CN113836665A - Non-circular gear pitch curve design method for driving sine mechanism to do uniform reciprocating motion - Google Patents

Non-circular gear pitch curve design method for driving sine mechanism to do uniform reciprocating motion Download PDF

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CN113836665A
CN113836665A CN202111142910.XA CN202111142910A CN113836665A CN 113836665 A CN113836665 A CN 113836665A CN 202111142910 A CN202111142910 A CN 202111142910A CN 113836665 A CN113836665 A CN 113836665A
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刘琼
史诺
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Xian Aeronautical University
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Abstract

The invention discloses a non-circular gear pitch curve design method for driving a sine mechanism to do uniform reciprocating motion, which comprises the following steps: drawing an ideal motion speed curve in CREO software; converting the speed curve into a point set; extracting coordinate values of the point set; extracting point set coordinate data corresponding to the working stroke; integrating in ORIGIN, converting to obtain displacement value, and obtaining crank length; calculating the driven wheel rotation angle corresponding to each displacement value; calculating a transmission ratio; calculating the radial directions of the driving wheel and the driven wheel; calculating in EXCEL, and converting the rotating angles and corresponding radial values of the driving wheel and the driven wheel into Cartesian coordinate values; and (4) introducing the coordinate points into UG NX software in a spline curve mode to obtain a driving wheel pitch curve and a driven wheel pitch curve. The motion curve output by the sine mechanism is drawn in drawing software, data processing is carried out after coordinate points are derived, key structure parameters of the mechanism are obtained, the pitch curve of the non-circular gear is solved reversely, calculation is simple and convenient, and serialized rapid design can be achieved.

