CN207830468U - The oblique line gear mechanism of active line tooth is constructed with plane spiral of Archimedes - Google Patents

Abstract

The utility model discloses a kind of oblique line gear mechanisms constructing active line tooth with plane spiral of Archimedes, including driving wheel and driven wheels at transmission, active exposure line construction is carried out using plane spiral of Archimedes, meet line gear space curve mesh theory, i.e. the active exposure line of spatial conjugation and driven contact line realize engaged transmission in the form of point contact, the active exposure line and driven contact line rely on active line tooth and respectively from moving-wire teeth, the active line tooth and from the wheel body that moving-wire tooth is distributed in driving wheel and driven wheel.The axis of the driving wheel and driven wheel is intersected with any angle, and any angle refers to unspecified angle in 0 ° 180 °.The circular helix that the utility model is commonly used for active exposure line from original line gear pair becomes plane spiral of Archimedes, reduce the Spatial Dimension of active exposure line, convenient for plane machining in minute manufacturing based on technique combined, be more advantageous to application of the line gear in small transmission field.

Description

Oblique line gear mechanism with driving line teeth constructed by planar Archimedes spiral

technical field

The utility model relates to the field of novel gear transmissions with small power and small size, in particular to an oblique axis gear mechanism with planar Archimedes spirals to construct active wire teeth.

Background technique

Gear transmission is the most widely used transmission and speed change technology. Different from the conjugate surface meshing theory of the traditional involute gear pair, a new type of gear mechanism - the linear gear transmission pair, applies the space conjugate curve meshing theory, which can realize the transmission of axes intersecting or interlacing at any angle and the transmission of large transmission ratio. The wire gear is also called the space curve meshing wheel. During the transmission process, a pair of conjugated space curves participate in the meshing. The pair of space curves are respectively used as the active contact line and the driven contact line in the wire gear pair. The existing linear gear mechanism adopts the active contact line of the cylindrical helical structure regardless of whether the axis of the driving and driven wheels is parallel, vertically intersected or staggered, and the design requirement is constant speed transmission or variable speed transmission, such as Chinese patent (patent application number CN201010105902) The disclosed "a kind of oblique gear mechanism"; the disclosed "a space staggered shaft gear mechanism" of Chinese patent (patent application number CN201210449290); ". Considering the processing difficulty of conventional size transmission pairs, the cylindrical helix is easier to realize CNC machining and guarantees higher precision than other spatial curves. However, the core problem to be solved by the wire gear is the transmission in a small space. The prerequisite for the wire gear to mesh and drive correctly in a small size is that the configuration of the wire gear is suitable for the micro-nano machining process. The micro-nano machining method is easier to process the planar configuration and has high precision. In the current cross-axis gear pair, there is no transmission form in which the driving wheel is constructed in a planar shape.

Utility model content

The utility model aims at the problems existing in the prior art in the micro-transmission field, and proposes an oblique line gear mechanism which uses a planar Archimedes spiral to construct an active contact line. The structure of the active contact wire is changed from the original cylindrical helix to the planar Archimedes helix, which reduces the spatial dimension of the contact wire, reduces the difficulty of micro-machining, and facilitates the combination with the plane processing-based process in micro-nano manufacturing. The utility model is beneficial to the application of the wire gear in the micro transmission field. This new wire gear pair follows the principle of space curve meshing, relying on the continuous meshing between the driving wire teeth and the driven wire teeth on the driving wheel and the driven wheel to realize stable transmission.

The concrete technical scheme of the utility model is as follows:

A kind of oblique line gear mechanism with active line teeth constructed by planar Archimedes spiral, including a transmission pair composed of a driving wheel and a driven wheel. The active contact line and the driven contact line of the yoke realize the meshing transmission in the form of point contact, and the active contact line and the driven contact line are respectively supported on the driving line teeth and the driven line teeth, and the driving line teeth and the driven line teeth The teeth are respectively distributed on the wheel body of the driving wheel and the driven wheel. The axes of the driving wheel and the driven wheel can intersect at any angle according to the design requirements, forming the angle θ between the rotation axis of the driving wheel and the driven wheel, and realizing the intersecting axis at any angle in space. The transmission, the arbitrary angle refers to any angle between 0° and 180°; the active contact line is a plane Archimedes spiral, and the driven contact line adopts a plane Archimedes spiral according to the different design requirements of the included angle of the axes. Helix, Cylindrical Helix, or Conical Helix.

