Pure rolling gear rack mechanism based on cycloid tooth profile and cycloid tooth trace

Abstract

The utility model provides a pure rolling gear rack mechanism based on a cycloid tooth profile and a cycloid tooth trace, which relates to the technical field of gear transmission and comprises a gear and a rack with pitch circles tangent to pitch lines, end face tooth profiles of the gear and the rack are composed of end face working tooth profile curves and tooth root transition curves, and the end face working tooth profile curves of the gear and the rack are cycloids; the tooth surfaces of the gear and the rack are provided with cycloid tooth trace structures; at least one pair of gear tooth meshing points of the gear and the rack are located at nodes to achieve pure rolling meshing contact, and meshing lines formed by moving tracks of the meshing points of the gear and the rack form two contact lines on the tooth surfaces of the gear and the rack respectively. The gear rack has the beneficial effects that the gear rack adopts symmetrical tooth lines, so that the axial force existing when the gear rack is meshed is eliminated, and the service life of a bearing is favorably prolonged.

Description

Technical Field

[0001] The utility model relates to the technical field of gear transmission, in particular to a pure rolling gear-rack mechanism based on a cycloidal tooth profile and a cycloidal tooth line. Background Art

[0002] In the field of mechanical engineering, gears and racks, as important components of transmission devices, are widely used in various mechanical equipment to achieve functions such as power transmission, speed transformation, and motion direction conversion. For example, the Chinese patent with the application number 201710016238.7 discloses "a concave-convex meshing circular arc gear-rack mechanism without relative sliding", and the Chinese patent with the application number 201710016207.1 discloses "a convex-concave meshing circular arc gear-rack mechanism without relative sliding". The tooth profiles of these gear-racks are all circular arc tooth profiles. Although the gear-rack transmission method has advantages such as high transmission efficiency and accurate transmission ratio, the meshing point is designed near the upper edge of the concave circular arc tooth profile, which is prone to stress concentration and causes tooth breakage. At the same time, since its tooth line does not adopt a symmetric tooth line, there is an axial force on the gear during transmission, which improves the requirements for the use of gear bearings and affects the accuracy and service life of the transmission system. Content of the Utility Model

[0003] In view of this, in order to solve the problems of axial force in the gear-rack mechanism of the existing gear transmission technology and the stress concentration prone to occur in the concave circular arc tooth profile, the embodiments of the utility model provide a pure rolling gear-rack mechanism based on a cycloidal tooth profile and a cycloidal tooth line.

[0004] The embodiments of the utility model provide a pure rolling gear-rack mechanism based on a cycloidal tooth profile and a cycloidal tooth line, including a gear and a rack with a pitch circle tangent to a pitch line. The end face tooth profiles of the gear and the rack are composed of an end face working tooth profile curve and a tooth root transition curve, and the end face tooth profiles of the gear and the rack are symmetric about the left and right sides; the end face working tooth profile curves of the gear and the rack are cycloids; the tooth surfaces of the gear and the rack have a cycloidal tooth line structure; at least one pair of tooth meshing points of the gear and the rack are located at the pitch point to achieve pure rolling meshing contact, and the meshing lines formed by the trajectories of the meshing points of the gear and the rack respectively form two contact lines on the tooth surfaces of the gear and the rack.

[0005] Further, the tooth surface structures of the gear and the rack are formed by sweeping the end face tooth profiles along the contact line, and the contact line of the gear is a cycloid symmetric about the z-axis after being unfolded along the pitch cylinder surface, and the contact line of the rack is a cycloid when unfolded at the pitch plane.

[0006] Further, the right working tooth profile curves of the gear and the rack are both formed by cycloid function curves, and the tooth root transition curve is composed of Hermite curves; the tooth tip control point of the end face working tooth profile curve is determined by the intersection point of the tooth tip circle and the cycloid function curve, and the starting control point of the tooth root transition curve is formed by the intersection of the cycloid function curve and the tooth root transition starting circle to form an intersection point P G4 , and the contact control point of the tooth root transition curve is formed by the intersection of the tooth root circle and the oblique line passing through point P G4 and having a slope of 1 to form P G3 ; Connect point P G4 and point P G3 according to the Hermite curve equation to form the tooth root curve.

