CN106774153B - A kind of profile tolerance compensation method of S-shaped rose cutter - Google Patents
A kind of profile tolerance compensation method of S-shaped rose cutter Download PDFInfo
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- 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
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- 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
- G05B19/404—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 control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract
The present invention provides a kind of profile tolerance compensation method of S-shaped rose cutter, comprising: chooses several profile tolerances point to be compensated according to S-shaped rose cutter profile diagram, and determines the coordinate of compensation point；Appropriate interpolation or approximating method are chosen to approach compensation point, obtains radius transition curve；The radius correction value of each grinding points is obtained according to the radius transition curve；According to the radius correction value along the relief angle Surface by Tangent Plane Method at the grinding points to moving grinding wheel.The method of the present invention can be effectively controlled the profile tolerance of bulb, improve the processing quality of bulb S-shaped sword line.
Description
Technical field
The present invention relates to rose cutter technical field more particularly to a kind of profile tolerance compensation methodes of S-shaped rose cutter.
Background technique
Rose cutter is the various complex-curved important cutters of milling, especially with the increasing of numerically-controlled machine tool, this
The demand of kind cutter will increase severely with day.Conventional rose cutter is straight line edge, is not easy chip removal during the cutting process, and chip is held
It easily accumulates near cutting edge, blocks milling cutter, not only influence machining accuracy, but also reduce cutting-tool's used life.Currently, domestic purchase more
The S-shaped rose cutter of foreign-made, rake face are waved surfaces, are easy to chip removal.Some domestic experts and factory are in S-shaped bulb
Made a large amount of work on the processing mechanism and mathematical model of milling cutter, but these work be all based on it is ideal, it is any partially
It is realized under the premise of difference.And during actual industrial is realized, there are many inevitable deviations, loss.
Rose cutter belongs to die mill, is made of bulb and cylinder (circular cone) two parts, and the S-shaped ball sword of rose cutter is
Refer to that the S-shaped blade curve of bulb is referred to as S line for convenience of description, S line is a spherical curve, it is ball sword rake face
With the intersection of ball sword flank, in order to solve the problems, such as the chip removal of rose cutter, ball sword should be ideal S-shaped, bulb
Profile tolerance deviates a Xiang Zhibiao of spherical surface entirety deviation as S line is measured, therefore many cutter producers are all to the profile tolerance of bulb
There are strict requirements.During actual processing, accuracy, the abrasion of grinding wheel degree, numerical control of the main installation dimension of organisation of working
The factors such as the deviation that interpolation algorithm, rake face and the flank that system uses position twice, can all influence the profile of rose cutter
Degree, the index passing rate of processing not up to standard that can seriously reduce rose cutter.
Summary of the invention
The present invention provides a kind of profile tolerance compensation method of S-shaped rose cutter, solves in rose cutter grinding process,
Due to machine dynamic performance, geometric precision of machine tool, lathe position error and grinding wheel parameter measurement are inaccurate etc., caused ball
The overproof problem of bulb profile tolerance of head milling cutter.
The profile tolerance compensation method of S-shaped rose cutter of the present invention, comprising:
Several profile tolerances point to be compensated is chosen according to S-shaped rose cutter profile diagram, and determines the coordinate of compensation point；
It chooses appropriate interpolation or approximating method and obtains radius transition curve to approach compensation point；
The radius correction value of each grinding points is obtained according to the radius transition curve；
According to the radius correction value along the relief angle Surface by Tangent Plane Method at the grinding points to moving grinding wheel.
Further, described that several profile tolerances point to be compensated is chosen according to S-shaped rose cutter profile diagram, and determine and mend
Repay coordinate a little, comprising:
It is distributed according to the radius wave pattern monotonicity in a certain section of section of S-shaped rose cutter profile diagram by the profile diagram
Entire value interval is divided into several minizones；
According to angle, mutually the endpoint in section each on profile diagram is converted into the point on S line by remaining relationship；
According to the actual processing radius deviateed at two maximum points of target radius of machining on profile diagram, each section is estimated
Actual processing radius at endpoint；
It takes each interval endpoint as compensation point, and the angle θ put on S line is corresponded to as abscissa using it, the actual processing is partly
Diameter is ordinate, determines the coordinate of compensation point.
Further, the selection linear interpolation method approaches compensation point, obtains radius transition curve, comprising:
Using the coordinate of compensation point as interpolation knot, formula is substituted into
Obtain the corresponding radius transition curve of radius that value range is [0 °, 90 °], wherein y (x) is each in section
The real radius of point, x ∈ [0 °, 90 °], xiThe angle θ for being i-th of compensation point on S line, yiFor the corresponding reality of i-th of compensation point
Radius, xi-1For θ angle of (i-1)-th compensation point on S line, yi-1For the corresponding real radius of (i-1)-th compensation point.
