阅读说明：本技术 锥形内啮合线齿轮机构及其构建方法和模拟仿真验证方法 (Conical internal meshing line gear mechanism, construction method thereof and simulation verification method ) 是由 何恩义 何迪 叶喜葱 于 2020-07-14 设计创作，主要内容包括：本发明提供一种锥形内啮合线齿轮机构,包括组成齿轮副的圆柱小齿轮和锥形齿圈,圆柱小齿轮的轴线与锥形齿圈的轴线相交,夹角为0°～90°。同时还提供一种锥形内啮合线齿轮机构的构建方法,包括如下步骤：步骤一,建立齿轮坐标系；步骤二,建立圆柱小齿轮和锥形齿圈接触线；步骤三,选择圆柱小齿轮齿廓半径<I>ρ</I><Sub>1</Sub>、锥形齿圈的齿廓半径<I>ρ</I><Sub>2</Sub>以及接触角<I>φ</I>；步骤四,圆柱小齿轮齿廓沿着圆柱螺旋线扫掠得到螺旋状凸齿,圆锥螺旋线齿廓沿着圆锥螺旋线扫掠得到螺旋状的凹齿。该机构能实现传动轴夹角0?<<I>θ</I><90?的任意角的相交轴传动,提供一种结构简单、小体积且能实现正反转连续稳定传动的内啮合线齿轮机构。(The invention provides a conical inner meshing line gear mechanism which comprises a cylindrical pinion and a conical gear ring, wherein the cylindrical pinion and the conical gear ring form a gear pair, the axis of the cylindrical pinion is intersected with the axis of the conical gear ring, and the included angle is 0-90 degrees. Meanwhile, a construction method of the conical inner meshing line gear mechanism is also provided, and comprises the following steps: step one, establishing a gear coordinate system; step two, establishing a contact line between the cylindrical pinion and the conical gear ring; step three, selecting the radius of the tooth profile of the cylindrical pinion ρ 1 Radius of tooth profile of conical gear ring ρ 2 And contact angle φ (ii) a Step four, the cylindrical pinion tooth profile is swept along the cylindrical spiral line to obtain a spiral convex tooth, and the conical spiral line tooth profile edgeThe helical concave teeth are obtained by sweeping along the conical spiral line. The mechanism can realize the 0 degree of included angle of the transmission shaft< θ <90, provides an inner meshing linear gear mechanism which is simple in structure, small in size and capable of achieving positive and negative rotation continuous stable transmission.)

1. The conical inner engaged line gear mechanism is characterized by comprising a cylindrical pinion and a conical gear ring which form a gear pair, wherein the axis of the cylindrical pinion is intersected with the axis of the conical gear ring, and the included angle is 0-90 degrees.

2. The conical internal engaged gear mechanism according to claim 1, wherein helical convex teeth and concave teeth are uniformly distributed on the cylindrical pinion and the conical gear ring, respectively, the convex teeth and the concave teeth are engaged with each other, a contact line of the convex teeth is a cylindrical helical line, and a contact line of the concave teeth is a conical helical line.

3. The conical internal-meshing-line gear mechanism according to claim 2, wherein the convex tooth profile of the cylindrical pinion is formed by a section of circular arc, and the concave tooth profile of the conical ring gear is formed by two symmetrical circular arcs as a forward-rotation working tooth profile and a reverse-rotation working tooth profile.

4. A construction method of a conical internal meshing line gear mechanism is characterized by comprising the following steps:

step one, establishing a gear coordinate system;

step two, establishing a contact line between the cylindrical pinion and the conical gear ring;

step three, selecting the radius rho of the tooth profile of the cylindrical pinion₁Tooth profile radius rho of conical gear ring₂And a contact angle phi;

and step four, sweeping the cylindrical pinion gear tooth profile along the cylindrical spiral line to obtain spiral convex teeth, and sweeping the conical gear tooth profile along the conical spiral line to obtain spiral concave teeth.

5. A awl according to claim 4 The method for constructing the annular inner meshing line gear mechanism is characterized in that: in the first step, o-xyz and o-x_py_pz_pIs a fixed coordinate system, o-x₁y₁z₁And o-x₂y₂z₂Is a coordinate system fixedly connected with the cylindrical pinion and the conical gear ring respectively, xoz and x_po_pz_pCoplanar; z-axis and z_pThe axis coincides with the axes of rotation of the cylindrical pinion and the conical ring gear, respectively, the z-axis and the z-axis_pThe included angle of the axes being theta (0 DEG)<θ<90 degrees); at the initial moment of engagement, o-xyz and o-x_py_pz_pAre each independently of o-x₁y₁z₁And o-x₂y₂z₂Overlapping; the cylindrical pinion and the conical ring gear each having an angular velocity ω₁、ω₁Around z₀、z_pThe shaft rotates at a constant speed, the steering is the same, and the rotating angle is theta after t steps₁And theta₂(ii) a The components of the center-to-center distances in the x-axis and z-axis are a, b.