Description

Non-circular gear pitch curve design method for driving sine mechanism to do uniform reciprocating motion
Technical Field
The invention belongs to the technical field of mechanical design and manufacturing, and relates to a design method of a driving gear of a sine mechanism, in particular to a design method of a non-circular gear pitch curve for driving the sine mechanism to do uniform reciprocating motion.
Background
The sine mechanism is a relatively common motion mechanism and can be applied to textile machinery, printing machinery and papermaking machinery, if the sine mechanism is driven by a common cylindrical gear, the speed of a rack of the sine mechanism presents a typical sine change rule, but in many occasions, the sine mechanism is required to output constant-speed reciprocating linear motion, the sine mechanism is required to be driven by variable input rotating speed, and the frequently-adopted modes are three types: the sine mechanism is driven to move by the non-circular gear with a free pitch curve, which is an ideal choice for improving the motion characteristic and realizing accurate constant-speed reciprocating linear motion.
The design of free pitch curve is difficult in engineering, the scheme of the prior art is that main structural parameters or motion parameters such as crank length, center distance, lift angle of acceleration and deceleration motion sections and the like are set firstly, then a program is programmed, motion speed is expressed by a piecewise function according to the reciprocating motion rule of a rack, the pitch curve of the non-circular gear is calculated on the basis, the constraint relation is more, the calculation process is complicated, the program is required to be programmed for calculation, the programming difficulty is higher for wide engineering personnel, and the application of the non-circular gear of the free pitch curve in practice is limited.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for designing a pitch curve of a non-circular gear for driving a sine mechanism to do uniform reciprocating motion, which realizes the design of the pitch curve by jointly applying CREO, EXCEL, ORIGIN and UG NX, does not need programming, has simple and convenient calculation and can realize the rapid design of serialization.
In order to achieve the purpose, the invention adopts the following technical scheme:
the design method of the non-circular gear pitch curve for driving the sine mechanism to do uniform reciprocating motion comprises the following steps:
the method comprises the following steps: drawing an ideal motion speed curve in CREO software, wherein the abscissa of the curve is the corner of the driving wheel, and the ordinate is the translation speed of the rack;
step two: extracting a starting point on the ideal movement speed curve, carrying out point array along the ideal movement speed curve, converting the ideal movement speed curve into a point set, and storing the point set in an IGES format;
step three: and (3) extracting coordinate values of the point set: newly building a model file in CREO software, importing a point set file in an IGES format, expressing points in the point set in a Cartesian coordinate form, storing the point set in a PTS format, opening the PTS format file by using a notebook, and extracting coordinate values of the points;
step four: extracting point set coordinate data corresponding to the working stroke: importing the coordinate data of the points into an EXCEL file, and converting the angle value of the rotating angle of the driving wheel into a camber value;
step five: acquiring the length of a crank: importing the data in the fourth step into an ORIGIN, clicking an Analysis-Mathematics-integration to perform integration operation, dividing the integration value by the rotating speed of the driving wheel to obtain a displacement value, viewing the maximum displacement value to obtain crank length data, wherein the maximum displacement of the working stroke is 2 times of the crank length;
step six: and calculating the driven wheel rotation angle corresponding to each displacement value: copying the displacement values into EXCEL for calculation, and calculating the driven wheel rotation angle corresponding to each displacement value
Figure BDA0003284393580000021
Driven wheel corner
Figure BDA0003284393580000022
The relationship satisfied by the displacement s and the crank length e is as follows:
Figure BDA0003284393580000023
step seven: calculating a transmission ratio: calculating the increment of the rotation angle of the driving wheel in each group of data relative to the previous group of data
Figure BDA0003284393580000024
Increment of driven wheel angle
Figure BDA0003284393580000025
The transmission ratio of the main driving wheel and the driven wheel is as follows:
Figure BDA0003284393580000026
step eight: calculating the radial direction of the driving wheel and the radial direction of the driven wheel: setting a reasonable center distance a of the non-circular gear according to the length e of the crank, and calculating the radial direction r of the driving wheel according to the following formula1Radial direction r of driven wheel2；
Figure BDA0003284393580000027
Figure BDA0003284393580000031
Step nine: the turning angles and corresponding radial values of the driving wheel and the driven wheel are converted into Cartesian coordinate values, and calculation is carried out in EXCEL, wherein the calculation formula is as follows:
Figure BDA0003284393580000032
Figure BDA0003284393580000033
step ten: and (3) introducing the coordinate points into UG NX software in a spline curve mode, respectively mirroring the two curves to obtain a driving wheel pitch curve and a driven wheel pitch curve, and translating the driven wheel pitch curve to obtain tangent driving wheel pitch curves and driven wheel pitch curves.
Preferably, in the first step, rounding operation is performed at the straight line intersection of the ideal motion speed curve.
Preferably, the array in the second step is in the form of a curve array, and the motion curve is equally divided into 360 parts.
Preferably, the first 181 groups of data are extracted from the fourth step for analysis.
Preferably, in the seventh step, the rotation angle of the driving wheel is adjusted
Figure BDA0003284393580000034
Angle of time driven wheel
Figure BDA0003284393580000035
The gear ratio at this position can be considered as
Figure BDA0003284393580000036
Is calculated according to the law of luobida, the formula is as follows:
Figure BDA0003284393580000037
preferably, in the step ten, a cubic spline curve is adopted to pour the coordinate points into UG NX software.
Preferably, the distance of the curvilinear translation of the driven wheel joint in the step ten is the center distance between the driving wheel and the driven wheel.
Compared with the prior art, the invention has the following technical effects:
the method directly draws a motion curve output by a sine mechanism in drawing software, then conducts a series of data processing after deriving a coordinate point, finally obtains key structure parameters of the mechanism, and reversely calculates a pitch curve of the non-circular gear; the method realizes the design of the pitch curve by jointly applying CREO, EXCEL, ORIGIN and UG NX, does not need programming, has simple and convenient calculation and can realize the rapid design of serialization.