[0007] Further, the contact line between the gear and the rack is determined according to the following method:

[0008] Establish four spatial coordinate systems of O0-x0,y0,z0, O k -x k ,y k ,z k , O1-x1,y1,z1 and O2-x2,y2,z2. The z0 axis and the z1 axis coincide with the rotation axis of the gear, the z k axis coincides with the meshing line of the gear and the rack, the z2 axis is on the rack and is k away from the z axis, and the distance between the z k axis and the z0 axis is R1; The coordinate system O0-x0,y0,z0 is fixedly connected to the gear, the coordinate system O2-x2,y2,z2 is fixedly connected to the rack, the gear rotates around the z0 axis at a constant angular velocity ω1, and the rack moves along the y2 axis at a constant linear velocity v1. After a period of time from the starting position, the coordinate system O0-x0,y0,z0 rotates around the z0 axis with the gear, and the coordinate system O2-x2,y2,z2 moves along the y2 axis with the rack;

[0009] In the coordinate system O k -x k ,y k ,z k , let the meshing line parametric equation of the meshing point movement of the gear and the rack be:

[0010]

[0011] The relationship between the rotation angle of the gear and the movement of the rack is:

[0012]

[0013] When the meshing point moves along the meshing line, contact lines are formed on the tooth surfaces of the gear and the rack respectively; according to the coordinate transformation principle, the coordinate transformation matrices of the three space coordinate systems O0-x0,y0,z0, O1-x1,y1,z1 and O2-x2,y2,z2 are as follows:

[0014] M 1k = M 10 × M 0k (3)

[0015]

[0016] where,

[0017]

[0018] In equations (4) and (6), R1 is the pitch circle radius of the gear, is the rotation angle of the gear;

[0019] The parametric equation of the contact line of the gear tooth surface is obtained from equations (1) and (5) as follows:

[0020]

[0021] The parametric equation of the contact line of the rack tooth surface is obtained from equations (1) and (4) as follows:

[0022]

[0023] Furthermore, the end face tooth profiles of the gear and the rack are determined by the following method:

[0024] In the coordinate system O k -x k ,y k ,z k the parametric equation of the right working tooth profile of the gear is:

[0025]

[0026] In the coordinate system O k -x k ,y k ,z k the parametric equation of the right working tooth profile of the rack is:

[0027]

[0028] In the coordinate system O k -x k ,y k ,z k the parametric equation of the left working tooth profile of the rack is:

[0029]

[0030] In the coordinate system O1 - x1, y1, z1, the parametric equation of the right working tooth profile of the gear is as follows:

[0031]

[0032] In the coordinate system O1 - x1, y1, z1, the parametric equation of the left working tooth profile of the gear is as follows:

[0033]

[0034] Furthermore, the tooth surfaces of the gear and the rack are determined as follows:

[0035] The formation of the gear tooth surface is swept along the motion law of the meshing point M. The parametric equation of the working left tooth surface of the gear:

[0036]

[0037] The formation of the gear tooth surface is swept along the motion law of the meshing point M. The parametric equation of the working right tooth surface of the gear:

[0038]

[0039] The formation of the rack tooth surface is realized along the motion track of the rack contact curve. The parametric equation of the working left tooth surface of the rack:

[0040]

[0041] The formation of the rack tooth surface is realized along the parallel motion of the rack contact curve. The parametric equation of the working right tooth surface of the rack:

[0042]

[0043] Furthermore, the root fillet curves of the gear and the rack are determined as follows:

[0044] The right - hand root fillet of the gear end face uses a Hermite curve as the fillet curve, where the Hermite curve is determined by points P F3 and P F4 , and the tangent vectors of points P F3 and P F4 are T F3 and T F4 respectively. The P F3 point is determined by the right - hand working tooth profile curve of the gear and the starting radius P h1 of the root fillet. The P F4 point is determined by the root circle radius Rf1 and the skew line passing through point P F3 with a slope of 1 determines that the parametric equation of the Hermite curve is:

[0045]

[0046] The right tooth root of the end face of the rack uses the Hermite curve as the transition curve, where the Hermite curve is determined by point P G3 and P G4 , and the tangent vectors of point P G3 and P G4 are T G3 and T G4 respectively. Point P G3 is determined by the working tooth profile curve on the right side of the gear and the starting radius R h2 of the tooth root transition fillet. Point P G4 is determined by the tooth root circle radius R f2 and the skew line passing through point P G3 with a slope of 1. The parametric equation of the Hermite curve is:

[0047]

[0048] Among them,

[0049]

[0050] The beneficial effects brought by the technical solution provided by the embodiment of the present invention are:

[0051] 1. A cycloidal tooth profile and cycloidal tooth line pure rolling gear-rack mechanism of the present invention, an active design method based on the parametric equation of the line of action. By setting the meshing point at the pitch point, the line of action is constructed through the motion law of the meshing point, and the gear contact line is a cycloid after being developed on the pitch cylinder surface; similarly, the rack contact line is a cycloid at the rack pitch surface, and the contact line is an axisymmetric cycloid after being developed on the pitch cylinder surface to eliminate the axial force, which can significantly reduce the frictional loss of the bearing, thereby improving the transmission efficiency.