6. The method of constructing a tapered internal-meshing-line gear mechanism according to claim 4, wherein: the contact line parameter equation on the tooth surface of the cylindrical pinion is as follows:

calculating a contact line equation of the tooth surface of the conical gear ring according to a space curve meshing equation as follows:

in the formula: m-helical radius of the cylindrical pinion contact line;

p-pitch coefficient;

t is the parameter of the helix;

i₁,j₁,k₁coordinate system o-x₁y₁z₁The base vector of (2);

i₂,j₂,k₂-coordinate systemo-x₂y₂z₂The base vector of (2);

i₁₂-a transmission ratio;

a. b-the components of the center-to-center distances in the x-axis and z-axis;

Theta is the included angle between the input shaft and the output shaft;

t_S、t_E-the respective values of the contact lines entering and exiting the mesh.

7. The method of claim 4, wherein the tooth profile radius ρ of the three-step convex tooth is₁Should be smaller than the tooth profile radius ρ of the concave teeth₂。

8. A simulation and verification method for a conical internal meshing line gear mechanism is characterized in that 'a conical internal meshing line gear mechanism' after being assembled is led into a motion simulation module of NX software to be subjected to kinematic simulation, and comprises the following steps:

the method comprises the following steps: the cylindrical pinion and the conical gear ring are respectively arranged to be rigid connecting rods L001 and L002;

step two: the kinematic pairs of the cylindrical pinion and the conical gear ring are respectively defined as revolute pairs J001 and J002;

step three: setting a contact mode of the cylindrical pinion and the conical gear ring to be 3D contact;

step four: applying a driving force to the cylindrical pinion gear with a given angular velocity of ω₁；

Step five: setting a solving scheme to solve, and recording the angular velocity omega of the conical gear ring in the motion process₂Obtaining an instantaneous angular velocity curve chart;

step six: by calculating the formula i- ω from the transmission ratio₁/ω₂The instantaneous transmission ratio during the movement is obtained.

Technical Field

The invention belongs to the field of gear transmission, and particularly relates to a conical internal meshing line gear mechanism, a construction method thereof and an analog simulation verification method.

Background

Gears are important basic elements in mechanical transmission, and have been widely applied to the fields of aerospace vehicles, new energy equipment, high-speed rails, ships and the like. At present, gear mechanisms based on the conjugate curved surface meshing theory have been widely used, such as spur gears, helical gears, worm gears, herringbone gears, and the like. The gear can realize high power, large transmission ratio, high-power movement and power transmission. With the rapid development of industrial production in the current society, micro-electromechanical products are sought by consumers. The miniature electromechanical product puts forward the requirements of small occupied space, light weight, stable transmission and the like on the transmission mechanism, and the development of the gear meshing theory is promoted.

In recent years, scholars at home and abroad have developed a novel gear mechanism suitable for a micro machine. For example, chinese patent application No. 200810029646.0 discloses "a space curve meshing transmission mechanism", application No. 201110009692.2 discloses "a parallel multi-output shaft micro transmission", patent No. 201210449290.9 discloses "a space staggered shaft gear mechanism". The gear mechanisms are all linear gear mechanisms based on the space curve meshing theory and mainly comprise a driving wheel and a driven wheel, hook rods are uniformly distributed on the driving wheel and the driven wheel, and stable transmission is realized by means of the engagement of the hook rods.

Although the line gear mechanism can realize continuous and stable transmission in a small space, the gear teeth are hook rods in convex contact, so that the tooth surface contact strength is low and the lubrication is difficult; in addition, the hook rod and the gear matrix form a cantilever beam structure, so that the hook rod of the linear gear pair is easy to deform in the meshing process, and even the hook rod is broken. These drawbacks result in a limited range of applications for the line gear mechanism, mostly for light load conditions.

Disclosure of Invention

The invention aims to solve the technical problem of providing a conical inner meshing line gear mechanism, a construction method and an analog simulation verification method thereof, which can realize the transmission of intersecting shafts at any angle of a transmission shaft included angle of 0 degree < theta <90 degrees, and provide the inner meshing line gear mechanism which has a simple structure and small volume and can realize forward and reverse continuous and stable transmission.