Further, the parameter equations of the active contact line and the driven contact line are:

In the formula, _t1 is the parameter, m is the parameter of the Archimedes spiral, n is the intercept of the Archimedes spiral, a and b are between the origins of the two reference systems consolidated by the master-slave contact line between the horizontal distance and the vertical distance, θ is the angle between the rotating shaft of the main driven wheel, and i ₂₁ is the transmission ratio. k is the polar angle coefficient.

Further, according to the design requirements of the axis angle θ of the transmission pair, when θ is 0° or 180°, the driven contact line is a plane Archimedes spiral; when θ is 90°, the The driven contact line is a cylindrical helix; when θ is other angles, the driven contact line is a conical helix.

Further, the sweep construction process of the active wire tooth entity and the driven wire tooth entity is as follows:

First construct the active and driven centerlines:

When external meshing, the centerline of the driving line tooth is obtained by moving the active contact line along its normal line to the center of curvature for a distance r ₁ , and the center line of the driven line tooth is the direction of the driven contact line along the normal line of the active contact line to the center of curvature Reversely translate a distance r ₂ to get, when internal meshing, the direction of translation is opposite;

Wherein, the parametric equation of the tooth centerline of the active wire is:

The parametric equation of the tooth center line of the driven line is:

Among them, r ₁ and r ₂ represent the radius of curvature of the driving line teeth and the driven contact line at the contact line perpendicular to the plane of the contact line.

Then sweep to get the wire tooth entity:

A cross-sectional circle is made from the starting point of the active center line to the vertical direction of the active contact line, and a cross-sectional circle is made from the starting point of the driven center line to the vertical direction of the driven contact line, and then the line tooth entity is obtained by sweeping the cross-sectional circle along the center line. The radius of curvature of the wire tooth is selected according to the design requirements. The main-slave contact line and the main-slave center line ensure the shape and curvature radius of the main-slave teeth near the contact line, and the shapes of the driving wheel and the driven wheel body, the driving and the driven teeth can be according to Design for actual conditions.

In the oblique gear mechanism with the active contact line constructed by the planar Archimedes spiral, a certain pair of active line teeth and driven line teeth are meshed at a certain moment of transmission. The contact line enters the meshing, which ensures the continuous and stable meshing transmission of the transmission pair.

Compared with the previous consistent use of cylindrical helix as the active contact line, the utility model uses the planar Archimedes helix as the active contact line, which reduces the spatial dimension of the active contact line and is convenient for the process of plane processing in micro-nano manufacturing. Combined, it is more conducive to the application of wire gears in the field of micro transmission, because in micro-scale processing, it is limited by micro-scale material properties, structural strength and stiffness, shape and size (size effect), difficulty of clamping and releasing, residual stress and Surface integrity, etc. The processing of three-dimensional curved surfaces requires one more dimension of control or movement, which is difficult and expensive; the processing technology for processing 2D or 2.5D is relatively mature. On the one hand, silicon micromachining technology developed from integrated circuit processing technology is inherently suitable for plane Processing, such as silicon anisotropic etching, photolithography, reactive ion etching, etc. On the other hand, non-silicon processing technology is easier to process planar graphics, such as planar EDM, electrolytic milling, ion beam processing, etc.

Description of drawings

FIG. 1 is a schematic diagram of an oblique line gear mechanism with a planar Archimedes spiral as the active contact line in an embodiment.

Fig. 2 is a top view of the driving wheel of the oblique line gear mechanism with the planar Archimedes spiral as the active contact line.

Fig. 3 is a top view of the driven wheel of the oblique line gear mechanism with the planar Archimedes spiral as the active contact line.

Fig. 4 is a side view of the driven wheel of the oblique line gear mechanism with the planar Archimedes spiral as the active contact line.

Fig. 5 is a schematic cross-sectional view of the upper wire teeth of the driving wheel described in Figs. 2 and 3 .

FIG. 6 is a schematic diagram of the corresponding coordinate system in FIG. 1 .

Detailed ways

The specific implementation of the utility model will be further described below in conjunction with the accompanying drawings, and the implementation of the utility model is not limited thereto.

As shown in Figure 1, an oblique line gear mechanism with planar Archimedes helix to construct active line teeth includes a transmission pair composed of a driving wheel and a driven wheel, and the driving wheel and driven wheel satisfy the line gear space curve The meshing theory, that is, the active contact line and the driven contact line of the space conjugate realize the meshing transmission in the form of point contact. The wire teeth and the driven wire teeth are respectively distributed on the wheel body of the driving wheel and the driven wheel. The axes of the driving wheel and the driven wheel can cross at any angle according to the design requirements to form the angle θ between the rotation axis of the driving wheel and the driven wheel to realize space The transmission between the cross shafts at any angle, the arbitrary angle refers to any angle between 0° and 180°; the active contact line is a plane Archimedes spiral, and the driven contact line is designed according to the different design requirements of the included angle of the axes Use a planar Archimedean, cylindrical or conical helix. Wherein, the driving wheel 3 is fixedly connected with the driving shaft 2, the driven wheel 4 is fixedly connected with the driven shaft 5, and the driving shaft 2 is fixedly connected with the motor 1. As shown in FIG. On the body, as shown in FIG. 4 , the driven wire teeth 7 are evenly arranged on the wheel body of the driven wheel 4 .