[0052] 2. A cycloidal tooth profile and cycloidal tooth line pure rolling gear-rack mechanism of the present invention, the gear tooth profile and the rack tooth profile are both tooth profiles based on the cycloid, and the tooth roots of the gear and the rack use the Hermite curve, which enhances the bending strength of the tooth root, makes the gear not prone to tooth root breakage, and enhances the service life of the gear and the rack.

[0053] 3. A cycloidal tooth profile and cycloidal tooth line pure rolling gear-rack mechanism of the present invention, the gear contact ratio design is free, and the structural shape of the tooth profile can be determined by setting the contact ratio value, realizing the uniform distribution of the load and improving the dynamic characteristics. Brief Description of the Drawings

[0054] Figure 1 It is a schematic diagram of a pure rolling gear-rack mechanism based on a cycloidal tooth profile and cycloidal tooth line in Embodiment 1 of the present utility model;

[0055] Figure 2 It is a schematic diagram of a spatial meshing coordinate system of a pure rolling gear-rack mechanism based on a cycloidal tooth profile and cycloidal tooth line in Embodiment 1;

[0056] Figure 3 It is an end view schematic diagram of a pure rolling gear-rack mechanism based on a cycloidal tooth profile and cycloidal tooth line in Embodiment 1;

[0057] Figure 4 It is a schematic diagram of the tooth profiles of the gear and the rack in Embodiment 1;

[0058] Figure 5 It is a schematic diagram of the gear in Embodiment 1;

[0059] Figure 6 It is a schematic diagram of the rack in Embodiment 1;

[0060] Figure 7 It is a schematic diagram of a pure rolling gear-rack mechanism based on a cycloidal tooth profile and cycloidal tooth line in Embodiment 2.

[0061] In the figure: 1. Driver; 2. Input shaft; 3. Coupling; 4. Output shaft; 5. Gear; 6. Rack; 7. Meshing line; 8. Pitch cylinder; 9. Rack pitch surface; 10. Gear contact line; 11. Rack contact line; 12. Tooth root transition curve; 13. End face working tooth profile curve. Detailed implementation manners

[0062] To make the objectives, technical solutions and advantages of the present utility model clearer, the following will further describe the embodiments of the present utility model with reference to the accompanying drawings. The following describes a relatively better one among multiple possible embodiments of the present utility model, aiming to provide a basic understanding of the present utility model, but not aiming to identify the key or decisive elements of the present utility model or limit the scope to be protected.

[0063] In all the examples shown and discussed here, any specific value should be interpreted as merely exemplary, rather than as a limitation. Therefore, other examples of the exemplary embodiments may have different values.

[0064] For technologies, methods and devices known to those of ordinary skill in the relevant art, they may not be discussed in detail, but where appropriate, the said technologies, methods and devices should be regarded as part of the specification.

[0065] It should be noted that like reference numerals and letters denote like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof in subsequent figures is not required. At the same time, it should be understood that, for the sake of convenience of description, the dimensions of the various parts shown in the figures are not drawn in actual proportional relationship.

[0066] In the description of the present utility model, it should be noted that the circuits, electronic components and modules involved in the present utility model are all prior arts, and those skilled in the art can fully implement them without further elaboration.

[0067] Furthermore, it should be noted that unless otherwise clearly defined and limited, the terms "installation" and "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present utility model can be understood according to specific circumstances.

[0068] The present utility model provides a cycloidal tooth profile and cycloidal tooth line pure rolling gear-rack mechanism, including a gear 5 and a rack 6 whose pitch circles are tangent to the pitch lines. The end face tooth profiles of the gear 5 and the rack 6 are composed of an end face working tooth profile curve 13 and a tooth root transition curve 12. The end face tooth profiles of the gear 5 and the rack 6 are symmetric about both the left and right sides; the end face working tooth profile curves 13 of the gear 5 and the rack 6 are cycloids; the tooth surfaces of the gear 5 and the rack 6 have a cycloidal tooth line structure; at least one pair of tooth engagement points of the gear 5 and the rack 6 are located at the pitch point to achieve pure rolling engagement contact. The engagement lines formed by the trajectories of the engagement points of the gear 5 and the rack 6 form two contact lines, namely a gear contact line 10 and a rack contact line 11, on the tooth surfaces of the gear 5 and the rack 6 respectively. The tooth surface structures of the gear 5 and the rack 6 are formed by sweeping the end face tooth profiles along the contact lines. After the gear contact line 10 is unfolded along the pitch cylinder surface, it is a cycloid symmetric about the z-axis, and the rack contact line 11 is a cycloid when unfolded at the pitch plane.

