Pure rolling external meshing gear based on parabolic tooth profile and gear pump

Abstract

The invention provides a pure rolling external meshing gear based on a parabola tooth profile and a gear pump, and relates to the technical field of gear transmission, the gear comprises a driving parabola tooth profile pure rolling bevel gear and a driven parabola tooth profile pure rolling bevel gear, an end face tooth profile curve is composed of an end face working tooth profile curve and an end face tooth root transition curve, the end face working tooth profile curve is composed of parabolic functions, the end face tooth root transition curve is composed of Hermite curves, meshing points are located at the tangent point of two reference circles, and meshing lines formed by the meshing points form two contact lines on the tooth surface of the driving bevel gear and the tooth surface of the driven bevel gear respectively during rotation. The external gear pump has the beneficial effects that the meshing points are arranged at the joints, the meshing lines are constructed according to the movement rule of the meshing points, the contact lines are spiral lines after being unfolded on the joint cylindrical surface, the contact points on the contact lines are in a pure rolling mode, the theoretical end face overlap ratio is zero, the oil trapping phenomenon of a traditional external gear pump is effectively eliminated, and the service life of the gear pump is prolonged. And the problems of noise and cavitation can be effectively avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of gear transmission, and in particular to a pure rolling external meshing gear based on a parabolic tooth profile and a gear pump. Background Art

[0002] As an important component in hydraulic systems, external gear pumps are widely used in industrial automation, metallurgy, chemical industry, aerospace and other fields. They have the advantages of simple structure, strong self-priming ability, and strong resistance to oil contamination. External gear pumps are mainly composed of active parabolic tooth profile pure rolling helical gears, driven parabolic tooth profile pure rolling helical gears, pump body, pump cover and safety valve. During operation, the two gears mesh with each other and rotate in the pump body to form a sealed working volume, and the suction and discharge of liquid are achieved through the change of volume. However, traditional external gear pumps have problems such as oil entrapment, leakage, and radial force imbalance. Among them, in traditional external gear pumps, a closed cavity is formed between the gear teeth when the gears mesh, and the cavity will change, which causes oil entrapment and cavitation. The oil entrapment problem will cause the oil pressure to fluctuate sharply, generating noise and cavitation problems.

[0003] In order to solve the problem of oil trapping in gear pumps, a variety of improvement methods have been adopted in the prior art. For example, Chinese patent application number 201811173572.4 discloses a / / -shaped unloading groove of an external gear pump, and Chinese patent application number 201680070594.0 discloses an external gear pump. Both methods have unloading grooves on the pump casing to eliminate the oil trapping phenomenon. However, the setting of the unloading groove may affect the volumetric efficiency of the pump and cannot effectively solve the sharp fluctuations in oil pressure caused by oil trapping in the external gear pump, resulting in noise and cavitation problems. Summary of the Invention

[0004] In view of this, in order to solve the problem of oil trapping in existing gear pumps, which causes rapid fluctuations in oil pressure, noise and cavitation, an embodiment of the present invention provides a pure rolling external meshing gear and a gear pump based on a parabolic tooth profile.

[0005] An embodiment of the present invention provides a pure rolling external meshing gear based on a parabolic tooth profile, comprising a driving helical gear and a driven helical gear with parallel axes, wherein the driving helical gear and the driven helical gear are in pure rolling meshing transmission, and the end face tooth profile curves of the driving helical gear and the driven helical gear are both composed of an end face working tooth profile curve and an end face tooth root transition curve, the end face working tooth profile curve is composed of a parabolic function, the end face tooth root transition curve is composed of a Hermite curve, and the end face tooth profile curves of the driving helical gear and the driven helical gear are both symmetrical on the left and right sides; the tooth surfaces of the driving helical gear and the driven helical gear have a helical structure; the meshing point of the driving helical gear is at a pitch circle, and the meshing point of the driven helical gear is at a pitch circle, and the two pitch circles are tangent to achieve pure rolling meshing contact, and the meshing lines formed by the meshing points when the driving helical gear and the driven helical gear rotate relative to each other form two contact lines on the tooth surfaces of the driving helical gear and the driven helical gear respectively.

[0006] Furthermore, the tooth surface structures of the driving helical gear and the driven helical gear are formed by the movement of the tooth profile curves of the respective gear end faces along the tooth surface contact lines along the contact points, and the contact lines are straight lines passing through the origin and having a slope greater than 0 after being unfolded along the gear pitch cylinder.

[0007] Furthermore, the working tooth profile curve on the left side of the end face of the active helical gear is composed of a parabolic function, wherein the tooth top control point P3 is formed by the intersection of the tooth top circle and the parabolic function, the tooth root transition fillet starting point P1 is formed by the intersection of the tooth root transition fillet starting circle and the parabolic function, and the tooth root control point is formed by the intersection of the tooth root circle radius and the oblique line passing through the point P1 and with a slope of 1.

[0008] Furthermore, the working tooth profile curve on the right side of the end face of the driven helical gear is composed of a parabolic function, wherein the driven gear tooth top control point G3 is formed by the intersection of the tooth top circle and the parabolic function, the tooth root transition fillet starting point G1 is formed by the intersection of the tooth root transition fillet starting circle and the parabolic function, and the tooth root control point G2 is formed by the intersection of the tooth root circle radius and the oblique line passing through point G1 and with a slope of 1.