Further, the selection Hermite interpolation method approaches compensation point, obtains radius transition curve, comprising:
Using the coordinate of compensation point as interpolation knot, formula is substituted into
Obtain the radius transition curve that value range is [0 °, 90 °], wherein
The xiThe angle θ for being i-th of compensation point on S line, the yiFor real radius, the y 'iFor xiThe derivative at place
Value, and meet y 'i=0, x ∈ [0 °, 90 °].
Further, described that the radius correction value of each grinding points on S line is obtained according to the radius transition curve, packet
It includes:
The actual processing radius of any point on S line is obtained according to radius approximating function, the actual processing radius is subtracted
Target radius of machining obtains the radius correction value of each grinding points, and the S line is bulb sword line.
The present invention is inserted into several compensation points in bulb profile full section, one additional to the compensation point at profile tolerance not best placement
Radius correction value, then compensation point is approached with continuous function (or piecewise function), it is flat to guarantee that the radius value at each compensation point is realized
Sliding linking.The present invention realizes the profile tolerance of effectively adjusting ball head milling cutter, effectively controls the profile tolerance of bulb, improves bulb S
The processing quality of shape sword line.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is this hair
Bright some embodiments for those of ordinary skill in the art without any creative labor, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of profile tolerance compensation method flow chart of S-shaped rose cutter of the present invention；
Fig. 2 is rose cutter S line schematic diagram of the present invention；
The profile diagram of Fig. 3 sword rose cutter；
The radius transition curve that Fig. 4 uses different approach methods to acquire；
Fig. 5 uses the compensated profile diagram of linear method；
Fig. 6 uses the compensated profile diagram of step method；
Fig. 7 uses the compensated profile diagram of cubic spline；
Fig. 8 uses the compensated profile diagram of Hermite method；
Fig. 9 uses the compensated profile diagram of bezier method；
Probe-radius amendment when Figure 10 compensation points are 10；
Figure 11 is based on 10 compensated profile diagrams of point using Hermite interpolation.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
Fig. 1 is a kind of profile tolerance compensation method flow chart of S-shaped rose cutter of the present invention, as shown in Figure 1, the present embodiment side
Method, comprising:
Step 101 chooses several profile tolerances point to be compensated according to S-shaped rose cutter profile diagram, and determines compensation point
Coordinate；
Further, described that several profile tolerances point to be compensated is chosen according to S-shaped rose cutter profile diagram, and determine and mend
Repay coordinate a little, comprising:
It is distributed according to the radius wave pattern monotonicity in a certain section of section of S-shaped rose cutter profile diagram by the profile diagram
Entire value interval is divided into several minizones；
According to angle, mutually the endpoint in section each on profile diagram is converted into the point on S line by remaining relationship；
According to the actual processing radius deviateed at two maximum points of target radius of machining on profile diagram, each section is estimated
Actual processing radius at endpoint；
It takes each interval endpoint as compensation point, and the angle θ put on S line is corresponded to as abscissa using it, the actual processing is partly
Diameter is ordinate, determines the coordinate of compensation point.
Specifically, as shown in Fig. 2, the sigmoid curve on hemisphere face is S line, the S line of rose cutter is a spherical surface song
Line, therefore every bit is all satisfied spherical equation on ball sword, establishes rectangular coordinate system O-XYZ, the axis weight of Z axis and rose cutter
It closes, origin is the centre of sphere, and in this coordinate system, hemispherical equation is expressed as
Wherein, R is Probe-radius, the diameter arrow that θ is a point M on spherical surfaceWith the angle of Z axis positive direction,For Y-axis pros
To withProjection vector on XOY planeFormed directed angle.
Each grinding points is all satisfied spherical equation on S line, therefore can divide S line by the angle θ, and value range is 0 ° and arrives
90 °, each angle θ corresponds to only one grinding points on S line, corresponds to S line starting point, i.e. bulb central point when wherein the angle θ is 0 °,
The terminal when angle θ is 90 ° corresponding to S line, i.e. ball sword and all sword interface points.The profile diagram of rose cutter is for showing rose cutter
Every bit actual processing radius deviates the size of target radius of machining on S line, with 2 swords for uniformly dividing tooth, bulb principal radii is 6
For rose cutter, Fig. 3 is the profile diagram and related data that the rose cutter measures in Tool monitoring equipment.Left side profile diagram
In between 0 ° and 90 ° region be that the S line profile of tooth 1 is distributed, region is that the S line profile of tooth 2 is distributed between 90 ° and 180 °, because equal
The profile diagram of even point of tooth, two S lines is symmetric using 90 ° of positions as line of demarcation, therefore it may only be necessary to consider the profile point of monodentate
Cloth.By taking tooth 1 as an example, as shown in figure 3,90 ° of positions actually bulb center in profile diagram, when taking 0 ° corresponding to the angle θ on S line
Grinding points, 0 ° of position actually ball sword and all sword delivery positions in profile diagram, grinding when taking 90 ° corresponding to the angle θ on S line
Point, therefore, when taking will mutually the point on profile diagram be converted into the point on S line by remaining relationship according to angle.