[0069] Please refer to Figure 1 , in the cycloidal tooth profile and cycloidal tooth line pure rolling gear-rack mechanism provided by Embodiment 1 of the present utility model, the contact ratio of the gear 5 and the rack 6 is ε = 1.6. The gear 5 and the rack 6 form a pair of gear-rack pairs. The gear 5 is connected to an output shaft 4. The input shaft 2 is fixedly connected to the output shaft 4 through a coupling 3, the input shaft 2 is fixedly connected to a driver 1, and the rack 6 is connected to a driven load.

[0070] See Figures 1 to 6 , the radius of the pitch cylinder 8 of the gear 5 is R1, and the radius of the addendum circle of the rack 6 is R a1, the root circle radius is R f1 , the teeth of the outer surface of the root cylinder of the gear 5 are uniformly distributed with teeth of cycloidal tooth lines. After the gear contact line 10 is unfolded along the pitch cylinder surface of the gear 5, it is an axisymmetric cycloid. The rack contact line 11 is an axisymmetric cycloid after being unfolded along the pitch surface 9 of the rack. The end face tooth profile of the gear 5 consists of a cycloid curve 11 and a left end face root transition curve 12, that is, a Hermite curve, in sequence from the tooth top to the tooth root.

[0071] The end face working tooth profiles and the root transition fillets of the gear 5 and the rack 6 are symmetric about the left and right sides. The left end face tooth profile is obtained by symmetry from the right end face tooth profile. Similarly, the left root transition fillet can be obtained by symmetry from the right root transition fillet. The tooth top control point P of the right end face working tooth profile of the gear 5 U3 is determined by the intersection of the addendum circle radius R a1 and the end face working tooth profile; the root transition start control point P of the right end face working tooth profile of the gear 5 F3 is determined by the intersection of the root transition start circle radius R h1 and the end face working tooth profile; the root control point P of the right end face root transition curve 12 of the gear 5 F4 is the intersection of the root circle radius and the oblique line passing through the point P F3 and having a slope of 1. Similarly, the tooth top control point P of the right end face working tooth profile of the rack 6 U2 is determined by the intersection of the addendum position length R of the rack 6 a2 and the end face working tooth profile; the root transition start control point P of the right end face working tooth profile of the rack 6 G3 is determined by the intersection of the root transition start position length R of the rack 6 h2 and the end face working tooth profile; the root control point P of the right end face root transition curve 12 of the rack 6 G4 is the intersection of the root transition start position length R h2 and the oblique line passing through the point P G3 and having a slope of 1.

[0072] The gear 5 rotates driven by the drive motor 1, causing the rack 6 to perform a translational motion, realizing the transmission of motion and power between the gear 5 and the rack 6. In this embodiment, the driver 1 is an electric motor.

[0073] The contact lines of the gear 5 and the rack 6, the gear contact line 10 and the rack contact line 11 are determined according to the following method:

[0074] Establish four space coordinate systems of O0-x0,y0,z0, O k -x k ,y k ,z k , O1-x1,y1,z1 and O2-x2,y2,z2. The z0 axis and the z1 axis coincide with the rotation axis of the gear 5, zk The meshing line 7 of the shaft with the gear 5 and the rack 6 coincides, the z2 axis is on the rack 6, and the distance from the z k axis is the distance of, z k The distance between the axis and the z0 axis is R1; the coordinate system O0-x0, y0, z0 is fixedly connected to the gear 5, and the coordinate system O2-x2, y2, z2 is fixedly connected to the rack 6. The gear rotates around the z0 axis at a uniform angular velocity ω1, and the rack 6 moves along the y2 axis at a uniform linear velocity v1. After a period of time from the starting position, the coordinate system O0-x0, y0, z0 rotates around the z0 axis with the gear 5, and the coordinate system O2-x2, y2, z2 moves along the y2 axis with the rack 6;