[0009] Furthermore, the contact line between the driving helical gear and the driven helical gear is determined according to the following method:

[0010] Establish O0-x0,y0,z0,O k -x k ,y k ,z k In the four spatial coordinate systems O1-x1, y1, z1 and O2-x2, y2, z2, the z0 axis and the z1 axis coincide with the rotation axis of the driving helical gear. k The axis coincides with the meshing line of the driving helical gear, the z2 axis is on the driven helical gear, and the driven helical gear moves along the z axis at a uniform angular velocity ω2. pAxis rotation, z k Axis and z1, z k The distance between the axes is R1; the coordinate system O0-x0, y0, z0 is fixedly connected to the driving helical gear, and the coordinate system O2-x2, y2, z2 is fixedly connected to the driven helical gear. The driving helical gear rotates around the z0 axis at a uniform angular velocity ω1, and the driven helical gear rotates around the z0 axis at a uniform angular velocity ω2. p The axis rotates, and after a period of time from the starting position, the coordinate system O0-x0, y0, z0 rotates around the z1 axis along with the driving helical gear, and the coordinate system O p -x p ,y p ,z p Rotates along the z2 axis along with the driven helical gear;

[0011] In coordinate system O k -x k ,y k ,z k In the equation, the meshing line parameter equation of the meshing point motion of the driving helical gear and the driven helical gear is:

[0012]

[0013] The relationship between the rotation angles of the driving helical gear and the driven helical gear is:

[0014]

[0015] When the meshing point moves along the meshing line KK, contact lines are formed on the tooth surfaces of the driving helical gear and the driven helical gear respectively. According to the coordinate transformation principle, the coordinate transformation matrices of the three spatial coordinate systems O0-x0, y0, z0, O1-x1, y1, z1 and O2-x2, y2, z2 are formed as follows:

[0016] M 1k =M 10 ×M 0k (3)

[0017]

[0018] in,

[0019]

[0020] In formulas (4) and (6), R1 is the pitch radius of the driving helical gear, is the rotation angle of the active helical gear;

[0021] The parametric equation of the contact line of the active helical gear tooth surface is obtained from equations (1) and (5):

[0022]

[0023] The parametric equation of the contact line of the driven helical gear tooth surface is obtained from equations (1) and (4):

[0024]

[0025] Furthermore, the end face tooth profiles of the driving helical gear and the driven helical gear are determined by the following method:

[0026] In coordinate system O k -x k ,y k ,z k The parametric equation of the right working tooth profile of the driven helical gear is as follows:

[0027]

[0028] In coordinate system O k -x k ,y k ,z k The parametric equation of the right working tooth profile of the active helical gear is:

[0029]

[0030] The parametric equation of the right working tooth profile of the active helical gear in the coordinate system O2-x2, y2, z2 is:

[0031]

[0032] The parametric equation of the right working tooth profile of the driven helical gear in the coordinate system O1-x1, y1, z1 is:

[0033]

[0034] The parametric equation of the left working tooth profile of the active helical gear in the coordinate system O2-x2, y2, z2 is:

[0035]

[0036] The parametric equation of the left working tooth profile of the driven helical gear in the coordinate system O1-x1, y1, z1 is:

[0037]

[0038] Furthermore, the tooth surfaces of the driving helical gear and the driven helical gear are determined according to the following method:

[0039] The parametric equation of the working left tooth surface of the driven helical gear is:

[0040]

[0041] The parametric equation of the working right tooth surface of the driven helical gear is:

[0042]

[0043] The parametric equation of the working left tooth surface of the active helical gear is:

[0044]

[0045] The parametric equation of the working right tooth surface of the active helical gear is:

[0046]

[0047] in,

[0048] T=c m σ (19).

[0049] Furthermore, the tooth root transition curves of the driving helical gear and the driven helical gear are determined according to the following method:

[0050] The right tooth root of the end face of the active helical gear uses the Hermite curve as the transition curve, wherein the Hermite curve is composed of points P1 and P2, and the tangent vectors of points P1 and P2 are T P1 and T P2 Point P1 is determined by the right working tooth profile curve of the active helical gear and the starting radius R of the tooth root transition fillet. h1 Point P2 is determined by the tooth root radius R f1 And the slope line passing through point P1 with a slope of 1 determines the parametric equation of the Hermite curve:

[0051]

[0052] The right tooth root of the driven helical gear uses a Hermite curve as a transition curve, wherein the Hermite curve is composed of points G1 and G2, and the tangent vectors of points G1 and G2 are T G1 and T G2 The G1 point is determined by the right working tooth profile curve of the driven helical gear and the starting radius R of the tooth root transition fillet. h2 The G2 point is determined by the tooth root radius R f2 And the slope line passing through point G1 with a slope of 1 determines the parametric equation of the Hermite curve:

[0053]

[0054] in,

[0055]

[0056] In addition, an embodiment of the present invention further provides a gear pump, comprising the above-mentioned pure rolling external meshing gear based on a parabolic tooth profile, and also comprising a housing, a driving shaft and a driven shaft, wherein the driving shaft is rotatably mounted in the housing and one end extends out of the housing, the driving helical gear is mounted on the driving shaft, the driven shaft is rotatably mounted in the housing, the driven helical gear is mounted on the driven shaft, the driving helical gear and the driven helical gear are meshed, and a sealed working chamber is formed between the meshing gear teeth of the driving helical gear and the driven helical gear.