In order to solve the technical problem, the technical scheme adopted by the invention is that the conical internal meshing line gear mechanism comprises a cylindrical pinion and a conical gear ring which form a gear pair, wherein the axis of the cylindrical pinion is intersected with the axis of the conical gear ring, and the included angle is 0-90 degrees.

In a preferred scheme, spiral convex teeth and spiral concave teeth are respectively distributed on the cylindrical pinion and the conical gear ring, the convex teeth and the concave teeth are meshed, a contact line of the convex teeth is a cylindrical spiral line, and a contact line on the concave teeth is a conical spiral line.

In a further scheme, the convex tooth profile of the cylindrical pinion is formed by a section of circular arc, and the concave tooth profile of the conical gear ring is formed by two symmetrical circular arcs and respectively used as a forward rotation working tooth profile and a reverse rotation working tooth profile.

The invention also provides a construction method of the conical internal meshing line gear mechanism, which comprises the following steps:

step one, establishing a gear coordinate system;

step two, establishing a contact line between the cylindrical pinion and the conical gear ring;

step three, selecting the radius rho of the tooth profile of the cylindrical pinion₁Tooth profile radius rho of conical gear ring₂And contact angle

And step four, sweeping the cylindrical pinion gear tooth profile along the cylindrical spiral line to obtain spiral convex teeth, and sweeping the conical gear tooth profile along the conical spiral line to obtain spiral concave teeth.

In a preferred embodiment, in step one, o-xyz and o-x_py_pz_pIs a fixed coordinate system, o-x₁y₁z₁And o-x₂y₂z₂Is a coordinate system fixedly connected with the cylindrical pinion and the conical gear ring respectively, xoz and x_po_pz_pCoplanar; z-axis and z_pThe axis coinciding with the axes of rotation of the pinion and the ring gear, respectively, the z-axis and the z-axis_pThe included angle of the axes being theta (0 DEG)<θ<90 degrees); at the initial moment of engagement, o-xyz and o-x_py_pz_pAre each independently of o-x₁y₁z₁And o-x₂y₂z₂Overlapping; the cylindrical pinion and the conical ring gear each having an angular velocity ω₁、ω₁Around z ₀、z_pThe shaft rotates at a constant speed, the steering is the same, and the rotating angle is theta after t steps₁And theta₂(ii) a The components of the center-to-center distances in the x-axis and z-axis are a, b.

In a preferred embodiment, the contact line parameter equation on the tooth surface of the cylindrical pinion is:

calculating a contact line equation of the tooth surface of the conical gear ring according to a space curve meshing equation as follows:

in the formula: m-helical radius of the cylindrical pinion contact line;

p-pitch coefficient;

t is the parameter of the helix;

i₁,j₁,k₁coordinate system o-x₁y₁z₁The base vector of (2);

i₂,j₂,k₂coordinate system o-x₂y₂z₂The base vector of (2);

i₁₂-a transmission ratio;

a. b-the components of the center-to-center distances in the x-axis and z-axis;

theta is the included angle between the input shaft and the output shaft;

t_S、t_E-the respective values of the contact lines entering and exiting the mesh.

In a preferred scheme, the tooth profile radius rho of the convex tooth in the third step₁Should be smaller than the tooth profile radius ρ of the concave teeth₂。

The invention also provides a simulation and verification method of the conical internal meshing line gear mechanism, which guides the assembled conical internal meshing line gear mechanism into a motion simulation module of NX software for performing kinematic simulation and comprises the following steps:

the method comprises the following steps: the cylindrical pinion and the conical gear ring are respectively arranged to be rigid connecting rods L001 and L002;

step two: the kinematic pairs of the cylindrical pinion and the conical gear ring are respectively defined as revolute pairs J001 and J002;

Step three: setting a contact mode of the cylindrical pinion and the conical gear ring to be 3D contact;

step four: applying a driving force to the cylindrical pinion gear with a given angular velocity of ω₁；

Step five: setting a solving scheme to solve, and recording the angular velocity omega of the conical gear ring in the motion process₂Obtaining an instantaneous angular velocity curve chart;

step six: by calculating the formula i- ω from the transmission ratio₁/ω₂The instantaneous transmission ratio during the movement is obtained.

The conical internal meshing line gear mechanism and the construction method thereof provided by the invention have the following advantages:

1. the conical internal meshing line gear mechanism has the advantages of compact structure, small volume and light weight, and can realize stable transmission of forward and reverse rotation.

2. The minimum tooth number of the small gear of the conical inner meshing linear gear mechanism can be 1, and the conical inner meshing linear gear mechanism has larger transmission ratio and coincidence ratio compared with the existing inner meshing straight gears and helical gears.

3. Compared with the early line gear taking the hook rod as the gear tooth, the conical internal meshing line gear mechanism has higher tooth surface contact strength and transmission precision and can bear larger load.

