WO2019104777A1

WO2019104777A1 - Arc-shaped surface contact-based worm and worm gear transmission type power device

Info

Publication number: WO2019104777A1
Application number: PCT/CN2017/117416
Authority: WO
Inventors: 吉卫喜; 范小斌; 李春涛; 马玉娟; 李申
Original assignee: 海安县申菱电器制造有限公司; 江南大学
Priority date: 2017-11-29
Filing date: 2017-12-20
Publication date: 2019-06-06
Also published as: CN107965550A

Abstract

An arc-shaped surface contact-based worm and worm gear transmission type power device, relating to the field of speed reducers for escalators. In arc-shaped surface contact-based worm and worm gear transmission, the worm is a multi-head arc-shaped cylindrical worm; a worm and worm gear optimized mathematical model is established based on an evolutionary fish swarm algorithm to optimize parameters of a worm pair, so as to obtain engagement performance of tooth surfaces; the tooth surface curvature of the worm is corrected on the basis of grinding machining, so that the tooth surfaces are engaged to form an arc-shaped surface contact, and the line of instantaneous contact between the worm gear and the worm is changed gradually and stably and distributed uniformly; the line of instantaneous contact between the tooth surfaces is perpendicular to the direction of relative movement direction between the tooth surfaces of the worm gear and the worm. According to the apparatus, after the design of the worm gear and the worm engaged with each other is optimized, the tooth surface curvature of the worm is corrected, so that the tooth surfaces are engaged to form an arc-shaped surface contact, and mounting errors are eliminated; moreover, the normal direction of the tooth surface of the worm pair is perpendicular to the direction of relative movement between the tooth surfaces of the worm gear and the worm, so that good lubricity is achieved for the worm gear and the worm engaged with each other.

Description

Curved surface contact worm gear transmission power unit

Technical field

The invention is applied to the field of escalator reducers, in particular to a curved surface contact worm and worm gear transmission power device for an escalator.

Background technique

The reducer functions as a matching speed and a torque transmission between the prime mover and the working machine or the actuator. With the application and development of the reducer in the industry, the design and manufacturing level of the reducer in China is becoming more and more perfect. However, for the worm gear drive of the worm reducer, the shape of the gear not only affects the motion characteristics of the worm drive, but also Affects the dynamic performance of the worm gear drive. In order to adapt to the development trend of modern large-scale production, people continue to explore new tooth profile. Under the prior art, there will always be meshing impact at the root and the top of the worm pair, which will greatly reduce the bearing capacity of the worm drive. The service life also increases the transmission noise of the reducer and affects the transmission accuracy.

Summary of the invention

In view of the above existing problems, the present invention provides a curved surface contact worm gear transmission power device, which has the advantages of compact structure, good bearing performance, stable operation, low noise and high life.

The invention comprises a turbine, a worm and a worm. The worm is a multi-headed cylindrical worm. The tooth surfaces of the turbine and the worm mesh with a curved surface contact. The instantaneous contact line of the tooth surface is perpendicular to the direction of relative movement of the tooth surface of the turbine and the worm;

Based on the evolutionary fish swarm algorithm, a mathematical model of worm optimization is established. The mathematical model of worm optimization is obtained as follows:

Where: σ is the penalty coefficient, f(x) is the unified objective function, and g _i (x) is the constraint;

The above parameters are optimized for the worm. The circular arc radius ρ, the axial modulus m, and the lead angle γ of the grinding wheel are used as design variables. The induced curvature and the meshing area are the objective functions, and the two targets are linearly weighted. The function is processed into a unified objective function, and the upper and lower bounds of the design variables are constrained, and the top of the worm gear is used as a performance constraint.

The invention corrects the tooth surface curvature of the worm based on the grinding process, so that the tooth surface meshing becomes a curved surface contact, eliminates the installation error, and simultaneously makes the instantaneous contact surface of the worm gear worm smoothly and evenly distributed, and makes the instantaneous contact line perpendicular to the worm wheel. The direction of relative movement of the tooth surface of the worm to achieve good lubrication of the intermeshing worm gear and worm.

The multi-head curved cylindrical worm of the invention adopts a disc-shaped grinding wheel for grinding, and derives the contact surface equation of the worm according to the working surface equation of the disc-shaped grinding wheel and the actual processing parameters.

