Non-circular gear pair pitch curve design method without function expression

Abstract

The invention discloses a non-circular gear pair pitch curve design method without a function expression, and the method comprises the following steps: S1, drawing a driving wheel rotation angle-radial curve; s2, extracting point set coordinates; s3, setting a center distance; s4, calculating the rotating angle of the driven wheel; s5, driven wheel pitch curve closure judgment; s6, a driving wheel pitch curve is constructed through spiral lines; s7, a planet carrier is constructed; s8, creating a pitch curve contact point tracking circle; s9, tracking a pitch curve contact point; and S10, connecting the pitch curve contact points in series to form a driven wheel pitch curve. According to the method, any spline curve is drawn to serve as a driving wheel rotation angle-radial curve, data calculation is conducted after point set coordinates are extracted, the driving wheel pitch curve and the driven wheel pitch curve are obtained through spiral line fitting and motion simulation means, complex pitch curve function expression derivation is avoided, design efficiency is high, and the method is easy to implement. And the whole design process is more free, and the method has a good application prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mechanical design, in particular to a non-circular gear pair pitch curve design method without function expression. BACKGROUND

[0002] Compared with the circular gear mechanism, the non-circular gear mechanism has the advantage of non-uniform speed ratio transmission, and can be widely applied in the fields of food machinery, agricultural machinery, textile machinery, etc. The non-uniform speed motion characteristic of the non-circular gear is determined by the pitch curves of the driving wheel and the driven wheel. The traditional design method is to list the function expression according to the meshing principle and differential geometry, and then form the special shape of the pitch curve. In the traditional design method, the derivation process of the curve equation is complex, and the design efficiency is low. SUMMARY

[0003] The purpose of the present application is to provide a non-circular gear pair pitch curve design method without function expression, which has simple design process, high efficiency, and more freedom in the whole design.

[0004] In order to achieve the above purpose, the technical scheme of the present application is a non-circular gear pair pitch curve design method without function expression, comprising the following steps:

[0005] S1: draw an arbitrary spline curve as the driving wheel rotation angle-arc length curve in UG NX, the horizontal coordinate of the driving wheel rotation angle-arc length curve is the rotation angle, the minimum value of the horizontal coordinate is 0, and the maximum value of the horizontal coordinate is 360, the vertical coordinate of the driving wheel rotation angle-arc length curve is the arc length, and the arc length at the rotation angle of 0 of the spline curve is the same as the arc length at the rotation angle of 360;

[0006] S2: insert a point set on the driving wheel rotation angle-arc length curve, divide the driving wheel rotation angle-arc length curve in an equal arc length manner, obtain the coordinates of each point, and the X-axis coordinate of the point corresponds to the rotation angle of the driving wheel rotation angle-arc length curve, and the Y-axis coordinate corresponds to the arc length of the driving wheel rotation angle-arc length curve;

[0007] S3: set the center distance between the driving wheel and the driven wheel as a;

[0008] S4: the arc lengths of the driving wheel and the driven wheel are r1 and r2 respectively, then r2=a-r1, the angular velocities of the driving wheel and the driven wheel are ω1 and ω2 respectively, then ω2=ω1×r1 / r2=ω1×r1 / (a-r1), the motion time is t, the rotation angle of the driving wheel is then the rotation angle of the driven wheel is the time for the driving wheel to rotate one revolution is t1, then and record the rotation angle of the driven wheel at each time

[0009] S5: set the allowable error as ε, and judge the condition expression if yes, then performing S6, if no, then performing S3;

[0010] S6: inserting a spiral line, specifying the center position of the spiral line, setting the spiral line radius to vary according to the driving wheel rotation angle - radial curve, and obtaining the driving wheel pitch curve;

[0011] S7: drawing a straight line with the center of the driving wheel pitch curve as the starting point, and the length of the straight line being the center distance a, and the straight line being the planet carrier;

[0012] S8: drawing a circle with the intersection point between the driving wheel pitch curve and the planet carrier as the center, and forming the contact point tracking circle of the driving wheel and the driven wheel pitch curve;