Drawings
FIG. 1 is a schematic view of a non-circular gear driven sinusoidal mechanism;
FIG. 2 is a graph of ideal movement velocity;
FIG. 3 is a set of array points for an ideal motion velocity profile;
FIG. 4 is a schematic view of the pitch curve of the driving wheel and the driven wheel obtained;
the meaning of each reference number in the figures is: the device comprises a driving wheel 1, a driven wheel 2, a crank 3, a sliding block 4, a guide rail 5, a rack 6 and a supporting seat 7.
Detailed Description
The present invention will be explained in further detail with reference to examples.
As shown in fig. 1 to 4, the present embodiment provides a method for designing a non-circular gear pitch curve for driving a sinusoidal mechanism to reciprocate at a uniform speed, including the following steps:
the method comprises the following steps: setting the rotation speed omega of the driving wheel1Setting the current example as 360 degree/s, drawing ideal motion speed curve output by sine mechanism in CREO software, the abscissa of the curve is the rotation angle of the driving wheel
Figure BDA0003284393580000041
The unit is DEG, the ordinate is the translational speed v of the frame, and the unit is cm/s;
in order to avoid rigid impact, it is necessary to ensure the smoothness of the motion curve, and to perform a rounding operation at the intersection of straight lines, thus ensuring that the speed is smoothly transited, as shown in fig. 2;
step two: extracting a starting point on the ideal movement speed curve, carrying out point array along the ideal movement speed curve, converting the ideal movement speed curve into a point set, and storing the point set in an IGES format; the number of arrays was 361, thus dividing the motion curve equally into 360, as shown in FIG. 3;
step three: and (3) extracting coordinate values of the point set: newly building a model file in CREO software, importing a point set file in an IGES format, expressing points in the point set in a Cartesian coordinate form, storing the point set in a PTS format, opening the PTS format file by using a notebook, extracting coordinate values of the points, wherein the coordinate data are shown in a table 1;
table 1 points coordinate values
Figure BDA0003284393580000051
Step four: extracting point set coordinate data corresponding to the working stroke: coordinates of the points shown in Table 1The data is imported into the EXCEL file, because the working stroke and the return stroke have the same speed and opposite directions, only the front 181 groups of data need to be extracted, and the rotation angle of the driving wheel is turned
Figure BDA0003284393580000052
The angle values of (a) are converted into camber values, as shown in table 2;
TABLE 2 motion law of working stroke
Figure BDA0003284393580000053
Figure BDA0003284393580000061
Step five: acquiring the length of a crank: importing the data shown in the table 2 in the fourth step into ORIGIN, clicking Analysis-Mathematics-integration to perform integration operation, and dividing the integration value by the rotating speed of the driving wheel, namely 2 pi (rad/s), to obtain a displacement value shown in the table 3;
TABLE 3 Displacement values for working Stroke
Figure BDA0003284393580000062
The maximum displacement of the working stroke is 2 times of the length e of the crank, the front 181 groups of data points are checked, the maximum displacement value is 17.16451843cm, and therefore the length of the crank of the sine mechanism is 85.82259215 mm;
step six: and calculating the driven wheel rotation angle corresponding to each displacement value: copying the displacement values into EXCEL for calculation, and calculating the driven wheel rotation angle corresponding to each displacement value
Figure BDA0003284393580000063
Driven wheel corner
Figure BDA0003284393580000064
The relationship satisfied by the displacement s and the crank length e is as follows:
Figure BDA0003284393580000065
step seven: calculating a transmission ratio: calculating the increment of the rotation angle of the driving wheel in each group of data relative to the previous group of data
Figure BDA0003284393580000066
Increment of driven wheel angle
Figure BDA0003284393580000067
The calculation formula of the transmission ratio of the main driving wheel and the driven wheel is as follows:
Figure BDA0003284393580000068
for the corner of the driving wheel
Figure BDA0003284393580000069
Angle of time driven wheel
Figure BDA00032843935800000610
The gear ratio at this position can be considered as
Figure BDA0003284393580000071
According to the law of luoba, the calculation formula of the transmission ratio at this position is:
Figure BDA0003284393580000072
step eight: calculating radial r of driving wheel1Radial direction r of driven wheel2: setting a reasonable center distance a of the non-circular gear according to the length e of the crank, and calculating the radial direction r of the driving wheel according to the following formula under the assumption that the center distance is 80mm1Radial direction r of driven wheel2；
Figure BDA0003284393580000073
Figure BDA0003284393580000074
Step nine: the turning angles and corresponding radial values of the driving wheel and the driven wheel are converted into Cartesian coordinate values, and calculation is carried out in EXCEL, wherein the calculation formula is as follows:
Figure BDA0003284393580000075
Figure BDA0003284393580000076
the calculated coordinate data of the driving wheel pitch curve is shown in table 4, and the coordinate data of the driven wheel pitch curve is shown in table 5;
TABLE 4 coordinate data of active wheel pitch curve
Figure BDA0003284393580000077
Figure BDA0003284393580000081
TABLE 5 driven wheel knuckle coordinate data
Serial number x2 y2 z2
1 33.947254 0 0
2 33.94589 0.490568 0
3 33.925687 0.981001 0
4 33.917261 1.471532 0
5 33.883612 1.961197 0
…… …… …… ……
180 -33.94727 0.490589 0
181 -33.93717 0 0
Step ten: and (3) introducing the coordinate points into UG NX software in the form of spline curves, respectively mirroring the two curves to obtain a driving wheel pitch curve and a driven wheel pitch curve, translating the driven wheel pitch curve by the length of the center distance of 80mm to obtain tangent driving wheel pitch curves and driven wheel pitch curves, as shown in figure 4.
Then other data are designed to complete the design of the non-circular gear driven sine mechanism with uniform reciprocating motion, as shown in fig. 1, the working principle of the non-circular gear driven sine mechanism with uniform reciprocating motion is as follows: the driving wheel 1 drives the driven wheel 2 to rotate, the driven wheel 2 drives the crank 3 to rotate in a speed changing manner, the slide block 4 moves in the guide rail 5, the rack 6 is driven to reciprocate, and the supporting seat 7 plays a role in supporting the rack 6.
It should be noted that the above embodiments are not all embodiments of the present invention, and those skilled in the art can make various changes, substitutions and alterations without departing from the spirit of the present invention.

