CN104615800B - The design method and its transmission device of alternating axis non-circular gear - Google Patents

Abstract

A design method of non-circular gears with crossed axes and its transmission device. According to the principle of space meshing and the method of relative motion, the design method of non-circular gears with crossed shafts is obtained. The method is simple and practical. The frame of the staggered shaft non-circular gear transmission device is equipped with an input shaft and an output shaft vertically staggered in space. The input shaft and the output shaft are respectively fixed with an input staggered shaft non-circular gear and an output staggered shaft non-circular gear through key grooves. The input staggered Shaft non-circular gears and output staggered shaft non-circular gears mesh with each other. Only one stage of non-circular gear transmission is used, that is, the variable speed ratio transmission between the spatially interleaved shafts is realized, and it has the characteristics of simple structure, high transmission efficiency, and good support rigidity.

Description

Design method and transmission device of non-circular gears with crossed axes

technical field

The invention relates to a gear design method and a mechanical transmission device, in particular to a design method for a non-circular gear with crossed axes and a transmission device thereof.

Background technique

The internal and external meshing non-circular gear transmission can transmit the speed ratio movement between parallel shafts, and the non-conical gear can transmit the speed ratio movement between intersecting shafts. If it is necessary to transmit the variable speed ratio movement of the spatially interleaved shafts, the above two must be combined to form a two-stage transmission, which has a long transmission chain, a complex structure, and low efficiency.

At the same time, because the axes of the non-conical gears intersect, the general gears should be installed in a cantilever structure. During high-speed movement, the gear shaft is not rigid enough, and the deflection is large, which seriously affects the meshing of the tooth surfaces, resulting in shock and vibration. Vibration, affecting high-speed dynamic performance.

Staggered axis non-circular gear transmission and its design principle can be derived from the basic definition of space meshing, but due to the considerable complexity of its mathematical model, its instantaneous axis surface is a space non-developable surface, and the helix angle of the occurrence surface of its tooth profile presents Very large non-linear, enveloped tools are difficult to build.

Contents of the invention

The object of the present invention is to provide a design method of a non-circular gear with crossed shafts, which has the characteristics of simple structure, high transmission efficiency and good support rigidity.

The steps of its design method are as follows:

1. According to the space meshing principle, calculate the instantaneous axial surface of the input non-circular gear with staggered shafts and the non-circular gear with output staggered shafts;

2. Determine the tooth profile shape of the enveloping tool according to the helical condition of the instantaneous axis surface;

3. Solve the movement speed of the tool;

4. Determine the modulus of the tool in different radial directions;

5. Obtain the envelope solution of the tooth profile of the non-circular gear with staggered axes by using the envelope of the above tool model;

6. Solve the tooth profile of non-circular gear with staggered axes by numerical method;

7. Carry out three-dimensional modeling, analysis, and production processing according to the tooth profile data.

According to the scheme, the steps of the design method are specifically:

In the first step, the instantaneous axis-surface equation of the input staggered-axis non-circular gear and the output staggered-axis non-circular gear's instantaneous axis-surface equation are respectively:

In the formula:

a is the length of the smallest common vertical line segment of the axis of the two non-circular gears with staggered axes, that is, the wheelbase.

Σ is the acute angle between the axes of two non-circular gears with staggered shafts, that is, the shaft intersection angle.

t is the radial parameter of the instantaneous axial surface, and the instantaneous axial surface can be regarded as a collection of instantaneous axes under different radial directions.

It is to input the rotation angle of the non-circular gear with crossed axes, and its range is 0～2π.

is the transmission ratio function, which characterizes the speed change relationship between the input wheel and the output wheel, and it is the input wheel rotation angle The function, its form can be a sine function, an exponential function, a proportional function.

is the rotation angle of the output staggered shaft non-circular gear, which is function, and its range is 0～2π. Its calculation formula is as follows:

In the second step, the helical parameter of the instantaneous axial surface is

In the third step, the movement speed of the tool is:

In the formula, is the motion speed of the instantaneous axis, is the common movement speed of the instantaneous axis surface and the tool.

when hour,

In the fourth step, the modulus of the tool in different radial directions is:

In the formula, S _t (2π,t) is the total arc length passed by the tool, which can be obtained from the arc integral formula:

z is the number of teeth of the gear, which is determined comprehensively by the strength and coincidence degree.

In the fifth step, the envelope solutions of the input staggered axis non-circular gear and the output staggered axis non-circular gear tooth profile are respectively:

In the formula: r _a is the tool tooth profile solved above. are the corresponding transformation matrices.

