CN104816045B - Non-circular gear Gear Shaping method - Google Patents

Abstract

A kind of non-circular gear Gear Shaping method, according to the parameter (pitch curve of non-circular gear, modulus, centre-to-centre spacing) and machined parameters, consider the movement locus that cutting output, withdrawing, positioning datum etc. calculate each axle of non-circular gear digital control gear shaper, generate machining code, non-circular gear can be processed on common digital control gear shaper, with the features such as high in machining efficiency, good processing accuracy, integrated cost is low.

Description

Shaping method of non-circular gear

technical field

The invention relates to a gear shaping processing method, in particular to a non-circular gear shaping processing method.

Background technique

Non-circular gears are used to transmit non-uniform motion between two shafts. Compared with other non-uniform speed ratio transmission mechanisms (such as cams, connecting rods, etc.), they have the advantages of stable transmission, compact structure, and high motion precision. They are widely used in textile, Cigarette, paper and other machinery and equipment. However, because the pitch curve is non-circular, the design and manufacture are much more complicated than circular gears, and three-dimensional modeling is particularly difficult.

The motion characteristic of non-circular gears is that it can realize the nonlinear relationship between the rotation angles of the active mechanism and the driven mechanism, so it has been paid more and more attention in light industry, heavy industry, instrumentation, engineering machinery and other industries. In many industries, non-circular gear transmission mechanisms are usually used instead of linkage mechanisms, cam mechanisms or other motion mechanisms to achieve specific motion laws. The structure of the non-circular gear transmission mechanism is compact, and the transmission is precise and stable. It can be used in non-circular gear mechanism to realize variable transmission ratio transmission, and can realize some special movements when combined with some mechanisms. If other mechanisms are used for these movements, the mechanism will often become huge and complicated. After adopting the non-circular gear mechanism, the motion performance and power performance of the mechanism are greatly improved. For example: in textile machinery, non-circular gears are used to change the density of warp and weft yarns to obtain different patterns. In the transmission chain of the main conveyor belt of the linkage machine, the Martensis sheave mechanism is used to drive the conveyor belt to make intermittent stop motion or indexing motion to complete the work on the station and the subsequent indexing motion. On the conveyor belt of the "cigarette holder paper cigarette" machine, an elliptical gear drive is used to replace the original intermittent drive mechanism, etc. Such an application not only simplifies the transmission mechanism, but also improves the production efficiency. Including oval gear mechanisms in packaging machinery, oval gears in hydraulic fluid meters, etc., all have specific applications for non-circular gears.

Due to the non-circular pitch curve feature, the machining of non-circular gears is much more difficult than that of general gears. At present, wire cutting and CNC machining centers are mostly used for processing, and there are generally disadvantages such as low processing efficiency and low processing accuracy. Transmission gear processing methods are mainly gear hobbing and gear shaping, but hobbing cannot process non-circular gears with concave pitch curves, and its versatility is not good.

According to the traditional method for gear shaping processing of non-circular gears, if the table rotates at a constant speed, the slotting tool must move in both horizontal and vertical directions to ensure normal meshing. In this way, the control is better realized and more intuitive, but the machine tool needs four-axis linkage control, and its electrical system and mechanical device are relatively complicated.

Contents of the invention

The object of the present invention is to provide a gear shaping method for non-circular gears. By using this method, the non-circular gears can be calculated according to the parameters (pitch curve, modulus, center distance) and processing parameters (feed rate, cutting amount) of non-circular gears. The motion trajectory of each axis of the circular gear CNC gear shaping machine generates processing codes, and non-circular gears can be processed on ordinary CNC gear shaping machines. It has the characteristics of high processing efficiency, good processing accuracy, and low comprehensive cost.

The technical scheme that the present invention realizes above-mentioned purpose is:

Using this method to process non-circular gears on a three-axis CNC gear shaping machine requires that the gear shaping machine must have the following basic functions. If the gear shaping machine does not have these functions, corresponding electrical transformations are required.

1. The CNC gear shaping machine has three feed axes and one main shaft. The definition of each axis is arranged according to the definition of the machine tool system itself. The general definition is as follows: X-axis—beam or table movement, A—worktable rotation, B—gear shaper cutter rotation.

