-circular gear A according to an embodiment of the present invention;

[0057] Figure 2 Schematic diagram of the basic tooth profile of the non-circular gear B according to an embodiment of the present invention;

[0058] Figure 3 A schematic diagram of meshing of second-order elliptical gears according to an embodiment of the present invention;

[0059] Figure 4 Schematic diagram of the meshing of three-stage gears according to an embodiment of the present invention. DETAILED DESCRIPTION

[0060] like Figures 1 to 4As shown, the present invention provides a three-point contact non-circular gear pair, comprising: a non-circular gear A and a non-circular gear B meshing with the non-circular gear A, wherein the tooth profile curve of the non-circular gear A comprises a transition arc curve segment A1 and a working arc curve segment A2 connected to the end of the transition arc curve segment A1; the tooth profile curve of the non-circular gear B comprises a tooth top chamfered straight line segment B1, a convex arc curve segment B2, a spline curve segment B3, a parabola curve segment B4, a convex arc curve segment B5, and a tooth root chamfered arc segment B6, wherein the upper and lower ends of the spline curve segment B3 are smoothly transitioned to the convex arc curve segment B2. and the parabolic curve segment B4, the upper and lower ends of the convex arc curve segment B5 are smoothly connected to the parabolic segment B4 and the tooth top chamfered arc segment B6, the working arc curve segment A2 and the convex arc curve segment B2, the spline curve segment B3, the parabolic curve segment B4 and the convex arc curve segment B5 form three-point contact at points CT1, CT2 and CT3, among which points CT1, CT2 and CT3 are the connection points of the convex arc curve segment B2 and the spline curve segment B3, the connection points of the spline curve segment B3 and the parabolic curve segment B4, and the connection points of the parabolic curve segment B4 and the convex arc curve segment B5 respectively.

[0061] A design method for a three-point contact non-circular gear pair was developed, and the following design parameters were optimized:

[0062] Z1=Z2=51,m n =6,α=20°,h a1 =1.234m n , h a2 =0.166m n , h f1 =0.266m n , h f2 =1.354m n , ρ a =1.5m n , ρ f =1.65m n ,ρ b =0.6m n , l a =0.5895m n , l f =0.5595m n , β=25.84°, Among them, m n is the gear module; Z1 and Z2 represent the number of teeth of non-circular gear A and non-circular gear B respectively; h a2 is the tooth top height of the basic tooth profile of non-circular gear B; h f1 is the tooth root height.

[0063] The non-circular gear pair designed in this embodiment is a second-order elliptical gear. According to the design principles and relevant requirements of the non-circular gear pitch curve, the major semi-axis a of the non-circular gear pair pitch curve can be obtained as a=133.2, the minor semi-axis b=126.9, and the eccentricity e=0.3;

[0064] like Figure 1 As shown, a basic tooth profile diagram of the non-circular gear A is established. The general expression of the transition arc curve segment A1 in the tooth profile curve of the non-circular gear A is:

[0065]

[0066] Where θ b The value range is [4.05°,89.95°];

[0067] The general expression of the working arc curve segment A2 in the tooth profile curve of the non-circular gear A is:

[0068]

[0069] Where, α a The value range is [4.05°,55.35°].

[0070] Among them, the equation of the transition arc tooth surface W1 is:

[0071]

[0072] The equation of the working arc tooth surface W2 is:

[0073]

[0074] Where, The value range is [0,80°].

[0075] like Figure 2 As shown in the figure, a basic tooth profile diagram of the non-circular gear B is established. The general expression of the tooth top chamfer straight line segment B1 in the tooth profile curve of the non-circular gear B is:

[0076]

[0077] Wherein, the value range of l is [0, 2.6813].

[0078] The general expression of the convex arc curve segment B2 in the tooth profile curve of the non-circular gear B is:

[0079]

[0080] Where, α f (Ι) The value range is [10°,18°].

[0081] The general expression of the spline curve B3 in the tooth profile curve of the non-circular gear B is:

[0082]

[0083] Wherein, the value range of t1 is [0,1].

[0084] The general expression of the parabolic curve segment B4 in the tooth profile curve of the non-circular gear B is:

[0085]

[0086] Where, the value range of t1 is [-0.5494, 0.5494].

[0087] The general expression of the convex arc curve segment B5 in the tooth profile curve of the non-circular gear B is:

[0088]

[0089] Where, α f (V) The value range is [35°,55°].

[0090] The general expression of the tooth root chamfer arc segment B6 in the tooth profile curve of the non-circular gear B is:

[0091]

[0092] Where, The value range is [0,37.04°].

[0093] The equation of the tooth surface M1 of the tooth top chamfer straight line segment is:

[0094]

[0095] The equation of the convex arc curve segment tooth surface M2 is:

[0096]

[0097] The equation of the spline curve segment tooth surface M3 is:

[0098]

[0099] The equation of the parabolic segment tooth surface M4 is:

[0100]

[0101] The equation of the convex arc curve segment tooth surface M5 is:

[0102]

[0103] The equation of the tooth surface M6 of the tooth root chamfered arc segment is:

[0104]

[0105] Where, The value range is [0,16°].