The sixth step is to use the numerical method to solve the tooth profile of the non-circular gear with staggered axes.

The numerical method is based on the solution of the meshing equation, which represents the normal vector n _a (s) of the tooth surface of the tool and the velocity of the tooth surface relative to the tool in Based on the derivative of the envelope equation:

In input staggered shaft non-circular gears:

In output staggered shaft non-circular gears:

Performance of meshing equation: input wheel:

Output wheel:

The coordinate data of the tooth surface can be obtained by solving the meshing equation by numerical method.

The seventh step is to carry out three-dimensional modeling, analysis, and production processing according to the tooth profile data.

The object of the present invention is also to provide a staggered shaft non-circular gear transmission designed using the design method of staggered shaft non-circular gears, which can realize the transmission of variable speed ratio between spatially staggered shafts through one-stage gear transmission, and has a simple structure, High transmission efficiency, good support rigidity and so on.

The technical solution of the present invention to achieve the above object is to include a frame, which is characterized in that: the frame is provided with input shafts and output shafts arranged vertically and staggered in space, and the input shafts and output shafts are respectively fixed with input staggered shafts through key grooves The non-circular gear and the output non-circular gear with crossed shafts, and the non-circular gear with the input crossed shafts and the non-circular gear with output crossed shafts mesh with each other.

According to the above scheme, the speed relationship between the input shaft and the output shaft satisfies a specific transmission ratio function; the power drives the input shaft to rotate at a constant speed, and through the transmission of a non-circular gear with interlaced shafts, the specific transmission ratio function requirements are obtained on the output shaft motion output.

Beneficial effects of the present invention: According to the principle of space meshing and the method of relative motion, the design method of non-circular gears with crossed axes is obtained, and the method is simple and practical. The staggered shaft non-circular gear transmission only adopts one-stage non-circular gear transmission, which realizes the variable speed ratio transmission between the space staggered shafts, and has the characteristics of simple structure, high transmission efficiency, and good support rigidity;

Description of drawings

FIG. 1 is a schematic structural view of the cross-axis non-circular gear transmission of the present invention.

Fig. 2 is the transmission ratio function of the crossed shaft non-circular gear of the present invention.

Fig. 3 is a schematic diagram of the instantaneous axial plane of the input crossed shaft non-circular gear of the present invention.

Fig. 4 is a schematic diagram of the instantaneous axis plane of the output staggered shaft non-circular gear of the present invention.

Fig. 5 is a schematic diagram of the end surface shape of the sinusoidal tool rack of the present invention.

Fig. 6 is a schematic diagram of the envelope solution of the input cross-axis non-circular gear tooth profile when t=35 according to the present invention.

Fig. 7 is a schematic diagram of the envelope solution of the output staggered axis non-circular gear tooth profile when t=35 according to the present invention.

Fig. 8 is a schematic diagram of a three-dimensional model of an input cross-axis non-circular gear of the present invention.

Fig. 9 is a schematic diagram of a three-dimensional model of a non-circular gear with staggered axes output in the present invention.

detailed description

The design method of non-circular gears with crossed shafts includes the following steps: with the transmission ratio function Shaft angle Take the center distance a=10 as an example.

1. Use the above formula to derive the instantaneous axis plane of the input non-circular gear with staggered shafts and the output non-circular gear with staggered shafts, and obtain the final equation as follows:

is obtained by numerical integration.

2. Determine the shape of the tooth profile of the enveloping tool according to the helical condition of the instantaneous axis surface. Here, a sine tool rack is taken as an example.

3. To solve the movement speed of the tool, the equation is as follows:

4. Determine the modulus of the tool in different radial directions, and take the number of teeth as z=24

is obtained by numerical integration.

5. Using the envelope of the tool model above, the envelope solution of the tooth profile of the non-circular gear with staggered axes is obtained.

In the formula, r _a is the tool tooth profile solved above. For each corresponding transformation matrix, the correspondence is as follows:

6. Solve the tooth profile of non-circular gear with staggered axes by numerical method.

The numerical method is based on the solution of the meshing equation, which in this case represents the normal vector n _a (s) of the tooth surface of the tool and the velocity of the tooth surface relative to the tool in Based on the derivative of the envelope equation:

In input staggered shaft non-circular gears:

In output staggered shaft non-circular gears:

Performance of meshing equation: input wheel:

Output wheel:

The coordinate data of the tooth surface can be obtained by solving the meshing equation by numerical method.