[0013] S9: in the UG NX motion simulation module, setting the driving pitch curve as the motion body 1, the pitch curve contact point tracking circle as the motion body 2, and the planet carrier as the motion body 3, establishing a relative rotation pair between the center of the driving wheel pitch curve and the end point of the planet carrier, inputting the driving wheel angular velocity ω1, and establishing a ground rotation pair at the other end point of the planet carrier, and inputting the angular displacement of the planet carrier at each moment, i.e. the rotation angle of the driven wheel at each moment the center of the pitch curve contact point tracking circle is set as a marker point, and the trajectory of the marker point in the simulation process is tracked;

[0014] S10: connecting the pitch curve contact points at each moment through a spline curve to obtain the driven wheel pitch curve, and finally hiding the marker point to obtain the non-circular gear pair pitch curve formed by the driving wheel pitch curve and the driven wheel pitch curve.

[0015] Further, the specific steps for obtaining the coordinates of each point in S2 are to save the entire file as an igs format, open it with Notepad, and read the coordinates of each point in the point set.

[0016] Further, in S6, the spiral line radius is set to vary according to the driving wheel rotation angle - radial curve, wherein the step distance is 0 and the number of turns is 1.

[0017] Further, in S9, a constant drive is adopted on the relative rotation pair, and a curve 2D drive is adopted on the ground rotation pair.

[0018] Compared with the prior art, the present application has the following beneficial effects:

[0019] The application draws an arbitrary spline curve as the rotation angle-pitch curve of the driving wheel, extracts the point set coordinates, and obtains the driving wheel pitch curve and the driven wheel pitch curve through helix fitting and motion simulation, thereby avoiding complex derivation of the pitch curve function expression, simplifying the design process, and improving the efficiency; and the arbitrary spline curve can obtain the corresponding driving wheel pitch curve and driven wheel pitch curve, and the whole design is more free, and has a good application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 The figure is a design flowchart of the application;

[0021] Figure 2 The figure is the rotation angle-pitch curve of the driving wheel drawn in the embodiment;

[0022] Figure 3 The figure is the point set on the rotation angle-pitch curve of the driving wheel in the embodiment;

[0023] Figure 4 The figure is the driving wheel pitch curve in the embodiment;

[0024] Figure 5 The figure is the planetary carrier in the embodiment;

[0025] Figure 6 The figure is the pitch curve contact point tracking circle in the embodiment;

[0026] Figure 7 The figure is the relative rotation pair between the driving wheel pitch curve and the planetary carrier and the ground rotation pair of the planetary carrier in the embodiment;

[0027] Figure 8 The figure is the marked point trajectory a in the simulation process in the embodiment;

[0028] Figure 9 The figure is the marked point trajectory b in the simulation process in the embodiment;

[0029] Figure 10 The figure is the marked point trajectory c in the simulation process in the embodiment;

[0030] Figure 11 The figure is the marked point trajectory d in the simulation process in the embodiment;

[0031] Figure 12 The figure is the marked point trajectory e in the simulation process in the embodiment;

[0032] Figure 13 The figure is the driven wheel pitch curve in the embodiment;

[0033] Figure 14 The figure is the non-circular gear pair pitch curve schematic diagram in the embodiment. DETAILED DESCRIPTION

[0034] The application will be described in further detail below with reference to the accompanying drawings and embodiments.

[0035] As Figure 1 shown in a non-circular gear pair pitch curve design method without function expression, comprising the following steps:

[0036] S1: draw the driven wheel rotation angle-lead curve;

[0037] Referring to Figure 2 Draw an arbitrary spline curve in UG NX as the driven wheel rotation angle-lead curve, the horizontal coordinate of the spline curve is the rotation angle, the minimum value of which is 0 and the maximum value of which is 360, representing the change range of the driven wheel rotation angle is 0-360°, and the vertical coordinate of the spline curve is the lead, the lead at the rotation angle of 0 is the same as the lead at the rotation angle of 360, so as to ensure that the driven wheel pitch curve is a closed curve;

[0038] S2: extract point set coordinates;