[0057] Furthermore, it also includes four bearings and seals arranged in the housing, wherein every two bearings are installed in the housing through a bearing seat, and two of the bearings are sleeved on the driving shaft and located at both ends of the driving helical gear, and the other two bearings are sleeved on the driven shaft and located at both ends of the driven helical gear, and the seals are used to seal the connection position between the bearing seat and the driving shaft and the housing.

[0058] The beneficial effects brought about by the technical solution provided by the embodiments of the present invention are:

[0059] 1. The present invention is a pure rolling external meshing gear and gear pump based on a parabolic tooth profile, and an active design method based on the meshing line parameter equation. By setting the meshing point at the node, the meshing line is constructed according to the motion law of the meshing point, and the contact line is a spiral line after being unfolded on the pitch cylindrical surface, so that the contact point on the contact line is in a pure rolling form and the theoretical end face overlap is zero.

[0060] 2. The present invention is a pure rolling external meshing gear and gear pump based on a parabolic tooth profile. When the driving helical gear and the driven helical gear are meshing for transmission in the gear pump, the theoretical end face overlap is zero. The driving helical gear and the driven helical gear end faces have only one meshing point. After meshing, there is a gap between the driving helical gear and the driven helical gear end faces, and oil trapping will not occur. This can effectively eliminate the oil trapping phenomenon of traditional external meshing gear pumps, and can effectively avoid the problems of rapid fluctuations in oil pressure, noise and cavitation caused by traditional external meshing gear pumps.

[0061] 3. The present invention is a pure rolling external meshing gear based on a parabolic tooth profile. The tooth profile is established based on a parabolic function, and the gear tooth root uses a Hermite curve to enhance the tooth root bending strength, making the gear less likely to have a tooth root breakage and extending the gear service life.

[0062] 4. The present invention is a pure rolling external meshing gear based on a parabolic tooth profile. The gear overlap can be designed freely. The structural shape of the tooth profile can be determined by setting the overlap value, thereby achieving uniform load distribution and improving dynamic characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Schematic diagram of a pure rolling external meshing gear based on a parabolic tooth profile according to the present invention;

[0064] Figure 2 It is a schematic diagram of the spatial meshing coordinate system of the driving helical gear and the driven helical gear;

[0065] Figure 3 It is a schematic diagram of the end faces of the driving helical gear and the driven helical gear.

[0066] Figure 4 It is a schematic diagram of the tooth profile of the driving helical gear and the driven helical gear;

[0067] Figure 5 It is a schematic diagram of a gear pump of the present invention;

[0068] Figure 6 It is an exploded view of a gear pump of the present invention.

[0069] In the figure: 1. Driving shaft; 2. Front pump cover; 3. First sealing ring; 4. Second sealing ring; 5. Bearing seat; 6. Pump body; 7. Driven shaft; 8. Driving bevel gear; 9. Locating pin; 10. Liquid inlet; 11. Rear pump cover; 12. Driving shaft key; 13. Driven shaft key; 14. Liquid outlet; 15. Driven bevel gear; 16. Fastening bolts; 17. Bearing. DETAILED DESCRIPTION

[0070] To make the objectives, technical solutions, and advantages of the present invention more apparent, embodiments of the present invention will be further described below with reference to the accompanying drawings. The following describes a preferred embodiment of the present invention among multiple possible embodiments, which is intended to provide a basic understanding of the present invention but is not intended to identify the key or decisive elements of the present invention or to limit the scope of protection.

[0071] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0072] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered part of the specification.

[0073] It should be noted that similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further discussed in the subsequent drawings. At the same time, it should be understood that for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual scale.

[0074] In the description of the present invention, it should be noted that the circuits, electronic components and modules involved in the present invention are all existing technologies and can be fully implemented by those skilled in the art without further elaboration.

[0075] It should be further noted that, unless otherwise expressly specified or limited, the terms "mounted" and "connected" should be understood broadly. For example, they can refer to fixed, removable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediary; and internal communication between two components. Those skilled in the art will understand the specific meanings of these terms in the present invention based on the specific circumstances.

[0076] The present invention provides a pure rolling external meshing gear based on a parabolic tooth profile, comprising a driving helical gear 8 and a driven helical gear 15 with parallel axes, wherein the driving helical gear 8 and the driven helical gear 15 are in pure rolling meshing transmission, and the end face tooth profile curves of the driving helical gear 8 and the driven helical gear 15 are composed of an end face working tooth profile curve and an end face tooth root transition curve, the end face working tooth profile curve is composed of a parabolic function, and the end face tooth root transition curve is composed of a Hermite curve, and the driving helical gear 8 and the driven helical gear 15 are in pure rolling meshing transmission. The end face tooth profile curves of the driven helical gear 15 are symmetrical on both sides. The tooth surfaces of the driving helical gear 8 and the driven helical gear 15 have a helical structure. The meshing point of the driving helical gear 8 is at the pitch circle, and the meshing point of the driven helical gear 15 is at the pitch circle. The two pitch circles are tangent to achieve pure rolling meshing contact. When the driving helical gear 8 and the driven helical gear 15 rotate relative to each other, the meshing line formed by the meshing point forms two contact lines on the tooth surfaces of the driving helical gear 8 and the driven helical gear 15, respectively. The tooth surface structure of the driving helical gear 8 and the driven helical gear 15 is formed by the movement of the tooth profile curves of the respective gear ends along the tooth surface contact line with the contact point. When the contact lines are expanded along the gear pitch cylinder, they are straight lines passing through the origin and with a slope greater than 0.