2. The machine tool has a CNC system with more than three axes of Siemens or Farak CNC system, and has three-axis linkage control function at the same time. New CNC gear shaping machines generally have these configurations. For older gear shaping machines, the control system of the gear shaping machine needs to be modified to achieve three-axis linkage.

3. The machine tool spindle must have two upper and lower stop points. The upper stop point is the basic configuration of a general gear shaping machine, but the lower stop point is an optional part, which can be purchased by contacting the machine tool factory. After the components are selected, it is necessary to program the PLC of the machine tool. Through the corresponding registers, program the corresponding M codes of the upper stop point and the lower stop point in place in a way that prohibits reading and writing, for the CNC program to call.

To process non-circular gears correctly, special designs of tools and fixtures are required:

1. The tooth shape, pressure angle and other parameters of the gear shaper cutter are the same as those of ordinary gear shaper cutters, but there must be a foundation on the gear shaper cutter that can align the circumferential tooth shape position of the gear shaper cutter, such as processing a base plane etc.

2. The fixture is designed according to the requirements of the processed wheel blank, but since the non-circular gear wheel blank has a circumferential positioning foundation, such as keyway, plane, etc., to make the workpiece can be correctly aligned on the machine tool, the corresponding fixture There must also be a datum that has a certain positional relationship with the wheel blank, such as a plane, a stepped surface, etc.

With the preparation of the above hardware conditions, the programming of the non-circular gear processing code can be carried out. The specific steps are as follows:

1. According to the modulus of the gear and the characteristics of the machine tool, refer to the processing technology of the cylindrical gear to determine the number of processing cycles as N, then the radial feed of each cycle i is Δh _i (i=1,2...N). Define the circumferential feed rate fθ _i and the radial feed rate fh _i in cycle i,

Since the instantaneous contact area will increase with the deepening of the radial shaper, and the force on the machine tool and the tool will increase, so the radial feed generally adopts a decreasing feed method, that is, the feed rate increases with the number of cycles. The increase is continuously decreasing.

Therefore, the feed rate in each cycle satisfies the law of decreasing, that is:

On the other hand, with the deepening of the radial cutting, the area integral of the circumferential cutting increases. Therefore, the radial feed in each cycle is reduced.

Δh _i+1 <Δh _i (i=1...N _i -1) (2)

Its specific value should be determined according to the actual situation. On the other hand, the general gear shaping process uses a gear shaping cutter to complete the finishing and rough machining, so the last cycle has the greatest impact on the precision and smoothness of the tooth surface. In one cycle, the feed rate should be very small.

2. According to the pitch curve equation of the non-circular gear to be processed is then its independent variable The first derivative of is The minimum radius of the gear shaper cutter is selected from the curvature of the pitch curve of the non-conical gear and the least undercut condition, and the number of teeth is rounded according to the modulus of the gear shaper cutter.

3. Design the non-circular gear tooth base according to the following equation.

In the formula:

h _a is the height of the addendum of the non-circular gear.

4. According to the above parameters, the position equation of each axis of non-circular gear shaping can be determined, and the position equation is as follows:

The movement speed of each axis is divided into two directions: radial direction and circumferential direction, and its circumferential movement speed is:

Its radial motion speed is:

In the formula, f _h are the circumferential and radial feed rates, respectively, is the gear rotation angle, h ₀ is the gear shape processing

radial displacement.

5. The feed model of each axis obtained above is based on the non-circular gear rotation angle as the independent variable, at a constant circumferential feed rate The area of the cutting area is constantly changing, which is unfavorable to the machining accuracy and the cutting tool. In order to keep the cutting area constant, the above mathematical model needs to be converted into the angle of the gear shaper cutter as the independent variable.

The rotation angle between the gear shaper cutter and the non-circular gear satisfies the relationship:

In the formula, θ is the rotation angle of the gear shaper cutter under equal arc length cutting;

The above equation can be solved by the difference method, and by solving the above equation, it can be solved which is

By substituting the above equations, the position equations of each axis of non-circular gear shaper processing with equal arc length cutting can be obtained;

The speed governing equations for the two directions of each axis:

In the formula, f _θ is the circumferential feed rate under equal arc length cutting, and θ is the rotation angle of the gear shaper cutter under equal arc length cutting;

6. Determine the position equation of each axis when retracting the tool. The retraction of non-circular gears is realized by the CNC program. When the CNC system detects that the gear shaper cutter moves to the lower stop point, it executes the tool retraction interpolation. The tool retraction on the machine tool spindle The distance is: ΔE, then the retraction position It can be obtained by solving the nonlinear equation according to the following formula.