4. The pinion of the conical internal meshing line gear mechanism can be used for conical internal meshing line gear pairs with different transmission ratios.

5. The conical inner meshing line gear mechanism has the advantages of simple structure, convenience in manufacturing, good economical efficiency and manufacturability, and can be produced to be used as a micro mechanical transmission mechanism.

Drawings

The invention is further illustrated with reference to the accompanying drawings and examples:

FIG. 1 is a schematic structural view of a tapered internal meshing linear gear mechanism of the present invention;

FIG. 2 is a solid model of a cylindrical pinion;

FIG. 3 is a top view of a solid model of a cylindrical pinion;

FIG. 4 is a front view of a solid model of a cylindrical pinion;

FIG. 5 is a solid model of a bevel ring gear.

FIG. 6 is a phantom elevation view of a bevel ring gear.

FIG. 7 is a cylindrical contact line on a cylindrical pinion and a conical contact line on a conical ring gear;

FIG. 8 is a schematic diagram of a space curve engagement coordinate system in an embodiment;

FIG. 9 is a schematic illustration of the normal profile meshing of a cylindrical pinion and a bevel ring gear;

FIG. 10 is a graph of instantaneous angular velocity of a bevel ring gear;

in the figure: the device comprises a driver 1, an input shaft 2, a cylindrical pinion 3, a convex tooth 4, a concave tooth 5, a conical gear ring 6, a coupling sleeve 7, an output shaft 8, a cylindrical contact line 9 and a conical contact line 10.

Detailed Description

As shown in fig. 1 to 6, a conical inner meshing line gear mechanism comprises a cylindrical pinion and a conical gear ring which form a gear pair, wherein the axis of the cylindrical pinion is intersected with the axis of the conical gear ring, and the included angle is 0-90 degrees.

Spiral convex teeth and concave teeth are respectively distributed on the cylindrical pinion and the conical gear ring, the convex teeth and the concave teeth are meshed, contact lines of the convex teeth are cylindrical spiral lines, and contact lines of the concave teeth are conical spiral lines. When one or more pairs of teeth are meshed but not completely disengaged, adjacent teeth are meshed, so that continuous stable transmission of the conical internal meshing linear tooth mechanism in a spatial intersecting axis is realized. The main elements participating in the meshing are the contact lines on the tooth flanks.

The driver is connected with the input shaft, the cylindrical pinion is sleeved on the input shaft, the driver rotates to drive the cylindrical pinion to rotate, the conical gear ring is driven to rotate by the engagement of the convex teeth and the concave teeth, and the conical gear ring drives the output shaft to rotate through the connecting sleeve, so that the stable transmission of the spatial crossed shaft is realized.

The spiral convex teeth are uniformly distributed on the outer part of the cylindrical base body of the cylindrical pinion, and the tooth width is as follows: b ═ p Δ t, i.e., B ═ p (t)_E-t_S) The tooth width of the convex tooth is determined by the parameters of the cylindrical contact line, and when the cylindrical contact line is determined, the tooth width of the convex tooth is also determined.

The conical gear ring is uniformly distributed with spiral concave teeth in the conical base body, and the tooth width of the conical gear ring is the same as that of the cylindrical pinion.

The tooth profile shapes of the convex teeth of the cylindrical pinion and the concave teeth of the conical gear ring gear are shown in FIG. 9, and the tooth profile of the convex teeth is that the radius is rho ₁A section of circular arc is cut on the circle of the gear, and the tooth profile of the concave tooth is formed by the radius rho₂The two sections of the arc are symmetrical, wherein AB is a positive rotation working tooth profile, CD is a negative rotation working tooth profile, and vice versa. The positive and negative rotating mesh points are respectively M₁，M₂Contact angleAnd determining the position of the meshing point on the tooth profile.

Tooth profile radius ρ of convex tooth₁Should be smaller than the tooth profile radius ρ of the concave teeth₂。

A construction method of a conical internal meshing line gear mechanism comprises the following steps:

step one, establishing a gear coordinate system, as shown in FIG. 8, o-xyz and o-x_py_pz_pIs a fixed coordinate system, o-x₁y₁z₁And o-x₂y₂z₂Is a coordinate system fixedly connected with the cylindrical pinion and the conical gear ring respectively, xoz and x_po_pz_pCoplanar; z-axis and z_pThe axis coinciding with the axis of rotation of the pinion and the bevel gear, respectively, and the z-axis_pThe included angle of the axes being theta (0 DEG)<θ<90 degrees); at the initial moment of engagement,o-xyz and o-x_py_pz_pAre each independently of o-x₁y₁z₁And o-x₂y₂z₂Overlapping; the cylindrical pinion and the conical ring gear each having an angular velocity ω₁、ω₁Around z₀、z_pThe shaft rotates at a constant speed, the steering is the same, and the rotating angle is theta after t steps₁And theta₂(ii) a The components of the center-to-center distances in the x-axis and z-axis are a, b.