[0077] Please refer to Figure 1 In a pure rolling external meshing gear based on a parabolic tooth profile provided by an embodiment of the present invention, the driving helical gear 8 and the driven helical gear 15 are applied to a mechanical transmission with a transmission ratio of 1, and the axial overlap between the driving helical gear 8 and the driven helical gear 15 is ε β =1.4. The driving helical gear 8 and the driven helical gear 15 form a pair of gears. The driving helical gear 8 is driven to rotate by driving the driving helical gear 8. The driving helical gear 8 and the driven helical gear 15 are engaged with each other and transmit power.

[0078] Please refer to Figures 1 to 4 The pitch circle radius of the active helical gear 8 is R1, and the top circle radius is R a1 , tooth root radius is Rf1 The contact line of the active helical gear 8 is a straight line, and the contact line developed according to the motion law of the active helical gear 8 is a helical line. The end face tooth profile of the active helical gear 8 is axisymmetric, that is, the left and right end face tooth profiles are axisymmetric. Taking the left end face tooth profile of the active helical gear 8 as an example, from the tooth top to the tooth root, it is composed of a parabolic function curve of the gear tooth's left end face working tooth profile and a Hermite curve, a transition curve to the left end face tooth root.

[0079] The end face working tooth profiles of the driving helical gear 8 and the driven helical gear 15 are end face parabolic tooth profiles, and the left and right sides of the tooth profiles are axially symmetrical. The tooth profile on the left side of the end face can be obtained by the axial symmetry of the tooth profile on the right side of the end face; specifically, the tooth root transition part is a Hermite curve, which is obtained by controlling point P1 and point P2 and calculating the tangent vector of the two points.

[0080] The working tooth profile curve on the right side of the end face of the active helical gear 8 is composed of a parabolic function, wherein the tooth top control point P3 is formed by the intersection of the tooth top circle and the parabolic function, the tooth root transition fillet starting point P1 is formed by the intersection of the tooth root transition fillet starting circle and the parabolic function, and the tooth root control point is formed by the intersection of the tooth root circle radius and the oblique line passing through the point P1 and with a slope of 1.

[0081] The working tooth profile curve on the right side of the end face of the driven helical gear 15 is composed of a parabolic function, wherein the driven gear tooth top control point G3 is formed by the intersection of the tooth top circle and the parabolic function, the tooth root transition fillet starting point G1 is formed by the intersection of the tooth root transition fillet starting circle and the parabolic function, and the tooth root control point G2 is formed by the intersection of the tooth root circle radius and the oblique line passing through the point G1 and with a slope of 1.

[0082] The tooth surface contact line c1 and the tooth surface contact line c2 of the driving helical gear 8 and the driven helical gear 15 are determined according to the following method:

[0083] Establish O0-x0,y0,z0,O k -x k ,y k ,z k In the four spatial coordinate systems O1-x1, y1, z1 and O2-x2, y2, z2, the z0 axis and the z1 axis coincide with the rotation axis of the driving helical gear 8, and the z k The axis coincides with the meshing line of the driving helical gear 8, and the z2 axis is on the driven helical gear 15. The driven helical gear 15 moves along the z axis at a uniform angular velocity ω2. p Axis rotation, z k Axis and z1, z kThe distance between the axes is R1; the coordinate system O0-x0, y0, z0 is fixedly connected to the driving helical gear 8, and the coordinate system O2-x2, y2, z2 is fixedly connected to the driven helical gear 15. The driving helical gear 8 rotates around the z0 axis at a uniform angular velocity ω1, and the driven helical gear 15 rotates around the z0 axis at a uniform angular velocity ω2. p The axis rotates, and after a period of time from the starting position, the coordinate system O0-x0, y0, z0 rotates around the z1 axis along with the driving helical gear 8, and the coordinate system O p -x p ,y p ,z p Rotates along the z2 axis along with the driven helical gear 15;

[0084] When the driving helical gear 8 and the driven helical gear 15 are meshed and driven, the meshing point M is set from O k Point starts to move along the meshing line KK at a uniform speed. k -x k ,y k ,z k In the equation, the meshing line parameter equation of the meshing point motion of the driving helical gear 8 and the driven helical gear 15 is:

[0085]

[0086] In order to ensure that the driving helical gear 8 and the driven helical gear 15 are meshed at a fixed transmission ratio, the movement of the angular meshing point between the driving helical gear 8 and the driven helical gear 15 must be a linear relationship. The relationship between the angular positions of the driving helical gear 8 and the driven helical gear 15 is:

[0087]

[0088] When the meshing point moves along the meshing line KK, contact lines are formed on the tooth surfaces of the driving helical gear 8 and the driven helical gear 15 respectively. According to the coordinate transformation principle, the coordinate transformation matrices of the three spatial coordinate systems O0-x0, y0, z0, O1-x1, y1, z1 and O2-x2, y2, z2 are formed as follows:

[0089] M 1k =M 10 ×M 0k (3)

[0090]

[0091] in,

[0092]

[0093] In formulas (4) and (6), R1 is the pitch radius of the driving helical gear 8, is the rotation angle of the active helical gear 8;

[0094] The parametric equation of the contact line of the tooth surface of the active helical gear 8 is obtained from equations (1) and (5):

[0095]

[0096] The parametric equation of the contact line of the tooth surface of the driven helical gear 15 is obtained from equations (1) and (4):