Profile diagram is radius distribution figure of the entire bulb S line in different location, as shown in figure 3, in figure half-round curve half
Diameter is bulb target radius of machining, and the present embodiment value is 6, and surge area is that each point is real on S line up and down near half-round curve
The waveform diagram of border radius of machining, as we can see from the figure on S line each point actual processing radial offset theory radius of machining displacement,
It and is in regularity distribution in a bit of section.Two particular points marked in the figure are respectively the external maximum of deviation theory radius
It is worth point (mark point in semicircle outside portion) and inner maximum point (mark point inside semicircle), is read most from the data on right side
Big external deviation is 0.01, and it is -0.009 that maximum internal, which deviates, illustrates that the actual processing radius of two o'clock is respectively 6.01 Hes
5.991, two o'clock is estimated according to profile diagram and is located near 5 ° and 40 °, mutually remaining relationship is converted on S line according to angle
Point corresponds to the grinding points when angle θ on S line takes 85 ° and 50 °.Using the angle θ of grinding points on S line as abscissa, at grinding points
Actual processing radius is ordinate, establishes coordinate system, obtains two and deviates maximum compensation point, coordinate is respectively (85,6.01)
(50,5.991).
Observation profile diagram is it is found that the radius wave pattern in a certain section of minizone substantially moves towards the dullness in increasing or decreasing
Property distribution, therefore, the entire value interval of profile diagram can be divided into 6 minizones by this rule: [0 °, 5 °], [5 °, 20 °],
[20 °, 40 °], [40 °, 65 °], [65 °, 90 °].The endpoint in each section is converted into the point on S line, that is, corresponds to the angle θ on S line
Value is followed successively by 90 °, 85 °, 70 °, 50 °, 25 °, 0 °, according to the real radius for deviateing maximum two compensation points, estimates each
Actual processing radius at a interval endpoint is followed successively by 6.005,6.01,6,5.991,6,6.006, chooses this six particular points
For compensation point, coordinate is followed successively by (90,6.005), (85,6.01), (70,6), (50,5.991), (25,6), (0,6.006).
Step 102, the appropriate interpolation of selection or approximating method obtain radius transition curve to approach compensation；
The concept of function approximation is to be approached more according to certain criterion with simple continuous function (or piecewise function)
Complicated function or one group of discrete point, interpolation and fitting are two kinds of important methods of function approximation.From geometric meaning, for
One group of given data point, interpolation are to find the full curve of one (or several piecewise smoothes) to come across these several points, fitting
It is to find the full curve of a form known unknown parameter to approach these points to greatest extent.There are commonly linear interpolation sides
Method, step method, Cubic Spline Method, Herimite interpolation, bezier method.To obtain the reality of each grinding points on S line
Radius of machining, the coordinate that step 101 is obtained compensation point by us carry out interpolation or fitting as interpolation or the node of fitting, from
And obtain a functional relation across or close to these points.The function is using the angle θ of grinding points on S line as independent variable, with mill
An actual processing radius at cutting is dependent variable, and image is the full curve that a value range is [0 °, 90 °], describes packet
Radius change rule containing each point on the entire S line including compensation point, is known as radius transition curve for the curve.
Fig. 4 is the radius transition curve that distinct methods are respectively adopted and obtain, and fig.1 is that compensation point radius takes target to process
Radius transition straight line is obtained when radius 6, is equivalent to no radius compensation, and each point radius of machining is target radius of machining on S line；
Fig.2 is the radius transition curve obtained using linear interpolation method, and feature is between adjacent compensation point with straight transitions；
Fig.3 is the radius transition curve obtained with step method, and feature is that a certain region inside radius since compensation point is constant, is arrived
With the biggish straight transitions of slope when close to next compensation point；Fig.4 is the radius transition song obtained using cubic spline interpolation
Line, with curve transition between adjacent compensation point；Fig.5 is the radius transition curve obtained using Herimite interpolation, adjacent benefit
It repays between a little with curve transition, and guarantees that the derivative at each compensation point is 0；Fig.6 is the radius obtained using bezier method
Easement curve, compared with above four kinds of interpolation methods, it cannot be guaranteed that curve strictly passes through each compensation point, curve shape is also not easy
Control.In practical applications, it answers concrete condition to make a concrete analysis of, according to actual profile diagram radius fluctuating characteristic, and combines each
The radius transition curve feature of method selects more matched approach method, for example, the footprint characteristic of Fig. 3 is each adjacent compensation
Radius change trend is in monotonicity increasing or decreasing between point, and with curve transition, therefore can be selected Cubic Spline Method or
Hermite method.