[0075] In the coordinate system O k -x k ,y k ,z k , let the parametric equation of the meshing line 7 of the meshing point movement of the gear 5 and the rack 6 be:

[0076]

[0077] The relationship between the rotation angle of the gear 5 and the movement of the rack 6 is:

[0078]

[0079] When the meshing point moves along the meshing line 7, a gear contact line 10 and a rack contact line 11 are formed on the tooth surfaces of the gear 5 and the rack 6 respectively; according to the coordinate transformation principle, the coordinate transformation matrices of the three space coordinate systems O0-x0, y0, z0, O1-x1, y1, z1 and O2-x2, y2, z2 are:

[0080] M 1k = M 10 ×M 0k (3)

[0081]

[0082] Among them,

[0083]

[0084] In formulas (4) and (6), R1 is the pitch circle radius of the gear 5, is the rotation angle of the gear 5;

[0085] The parametric equation of the contact line gear contact line 10 on the tooth surface of the gear 5 obtained from formulas (1) and (5) is:

[0086]

[0087] The parametric equation of the rack contact line 11 on the tooth surface of the rack 6 is obtained from equations (1) and (4) as follows:

[0088]

[0089] The end face tooth profiles of the gear 5 and the rack 6 are determined by the following method:

[0090] In the coordinate system O k -x k ,y k ,z k The parametric equation of the right working tooth profile of the gear 5 is:

[0091]

[0092] In the coordinate system O k -x k ,y k ,z k The parametric equation of the right working tooth profile of the rack 6 is:

[0093]

[0094] In the coordinate system O k -x k ,y k ,z k The parametric equation of the left working tooth profile of the rack 6 is:

[0095]

[0096] In the coordinate system O1 - x1, y1, z1, the parametric equation of the right working tooth profile of the gear 5 is:

[0097]

[0098] In the coordinate system O1 - x1, y1, z1, the parametric equation of the left working tooth profile of the gear 5 is:

[0099]

[0100] The tooth surfaces of the gear 5 and the rack 6 are determined by the following method:

[0101] The formation of the tooth surface of the gear 5 is swept along the motion law of the meshing point M. The parametric equation of the working left tooth surface of the gear 5:

[0102]

[0103] The formation of the tooth surface of the gear 5 is swept along the motion law of the meshing point M. The parametric equation of the working right tooth surface of the gear 5:

[0104]

[0105] The formation of the tooth surface of the rack 6 is achieved along the movement track of the rack contact curve. The parametric equation of the working left tooth surface of the rack 6 is:

[0106]

[0107] The formation of the tooth surface of the rack 6 is achieved by the parallel movement along the rack contact curve. The parametric equation of the working right tooth surface of the rack 6 is:

[0108]

[0109] The tooth root transition curve 12 of the gear 5 and the rack 6 is determined according to the following method:

[0110] The right end face tooth root of the gear 5 uses a Hermite curve as the transition curve, where the Hermite curve is determined by the points P F3 and P F4 , and the tangent vectors of the points P F3 and P F4 are T F3 and T F4 respectively. The point P F3 is determined by the right working tooth profile curve of the gear 5 and the starting radius R h1 of the tooth root transition fillet. The point P F4 is determined by the tooth root circle radius R f1 and a slant line passing through the point P F3 with a slope of 1. The parametric equation of the Hermite curve is:

[0111]

[0112] The right end face tooth root of the rack 6 uses a Hermite curve as the transition curve, where the Hermite curve is determined by the points P G3 and P G4 , and the tangent vectors of the points P G3 and P G4 are T G3 and T G4 respectively. The point P G3 is determined by the right working tooth profile curve of the gear 5 and the starting radius R h2 of the tooth root transition fillet. The point P G4 is determined by the tooth root circle radius R f2 and a slant line passing through the point P G3 with a slope of 1. The parametric equation of the Hermite curve is:

[0113]

[0114] Among them,

[0115]

[0116] In all the above formulas:

[0117] t - Parameter of the cycloid function parametric equation;

[0118] p - Set value of the cycloid function;

[0119] σ - Motion parameter variable of the meshing point M, and σ ∈ [0, Δσ];

[0120] Δσ - Maximum value of the motion parameter variable of the meshing point;

[0121] - Linear proportionality coefficient for the motion of the meshing point;

[0122] i - Contact ratio

[0123] m t - Transverse module;

[0124] Z1 - Number of teeth of the gear;

[0125] Z2 - Number of teeth passed by the rack after the gear rotates one week;