Claims (7)

1. The design method of the non-circular gear pitch curve for driving the sine mechanism to do uniform reciprocating motion is characterized by comprising the following steps of:
the method comprises the following steps: drawing an ideal motion speed curve in CREO software, wherein the abscissa of the curve is the corner of the driving wheel, and the ordinate is the translation speed of the rack;
step two: extracting a starting point on the ideal movement speed curve, carrying out point array along the ideal movement speed curve, converting the ideal movement speed curve into a point set, and storing the point set in an IGES format;
step three: and (3) extracting coordinate values of the point set: newly building a model file in CREO software, importing a point set file in an IGES format, expressing points in the point set in a Cartesian coordinate form, storing the point set in a PTS format, opening the PTS format file by using a notebook, and extracting coordinate values of the points;
step four: extracting point set coordinate data corresponding to the working stroke: importing the coordinate data of the points into an EXCEL file, and converting the angle value of the rotating angle of the driving wheel into a camber value;
step five: acquiring the length of a crank: importing the data in the fourth step into an ORIGIN, clicking an Analysis-Mathematics-integration to perform integration operation, dividing the integration value by the rotating speed of the driving wheel to obtain a displacement value, viewing the maximum displacement value to obtain crank length data, wherein the maximum displacement of the working stroke is 2 times of the crank length;
step six: and calculating the driven wheel rotation angle corresponding to each displacement value: copying the displacement values into EXCEL for calculation, and calculating the driven wheel rotation angle corresponding to each displacement value
Figure FDA0003284393570000011
Driven wheel corner
Figure FDA0003284393570000012
The relationship satisfied by the displacement s and the crank length e is as follows:
Figure FDA0003284393570000013
step seven: calculating a transmission ratio: calculating the increment of the rotation angle of the driving wheel in each group of data relative to the previous group of data
Figure FDA0003284393570000014
Increment of driven wheel angle
Figure FDA0003284393570000015
The transmission ratio of the main driving wheel and the driven wheel is as follows:
Figure FDA0003284393570000016
step eight: calculating the radial direction of the driving wheel and the radial direction of the driven wheel: setting a reasonable center distance a of the non-circular gear according to the length e of the crank, and calculating the radial direction r of the driving wheel according to the following formula1Radial direction r of driven wheel2；
Figure FDA0003284393570000021
Figure FDA0003284393570000022
Step nine: the turning angles and corresponding radial values of the driving wheel and the driven wheel are converted into Cartesian coordinate values, and calculation is carried out in EXCEL, wherein the calculation formula is as follows:
Figure FDA0003284393570000023
Figure FDA0003284393570000024
step ten: and (3) introducing the coordinate points into UG NX software in a spline curve mode, respectively mirroring the two curves to obtain a driving wheel pitch curve and a driven wheel pitch curve, and translating the driven wheel pitch curve to obtain tangent driving wheel pitch curves and driven wheel pitch curves.
2. The method as claimed in claim 1, wherein the first step is to round the corner at the straight line intersection of the ideal motion speed curve.
3. The method for designing the non-circular gear pitch curve which drives the sine mechanism to do uniform reciprocating motion according to claim 1, wherein the array in the second step is in a curve array form, and the motion curve is equally divided into 360 parts.
4. The method for designing a non-circular gear pitch curve for driving a sinusoidal mechanism to reciprocate at a constant speed according to claim 1, wherein the first 181 groups of data are extracted for analysis in the fourth step.
5. The method as claimed in claim 1, wherein step seven comprises turning the driving wheel about a rotational angle
Figure FDA0003284393570000025
Angle of time driven wheel
Figure FDA0003284393570000026
The gear ratio at this position can be considered as
Figure FDA0003284393570000027
Is calculated according to the law of luobida, the formula is as follows:
Figure FDA0003284393570000031
6. the method for designing a non-circular gear pitch curve for driving a sinusoidal mechanism to reciprocate at a uniform speed according to claim 1, wherein in the tenth step, a cubic spline curve is adopted to introduce coordinate points into UG NX software.
7. The method as claimed in claim 6, wherein the step ten is performed by translating the driven wheel pitch curve by the distance between the centers of the driving wheel and the driven wheel.
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