[0097]

[0098] Furthermore, the end face tooth profiles of the driving helical gear 8 and the driven helical gear 15 are determined by the following method:

[0099] In coordinate system O k -x k ,y k ,z k The parametric equation of the right working tooth profile of the driven helical gear 15 is:

[0100]

[0101] In coordinate system O k -x k ,y k ,z k The parametric equation of the right working tooth profile of the active helical gear 8 is:

[0102]

[0103] The parametric equation of the right working tooth profile of the active helical gear 8 in the coordinate system O2-x2, y2, z2 is:

[0104]

[0105] The parametric equation of the right working tooth profile of the driven helical gear 15 in the coordinate system O1-x1, y1, z1 is:

[0106]

[0107] The parametric equation of the left working tooth profile of the active helical gear 8 in the coordinate system O2-x2, y2, z2 is:

[0108]

[0109] The parametric equation of the left working tooth profile of the driven helical gear 15 in the coordinate system O1-x1, y1, z1 is:

[0110]

[0111] Furthermore, the tooth surfaces of the driving helical gear 8 and the driven helical gear 15 are determined according to the following method:

[0112] The parametric equation of the working left tooth surface of the driven helical gear 15 is:

[0113]

[0114] The parametric equation of the working right tooth surface of the driven helical gear 15 is:

[0115]

[0116] The parametric equation of the working left tooth surface of the active helical gear 8 is:

[0117]

[0118] The parametric equation of the working right tooth surface of the active helical gear 8 is:

[0119]

[0120] in,

[0121] T=c m σ (19).

[0122] Furthermore, the tooth root transition curves of the driving helical gear 8 and the driven helical gear 15 are determined according to the following method:

[0123] The right tooth root of the end face of the driving helical gear 8 uses a Hermite curve as a transition curve, wherein the Hermite curve is formed by points P1 and P2, and the tangent vectors of points P1 and P2 are T P1 and T P2 Point P1 is determined by the right working tooth profile curve of the active helical gear 8 and the starting radius R of the tooth root transition fillet. h1 Point P2 is determined by the tooth root radius R f1 And the slope line passing through point P1 with a slope of 1 determines the parametric equation of the Hermite curve:

[0124]

[0125] The right tooth root of the driven helical gear 15 uses a Hermite curve as a transition curve, wherein the Hermite curve is composed of points G1 and G2, and the tangent vectors of points G1 and G2 are T G1 and T G2 The G1 point is determined by the right working tooth profile curve of the driven helical gear 15 and the starting radius R of the tooth root transition fillet. h2 The G2 point is determined by the tooth root radius R f2And the slope line passing through point G1 with a slope of 1 determines the parametric equation of the Hermite curve:

[0126]

[0127] in,

[0128]

[0129] In all the above formulas:

[0130] p-parabolic function parameter;

[0131] σ-motion parameter variable of meshing point M, and σ∈[0,Δσ];

[0132] Δσ - the maximum value of the motion parameter variable of the meshing point;

[0133] - is the linear proportional coefficient of the meshing point movement;

[0134] m t -end face module;

[0135] Z1-number of teeth of the active helical gear;

[0136] Z2-number of teeth on the driven helical gear;

[0137] c m - kinematic coefficients of helical gears;

[0138] T H is the Hermite type line parameter, 0.2≤T H ≤1.5;

[0139] t H is the value range of the Hermite type line, 0≤t H ≤1;

[0140] P1-the intersection of the starting circle of the transition fillet of the active helical gear and the parameter equation of the working tooth profile of the active helical gear;

[0141] P2-the intersection of the root circle of the active helical gear and the oblique line passing through point P1 with a slope of 1;

[0142] G1-intersection point of the starting circle of the transition fillet of the driven helical gear and the parameter equation of the working tooth profile of the driven helical gear;

[0143] G2-the intersection of the root circle of the driven helical gear and the oblique line passing through point G1 with a slope of 1;

[0144] T P1 - tangent vector of point P1;

[0145] T P2 - tangent vector of point P2;

[0146] T G1 - tangent vector of point G1;

[0147] T G2 - tangent vector of point G2;

[0148] x p12 (P1) – x-coordinate of point P1;

[0149] y p12 (P1) – y coordinate of point P1;

[0150] z p12 (P1) – z coordinate of point P1;

[0151] x p12 (P2) – x-coordinate of point P2;

[0152] y p12 (P2) – y coordinate of point P2;

[0153] z p12 (P2) – z coordinate of point P2;

[0154] x G12 (G1) – x-coordinate of point G1;

[0155] y G12 (G1) – y coordinate of point G1;

[0156] z G12 (G1) – y coordinate of point G1;

[0157] x G12 (G2) – x-coordinate of point G2;

[0158] y G12 (G2) – y coordinate of point G2;

[0159] z G12 (G2) – z coordinate of point G2;

[0160] Δd-face width coefficient;

[0161] i-gear ratio;

[0162] b-helical gear tooth width, b=Δd×2R1; (23)

[0163] α n -normal pressure angle;

[0164] α t - end pressure angle,

[0165] β-helix angle, - tooth addendum coefficient,

[0166] - headspace coefficient,

[0167] R1- is the pitch radius of the helical gear, R1 = m t Z1 / 2; (26)

[0168] a-center distance, α=R1+iR1; (27)