[0126] T H is the Hermite curve parameter, 0.2 ≤ T H ≤ 1.5;

[0127] t H is the value range of the Hermite curve, 0 ≤ t H ≤ 1;

[0128] P F3 - Intersection point of the starting radius of the gear transition fillet and the parametric equation of the gear working tooth profile;

[0129] P F4 - Intersection point of the root circle radius and the oblique line passing through point P F3 and with a slope of 1;

[0130] P G3 - Intersection point of the starting length of the rack transition fillet and the parametric equation of the rack working tooth profile;

[0131] P G4 - Intersection point of the root position length of the rack and the oblique line passing through point P G3 and with a slope of 1;

[0132] T P1 - Unit tangent vector of point P1;

[0133] TP2 - Unit tangent vector of point P2;

[0134] T G1 - Unit tangent vector of point G1;

[0135] T G2 - Unit tangent vector of point G2;

[0136] x P (P F3 ) - x - coordinate of point P F3 ;

[0137] y p (P F3 ) - y - coordinate of point P F3 ;

[0138] z p (P F3 ) - z - coordinate of point P F3 ;

[0139] x p (P F4 ) - x - coordinate of point P F4 ;

[0140] y p (P F4 ) - y - coordinate of point P F4 ;

[0141] z p (P F4 ) - z - coordinate of point P F4 ;

[0142] x G (P G3 ) - x - coordinate of point P G3 ;

[0143] y G (P G3 ) - y - coordinate of point P G3 ;

[0144] z G (P G3 ) - z - coordinate of point P G3 ;

[0145] x G (P G4 ) - x - coordinate of point P G4 ;

[0146] y G (P G4 ) - y - coordinate of point P G4 ;

[0147] zG (P G4 ) - The z - coordinate of point P G4 ;

[0148] Δd - Face width coefficient;

[0149] b - Tooth width of the gear, b = Δd×2R1; (22)

[0150] α t - Transverse pressure angle, α t = 20°;

[0151] - Addendum coefficient,

[0152] - Clearance coefficient,

[0153] R1 - Pitch circle radius of the gear, R1 = m t Z1 / 2; (23)

[0154] R2 - Pitch line of the rack;

[0155] a - Center distance between the rack and the gear, a = R1 + R2; (24)

[0156] h a - Addendum,

[0157] h f - Dedendum,

[0158] R a1 - Addendum circle radius of the gear, R a1 = R1 + h a ; (27)

[0159] R f1 - Root circle radius of the gear, R f1 = R1 - h f ; (28)

[0160] R h1 - Starting radius of the fillet of the gear, R h1 = R1 - h a ; (29)

[0161] R a2 - Addendum position length of the rack, R a2 = R2 + h a ; (30)

[0162] R f2 - Root position length of the rack, R f2= R2 - h f ; (31)

[0163] R h2 - Rack transition fillet start length, R h2 = r2 - h a ; (32)

[0164] ε - Contact ratio,

[0165] p t - Transverse circular pitch, p t = πm t ; (34).

[0166] The relevant parameters are taken as Z1 = 16, i = 1, m t = 2, b = 32mm, α t = 20°, and Δσ = 0.2, R1 = 16mm, R2 = 38mm are obtained;

[0167] Then substituting the above values into equations (1) - (34), the contact line parameter equation and the transverse tooth profile parameter equation of the gear and the rack in this example can be obtained, the tooth surface structure of the gear and the rack can be obtained, and the assembly can be carried out according to the correct center distance.

[0168] Embodiment 2

[0169] As Figure 7 shown, Embodiment 2 of the present utility model further provides another cycloidal tooth profile and cycloidal tooth line pure rolling gear - rack mechanism. The gear 5 is connected to the output shaft 4, the output shaft 4 is connected to the input shaft 2 through a coupling 3, the input shaft 2 is fixedly connected to the driver 1, and the rack 6 is connected to the driven load. In this embodiment, the number of teeth of the gear 5 is 20. The number of teeth of the rack 6 is 30, and the designed contact ratio ε = 2. When the output shaft 4 drives the gear 5 to rotate, since two pairs of adjacent gears and racks of the gear 5 and the rack 6 are in the meshing state, and the pre - set contact ratio ε = 2 of the cycloidal tooth profile and cycloidal tooth line pure rolling gear - rack mechanism, it is ensured that at each instant, at least two pairs of teeth are simultaneously involved in the meshing transmission, thus realizing the continuous and stable meshing transmission of the cycloidal tooth profile and cycloidal tooth line pure rolling gear - rack mechanism in the rotational motion.