[0106] According to the above method, the tooth surface of the first gear of non-circular gear A and non-circular gear B can be constructed. Furthermore, the tooth surface data points are stored and imported into the three-dimensional modeling software UG. The spline curve command in the software is used in combination with the surface construction function to establish a complete single gear tooth. Finally, the tooth profile conversion method is used to modify the relevant parameters and repeat the above single tooth construction steps to complete the model construction of non-circular gear A and non-circular gear B. Figure 3 Schematic diagram of the meshing of the constructed second-order non-circular gear A and non-circular gear B. Figure 4 The figure is a meshing diagram of a third-order non-circular gear pair constructed using the above method.

[0107] The present embodiment proposes a three-point contact non-circular gear pair, which has the advantages of high load-bearing capacity, high transmission efficiency, and low friction and wear during the meshing process, and solves the problems of the existing non-circular gear pair with a single tooth profile form, large relative sliding wear, and high transmission noise.

[0108] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A three-point contact non-circular gear pair, comprising: Non-circular gears A and non-circular gears A Non-circular gears in meshing arrangement B， It is characterized in that: the non-circular gear A The tooth profile curve includes transition arc curve segments and transition arc curve segments Connected working arc curve segments , the non-circular gear B The tooth profile curve consists of consecutive tooth top chamfer straight line segments , convex arc curve segment , spline curve segment , parabolic curve segment , convex arc curve segment and tooth root chamfer arc segment , the non-circular gear A and non-circular gears B During the meshing process, the working arc curve segment With convex arc curve segment , spline curve segment , parabolic curve segment and convex arc curve segments Three-point contact is formed at points CT1, CT2 and CT3, where points CT1, CT2 and CT3 are convex arc curve segments. and spline segments Connection points, spline curve segments and parabolic curve segments The connection points and parabolic curve segments of and convex arc curve segments connection point.

2. The three-point contact non-circular gear pair according to claim 1, characterized in that: The non-circular gear A Transition arc curve segment in the tooth profile curve The general expression is: in, Is the working arc curve segment The arc radius, It is a transition arc curve segment The arc radius, It is a design parameter that determines the position of a point on the arc; is the minimum value of the design parameter, ; The non-circular gear A Working arc curve segment in the tooth profile curve The general expression is: in is the meshing parameter angle, satisfying , ; is the tooth top height; Indicates a point arrive Axis distance; " symbols represent the left and right tooth surfaces respectively.

3. The three-point contact non-circular gear pair according to claim 2, characterized in that: The non-circular gear A The profiled tooth surface includes the transition arc curve segment and working arc curve segments Corresponding transition arc tooth surfaces and working arc tooth surface ; The transition arc tooth surface The equation is: The working arc tooth surface The equation is: in, Non-circular gears A The base circle radius at the gear tooth position, Is a non-circular gear after a preset time A The angle of rotation, is the gear helix angle.

4. The three-point contact non-circular gear pair according to claim 3, characterized in that: The non-circular gear B The tooth top chamfer straight line segment in the tooth profile curve The general expression is: in, Indicates the straight line segment of the tooth top chamfer With convex arc curve segment The normal of the intersection point and The angle between the axes; is the straight line segment of the tooth top chamfer and The angle between the axes; is the straight line segment of the tooth top chamfer Straight line segment from any point on the tooth to the tooth top chamfer With convex arc curve segment The distance of the intersection; Represents a convex arc curve segment With spline segments The normal of the intersection point and The angle between the axes; Indicates a point arrive Axis distance. The non-circular gear B Convex arc curve segment in the tooth profile curve The general expression is: in is a convex arc curve segment The arc radius, is the design parameter that determines the position of the point on the arc; The non-circular gear B The spline curve segment in the tooth profile curve The general expression is: in As parameters, , 、 、 、 、 、 、 、 are the x-coordinate and y-coordinate of the control point respectively; The non-circular gear B The parabolic curve segment in the tooth profile curve The general expression is: in is the independent variable of the parabola, , ; is the parabola coefficient, ; From the vertex of the parabola to the origin distance, ; Represents a spline segment With parabolic curve segment The normal of the intersection point and The angle between the axes; Represents a parabolic curve segment With convex arc curve segment The normal of the intersection point and The angle between the axes, The non-circular gear B Convex arc curve segment in the tooth profile curve The general expression is: in is a convex arc curve segment The arc radius, is the design parameter that determines the location of the point; The non-circular gear B The tooth root chamfer arc segment in the tooth profile curve The general expression is: in The tooth root chamfer arc segment The arc radius, is the design parameter that determines the position of the point on the arc, is the tooth root height.

5. The three-point contact non-circular gear pair according to claim 4, characterized in that: The non-circular gear B The profiled tooth surface includes the straight line segment with the tooth top chamfer , convex arc curve segment , spline curve segment , parabolic curve segment , convex arc curve segment and tooth root chamfer arc segment The corresponding tooth surface of the straight line segment of the tooth top chamfer , convex arc curve segment tooth surface , spline curve segment tooth surface , parabolic segment tooth surface , convex arc curve segment tooth surface and tooth surface of tooth root chamfer arc segment ; Tooth surface of the tooth top chamfered straight line segment The equation is: The convex arc curve segment tooth surface The equation is: The spline curve segment tooth surface The equation is: The parabolic segment tooth surface The equation is: The convex arc curve segment tooth surface The equation is: Tooth surface of tooth root chamfered arc segment The equation is: Where, Non-circular gear B The base circle radius at the preset gear tooth position, Is a non-circular gear after a preset time B The angle of rotation.

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