[0169] h a - tooth top height,

[0170] h f -Tooth root height,

[0171] R a1 - Radius of the tooth tip circle of the driving helical gear, R a1 =R1+h a ; (30)

[0172] R f1 - Radius of tooth root circle of driving helical gear, R f1 =R1-h f ; (31)

[0173] R h1 - Radius of the starting circle of the transition fillet of the active helical gear, Rh1 = R1-h a ; (32)

[0174] R a2 - Radius of the tooth tip circle of the driven helical gear, R a2 =R2+h a ; (33)

[0175] R f2 - Radius of tooth root circle of driven helical gear, R f2 =R2-h f ; (34)

[0176] R h2 - Radius of the starting circle of the transition fillet of the driven helical gear, R h2 =R2-h a ; (35)

[0177] ε β - axial contact,

[0178] p t - Face pitch, p t =πmt ; (37)

[0179] p s - tooth thickness,

[0180] p e -tooth gap width,

[0181] The relevant parameters are Z1=14, i=1, m t =4.5151, b=37.927mm,α t =22.3350°, we get Δσ=0.2, R1=31.606mm, c m =189.639.

[0182] Then, substituting the above values ​​into equations (1) to (39), the contact line parameter equations and the end face tooth profile parameter equations of the driving helical gear and the driven helical gear in this example can be obtained, and the tooth surface structures of the driving helical gear and the driven helical gear can be obtained.

[0183] In addition, please refer to Figure 1 、 5 and 6. An embodiment of the present invention further provides a gear pump, comprising the above-mentioned pure rolling external meshing gear based on a parabolic tooth profile, and further comprising a housing, a driving shaft 1 and a driven shaft 7.

[0184] The driving shaft 1 is rotatably mounted in the housing and one end extends out of the housing. The driving bevel gear 8 is mounted on the driving shaft 1. The driven shaft 7 is rotatably mounted in the housing. The driven bevel gear 15 is mounted on the driven shaft 7. The driving bevel gear 8 and the driven bevel gear 15 are meshed, and a sealed working chamber is formed between the meshing gear teeth of the driving bevel gear 8 and the driven bevel gear 15.

[0185] The driving shaft 1 and the driven shaft gear are both mounted via bearings 17. Specifically, the gear pump further includes four bearings 17 disposed within the housing. The bearings 17 are sliding bearings 17, wherein every two bearings 17 are mounted within the housing via a bearing seat 5. Two of the bearings 17 are sleeved on the driving shaft 1 and located at both ends of the driving helical gear 8, and the other two bearings 17 are sleeved on the driven shaft 7 and located at both ends of the driven helical gear 15. The driving helical gear 8 is keyed to the driving shaft 1 via a driving shaft key 12, and the driven helical gear 15 is keyed to the driven shaft 7 via a driven shaft key 13.

[0186] The housing includes a front pump cover 2, a pump body 6, and a rear pump cover 11. The pump body 6 is open on both sides to form an 8-shaped inner cavity. The front pump cover 2 and the rear pump cover 11 are respectively connected to the two sides of the pump body 6 to seal the inner cavity. Here, a positioning pin 9 is provided on the front side of the pump body 6. The positioning pin 9 is connected to the front pump cover 2 and plays a positioning role for the front pump cover 2. The rear pump cover 11 is provided with a plurality of fastening bolts 16. The fastening bolts 16 pass through the pump body 6 and connect to the front pump cover 2, thereby assembling the front pump cover 2, the pump body 6, and the rear pump cover 11 into the housing.

[0187] The other two sides of the inner cavity are respectively provided with a liquid inlet 10 and a liquid outlet 14. The liquid inlet 10 and the liquid outlet 14 are approximately located on the same straight line, perpendicular to the end faces of the driving bevel gear 8 and the driven bevel gear 15, and aligned with the meshing portion of the driving bevel gear 8 and the driven bevel gear 15. The portion of the inner cavity near the liquid inlet 10 forms a liquid suction chamber, and the portion of the inner cavity near the liquid outlet 14 forms a liquid pressure chamber. Generally, the liquid inlet 10 and the liquid outlet 14 can be selected as tubular joints, embedded and installed on the outer wall of the inner cavity through a mounting seat.

[0188] The two bearing seats 5 are respectively embedded in both sides of the inner cavity, and the driving bevel gear 8 and the driven bevel gear 15 are arranged between the two bearing seats 5. The driving bevel gear 8 is located at the upper part of the inner cavity, and the driven bevel gear 15 is located at the lower part of the inner cavity. The driving bevel gear 8 and the driven bevel gear 15 are tightly matched with the inner wall of the inner cavity.

[0189] In addition, in order to ensure the sealing of the working space in the inner cavity, the gear pump also includes a seal, which is used to seal the connection between the bearing seat 5 and the driving shaft 1 and the housing. Specifically, the seal includes a first sealing ring 3 and two second sealing rings 4, wherein the first sealing ring 3 is arranged at the connection between the driving shaft 1 and the housing, and the first sealing ring 3 is sleeved on the driving shaft 1 and arranged at the contact position between the driving shaft 1 and the front pump cover 2. The two second sealing rings 4 are respectively sleeved on the outer edges of the two bearing seats 5, and the second sealing rings 4 are arranged at the contact positions between the two bearing seats 5 and the front pump cover 2 and the rear pump cover 11.