In the formula,

Solved according to the above formula According to the processing method of equal arc length, it is replaced by Then the position equation of each axis can be solved when the tool is withdrawn.

The speed control equations of the two directions of each axis when retracting the tool:

In the formula, f _θ is the circumferential feed rate under equal arc length cutting;

7. Determine the initial position of the tool setting: the initial position of the radial feed is: h _o = h+r _o , h is the radial feed, r ₀ is the radius of the gear shaper cutter, and the initial position of the circumferential feed is Substitute the two starting positions into the motion equation to get the position of each motion axis during tool setting.

8. Select different feed rates according to finishing and preliminary processing, write interpolation instructions in the form of spline curves, add M codes for auxiliary functions in the program, and determine the offset coordinate system register.

9. Position and install the tooth embryo of the non-circular gear on the fixture, first find the center of rotation of the non-circular gear according to the outer circular surface of the tooling, and then find the circumferential direction of the non-circular gear according to the circumferential plane, and adjust the machine tool to the sixth The starting position calculated by the step, and input the coordinate value of each axis into the offset coordinate system register.

10. According to each cycle, complete the shaping process of the non-circular gear segment by segment.

The beneficial effect of the invention is that the processing code generated by the method can be used to process non-circular gears on an ordinary numerical control gear shaping machine, and has the characteristics of high processing efficiency, good processing accuracy and low comprehensive cost.

Description of drawings

Fig. 1 is a wheel blank diagram of the driving wheel of the embodiment of the present invention.

Fig. 2 is a wheel blank diagram of the driven wheel of the embodiment of the present invention.

Fig. 3 is a graphics simulation diagram of the first processing cycle of the driving wheel according to the embodiment of the present invention.

Fig. 4 is a graphics simulation diagram of the second processing cycle of the driving wheel according to the embodiment of the present invention.

Fig. 5 is a graphics simulation diagram of the third processing cycle of the driving wheel according to the embodiment of the present invention.

Fig. 6 is a graphics simulation diagram of the fifth processing cycle of the driving wheel according to the embodiment of the present invention.

Fig. 7 is a graphics simulation diagram of the first processing cycle of the driven wheel according to the embodiment of the present invention.

Fig. 8 is a graphics simulation diagram of the second processing cycle of the driven wheel according to the embodiment of the present invention.

Fig. 9 is a graphics simulation diagram of the third processing cycle of the driven wheel according to the embodiment of the present invention.

Fig. 10 is a graphics simulation diagram of the fifth machining cycle of the driven wheel according to the embodiment of the present invention.

Fig. 11 is a speed curve diagram of the A-axis of the machine tool with the fifth processing cycle of the driving wheel according to the embodiment of the present invention.

Fig. 12 is a speed curve diagram of the B-axis of the fifth machining cycle of the driving wheel according to the embodiment of the present invention.

Fig. 13 is an X-axis speed graph of the fifth machining cycle of the driving wheel according to the embodiment of the present invention.

Fig. 14 is a speed graph of the A-axis of the fifth machining cycle machine tool for the driven wheel according to the embodiment of the present invention.

Fig. 15 is a speed curve diagram of the B-axis of the fifth machining cycle of the driven wheel according to the embodiment of the present invention.

Fig. 16 is an X-axis speed graph of the fifth machining cycle of the driven wheel according to the embodiment of the present invention.

detailed description

Here, a pair of sinusoidal transmission ratio third-order non-circular gear transmission is taken as an example, and the processing is carried out according to the above method. The parameters of the gear are shown in Table 1.