The invention grinds the worm by a disc type grinding wheel, and the worm shaft and the occurrence of the toroidal axis of the grinding wheel are installed with the worm indexing cylindrical spiral lifting angle as a mounting angle; when grinding, the worm is A certain spiral characteristic parameter is used for spiral motion, and the grinding wheel rotates around its own axis to perform worm tooth surface grinding.

The worm of the invention is processed by a disc-shaped grinding wheel, and the dynamic meshing performance is optimized, and the worm wheel hob is not required to be manufactured, which overcomes the problem that the worm wheel hob is difficult to manufacture in the conventional manufacturing, and the manufacturing cost is reduced.

The contact surface equation of the worm wheel is obtained by the following formula:

K ₂ = M ₂₁ · K ₁

In the above formula, K ₂ is the instantaneous contact surface equation of the worm wheel, K ₁ is the instantaneous contact surface equation of the worm, φ ₁ is the rotation angle of the worm, φ ₂ is the rotation angle of the worm wheel, a is the center distance of the worm gear, and the coordinate system S ₁ is a spatial dynamic coordinate system, which is fixed to the worm, and the k ₁ axis coincides with the worm axis; the coordinate system S _σ is also a spatial dynamic coordinate system, which is coupled with the toroidal disc-shaped grinding wheel, and the axis of the grinding wheel is exactly k _σ axis coincident; S _w is the spatial coordinate system fixed coordinate system, k _w k ₁ axis coincides with the axis; S _p is the spatial coordinate system to express the relationship between the worm and the worm wheel movement established by the auxiliary coordinate system fixed.

DRAWINGS

Figure 1 is a schematic view of a disc type grinding wheel machining worm;

2 is a schematic diagram of a coordinate system in which a worm wheel meshes with a worm;

Figure 3 is a schematic view of the engagement of the curved surface contact worm gear drive pair;

Figure 4 is a schematic view showing the distribution of the contact surface of the worm gear.

Detailed ways:

A curved surface contact worm gear transmission power device for an escalator, the worm is processed by a disc-shaped grinding wheel. Figure 1 is a schematic view of a disk-shaped grinding wheel machining worm. Firstly, according to the tooth surface equation of the disc-shaped grinding wheel and the actual machining parameters, combined with the worm design principle, the tooth surface equation of the worm is determined as shown in the figure. When the worm is processed, the worm shaft and the grinding wheel occur in the ring. The axis of the surface (production surface) is installed with the worm indexing cylindrical spiral angle as the installation angle; the worm is spirally moved with certain spiral characteristic parameters, while grinding the sand The wheel rotates around its own axis to grind the worm tooth surface to machine the worm. Then, according to the tooth surface equation of the worm and the space meshing theory, according to the installation position of the worm wheel and the worm, the tooth surface equation of the worm wheel completely conjugate with the worm is obtained.

As shown in Fig. 2, the worm rotates around the k ₁ axis, and the worm wheel rotates around the k _σ axis, S ₁ (O ₁ , i ₁ , j ₁ , k ₁ ), S _σ (O _σ , i _σ , j _σ , k _σ ), S _w (O _w , i _w , j _w , k _w ), S _p (O _p , i _p , j _p , k _p ). Wherein, the coordinate system S ₁ (O ₁ , i ₁ , j ₁ , k ₁ ) is a spatial dynamic coordinate system, which is fixed to the worm, and the k ₁ axis coincides with the worm axis; the coordinate system S _σ (O _σ , i _σ , j _σ , k _σ ) is also a spatial dynamic coordinate system, which is coupled with a toroidal disc-shaped grinding wheel, and the axis of the grinding wheel coincides exactly with the k _σ axis; the coordinate system S _w (O _w , i _w , j _w , k _w ) is a spatial fixed coordinate system, the k _w axis coincides with the k ₁ axis; the coordinate system S _p (O _p , i _p , j _p , k _p ) is a spatially assisted setting established to express the motion relationship between the worm and the worm wheel In the coordinate system, the k _p axis coincides with the k _σ axis, and the i _p axis coincides with the i _w axis. The multi-head curved cylindrical worm is ground by a disc-shaped grinding wheel. The instantaneous contact surface equation of the worm is derived from the working surface equation of the disc-shaped grinding wheel and the actual machining parameters. The instantaneous contact surface equation of the worm wheel is as follows:

K ₂ = M ₂₁ · K ₁

Based on the evolutionary fish swarm algorithm, the mathematical model of worm optimization is established, and the parameters of the worm are optimized to improve the meshing performance of the tooth surface. The circular arc radius ρ, the axial modulus m and the lead angle γ of the grinding wheel are used as design variables. The curvature of the induced method and the area of the meshing area are the objective functions, and the two objective functions are processed into a unified objective function by linear weighting method. The upper and lower boundary constraints are based on the worm gear top thickness as a performance constraint, and it must be ensured that no undercut occurs on the worm tooth surface. The mathematical model of the worm optimization is as follows:

Where: σ is the penalty coefficient, f(x) is the unified objective function, and g _i (x) is the constraint.