The transmission principle is: the rotation of the motor 1 makes the driving shaft 2 and the driving wheel 3 rotate, and the driving wheel 3 and the driven wheel 4 are meshed for transmission, and then the driven shaft 5 is rotated to realize the transmission process of the cross axis. At any time, a certain pair of driving wire teeth and driven wire teeth meshes, and when the meshing is not disengaged, the next pair of driving and driven contact wires enters into meshing, ensuring continuous and stable meshing transmission of the transmission pair.

The construction process of the driving wire teeth and the driven wire teeth in the utility model is further described below in conjunction with the accompanying drawings.

The coordinate system of the space conjugate curve shown in Figure 5 corresponds to the transmission position of the gear mechanism shown in Figure 1, and represents the reference coordinates of a pair of space conjugate curves in space and the movement reference coordinates when the transmission meshes. Specifically: the two space coordinate systems o-xyz and ox _p y _p z _p represent the fixed coordinate system where the driving wheel and the driven wheel are located, and the two space coordinate systems ox ₁ y ₁ z ₁ and ox ₂ y ₂ z ₂ are respectively It is solidified with the driving wheel and the driven wheel, and rotates together with the driving and driven wheels. Respectively coincide with the axis of rotation of the driving wheel and the driven wheel. The angle between the x _p axis and the x axis is θ. o The distance from point _p to the z-axis is a, and the distance to the x-axis is b. At the initial moment, ox ₁ y ₁ z ₁ and ox ₂ y ₂ z ₂ coincide with o-xyz and ox _p y _p z _p respectively, the driving wheel and the driven wheel are respectively at the angular velocity and Rotate around the z ₁ axis and z ₂ axis, after a certain period of time from the initial position, the driving wheel and the driven wheel have rotated respectively and horn.

Then the space curve equation of the active contact line and the driven contact line can be expressed as:

Chinese style is the kinematic condition at the meshing point, this equation is called the meshing equation, and its physical meaning is that the relative velocity of the driving contact line at the meshing point has zero component in the vertical direction of the plane where the active contact line is located, that is, the driven contact line Always keep in contact with the active contact line and do not leave the plane where the active contact line is located.

The curve parameter equation of the active contact line is:

The curve parameter of the active contact line is the space curve parameter equation of the plane Archimedes spiral.

The driven contact line equation is:

In the above two formulas:

The superscript (1) indicates that the reference coordinate system of the equation is ox ₁ y ₁ z ₁ , and the subscript M indicates the contact line equation. In this utility model, the planar Archimedes spiral is used as the active contact line, a special solution of the meshing equation for:

k—polar angle coefficient.

m—Archimedes spiral coefficient, which means the increase of the polar diameter every 1 degree of rotation, m>0.

n—Archimedes screw intercept, indicating the distance from the starting position to the dot.

t ₁ —polar angle, indicating the degree of rotation of the Archimedes spiral.

θ—the supplementary angle of the angle between the main and driven wheel axes, the range is 0°-180°;

a, b—o The distance from point _p to the z-axis is a, the distance to the x-axis is b, a>0, b>0;

i ₂₁ —the transmission ratio of the driving wheel and the driven wheel, that is, the ratio of the number of teeth on the driving wheel to the number of teeth on the driven wheel;

In the above two formulas, when the values of the parameters a, b, θ, and i ₂₁ of the transmission pair are determined, the parameter equation of the contact line curve of the driven line tooth that is conjugated with it is determined accordingly.

The transformation matrix between ox ₁ y ₁ z ₁ and ox ₂ y ₂ z ₂ can be obtained through the matrix transformation relation M ₂₁ =M _2p ·M _po ·M _o1 :

The active contact line equation is changed from the above conversion matrix to the driven contact line equation:

In the formula:

—The superscript (2) indicates that the reference coordinate system of the parametric equation is ox ₂ y ₂ z ₂ , and the subscript M indicates the contact line;

θ—the supplementary angle of the angle between the main and driven wheel axes, the range is 0°-180°;

a, b—o The distance from point _p to the z-axis is a, the distance to the x-axis is b, a>0, b>0;

The transmission condition expression that expresses that the driving wheel and the driven wheel rotate according to a given transmission ratio is:

In the formula:

i ₂₁ —the transmission ratio of the driving wheel and the driven wheel, that is, the ratio of the number of teeth on the driving wheel to the number of teeth on the driven wheel;

— Angular velocity of driving wheel and driven wheel rotation;

— After a certain period of time, the angles at which the driving wheel and the driven wheel turn respectively;

When the values of parameters a, b, θ, and i ₂₁ of the transmission pair are determined, the parametric equation of the contact line curve of the driven tooth coupled with it is determined accordingly.