[0190] When the gear pump is working, the motor drives the driving shaft 1 to rotate, driving the driving bevel gear 8 to rotate, and the driving bevel gear 8 drives the driven bevel gear 15 to rotate. As the gear teeth of the driving bevel gear 8 and the driven bevel gear 15 gradually disengage, the volume of the sealed working chamber between the gear teeth gradually increases, forming a partial vacuum. Under the action of atmospheric pressure, the fluid enters the liquid inlet chamber from the liquid inlet 10 and fills the inter-tooth grooves. The oil sucked into the inter-tooth grooves is brought to the pressure liquid chamber as the driving bevel gear 8 and the driven bevel gear 15 rotate. In the pressure liquid chamber, as the gear teeth gradually engage, the volume of the sealed working chamber gradually decreases, the fluid is squeezed, the pressure increases, and finally the high-pressure fluid is discharged through the liquid outlet 14.

[0191] In this document, directional terms such as front, back, top, and bottom are defined based on the positions of components in the accompanying drawings and relative to each other, and are intended for clarity and convenience in describing the technical solution. It should be understood that these terms are relative and may vary depending on usage and placement. The use of these directional terms should not limit the scope of protection claimed in this application.

[0192] The above embodiments and features of the embodiments may be combined with each other unless they conflict. The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A pure rolling external gear based on a parabolic tooth profile, comprising a driving helical gear and a driven helical gear with parallel axes, wherein the driving helical gear and the driven helical gear are in pure rolling meshing transmission, characterized in that: The end face tooth profile curves of the driving helical gear and the driven helical gear are both composed of an end face working tooth profile curve and an end face tooth root transition curve, the end face working tooth profile curve is composed of a parabolic function, the end face tooth root transition curve is composed of a Hermite curve, and the end face tooth profile curves of the driving helical gear and the driven helical gear are both symmetrical on the left and right sides; the tooth surfaces of the driving helical gear and the driven helical gear have a spiral line structure; the meshing point of the driving parabolic tooth profile pure rolling helical gear is at the tangent point of two pitch circles, and the meshing point of the driven parabolic tooth profile pure rolling helical gear is at the tangent point of two pitch circles. When the driving helical gear and the driven helical gear rotate relative to each other, the meshing line formed by the meshing point forms two contact lines on the tooth surfaces of the driving helical gear and the driven helical gear respectively.

2. A pure rolling external gear based on a parabolic tooth profile as claimed in claim 1, characterized in that: The tooth surface structures of the driving helical gear and the driven helical gear are formed by the movement of the tooth profile curves of the respective gear end faces along the tooth surface contact lines along the contact points, and the contact lines are straight lines passing through the origin and having a slope greater than 0 after being unfolded along the gear pitch cylinder.

3. The pure rolling external gear based on parabolic tooth profile according to claim 1, characterized in that: The working tooth profile curve on the left side of the end face of the active helical gear is composed of a parabolic function, wherein the tooth top control point P3 is formed by the intersection of the tooth top circle and the parabolic function, the tooth root transition fillet starting point P1 is formed by the intersection of the tooth root transition fillet starting circle and the parabolic function, and the tooth root control point is formed by the intersection of the tooth root circle radius and the oblique line passing through the point P1 and with a slope of 1.

4. The pure rolling external gear based on parabolic tooth profile according to claim 1, characterized in that: The working tooth profile curve on the right side of the end face of the driven helical gear is composed of a parabolic function, wherein the driven gear tooth top control point G3 is formed by the intersection of the tooth top circle and the parabolic function, the tooth root transition fillet starting point G1 is formed by the intersection of the tooth root transition fillet starting circle and the parabolic function, and the tooth root control point G2 is formed by the intersection of the tooth root circle radius and the oblique line passing through point G1 and with a slope of 1.

5. The pure rolling external gear based on parabolic tooth profile according to claim 1, characterized in that: The contact line between the driving helical gear and the driven helical gear is determined according to the following method: Establish O0-x0,y0,z0,O k -x k ,y k ,z k In the four spatial coordinate systems O1-x1, y1, z1 and O2-x2, y2, z2, the z0 axis and the z1 axis coincide with the rotation axis of the active helical gear. k The axis coincides with the meshing line of the driving helical gear, the z2 axis is on the driven helical gear, and the driven helical gear moves along the z axis at a uniform angular velocity ω2. p Axis rotation, z k Axis and z1, z k The distance between the axes is R1; the coordinate system O0-x0, y0, z0 is fixedly connected to the driving helical gear, and the coordinate system O2-x2, y2, z2 is fixedly connected to the driven helical gear. The driving helical gear rotates around the z0 axis at a uniform angular velocity ω1, and the driven helical gear rotates around the z0 axis at a uniform angular velocity ω2. p The axis rotates. After a period of time from the starting position, the coordinate system O0-x0, y0, z0 rotates around the z1 axis along with the driving bevel gear. p -x p ,y p ,z p Rotates along the z2 axis along with the driven helical gear; In the coordinate system O k -x k ,y k ,z k In the above, the meshing line parameter equation of the meshing point motion of the driving helical gear and the driven helical gear is assumed to be: The relationship between the rotation angles of the driving helical gear and the driven helical gear is: When the meshing point moves along the meshing line KK, contact lines are formed on the tooth surfaces of the active helical gear and the driven helical gear respectively; according to the coordinate transformation principle, the coordinate transformation matrices of the three spatial coordinate systems O0-x0, y0, z0, O1-x1, y1, z1 and O2-x2, y2, z2 are formed as follows: M 1k =M 10 ×M 0k (3) in, In formulas (4) and (6), R1 is the pitch radius of the active helical gear, is the rotation angle of the active bevel gear; The parametric equation of the contact line of the active helical gear tooth surface is obtained by equations (1) and (5): The parametric equation of the contact line of the driven helical gear tooth surface is obtained by equations (1) and (4):