Step two, establishing a contact line between the cylindrical pinion and the conical gear ring, wherein a contact line parameter equation on the tooth surface of the cylindrical pinion is as follows:

Calculating a contact line equation of the tooth surface of the conical gear ring according to a space curve meshing equation as follows:

in the formula: m-helical radius of the cylindrical pinion contact line;

p-pitch coefficient;

t is the parameter of the helix;

i₁,j₁,k₁coordinate system o-x₁y₁z₁The base vector of (2);

i₂,j₂,k₂coordinate system o-x₂y₂z₂The base vector of (2);

i₁₂-a transmission ratio;

a. b-the components of the center-to-center distances in the x-axis and z-axis;

theta is the included angle between the input shaft and the output shaft;

t_S、t_E-the respective values of the contact lines entering and exiting the mesh.

When determining the parameters a, b, theta, t_S、t_E、i₁₂And m and n rear cylindrical spiral contact lines and conical spiral contact lines can be determined.

Step three, selecting the radius rho of the tooth profile of the cylindrical pinion₁Tooth profile radius rho of conical gear ring₂And contact angleWhen determining the normal tooth profile radius ρ₁、ρ₂And contact angleThe normal tooth profile shapes of the pinion 3 and the ring gear 6 are also determined.

And step four, sweeping the cylindrical pinion gear tooth profile along the cylindrical spiral line to obtain spiral convex teeth, and sweeping the conical gear tooth profile along the conical spiral line to obtain spiral concave teeth.

According to the transmission ratio i₁₂The contact ratio and the actual load determine the number of teeth.

In this embodiment, the values of the relevant parameters are set as follows: theta 30 deg., a 12.8mm, b 12mm, m 8mm, p 4mm, p ₁＝1mm，ρ₂＝2mm，

i₁₂＝3，t_S＝-π/4,t_EPi/4, the number of teeth of the pinion is 6, and the contact ratio is 1.5;

substituting equation (1) results in the equation for the line of cylinder contact:

substituting equation (2) results in the conic contact line equation:

in the same way, different shapes of convex teeth and concave teeth can be obtained by selecting other parameters, wherein the cylindrical pinion is used for the bevel gear pair with the internal meshing line of the bevel gear rings with different transmission ratios.

A simulation and verification method for a conical inner meshing line gear mechanism guides an assembled conical inner meshing line gear mechanism into a motion simulation module of NX software for kinematic simulation, and comprises the following steps:

the method comprises the following steps: the cylindrical pinion and the conical gear ring are respectively arranged to be rigid connecting rods L001 and L002;

step two: the kinematic pairs of the cylindrical pinion and the conical gear ring are respectively defined as revolute pairs J001 and J002;

step three: setting a contact mode of the cylindrical pinion and the gear ring to be 3D contact;

step four: applying a driving force to the cylindrical pinion gear with a given angular velocity of ω₁In the present embodiment, the angular velocity is 900 °/s;

step five: setting a solving scheme to solve, and recording the angular velocity omega of the conical gear ring in the motion process₂Obtaining a graph of instantaneous angular velocity, as shown in fig. 10;

Step six: by calculating the formula i- ω from the transmission ratio₁/ω₂The instantaneous transmission ratio during the movement is obtained.

By recording the angular velocity of the bevel ring gear during the movement, an instantaneous velocity change value can be obtained, as shown in table 1,

TABLE 1 angular velocity data

Angular velocity of the cylindrical pinion gear is 900⁰The gear ratio of the gear pair is 3, and the angular speed of the conical gear ring should be 300 theoretically⁰And s. As can be seen from fig. 10, the rotation speed of the bevel ring gear is stable, and the angular velocity of the bevel ring gear is always stable at 300 during the movement⁰Around/s. From table 1, it can be seen that the maximum angular velocity of the bevel ring gear is 302.840⁰S, minimum angular velocity 299.046⁰S, calculating formula i ═ ω by transmission ratio₁/ω₂Can be obtained in motionInstantaneous drive ratio fluctuates at 2.972 ~ 3.010 in the in-process, and gear pair drive ratio changes very little, and its transmission error is only 0.013, can satisfy fixed drive ratio transmission demand, and simulation experiment has verified that toper internal meshing line gear mechanism can realize stable transmission.