The sweeping construction process of the active wire tooth entity and the driven wire tooth entity is as follows:

First construct the active centerline and the driven centerline: in external meshing, the active centerline is obtained by moving the active contact line along its normal to the center of curvature for a distance r ₁ , and the driven centerline is the driven contact line along the active contact line The normal line is reversely translated by a distance r ₂ in the direction of the curvature center, and the translation direction is opposite when the inner mesh is engaged;

Among them, the parametric equation of the centerline of the active wire tooth is:

In the formula The superscript (1) indicates that the reference coordinate system of the parametric equation is ox ₁ y ₁ z ₁ , and the subscript C indicates the center line; r ₁ indicates the radius of curvature of the active wire teeth at the contact line perpendicular to the plane of the contact line.

The parametric equation of the tooth centerline of the driven wire is:

In the formula The superscript (2) indicates that the reference coordinate system of the parameter equation is ox ₂ y ₂ z ₂ , the subscript C indicates the center line; r ₂ indicates the radius of curvature of the driven line tooth at the contact line perpendicular to the plane of the contact line, and the sign Depending on the external meshing or internal meshing, the translation direction of the center line is different;

After determining the curvature radii r ₁ and r ₂ of the driving line teeth at the contact line, the shape of the line teeth near the contact line is also determined. According to the meshing theory of space curves, as long as the accuracy of a pair of space conjugate curves, that is, the contact line of the master and slave can be guaranteed, the transmission accuracy of the wire gear pair can be guaranteed. It can be designed according to actual conditions, such as processing technology, processing accuracy, lubrication design, material utilization rate, stiffness and strength design, etc.

Then sweep to obtain the wire tooth entity: the wire tooth is formed by moving the main and driven contact lines to the positive and negative directions of the active contact line normal for a distance r ₁ and r ₂ respectively to form two wire tooth centerlines, and make a cross-sectional circle, Then the line tooth entity is obtained by sweeping the section circle along the center line.

As shown in Figure 5, it is a schematic cross-sectional view of the active wire teeth. The base of the wire teeth rests on the driving wheel 3, where 8 represents any point on the active contact line, and 9 is the corresponding point on the active center line and point 8, representing the active contact line. center of curvature, and the radius of curvature is r ₁ , according to the theory of space curve meshing, as long as the accuracy of a pair of space conjugate curves, that is, the contact line of the master and slave, can ensure the transmission accuracy of the linear gear pair, the wheel body of the driving wheel and the driven wheel The shape of the active and driven wire teeth can be designed according to actual conditions, such as processing technology, processing accuracy, lubrication design, material utilization rate, stiffness and strength design, etc.

Implementation example: wire gear pair suitable for 3D printing

In this implementation case, in order to ensure the rigidity of the wire teeth, the cross section of the active wire teeth is designed as a diagonally supported structure. The contact line is on the left side of the wire gear base, and the right side is the supporting structure. To save material under the premise of maintaining rigidity, the wire tooth adopts a partial circular cross section. As shown in Figure 5.

In the above two formulas: the parameter equation of the active contact line is

The given design parameters are θ=135°, m=10, n=100, a=10, b=10, i ₂₁ =0.25, Z ₁ =10, Z ₂ =40, r ₁ =2, r ₂ =2 .

According to the above method, the equation of the tooth contact line of the driven wire is obtained as:

The equation of the center line of the active wire tooth is:

The equation of the tooth centerline of the driven line is:

According to the above four formulas and the above-mentioned wire tooth construction method suitable for 3D printing, after adding the wheel body and D-shaped hole, the driving wheel is obtained as shown in Figure 2, and the driven wire teeth adopt the same wire tooth section as shown in Figure 5 configuration, after adding the spoked wheel body and the D-shaped hole, the driven wheel as shown in Figure 3 and 4 is obtained. Wherein Fig. 3 is a top view of the driven wheel, and Fig. 4 is a side view of the driven wheel.