[0170] The relevant parameters are respectively taken as: Z1 = 20, i = 1, m t = 2, ε = 2, b = 40mm, α t = 20°, and Δσ = 0.2, R1 = 20mm, R2 = 38mm are obtained;

[0171] Substituting the above numerical values into Equations (1)-(34), the parametric equations of the contact line and the end face profile of the gear and the rack in this example can be obtained. Then, according to the motion law of the meshing point respectively, the tooth surface structures of the gear and the rack can be obtained, and they can be assembled according to the correct center distance.

[0172] In this article, the orientation words such as front, back, up, and down are defined based on the positions of the components in the attached drawings and the positions of the components relative to each other, only for the sake of clarity and convenience in expressing the technical solution. It should be understood that they are relative concepts and can change accordingly according to different usage and placement methods. The use of the orientation words should not limit the scope claimed in this application.

[0173] Without conflict, the above embodiments and the features in the embodiments in this article can be combined with each other. The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A cycloidal tooth profile and cycloidal tooth line pure rolling gear-rack mechanism, characterized in that: It includes a gear and a rack where the pitch circle is tangent to the pitch line. The end face tooth profiles of the gear and the rack are composed of an end face working tooth profile curve and a tooth root transition curve. The end face tooth profiles of the gear and the rack are symmetric about the left and right sides. The end face working tooth profile curves of the gear and the rack are cycloids. The tooth surfaces of the gear and the rack have a cycloidal tooth line structure. At least one pair of tooth engagement points of the gear and the rack are located at the pitch point to achieve pure rolling engagement contact. The meshing lines formed by the trajectories of the engagement points of the gear and the rack respectively form two contact lines on the tooth surfaces of the gear and the rack.

2. The pure rolling gear-rack mechanism with cycloidal tooth profile and cycloidal tooth trace as claimed in claim 1, wherein: The tooth surface structures of the gear and the rack are formed by sweeping the end face tooth profiles along the contact lines. After the contact line of the gear is developed along the pitch cylinder surface, it is a cycloid symmetric about the z-axis. The contact line of the rack is a cycloid when developed at the pitch plane.

3. A cycloidal tooth profile and cycloidal tooth line pure rolling gear-rack mechanism according to claim 1, characterized in that: The right working tooth profile curves of the gear and the rack are both formed by cycloid function curves, and the tooth root transition curve is composed of Hermite curves; the tooth top control point of the end face working tooth profile curve is determined by the intersection point of the tooth top circle and the cycloid function curve, and the starting control point of the tooth root transition curve is formed by the intersection of the cycloid function curve and the tooth root transition starting circle to form an intersection point P G4 , and the contact control point of the tooth root transition curve is formed by the intersection of the tooth root circle and the oblique line passing through point P G4 and having a slope of 1 to form P G3 ; Connect point P G4 and point P G3 according to the Hermite curve equation to form the tooth root curve.

4. The cycloid tooth profile and cycloid tooth line pure rolling gear-rack mechanism according to claim 3, wherein: The contact lines of the gear and the rack are determined according to the following method: Establish four spatial coordinate systems O0-x0,y0,z0, O k -x k ,y k ,z k , O1-x1,y1,z1 and O2-x2,y2,z2. In these coordinate systems, the z0-axis and the z1-axis coincide with the rotational axis of the gear, the z k -axis coincides with the meshing line of the gear and the rack, the z2-axis is on the rack and is at a distance of k from the z -axis, and the distance between the z k -axis and the z0-axis is R1; the coordinate system O0-x0,y0,z0 is fixedly connected to the gear, the coordinate system O2-x2,y2,z2 is fixedly connected to the rack, the gear rotates around the z0-axis with a uniform angular velocity ω1, the rack moves along the y2-axis with a uniform linear velocity v1. After a period of time from the starting position, the coordinate system O0-x0,y0,z0 rotates around the z0-axis with the gear, and the coordinate system O2-x2,y2,z2 moves along the y2-axis with the rack; In the coordinate system O k -x k , y k , z k , let the parametric equation of the meshing line of the meshing point of the said gear and the said rack be: The relationship between the rotation angle of the gear and the movement of the rack is: When the engagement point moves along the meshing line, contact lines are respectively formed on the tooth surfaces of the gear and the rack. According to the coordinate transformation principle, the coordinate transformation matrices of the three space coordinate systems O0-x0,y0,z0, O1-x1,y1,z1 and O2-x2,y2,z2 are: M 1k = M 10 × M 0k (3) Where, In formulas (4) and (6), R1 is the pitch circle radius of the gear, is the rotation angle of the gear; The parametric equation of the contact line of the gear tooth surface is obtained from equations (1) and (5): The parametric equation of the contact line of the rack tooth surface is obtained from equations (1) and (4):