[0039] Referring to Figure 3 Insert a point set on the driven wheel rotation angle-lead curve, divide the spline curve in an equal arc length manner, and then save the entire file in igs format, open it with Notepad, read the coordinates of each point in the point set, the X-axis coordinate of the point corresponds to the rotation angle of the driven wheel, and the Y-axis coordinate corresponds to the lead of the driven wheel, and the coordinate data points are shown in Table 1;

[0040] Table 1: Spline curve coordinate point data

[0041]

[0042] S3: set the center distance;

[0043] Suppose the center distance between the driven wheel and the driven wheel is a;

[0044] S4: calculate the driven wheel rotation angle;

[0045] The driven wheel and the driven wheel lead are r1 and r2, respectively, so

[0046] r2=a-r1

[0047] The angular velocity of the driven wheel and the driven wheel is ω1 and ω2, respectively, so

[0048] ω2=ω1×r1 / r2=ω1×r1 / (a-r1)

[0049] The motion time is t, and the driven wheel rotation angle is Since the driven wheel rotates at a constant speed, then

[0050]

[0051] The rotation angle of the driven wheel is The time for the driving wheel to rotate one round is t1, then

[0052]

[0053] The rotation angle of the driven wheel at each moment is recorded

[0054] S5: Judgment of the closedness of the driven wheel cam curve;

[0055] According to the rotation angle of the driven wheel, it is judged whether the cam curve is closed or not. If the driven wheel cam curve is a non-closed curve; if the driven wheel cam curve has self-intersection phenomenon and cannot be transmitted; if the driven wheel cam curve is a closed curve, which can ensure the continuous and periodic transmission between the driving wheel and the driven wheel;

[0056] The allowable error is set as ε, and the judgment condition expression is

[0057]

[0058] If the condition is established, the rotation angle of the driven wheel tends to 360°, reaching the required accuracy, and then S6 is executed; if the condition expression is not established, S3 is executed, and the center distance a is reset so that the rotation angle of the driven wheel tends to 360° until the required accuracy is reached; the integral operation is carried out in Origin, the driving wheel angular velocity ω1 is set as 360° / s, the allowable error ε = 0.01 mm, and the calculated rotation angle of the driven wheel is 360.0001° under the condition that the center distance a is 131.4195 mm, which meets the accuracy requirement, as shown in Table 2;

[0059] Table 2: Calculation of the rotation angle of the driven wheel

[0060]

[0061]

[0062] S6: Constructing the driving wheel cam curve by using a spiral line;

[0063] Referring to Figure 4 the spiral line is inserted, the center position of the spiral line is specified, and the spiral line radius is set to vary according to the driving wheel rotation angle-pitch curve, wherein the step is 0 and the number of turns is 1, so as to obtain the driving wheel cam curve;

[0064] S7: Constructing the planet carrier;

[0065] Referring to Figure 5Draw a straight line with the center of the active gear pitch curve as the starting point, and its length is the center distance a. This straight line is the planet carrier.

[0066] S8: Create a circle to track the contact point of the nodal curve;

[0067] See Figure 6 Draw a circle with the intersection of the driving gear pitch curve and the planet carrier as the center to form a contact point tracking circle between the driving gear and the driven gear pitch curve;

[0068] S9: Tracking section curve contact point;

[0069] In the UG NX motion simulation module, set the active joint curve as motion body 1, the joint curve contact point tracking circle as motion body 2, and the planetary carrier as motion body 3;

[0070] See Figure 7 A relative revolute joint is established at the center of the driving gear pitch curve and the end point of the planetary carrier. A constant drive is used on the relative revolute joint, and the input angular velocity ω1 of the driving gear is 360° / s. A ground revolute joint is established at the other end point of the planetary carrier, and a 2D curve drive is used on the ground revolute joint. The input angular displacement of the planetary carrier at each moment is the rotation angle of the driven gear at each moment.

[0071] A point is set between the center of the pitch curve contact point tracking circle and the pitch curve of the driving wheel to constrain the online pair. Similarly, a point is set between the center of the pitch curve contact point tracking circle and the planetary carrier to constrain the online pair. The center of the pitch curve contact point tracking circle is set as a marker point, see [link to documentation]. Figures 8 to 12 Track the trajectory of marker points during the simulation process;

[0072] S10: The contact point of the tandem joint curve forms the driven wheel joint curve;

[0073] See Figure 13 Connecting the contact points of the pitch curves at various moments using spline curves forms the driven gear pitch curve. Finally, hiding the marker points yields the non-circular gear pair pitch curve composed of the driving gear pitch curve and the driven gear pitch curve, as shown below. Figure 14 As shown.