Fig. 5 to Fig. 9 is respectively the compensated profile diagram of above-mentioned five kinds of methods.Profile tolerance before the present embodiment does not compensate is
0.019mm.Fig. 5 be using the compensated profile diagram of linear method, it is maximum it is external to deviate be 0.007, maximum internal deviate for-
0.008, profile tolerance 0.015mm.Fig. 6 uses the compensated profile diagram of step method, and maximum external deviation is 0.01, most imperial palace
It is -0.009 that portion, which deviates, profile tolerance 0.019mm.Fig. 7 uses the compensated profile diagram of cubic spline, and maximum external deviation is
0.008, it is -0.006 that maximum internal, which deviates, profile tolerance 0.014mm.Fig. 8 uses the compensated profile diagram of Hermite method,
Maximum external deviation is 0.007, and it is -0.005 that maximum internal, which deviates, profile tolerance 0.012mm.Fig. 9 is mended using bezier method
Profile diagram after repaying, maximum external deviation is 0.007, and it is -0.005 that maximum internal, which deviates, profile tolerance 0.012mm.
Further, the selection linear interpolation method approaches compensation point, obtains radius transition curve, comprising:
Using the coordinate of compensation point as interpolation knot, formula is substituted into
Obtain the corresponding radius transition curve of radius that value range is [0 °, 90 °], wherein y (x) is each in section
The real radius of point, x ∈ [0 °, 90 °], xiThe angle θ for being i-th of compensation point on S line, yiFor the corresponding reality of i-th of compensation point
Radius, xi-1For θ angle of (i-1)-th compensation point on S line, yi-1For the corresponding real radius of (i-1)-th compensation point.
Specifically, when actual profile diagram radius change feature between each compensation point in broken line connection when, the present embodiment
It is approached using linear method.It obtains using the angle θ of any on S line as independent variable, the real radius of the point is dependent variable, value
Range is the linear interpolation function y (x) of [0 °, 90 °], and image is a continuous broken line, reflects and puts corresponding reality on S line
Radius change rule, referred to as radius transition curve.
Further, the selection Hermite interpolation method approaches compensation point, obtains radius transition curve, comprising:
Using the coordinate of compensation point as interpolation knot, formula is substituted into
Obtain the radius transition curve that value range is [0 °, 90 °], wherein
The xiThe angle θ for being i-th of compensation point on S line, the yiFor real radius, the y 'iFor xiThe derivative at place
Value, and meet y 'i=0, x ∈ [0 °, 90 °].It obtains using the angle θ of any on S line as independent variable, the real radius of the point is because becoming
Amount, value range are the Hermite interpolating function y (x) of [0 °, 90 °], and image is a full curve, reflects point on S line
Corresponding real radius changing rule, referred to as radius transition curve.
Specifically, Hermite interpolation method meets and is equal to given functional value on node, and leading on node
Numerical value is also equal to given derivative value.θ angle of the known n compensation point on S line is followed successively by x1,x2…xn(x1≤x2≤…≤xn,
x1=0, x=90), using the real radius of each compensation point as functional value, it is followed successively by y1,y2…yn, the derivative of function at each compensation point
Value is followed successively by y1′,y2′…yn', enable y1′,y2′…yn' it is 0, it is brought into the constructed fuction formula of cubic Hamiltonian symmetrical systems
(2)。
Step 103 obtains the radius correction value of each grinding points according to the radius transition curve；
Further, described that the radius correction value of each grinding points on S line is obtained according to the radius transition curve, packet
It includes:
The actual processing radius of any point on S line is obtained according to radius approximating function, the actual processing radius is subtracted
Target radius of machining obtains the radius correction value of each grinding points, and the S line is bulb sword line.
Step 104, according to the radius correction value along the relief angle Surface by Tangent Plane Method at the grinding points to moving grinding wheel.