Table 1 Basic parameters of gears

According to the above basic parameters and the basic definition of non-circular gears, the pitch curve of the driving wheel is obtained

Pitch curve of driven wheel:

Angle of driven wheel:

Number of teeth of the driven wheel:

The arc length of the driving pitch curve:

So the modulus of the gear:

Calculate the addendum h _a = h _a ^* m = 2.5 of the non-circular gear according to Table 1, and determine the wheel base of the non-circular gear according to formula (3), as shown in Fig. 1 and Fig. 2 . According to the formula (13), the non-circular gear, the starting position of the tool setting of the driving wheel and the tool setting point of the driving wheel can be determined. The final calculation results are shown in Table 2

Table 2 Tool setting position

Select the same gear shaper cutter to process the driving wheel and the driven wheel, and the basic parameters of the gear shaper cutter are shown in Table 3:

Table 3 Basic parameters of gear shaper cutter

The gear feed is divided into 5 cycles, the feed rate and cutting depth of each cycle are shown in Table 4. According to formula (8), the position of each axis of the non-circular gear can be obtained, and the processing code can be written by using this position number, and the above-mentioned non-circular gear can be processed by gear shaping. Using the method of graphics simulation, the envelope curve of the tooth profile of the gear shaping cutter on the gear wheel blank can be obtained in each cycle, as shown in Fig. 3-Fig. 10, Fig. 3-Fig. 7-Figure 10 is the enveloping tooth shape of the driven wheel. The speed curves of each axis can be obtained according to formula (9). Figure 11-Figure 16 shows the speed curves of each axis during circumferential feed in the last machining cycle. Fig. 11 and Fig. 14 are the speed curves of the A axis, Fig. 12 and Fig. 15 are the speed curves of the B axis, and Fig. 13 and Fig. 16 are the speed curves of the X axis.

Table.4 Machining feed parameters

Claims (1)