5. The cycloid tooth profile and cycloid tooth line pure rolling gear and rack mechanism according to claim 4, characterized in that: The end face tooth profiles of the gear and the rack are determined by the following method: In coordinate system O k -x k ,y k ,z k The parametric equation of the right working tooth profile of the gear described above is as follows: In coordinate system O k -x k , y k , z k The parametric equation of the right working tooth profile of the rack described therein is: In coordinate system O k -x k , y k , z k The parametric equation of the left working tooth profile of the rack described above is: The parametric equation of the right working tooth profile of the gear in the coordinate system O1-x1,y1,z1 is: The parametric equation of the left working tooth profile of the gear in the coordinate system O1-x1,y1,z1 is:

6. A cycloidal tooth profile and cycloidal tooth line pure rolling gear-rack mechanism according to claim 5, characterized in that: The tooth surfaces of the gear and the rack are determined according to the following method: The formation of the gear tooth surface is swept along the movement law of the engagement point M. The parametric equation of the working left tooth surface of the gear: The formation of the gear tooth surface is swept along the movement law of the engagement point M. The parametric equation of the working right tooth surface of the gear: The formation of the rack tooth surface is realized along the movement trajectory of the rack contact curve. The parametric equation of the working left tooth surface of the rack: The formation of the rack tooth surface is realized by the parallel movement along the rack contact curve. The parametric equation of the working right tooth surface of the rack:

7. A cycloidal tooth profile and cycloidal tooth line pure rolling gear and rack mechanism according to claim 6, characterized in that: The tooth root transition curves of the gear and the rack are determined according to the following method: The right tooth root of the end face of the said gear uses a Hermite curve as the transition curve, where the Hermite curve is determined by points P F3 and P F4 , and the tangent vectors of points P F3 and P F4 are T F3 and T F4 respectively. Point P F3 is determined by the working tooth profile curve on the right side of the gear and the starting radius R h1 of the tooth root transition fillet. Point P F4 is determined by the tooth root circle radius R f1 and a slant line passing through point P F3 with a slope of 1. The parametric equation of the Hermite curve is as follows: The right tooth root of the end face of the rack uses a Hermite curve as the transition curve, where the Hermite curve is determined by points P G3 and P G4 , and the tangent vectors of points P G3 and P G4 are T G3 and T G4 respectively. Point P G3 is determined by the working tooth profile curve on the right side of the gear and the starting radius R h2 of the tooth root transition fillet. Point P G4 is determined by the tooth root circle radius R f2 and a slant line passing through point P G3 with a slope of 1. The parametric equation of the Hermite curve is as follows: Where, In all the above equations: t - parameter of the cycloid function parametric equation; p - set value of the cycloid function parameter; σ - movement parameter variable of the engagement point M, and σ ∈ [0,Δσ]; Δσ - maximum value of the movement parameter variable of the engagement point; - The linear proportionality coefficient of the movement of the meshing point; i - contact ratio m t - Transverse module; Z1 - number of teeth of the gear; Z2 - number of teeth of the rack passed after the gear rotates one week; T H is the Hermite curve parameter; t H Value range for Hermite type curve Δd - face width coefficient; b - tooth width of the gear, b = Δd×2R1; (22) α t - End face pressure angle; - addendum coefficient; - Clearance coefficient; R1 - pitch circle radius of the gear, R1 = mtZ1 / 2; (23) R2 - pitch line of the rack; a - center distance between the rack and the gear, a = R1 + R2; (24) h a - Addendum height, h f - Dedendum height, R a1 - Pitch circle radius of gear teeth, R a1 = R1 + h a ; (27) R f1 - Pitch circle radius of gear teeth, R f1 =R1 - h f ; (28) R h1 - Starting radius of gear transition fillet, R h1 = R1 - h a ; (29) R a2 - Length of the tooth tip position of the rack, R a2 = R2 + h a ; (30) R f2 - Length of the root position of the rack tooth, R f2 = R2 - h f ; (31) R h2 - Starting length of rack transition fillet, R h2 = R2 - h a ; (32) ε-overlap degree, p t - Circular pitch of end face, p t = πm t ; (34).

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