As shown in Figure 1, the driving wheel and driven wheel of the oblique line gear mechanism designed in this example with planar Archimedes spiral to construct the driving line teeth are installed on the drive shaft 2 and the driven wheel according to the design angle and wheelbase. On the shaft 5, the transmission test can be carried out. After measurement, the instantaneous transmission ratio and the average transmission ratio of the gear pair are stable, and continuous and stable meshing transmission can be realized. This shows that the transmission method of the oblique line gear mechanism with the planar Archimedes spiral structure of the active line teeth developed by the utility model is feasible.

The utility model provides a new wire tooth construction method using the planar Archimedes spiral as the active contact wire under the theoretical framework of the online gear space conjugate curve meshing, which is different from the existing wire gear mechanism and adopts the cylindrical helix. Construct active contact lines. The mechanism can be used in the method and mechanism of continuous and stable meshing transmission of any cross axis. The mechanism has a series of advantages of the wire gear: simplifying the structure of the gear mechanism and the micromechanical transmission device, reducing the geometric size, reducing the mass, improving the flexibility of operation, and is simple to manufacture and low in cost. Moreover, since the structure of the active contact wire is changed from the original cylindrical helix to the planar Archimedes helix, the spatial dimension of the active contact wire is reduced, which is convenient to combine with the planar processing-based process in micro-nano manufacturing, which is more conducive to wire The processing and application of gears in the field of micro transmission.

The above-mentioned embodiments of the present utility model are only examples for clearly illustrating the present utility model, and are not intended to limit the implementation of the present utility model. For those of ordinary skill in the art, on the basis of the above description, other changes or changes in different forms can also be made. It is not necessary and impossible to exhaustively list all the implementation manners here. All modifications, equivalent replacements and improvements made within the spirit and principles of the utility model shall be included in the protection scope of the claims of the utility model.

Claims (4)

1. A kind of oblique wire gear mechanism with planar Archimedes helix structure active wire teeth, comprising the transmission pair that driving wheel and driven wheel form, it is characterized in that: described driving wheel and driven wheel satisfy the linear gear space curve The meshing theory, that is, the active contact line and the driven contact line of the space conjugate realize the meshing transmission in the form of point contact. The wire teeth and the driven wire teeth are respectively distributed on the wheel body of the driving wheel and the driven wheel. The axes of the driving wheel and the driven wheel can cross at any angle according to the design requirements to form the angle θ between the rotation axis of the driving wheel and the driven wheel to realize space The transmission between the cross shafts at any angle, the arbitrary angle refers to any angle between 0° and 180°; the active contact line is a plane Archimedes spiral, and the driven contact line is designed according to the different design requirements of the included angle of the axes Use a planar Archimedean, cylindrical or conical helix. 2. According to claim 1, the oblique line gear mechanism with planar Archimedes spiral to construct the driving line teeth is characterized in that: the parametric equations of the driving contact line and the driven contact line are: In the formula, _t1 is the parameter, m is the parameter of the Archimedes spiral, n is the intercept of the Archimedes spiral, a and b are between the origins of the two reference systems consolidated by the master-slave contact line The horizontal distance and the vertical distance between, θ is the included angle of the rotation axis of the driven wheel, i ₂₁ is the transmission ratio, and k is the polar angle coefficient. 3. According to claim 2, the oblique line gear mechanism with planar Archimedes spiral to construct the active line teeth is characterized in that: according to the design requirements of the axis angle θ of the transmission pair, when θ is 0° or 180°, the driven contact line is a plane Archimedes spiral; when θ is 90°, the driven contact line is a cylindrical helix; when θ is other angles, the driven contact line The line is a conic helix. 4. According to claim 3, the oblique line gear mechanism of driving line teeth constructed by planar Archimedes spiral is characterized in that: the sweeping construction process of the driving line tooth entity and the driven line tooth entity is as follows : First construct the active and driven centerlines: When external meshing, the centerline of the driving line tooth is obtained by moving the active contact line along its normal line to the center of curvature for a distance r ₁ , and the center line of the driven line tooth is the direction of the driven contact line along the normal line of the active contact line to the center of curvature Reversely translate a distance r ₂ to get, when internal meshing, the direction of translation is opposite; Wherein, the parametric equation of the tooth centerline of the active wire is: The parametric equation of the tooth center line of the driven line is: Among them, r ₁ and r ₂ represent the radius of curvature of the driving line teeth and the driven contact line at the contact line perpendicular to the plane of the contact line. Then sweep to get the wire tooth entity: A cross-sectional circle is made from the starting point of the active center line to the vertical direction of the active contact line, and a cross-sectional circle is made from the starting point of the driven center line to the vertical direction of the driven contact line, and then the line tooth entity is obtained by sweeping the cross-sectional circle along the center line.