CN114019908B - Spiral bevel gear tooth profile cambered surface chamfering control method - Google Patents
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/408—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by data handling or data format, e.g. reading, buffering or conversion of data
- G05B19/4083—Adapting programme, configuration
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F19/00—Finishing gear teeth by other tools than those used for manufacturing gear teeth
- B23F19/10—Chamfering the end edges of gear teeth
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
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Abstract
The invention provides a spiral bevel gear tooth profile cambered surface chamfering control method, which comprises the following steps: firstly, calculating tooth profile equations of the large end and the small end of a small spiral bevel gear path, accurately controlling the track of the arc surface chamfering of a chamfering tool, then integrating the track into software developed on the basis of C#, and automatically controlling an open type numerical control machine tool to process chamfering through a fixed high motion control card, wherein the tooth profile cambered surface chamfering of the two ends of the large spiral bevel gear is identical. The invention can truly eliminate the problem of the edge of the gear, and furthest reduce the stress concentration during the heat treatment of the gear, thereby improving the working effect of the gear; the man-machine interaction software is provided, so that the machining program of the spiral bevel gear tooth profile cambered surface chamfer can be automatically obtained, the machining difficulty is greatly reduced, and an operator can work more easily.
Description
Technical Field
The invention relates to the technical field of gear machining, in particular to a spiral bevel gear tooth profile cambered surface chamfering control method.
Background
The rapid development of modern technology makes spiral bevel gear widely used in various fields, but because the edge of gear teeth will be left with residual thorns when cutting the gear teeth, bumps and napping are generated in the process of carrying or assembling, the spiral bevel gear has certain defects, such as meshing noise, gear transmission accuracy reduction, gear service life shortening and the like. At present, the technology for chamfering the cambered surface of the spiral bevel gear has few technology, complex programming process and easy error, and certain difficulty exists in the operation of technicians, the traditional technology for chamfering the gear is to process the edge into an inclined plane of about 45 degrees, but simultaneously, a new smaller edge can be generated, the problem of stress concentration at the edge can not be completely eliminated all the time, and in the occasion of high-speed and heavy-load high-reliability transmission requirement, the requirement of chamfering the cambered surface is provided, and the chamfering of the cambered surface is to smoothly connect the meshing surface, the upper tooth surface, the lower tooth surface and the top circular surface by using circular surfaces or other quadric surfaces, so that the edge of the gear is completely eliminated. The chamfering technology of the spiral bevel gear is not mature at present, the chamfering program is complex to write, and the requirement on operators is high, so that development of automatic programming software is needed, and technicians can chamfer the spiral bevel gear only by performing simple operation.
Disclosure of Invention
The invention aims to provide a spiral bevel gear tooth profile cambered surface chamfering control method for solving the problems in the background technology.
The method combines the characteristics of tooth profile chamfering real-time performance, convenient and simple processing process and the like, and selects an improved NURBS curve interpolation algorithm and a GTS-VB series fixed height motion control card. Based on an open numerical control system platform, an operator operates software developed on the computer based on C# and comprises the steps of calculating tooth profile curve equations at two ends of a small gear of a spiral bevel gear, simulating chamfering processing tracks of cutters and the like, finally inputting parameters such as a machine tool, a workpiece, the cutters and the like, calling a dynamic link library in a fixed high-speed motion control card, sending a high-speed pulse instruction to the machine tool, driving a chamfering cutter on the machine tool to finish chamfering of cambered surfaces at two ends of the tooth profile of the small gear, and chamfering cambered surfaces at two ends of the large gear of the spiral bevel gear.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the spiral bevel gear tooth profile cambered surface chamfering control method is characterized by comprising the following steps of:
step 1: according to the spiral bevel gear structure and the tooth cutting method, calculating and obtaining tooth profile curve equations of the large end and the small end of the small wheel: obtaining tooth profile curve equations of a large end and a small end of a small wheel, firstly calculating a tooth crest line equation of a gear, and then calculating the tooth profile curve equations of the large end and the small end of the gear according to the structure of a spiral bevel gear and the coordinate relation of a machine tool;
step 2: simulating and extracting data points: simulating a three-dimensional curve graph in Matlab according to the tooth profile curve equation obtained in the step 1, and extracting a plurality of data points;
step 3: in combination with the modified NURBS curve interpolation algorithm:
in the interpolation process, any node parameter u E [ u ] of NURBS curve is given i ,u i+1 ]The curves are represented in matrix form, and the calculated i-th NURBS curve is:
wherein:
all coefficients in the formula (1) are determined by the weight factors, control vertexes and node vectors which are initially given, so that the interpolation efficiency is improved only by selecting the coefficients under the condition that the current interpolation point position is known;
performing parameter point densification on the feeding step length in the track space to convert the feeding step length into a node vector increment delta u of a one-dimensional parameter space i From formula u i+1 ＝u i +Δu i The parameter coordinates of the next interpolation point can be obtained;
according to a fourth-order Longger-Kutta algorithm, the node vector increment is calculated as follows:
calculated u i+1 And (3) carrying out NURBS curve interpolation equation (1), and obtaining the position parameter of the next interpolation point: p is p i+1 ＝p(u i+1 )；
Self-adaptive control of NURBS curve interpolation reduces interpolation step length by adjusting interpolation speed, thereby reducing chord height error; in each interpolation period, the chord height error is:
wherein: ρ i Radius of curvature, deltal i Interpolation is carried out to give step length, delta l i ＝v i T, and T is the interpolation period;
the feed speed v can thus be approximated i Chord height error delta i Relationship:
by machine tool maximum chord height error delta max Selecting a maximum allowable chord height error value
And finally, obtaining acceleration errors as follows:
the chamfering of the cutter is more stable and accurate according to the chord height error and the acceleration error formula;
finally, combining the obtained data points on the tooth profile of the spiral bevel gear with an improved NURBS curve interpolation algorithm to enable the chamfering tool to obtain an accurate and complete tooth profile cambered surface chamfering track;
step 4: all the control flows are integrated into software based on C# development:
opening a Windows window application program under a Visual C# template in VS2015 software, writing a control program, inputting a login name and a login password at a login interface by a user, and entering a functional interface, wherein the functional interface comprises functions of machine tool shaft state detection, machine tool management, workpiece management, tool management, database management, interpolation motion, NURBS curve and Matlab drawing call;
step 5: the fixed height operation control card controls the machine tool to finish chamfering the cambered surface of the tooth profile of the gear:
and after the operator inputs various required parameters into software on a computer, calling a dynamic link library in the fixed high-motion control card, and sending a high-speed pulse instruction to a machine tool so as to control the open type numerical control machine tool to finish chamfering of the tooth profile cambered surface of the gear.
The tooth crest line equation calculation process of the gear in the step 1 comprises the following steps:
comprehensively analyzing the tooth cutting principle of the spiral bevel gear and the technological parameters and the cutter parameters in the actual machining process to obtain parameters related to the pitch cone surface of the spiral bevel gear, solving an analytical equation of an imaginary tooth line on the pitch cone surface at the center of a tooth socket of the spiral bevel gear, and deducing an equation of a tooth top crest line according to the obtained relationship between the imaginary tooth line equation and the tooth top crest line under an equivalent gear.
In the step 2, a three-dimensional curve graph of a tooth profile curve is simulated in Matlab software, and a plurality of data points are extracted as follows:
setting configuration environments of C# and Matlab, calling Figure in Matlab by C# and embedding the Figure into a Winform window, drawing a three-dimensional graph according to a tooth profile curve equation calculated in the prior, extracting corresponding data points into a textBox control in C# and storing the data points into a txt file.
The chamfering tool in the step 3 is a chamfering tool: the traditional tooth profile chamfering process is to process the edge into an inclined plane with the angle of about 45 degrees, but a new smaller edge can be generated at the same time, so that a chamfering tool is selected, the tooth profile edge is chamfered by adopting an arc surface, and the two sides of the tooth profile edge line are connected by using the arc surface in a smooth manner, so that the edge of a gear can be completely eliminated.
And (3) finishing chamfering of the cambered surface of the tooth profile of the gear by the machine tool in the step (5): the spiral bevel gear is a spiral bevel gear, the axes of the two wheels are intersected, and the intersection angle is 90 degrees; the axis of the small spiral bevel gear is overlapped with the Z axis of the machine tool, and the C axis of the machine tool drives the gear to do rotary motion; firstly, a cutter executes a spiral tooth chamfering instruction at the small end of a gear, after a complete tooth profile is finished, the cutter is lifted to a certain height, at the moment, the machine tool C shaft rotates a certain angle, so that the gear to be machined rotates to the next complete tooth profile, the cutter starts to return to the chamfering starting position, the chamfering of the next tooth profile is started, and the steps are repeated until the gear teeth at the small end of the gear are completely machined, and the tooth profile cambered surface chamfering of the large end of the small spiral bevel gear and the tooth profile cambered surface chamfering of the large end of the large spiral bevel gear are all the same.