6. A pure rolling external gear based on a parabolic tooth profile as claimed in claim 5, characterized in that: The end face tooth profiles of the driving helical gear and the driven helical gear are determined by the following method: In the coordinate system O k -x k ,y k ,z k The parametric equation of the right working tooth profile of the driven helical gear is as follows: In the coordinate system O k -x k ,y k ,z k The right working tooth profile parameter equation of the active helical gear is as follows: The parametric equation of the right working tooth profile of the active helical gear in the coordinate system O2-x2, y2, z2 is: The parametric equation of the right working tooth profile of the driven helical gear in the coordinate system O1-x1, y1, z1 is: The parametric equation of the left working tooth profile of the active helical gear in the coordinate system O2-x2, y2, z2 is: The parametric equation of the left working tooth profile of the driven helical gear in the coordinate system O1-x1, y1, z1 is:

7. A pure rolling external gear based on a parabolic tooth profile as claimed in claim 6, characterized in that: The tooth surfaces of the driving helical gear and the driven helical gear are determined according to the following method: The parameter equation of the working left tooth surface of the driven helical gear is: The parametric equation of the working right tooth surface of the driven helical gear is: The parametric equation of the working left tooth surface of the active helical gear is: The parametric equation of the working right tooth surface of the active helical gear is: in, T=c m (19).

8. A pure rolling external gear based on a parabolic tooth profile as claimed in claim 7, characterized in that: The tooth root transition curves of the driving helical gear and the driven helical gear are determined according to the following method: The right tooth root of the end face of the active helical gear uses a Hermite curve as a transition curve, wherein the Hermite curve is composed of points P1 and P2, and the tangent vectors of points P1 and P2 are T P1 and T P2 Point P1 is determined by the right working tooth profile curve of the active helical gear and the starting radius R of the tooth root transition fillet. h1 The point P2 is determined by the root circle radius R f1 And the oblique line passing through point P1 with a slope of 1 determines the Hermite curve parameter equation: The right tooth root of the end face of the driven helical gear uses a Hermite curve as a transition curve, wherein the Hermite curve is composed of points G1 and G2, and the tangent vectors of points G1 and G2 are T G1 and T G2 The G1 point is determined by the right working tooth profile curve of the driven helical gear and the starting radius R of the tooth root transition fillet. h2 The G2 point is determined by the root circle radius R f2 And the oblique line passing through point G1 with a slope of 1 determines the Hermite curve parameter equation: in, t-parabolic function parameter equation parameters p-sets the parabolic function parameter value; σ-motion parameter variable of meshing point M, and σ∈[0,Δσ]; Δσ-the maximum value of the motion parameter variable of the meshing point; - is the linear proportional coefficient of the meshing point movement; m t -end modulus; Z1-number of teeth of active helical gear; Z2-number of teeth on the driven helical gear; c m - helical gear kinematic coefficient; T H is the Hermite type line parameter; t H The value range of the Hermite type line; Δd-face width coefficient; i- transmission ratio; b-helical gear tooth width, b=Δd×2R1; (23) α n - normal pressure angle; α t - end pressure angle, β-helix angle, -tooth addendum coefficient; -Head clearance coefficient; R1- is the pitch circle radius of the helical gear, R1 = m t Z1 / 2; (26) a-center distance, a=R1+iR1; (27) h a - Tooth top height, h f -Tooth root height, R a1 - Radius of the tooth tip circle of the active helical gear, R a1 =R1+h a ; (30) R f1 - Radius of the tooth root circle of the active helical gear, R f1 =R1-h f ; (31) R h1 - Radius of the starting circle of the transition fillet of the active helical gear, R h1 =R1-h a ; (32) R a2 - Radius of the tooth tip circle of the driven helical gear, R a2 =R2+h a ; (33) R f2 - Radius of tooth root circle of driven helical gear, R f2 =R2-h f ; (34) R h2 - Radius of the starting circle of the transition fillet of the driven helical gear, R h2 =R2-h a ; (35) ε β - axial overlap, p t - Face pitch, p t =πm t ; (37) p s -tooth thickness, p e -tooth gap width, 9. A gear pump, characterized in that: It comprises a pure rolling external meshing gear based on a parabolic tooth profile as described in any one of claims 1 to 8, and also comprises a housing, a driving shaft and a driven shaft, wherein the driving shaft is rotatably mounted in the housing and one end extends out of the housing, the driving bevel gear is mounted on the driving shaft, the driven shaft is rotatably mounted in the housing, the driven bevel gear is mounted on the driven shaft, the driving bevel gear and the driven bevel gear are meshed, and a sealed working chamber is formed between the meshing gear teeth of the driving bevel gear and the driven bevel gear.

10. A gear pump according to claim 9, characterized in that: It also includes four bearings and seals arranged in the housing, wherein every two of the bearings are installed in the housing through a bearing seat, and two of the bearings are sleeved on the driving shaft and located at both ends of the driving bevel gear, and the other two bearings are sleeved on the driven shaft and located at both ends of the driven bevel gear, and the seal is used to seal the connection position between the bearing seat and the driving shaft and the housing.

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