1. A non-circular gear shaping method, characterized in that: A. Hardware preparation: 1. The CNC gear shaping machine has three feed motion axes and one main shaft; the definition of each axis is arranged according to the definition of the machine tool system itself. The general definition is as follows: X axis—beam or table movement, A—worktable rotation , B—rotation of gear shaper cutter; 2. The machine tool has a CNC system with more than three axes of Siemens or Farak CNC system, and has three-axis linkage control function at the same time; 3. The spindle of the machine tool must have two upper and lower stop points; program the PLC of the machine tool, and program the corresponding M codes of the upper stop point and the lower stop point in place through the corresponding registers in a way that prohibits reading and writing, for CNC program call; 4. There must be a basis on the gear shaper cutter that can align the circumferential tooth profile position of the gear shaper cutter, and process a datum plane on the tool handle; 5. The fixture is designed according to the requirements of the processed wheel blank, but since the non-circular gear wheel blank has a circumferential positioning foundation, keyway or plane, to make the workpiece can be correctly aligned on the machine tool, the corresponding fixture must also have A datum, plane or stepped surface that has a certain positional relationship with the wheel blank; B. Program the non-circular gear processing code, the specific steps are as follows: 1. According to the modulus of the gear and the characteristics of the machine tool, refer to the processing technology of the cylindrical gear to determine the number of processing cycles as N, then the radial feed of each cycle i is Δh _i (i=1,2...N); definition In cycle i, the circumferential feed rate is fθ _i , and the radial feed rate is fh _i , Since the instantaneous contact area will increase with the deepening of the radial shaper, and the force on the machine tool and the tool will increase, so the radial feed generally adopts a decreasing feed method, that is, the feed rate increases with the number of cycles. increasing and decreasing continuously; Therefore, the radial feed rate fh _i and circumferential feed rate fθ _i in each cycle satisfy the law of decreasing, that is: <mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>fh</mi><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mi>fh</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>f&amp;theta;</mi><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mi>f&amp;theta;</mi><mi>i</mi></msub></mrow></mtd></mtr></mtable><mo>,</mo><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1...</mn><msub><mi>N</mi><mi>i</mi></msub><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow> On the other hand, with the deepening of the radial cut, the circumferential cutting area will increase; so the radial feed in each cycle decreases; Δh _i+1 <Δh _i (i=1...N _i -1) (2) Its specific value should be determined according to the actual situation. On the other hand, the general gear shaping process uses a gear shaping cutter to complete the finishing and rough machining, so the last cycle has the greatest impact on the precision and smoothness of the tooth surface. In one cycle, the feed rate should be very small; 2. According to the pitch curve equation of the non-circular gear to be processed is then its independent variable The first derivative of is is the gear rotation angle; the minimum radius of the gear shaping cutter is selected from the curvature of the pitch curve of the non-conical gear and the least undercut condition, and the number of teeth is rounded according to the modulus of the gear shaping cutter; 3. Design the non-circular gear tooth base according to the following equation; In the formula: h _a is the addendum height of the non-circular gear, x _a is the abscissa of the tooth base curve, and y _a is the ordinate of the tooth base curve; 4. According to the above parameters, the position equation of each axis of non-circular gear shaping can be determined, and the position equation is as follows: The movement speed of each axis is divided into two directions: radial direction and circumferential direction, and its circumferential movement speed is: Its radial motion speed is: In the formula, f _h are the circumferential and radial feed rates, respectively, is the gear rotation angle, h ₀ is the radial displacement of gear shaping process; 5. The mathematical model of each axis obtained above is based on the non-circular gear rotation angle as the independent variable, at a constant circumferential feed rate The area of the cutting area is constantly changing, which is unfavorable to the machining accuracy and the cutting tool. In order to keep the cutting area constant, the above mathematical model needs to be converted to the angle of the gear shaper cutter as the independent variable; The rotation angle between the gear shaper cutter and the non-circular gear satisfies the relationship: In the formula, θ is the rotation angle of the gear shaper cutter under equal arc length cutting; The above equation can be solved by the difference method, and by solving the above equation, it can be solved which is By substituting the above equations, the position equations of each axis of non-circular gear shaper processing with equal arc length cutting can be obtained; The speed governing equations for the two directions of each axis: 6. Determine the position equation of each axis when retracting the tool. The retraction of non-circular gears is realized by the CNC program. When the CNC system detects that the gear shaper cutter moves to the lower stop point, it executes the tool retraction interpolation. The tool retraction on the machine tool spindle The distance is: ΔE, then the retraction position It can be obtained by solving the nonlinear equation according to the following formula; In the formula, Solved according to the above formula According to the processing method of equal arc length, it is replaced by Then the position equation of each axis can be solved when the tool is retracted; The speed control equations of the two directions of each axis when retracting the tool: In the formula, f _θ is the circumferential feed rate under equal arc length cutting; 7. Determine the initial position of the tool setting: the initial position of the radial feed is: h _o = h+r _o , h is the radial feed, r ₀ is the radius of the gear shaper cutter, and the initial position of the circumferential feed is Substitute the two starting positions into the position equation to get the position of each movement axis during tool setting; <mrow><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>E</mi><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>=</mo><msqrt><mrow><mi>r</mi><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>2</mn></msup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>h</mi><mi>r</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow><msqrt><mrow><mi>r</mi><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>r</mi><mo>&amp;prime;</mo></msup><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup></mrow></msqrt></mfrac></mrow></msqrt></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>&amp;gamma;</mi><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>=</mo><mi>arctan</mi><mo>{</mo><mfrac><mrow><mo>-</mo><msup><mi>hr</mi><mo>&amp;prime;</mo></msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow><mrow><msub><mi>h</mi><mi>o</mi></msub><mi>r</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>+</mo><mi>r</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><msqrt><mrow><mi>r</mi><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>r</mi><mo>&amp;prime;</mo></msup><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup></mrow></msqrt></mrow></mfrac><mo>}</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>&amp;theta;</mi><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>=</mo><mo>-</mo><mi>arccos</mi><mfrac><mrow><mi>h</mi><mo>+</mo><mfrac><mrow><mi>r</mi><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup></mrow><msqrt><mrow><mi>r</mi><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>r</mi><mo>&amp;prime;</mo></msup><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup></mrow></msqrt></mfrac></mrow><msqrt><mrow><mi>r</mi><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>2</mn></msup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>h</mi><mi>r</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow><msqrt><mrow><mi>r</mi><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>r</mi><mo>&amp;prime;</mo></msup><msup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mn>2</mn></msup></mrow></msqrt></mfrac></mrow></msqrt></mfrac></mrow></mtd></mtr></mtable></mfenced><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>13</mn><mo>)</mo></mrow></mrow> 8. Select different feed rates according to finishing and preliminary processing, write interpolation instructions in the form of spline curves, add M codes for auxiliary functions in the program, and determine the register of the offset coordinate system; 9. Position and install the tooth embryo of the non-circular gear on the fixture, first find the center of rotation of the non-circular gear according to the outer circular surface of the fixture, and then find the circumferential direction of the non-circular gear according to the circumferential plane, and adjust the machine tool to the sixth The starting position calculated by the step, and input the coordinate values of each axis into the offset coordinate system register; 10. According to each cycle, complete the shaping process of the non-circular gear segment by segment.