The invention has the following advantages and benefits:
(1) The chamfering tool can avoid the problem that a new smaller edge can be left after chamfering of a common chamfering tool, and the edge of the gear can not be really eliminated, so that the stress concentration during heat treatment of the gear is reduced to the greatest extent, and the working effect of the gear is improved.
(2) The NURBS curve interpolation based on the fourth-order Dragon lattice-Kutta algorithm can enable the chamfering of the tooth profile cambered surface of the chamfering tool to be more accurate.
(3) The man-machine interaction software based on the C# is provided, and the machining program of the spiral bevel gear tooth profile cambered surface chamfer can be automatically obtained by inputting the machine tool model parameters, the offset parameters of each shaft, the parameters of the spiral bevel gear and the parameters of the cutter, so that the machining difficulty is greatly reduced, and an operator can work more easily.
Drawings
FIG. 1 is a general flow chart of a spiral bevel gear tooth profile cambered surface chamfering control method of the invention;
FIG. 2 is a NURBS curve interpolation flow chart of a spiral bevel gear tooth profile cambered surface chamfering control method of the invention;
FIG. 3 is a diagram showing the chamfering of the tooth profile of the chamfering tool in the method for controlling the chamfering of the tooth profile of the spiral bevel gear;
fig. 4 is a software design diagram of the spiral bevel gear tooth profile cambered surface chamfering control method.
Detailed Description
The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by persons skilled in the art without making creative efforts based on the embodiments in the present invention are all within the protection scope of the present invention.
As shown in fig. 1 to 4, in this embodiment, tooth profile equations of large and small ends of a spiral bevel gear pinion are calculated, the track of the arc surface chamfer of a chamfering tool is precisely controlled, all the tracks are integrated into software developed on the basis of c#, an open type numerical control machine tool is automatically controlled to perform chamfer processing through a fixed height motion control card, and the arc surface chamfer of the tooth profile at two ends of the spiral bevel gear pinion is identical.
A spiral bevel gear tooth profile cambered surface chamfering control method comprises the following steps:
step 1: according to the spiral bevel gear structure and the tooth cutting method, the tooth profile curve equation of the large end and the small end of the small wheel is obtained through calculation:
obtaining tooth profile curve equations of a large end and a small end of a small wheel, firstly calculating a tooth crest line equation of a gear, and then calculating the tooth profile curve equations of the large end and the small end of the gear according to the structure of a spiral bevel gear and the coordinate relation of a machine tool;
step 2: simulating and extracting data points:
simulating a three-dimensional curve graph in Matlab according to the tooth profile curve equation obtained in the step 1, and extracting a plurality of data points;
step 3: in combination with the modified NURBS curve interpolation algorithm:
during interpolation, any node giving NURBS curveParameter u e [ u ] i ,u i+1 ]The curves are represented in matrix form, and the calculated i-th NURBS curve is:
wherein:
all coefficients in the formula (1) are determined by the weight factors, the control vertexes and the node vectors which are originally given, so that the interpolation efficiency is improved only by selecting the coefficients under the condition that the current interpolation point position is known.
Performing parameter point densification on the feeding step length in the track space to convert the feeding step length into a node vector increment delta u of a one-dimensional parameter space i From formula u i+1 ＝u i +Δu i The parameter coordinates of the next interpolation point can be obtained.
According to a fourth-order Longger-Kutta algorithm, the node vector increment is calculated as follows:
calculated u i+1 And (3) carrying out NURBS curve interpolation equation (1), and obtaining the position parameter of the next interpolation point: p is p i+1 ＝p(u i+1 )
And (3) self-adaptive control of NURBS curve interpolation, wherein the interpolation step length is reduced by adjusting the interpolation speed, so that the chord height error is reduced. In each interpolation period, the chord height error is:
wherein: ρ i Radius of curvature, deltal i Interpolation is carried out to give step length, delta l i ＝v i T, and T is the interpolation period
The feed speed v can thus be approximated i Chord height error delta i Relationship:
by machine tool maximum chord height error delta max Selecting a maximum allowable chord height error value
And finally, obtaining acceleration errors as follows:
the chamfering of the cutter is more stable and accurate according to the chord height error and the acceleration error formula;
and finally, combining the obtained data points on the tooth profile of the spiral bevel gear with an improved NURBS curve interpolation algorithm to ensure that the chamfering tool obtains an accurate and complete tooth profile cambered surface chamfering track.