7. Carry out three-dimensional modeling, analysis, and production processing according to the tooth profile data.

The staggered shaft non-circular gear transmission designed by using the design method of staggered shaft non-circular gears includes a frame 0, which is characterized in that: there is space on the frame 0 with input shaft 1 and output shaft 2 vertically staggered, and input shaft 1 and The output shaft 2 is respectively fixed with an input staggered shaft non-circular gear 3 and an output staggered shaft non-circular gear 4 through key grooves, and the input staggered shaft non-circular gear 3 and the output staggered shaft non-circular gear 4 mesh with each other.

The power drives the input shaft 1 to rotate at a constant speed, and through a first-stage cross-axis non-circular gear transmission, the output shaft 2 can obtain the motion output required by a specific function.

Claims (3)

1. A kind of 1. design method of alternating axis non-circular gear, it is characterised in that：Its step is as follows：

   First, input alternating axis non-circular gear is obtained according to space meshing principle and exports the axode of alternating axis non-circular gear；

   2nd, according to the spiral situation of axode, the profile geometry of envelope cutter is determined；

   3rd, the movement velocity of cutter is solved；

   4th, modulus of the cutter on footpath not in the same direction is determined；

   5th, the envelope solution of alternating axis non-circular gear tooth profile is obtained with above-mentioned cutter model envelope；

   6th, with numerical method, the flank profil of alternating axis non-circular gear is solved；

   7th, according to flank profil data, three-dimensional modeling, analysis, and production and processing are carried out；

   Described step is specifically：

   The first step, input the axode equation and output alternating axis non-circular gear axode equation difference of alternating axis non-circular gear For：

   In formula：

   A is the length of the axis minimum common vertical line section of two alternating axis non-circular gears, i.e. wheelbase；

   Σ is the folded acute angle of the axis of two alternating axis non-circular gears, i.e. crossed axis angle；

   T be axode to footpath parameter, axode can regard the set that instantaneous axis line is formed under footpath not in the same direction as；

   To input the corner of alternating axis non-circular gear, in the range of 0~2 π；

   For transmission ratio function, the velocity variations relation of wheel for inputting and output wheel is characterized, it is wheel for inputting cornerLetter Number, its form can be SIN functions, exponential function, direct proportion function；

   To export the corner of alternating axis non-circular gear, it isFunction, in the range of 0~2 π；Its calculating formula is as follows：

   Second step, the helix parameter of axode are

   3rd step, the movement velocity of cutter are：

   In formula,For the movement velocity of axode,For axode and the common movement velocity of cutter；

   WhenWhen,

   4th step, modulus of the cutter on footpath not in the same direction are：

   S in formula_tTotal arc length that (2 π, t) are passed through by cutter, can be obtained by arc integral formula：

   Z is the number of teeth of gear, and by intensity, registration synthesis determines；

   5th step, input alternating axis non-circular gear, the envelope solution of output alternating axis non-circular gear tooth profile are respectively：

   In formula：r_aFor the cutter tooth-profile of above-mentioned solution； For each corresponding transformation matrix；

   6th step, with numerical method, solve the flank profil of alternating axis non-circular gear；

   For the numerical method based on the solution to mesh equation, mesh equation shows as the normal vector n of the cutter flank of tooth_aAnd flank of tooth phase (s) To the movement velocity of cutterWhereinBased on the derivation to Envelope equation：

   In alternating axis non-circular gear is inputted：

   In alternating axis non-circular gear is exported：

   The performance of mesh equation：Wheel for inputting：

   Output wheel：

   The coordinate data of the flank of tooth is can obtain by solution of the numerical method to mesh equation；

   7th step, according to flank profil data, carry out three-dimensional modeling, analysis, and production and processing.
2. 2. a kind of usage right requires the alternating axis non-circular gear drive dress of the design method design of the 1 alternating axis non-circular gear Put, it is characterised in that：Including a frame (0), it is characterised in that：There is the input shaft of space vertical interlaced arrangement in frame (0) (1) input alternating axis non-circular gear (3) and output shaft (2), is fixed with by keyway respectively on input shaft (1) and output shaft (2) With output alternating axis non-circular gear (4), input alternating axis non-circular gear (3) and output alternating axis non-circular gear (4) intermeshing.
3. 3. usage right according to claim 2 requires interlocking for the design method design of the 1 alternating axis non-circular gear Axle non-circular gear drive device, it is characterised in that：The length velocity relation of described input shaft (1) and output shaft (2) meets specific Transmission ratio function；Power drive input shaft (1) uniform rotation, by one-level alternating axis non-circular gear drive, it is on output shaft (2) Obtain the movement output of specific transmission ratio function requirement.