[0074] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for designing the pitch curve of a non-circular gear pair without a functional expression, characterized in that, Includes the following steps: S1: Draw an arbitrary spline curve in UG NX as the driving wheel rotation angle-radial curve. The horizontal coordinate of the driving wheel rotation angle-radial curve is the rotation angle, the minimum horizontal coordinate is 0, and the maximum horizontal coordinate is 360. The vertical coordinate of the driving wheel rotation angle-radial curve is the radial direction. The radial direction at the rotation angle of the spline curve is the same as the radial direction at the rotation angle of 360. S2: Insert a set of points on the driving wheel rotation angle-radial curve, divide the driving wheel rotation angle-radial curve equally using the method of equal arc length, and obtain the coordinates of each point. The X-axis coordinate of the point corresponds to the rotation angle of the driving wheel rotation angle-radial curve, and the Y-axis coordinate corresponds to the radial direction of the driving wheel rotation angle-radial curve. S3: Set the center distance between the driving wheel and the driven wheel to a; S4: The radial directions of the driving wheel and the driven wheel are r1 and r2 respectively, then r2 = a - r1. The angular velocities of the driving wheel and the driven wheel are ω1 and ω2 respectively, then ω2 = ω1 × r1 / r2 = ω1 × r1 / (a - r1). The motion time is t, and the rotation angle of the driving wheel is... but The driven wheel rotates at an angle of... If the time for the driving wheel to rotate one revolution is t1, then... And record the driven wheel rotation angle at each moment. S5: Set the allowable error to ε, and define the judgment condition expression. If the condition is true, then execute S6; otherwise, execute S3. S6: Insert a helix, specify the center position of the helix, and set the radius of the helix according to the change of the driving wheel rotation angle-radial curve to obtain the driving wheel pitch curve; S7: Draw a straight line starting from the center of the active gear pitch curve, with a length of center distance a. This straight line is the planet carrier. S8: Draw a circle with the intersection of the driving gear pitch curve and the planet carrier as the center to form the contact point tracking circle between the driving gear and the driven gear pitch curve; S9: In the UG NX motion simulation module, set the active pitch curve as motion body 1, the pitch curve contact point tracking circle as motion body 2, and the planetary carrier as motion body 3. Establish a relative revolute joint between the center of the active wheel pitch curve and the endpoint of the planetary carrier, and input the angular velocity ω1 of the active wheel. Establish a grounding revolute joint at the other endpoint of the planetary carrier, and input the angular displacement of the planetary carrier at each moment, i.e., the rotation angle of the driven wheel at each moment. The center of the contact point tracking circle of the pitch curve is constrained by the points set between the pitch curve of the driving wheel and the planet carrier on the line pair. The center of the contact point tracking circle of the pitch curve is set as a marker point to track the trajectory of the marker point during the simulation process. S10: Connect the contact points of the pitch curves at each moment using spline curves to obtain the driven gear pitch curve. Finally, hide the marker points to obtain the non-circular gear pitch curve formed by the driving gear pitch curve and the driven gear pitch curve.

2. The method for designing the pitch curve of a non-circular gear pair without a functional expression as described in claim 1, characterized in that: The specific steps for obtaining the coordinates of each point in S2 are as follows: save the entire file as an igs format, open it with Notepad, and read the coordinates of each point in the point set.

3. The method for designing the pitch curve of a non-circular gear pair without a functional expression as described in claim 1, characterized in that: In S6, the spiral radius is set according to the change of the driving wheel rotation angle-radial curve, where the step size is 0 and the number of revolutions is 1.

4. The method for designing the pitch curve of a non-circular gear pair without a functional expression as described in claim 1, characterized in that: In S9, constant drive is used on the relative rotating joint, and curved 2D drive is used on the grounded rotating joint.

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