Step 4: all the control flows are integrated into software based on C# development:
the method comprises the steps of opening a Windows window application program under a Visual C# template in VS2015 software, writing a control program, inputting a login name and a login password at a login interface by a user, and entering a functional interface, wherein the functional interface comprises functions of machine tool shaft state detection, machine tool management, workpiece management, tool management, database management, interpolation motion, NURBS curve and Matlab drawing.
Step 5: the fixed height operation control card controls the machine tool to finish chamfering the cambered surface of the tooth profile of the gear:
and after the operator inputs various required parameters into software on a computer, calling a dynamic link library in the fixed high-motion control card, and sending a high-speed pulse instruction to a machine tool so as to control the open type numerical control machine tool to finish chamfering of the tooth profile cambered surface of the gear.
The tooth crest line equation calculation process of the gear in the step 1 comprises the following steps:
comprehensively analyzing the tooth cutting principle of the spiral bevel gear and the technological parameters and the cutter parameters in the actual machining process to obtain parameters related to the pitch cone surface of the spiral bevel gear, solving an analytical equation of an imaginary tooth line on the pitch cone surface at the center of a tooth socket of the spiral bevel gear, and deducing an equation of a tooth top crest line according to the obtained relationship between the imaginary tooth line equation and the tooth top crest line under an equivalent gear.
In the step 2, a three-dimensional curve graph of a tooth profile curve is simulated in Matlab software, and a plurality of data points are extracted as follows:
setting configuration environments of C# and Matlab, calling Figure in Matlab by C# and embedding the Figure into a Winform window, drawing a three-dimensional graph according to a tooth profile curve equation calculated in the prior, extracting corresponding data points into a textBox control in C# and storing the data points into a txt file.
The chamfering tool in the step 3 is a chamfering tool:
the traditional tooth profile chamfering process is to process the edge into an inclined plane with the angle of about 45 degrees, but a new smaller edge can be generated at the same time, so that a chamfering tool is selected, the tooth profile edge is chamfered by adopting an arc surface, and the two sides of the tooth profile edge line are connected by using the arc surface in a smooth manner, so that the edge of a gear can be completely eliminated.
And (3) finishing chamfering of the cambered surface of the tooth profile of the gear by the machine tool in the step (5):
the spiral bevel gear in this embodiment is a spiral bevel gear, the axes of the two wheels intersect, and the angle of intersection is 90 degrees. The axis of the small spiral bevel gear is coincident with the Z axis of the machine tool, the C axis of the machine tool drives the gear to perform rotary motion, firstly, the cutter performs a curved tooth chamfering instruction at the small end of the gear, after a complete tooth profile is finished, the cutter is lifted to a certain height, at the moment, the C axis of the machine tool rotates a certain angle, the gear to be machined rotates to the next complete tooth profile, the cutter starts to return to the chamfering starting position, the chamfering of the next tooth profile is started, and the process is repeated until the gear teeth of the small end of the gear are completely machined, and the tooth profile cambered surface chamfering of the large end of the small spiral bevel gear and the tooth profile cambered surface chamfering of the large end of the large spiral bevel gear are all the same.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the foregoing embodiments, and that the foregoing embodiments and description are merely preferred embodiments of the invention, and are not intended to limit the invention, but that various changes and modifications may be made therein without departing from the novel spirit and scope of the invention, which is defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (1)
1. The spiral bevel gear tooth profile cambered surface chamfering control method is characterized by comprising the following steps of:
step 1: according to the spiral bevel gear structure and the tooth cutting method, calculating and obtaining tooth profile curve equations of the large end and the small end of the small wheel: obtaining tooth profile curve equations of a large end and a small end of a small wheel, firstly calculating a tooth crest line equation of a gear, and then calculating the tooth profile curve equations of the large end and the small end of the gear according to the structure of a spiral bevel gear and the coordinate relation of a machine tool;
step 2: simulating and extracting data points: simulating a three-dimensional curve graph in Matlab according to the tooth profile curve equation obtained in the step 1, and extracting a plurality of data points;
step 3: in combination with the modified NURBS curve interpolation algorithm:
in the interpolation process, any node parameter u E [ u ] of NURBS curve is given i ,u i+1 ]Representing the curve as a matrix, calculating the ith NURBS curveThe method comprises the following steps:
wherein:
all coefficients in the formula (1) are determined by the weight factors, control vertexes and node vectors which are initially given, so that the interpolation efficiency is improved only by selecting the coefficients under the condition that the current interpolation point position is known;
performing parameter point densification on the feeding step length in the track space to convert the feeding step length into a node vector increment delta u of a one-dimensional parameter space i From formula u i+1 ＝u i +Δu i The parameter coordinates of the next interpolation point can be obtained;
according to a fourth-order Longger-Kutta algorithm, the node vector increment is calculated as follows:
calculated u i+1 And (3) carrying out NURBS curve interpolation equation (1), and obtaining the position parameter of the next interpolation point: p is p i+1 ＝p(u i+1 )；
Self-adaptive control of NURBS curve interpolation reduces interpolation step length by adjusting interpolation speed, thereby reducing chord height error; in each interpolation period, the chord height error is:
wherein: ρ i Radius of curvature, deltal i Interpolation is carried out to give step length, delta l i ＝v i T, and T is the interpolation period, v i For speed, delta i Is chord height error;
the feed speed v can thus be approximated i Chord height error delta i Relationship:
by machine tool maximum chord height error delta max Selecting a maximum allowable chord height error value
And finally, obtaining acceleration errors as follows:
the chamfering of the cutter is more stable and accurate according to the chord height error and the acceleration error formula;
finally, combining the obtained data points on the tooth profile of the spiral bevel gear with an improved NURBS curve interpolation algorithm to enable the chamfering tool to obtain an accurate and complete tooth profile cambered surface chamfering track;
step 4: all the control flows are integrated into software based on C# development:
opening a Windows window application program under a Visual C# template in VS2015 software, writing a control program, inputting a login name and a login password at a login interface by a user, and entering a functional interface, wherein the functional interface comprises functions of machine tool shaft state detection, machine tool management, workpiece management, tool management, database management, interpolation motion, NURBS curve and Matlab drawing call;
step 5: the fixed height operation control card controls the machine tool to finish chamfering the cambered surface of the tooth profile of the gear:
after the operator inputs various required parameters into software on a computer, a dynamic link library in a fixed high-motion control card is called, and a high-speed pulse instruction is sent to a machine tool so as to control the open type numerical control machine tool to finish the chamfering processing of the tooth profile cambered surface of the gear;
the tooth crest line equation calculation process of the gear in the step 1 comprises the following steps: firstly, solving an analytical equation of an imaginary tooth line on a section conical surface at the center of a tooth socket of a spiral bevel gear, and then deducing an addendum crest line equation according to the obtained relationship between the imaginary tooth line equation and the addendum crest line under an equivalent gear;
in the step 2, a three-dimensional curve graph of a tooth profile curve is simulated in Matlab software, and a plurality of data points are extracted as follows:
setting configuration environments of C# and Matlab, calling Figure in Matlab by C# and embedding the Figure into a window form, drawing a three-dimensional graph according to a tooth profile curve equation calculated in the front, extracting corresponding data points into a textBox control in C# and storing the data points into a txt file;
the chamfering tool in the step 3 is a chamfering tool: the tooth profile edge is chamfered by adopting an arc surface, and the two sides of the tooth profile edge line are connected by using the arc surface in a smooth manner, so that the edge of the gear can be completely eliminated;
and (3) finishing chamfering of the cambered surface of the tooth profile of the gear by the machine tool in the step (5): the spiral bevel gear is a spiral bevel gear, the axes of the two wheels are intersected, and the intersection angle is 90 degrees; the axis of the small spiral bevel gear is overlapped with the Z axis of the machine tool, and the C axis of the machine tool drives the gear to do rotary motion; firstly, a cutter executes a spiral tooth chamfering instruction at the small end of a gear, after a complete tooth profile is finished, the cutter is lifted, and at the moment, the C-axis of the machine tool rotates by an angle, so that the gear to be machined rotates to the next complete tooth profile, the cutter starts to return to the chamfering starting position and starts the chamfering of the next tooth profile, the steps are repeated until the gear teeth of the small end of the gear are completely machined, and the tooth profile cambered surface chamfering of the large end of the small spiral bevel gear and the tooth profile cambered surface chamfering of the large end of the large spiral bevel gear are all the same.
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