Calculating the value of the induced curvature and the area of the meshing area before and after optimization, the optimized curvature value of the induced method becomes smaller than that before the optimization, and the area ratio of the meshing area becomes larger before optimization, indicating that the tooth surface optimization method is feasible.

As shown in Fig. 3, the meshing diagram of the curved surface contact worm gear transmission pair is shown, and the worm and the worm wheel mesh with the transmission. According to the spiral instantaneous contact surface equation of the worm and the space meshing theory, according to the installation position of the worm gear, the instantaneous contact surface equation of the worm wheel is obtained.

4 is a schematic diagram of the contact line of the worm gear meshing tooth surface. In FIG. 4, 1, 2, and 3 represent instantaneous contact lines, and the dot area represents the surface contact meshing area. The curvature of the flank surface of the worm is corrected so that the curvature correction law of the tooth surface is consistent with the change of the radius of curvature of the relative movement direction of the worm gear tooth surface, so that the tooth surface meshes into a curved surface contact to form a good lubrication state.

In the embodiment, during the worm machining, the worm is spirally moved with a certain spiral characteristic parameter, and the grinding wheel is rotated about its own axis to perform the worm tooth surface grinding.

The above description is illustrative of the invention and is not to be construed as limiting the scope of the invention, and the scope of the invention is defined by the appended claims. The invention may be modified in any form without departing from the basic structure of the invention.

Claims

A curved surface contact worm gear transmission power device, comprising a turbine and a worm, wherein the worm is a multi-head curved cylindrical worm, the tooth surfaces of the turbine and the worm mesh with a curved surface contact, and the instantaneous contact line of the tooth surface is perpendicular to the turbine The direction of relative movement of the tooth surface of the worm; the worm is processed by a disc type grinding wheel;

Based on the evolutionary fish swarm algorithm, a mathematical model of worm optimization is established. The mathematical model of worm optimization is obtained as follows:

Where: σ is the penalty coefficient, f(x) is the unified objective function, and g i (x) is the constraint condition; the above parameters are optimized for the worm, with the circular arc radius ρ of the grinding wheel profile, the axial modulus m, and the lead angle As the design variable, γ is used as the objective function of the induced curvature and the meshing area. The two objective functions are processed into a unified objective function by linear weighting method. The upper and lower bounds of the design variables are constrained, and the worm gear top thickness is used as the performance constraint.
A curved surface contact worm gear transmission power unit according to claim 1, wherein said multi-head curved cylindrical worm is ground by a disc-shaped grinding wheel, according to a working surface equation of the disc-shaped grinding wheel and actual machining parameters. The equation of the contact surface of the worm is derived.
A curved surface contact worm gear transmission power unit according to claim 1, wherein the disc type grinding wheel grinds the worm, the disc type grinding wheel and the worm shaft, the worm axis and the grinding wheel generate the toroidal axis The worm indexing cylinder spiral angle is installed for the installation angle; when grinding, the worm moves spirally with certain spiral characteristic parameters while grinding the sand The wheel rotates around its own axis to perform worm tooth surface grinding.
A curved surface contact worm gear transmission power unit according to claim 1, wherein the contact surface equation of the worm wheel is obtained by the following formula:

K 2 = M 21 · K 1

In the above formula, K 2 is the instantaneous contact surface equation of the worm wheel, K 1 is the instantaneous contact surface equation of the worm, φ 1 is the rotation angle of the worm, φ 2 is the rotation angle of the worm wheel, a is the center distance of the worm gear, and the coordinate system S 1 is a spatial dynamic coordinate system, which is fixed to the worm, and the k 1 axis coincides with the worm axis; the coordinate system S σ is also a spatial dynamic coordinate system, which is coupled with the toroidal disc-shaped grinding wheel, and the axis of the grinding wheel is exactly k σ axis coincident; S w is the spatial coordinate system fixed coordinate system, k w k 1 axis coincides with the axis; S p is the spatial coordinate system to express the relationship between the worm and the worm wheel movement established by the auxiliary coordinate system fixed.