Specifically, to reach target radius of machining, amendment direction should be contrary with radius change in profile diagram, even
Actual processing radius is greater than target radius of machining, should reduce direction toward radius and be modified, conversely, then repairing to radius augment direction
Just.The calculating of the part is realized on the basis of existing bulb flank algorithm, and the sand of each point on grinding flank S line has been calculated
After wheel positioning, grinding wheel is moved into corresponding radius to (i.e. perpendicular to rear corner surface direction) along the relief angle Surface by Tangent Plane Method at grinding points
Correction value is positive (it is positive direction that i.e. radius, which reduces direction), it is specified that being directed toward centre of sphere direction, thus half between realizing each adjacent grinding points
The continuously smooth transition of diameter value.For example, the actual processing radius of maximum external deviation point is 6.01 on S line, radius correction value
It is 0.01, therefore radius should be reduced 0.01, just can guarantee that actual processing radius reaches along relief angle Surface by Tangent Plane Method to translation 0.01
To target radius of machining；The actual processing radius of maximum internal deviation point is 5.991 on S line, and radius correction value is -0.009,
Therefore radius should be increased 0.009, just can guarantee that actual processing radius reaches mesh along relief angle Surface by Tangent Plane Method to translation -0.009
Mark radius of machining.
Fig. 5 to Fig. 9 illustrates that outline compensation function can effectively be adjusted the profile tolerance of rose cutter, with regard to this
For experimental data, Hermite method is more obvious to the improvement of profile tolerance, and on this basis, compensation point increase is by we
10, further processing test is done with Hermite method, processing result is as shown in figure 11, and profile tolerance can reach 0.006mm.One
As the profile tolerance of rose cutter is required as no more than 0.015mm, completely can be by profile by our outline compensation function
Degree control is within the scope of this.In actual processing, the rose cutter of same specification is produced in batches, grinding wheel or lathe etc.
The profile diagram of bulb sword line caused by measurement and machine error is generally all in regularity distribution, and user is in the early stage during toolsetting,
Can according to the profile diagram of profile tolerance cutter not up to standard, observe actual processing radius change rule, select suitable compensation method and
Compensation point can process the rose cutter of profile tolerance qualification in the subsequent manufacturing.
The present invention realizes the profile tolerance of effectively adjusting ball head milling cutter, effectively controls the profile tolerance of bulb, improves bulb S
The processing quality of shape sword line.
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (5)
1. a kind of profile tolerance compensation method of S-shaped rose cutter characterized by comprising
Several profile tolerances point to be compensated is chosen according to S-shaped rose cutter profile diagram, and determines the coordinate of compensation point；
It chooses appropriate interpolation method and obtains radius transition curve to approach compensation point；
The radius correction value of each grinding points is obtained according to the radius transition curve；
According to the radius correction value along the relief angle Surface by Tangent Plane Method at the grinding points to moving grinding wheel.
2. the method according to claim 1, wherein described choose several according to S-shaped rose cutter profile diagram
Profile tolerance point to be compensated, and determine the coordinate of compensation point, comprising:
It is according to the radius wave pattern monotonicity distribution in a certain section of section of S-shaped rose cutter profile diagram that the profile diagram is entire
Value interval is divided into several minizones；
According to angle, mutually the endpoint in section each on profile diagram is converted into the point on S line by remaining relationship；
According to the actual processing radius deviateed at two maximum points of target radius of machining on profile diagram, each interval endpoint is estimated
The actual processing radius at place；
It takes each interval endpoint as compensation point, and the angle θ put on S line is corresponded to as abscissa using it, the actual processing radius is
Ordinate determines the coordinate of compensation point.
3. the method according to claim 1, wherein the appropriate interpolation method of selection obtains to approach compensation point
Radius transition curve, comprising:
Using the coordinate of compensation point as interpolation knot, formula is substituted into
Obtain the corresponding radius transition curve of radius that value range is [0 °, 90 °], wherein y (x) is each point in section
Actual processing radius, x ∈ [0 °, 90 °], xiThe angle θ for being i-th of compensation point on S line, yiFor the corresponding reality of i-th of compensation point
Radius of machining, xi-1For θ angle of (i-1)-th compensation point on S line, yi-1For the corresponding actual processing radius of (i-1)-th compensation point.
4. the method according to claim 1, wherein the appropriate interpolation method of selection obtains to approach compensation point
Radius transition curve, comprising:
Using the coordinate of compensation point as interpolation knot, formula is substituted into
Obtain the radius transition curve that value range is [0 °, 90 °], wherein
The xiThe angle θ for being i-th of compensation point on S line, the yiFor real radius, the y 'iFor xiThe derivative value at place, and it is full
Sufficient y 'i=0, x ∈ [0 °, 90 °].
5. the method according to claim 1, wherein described obtain each grinding according to the radius transition curve
The radius correction value of point, comprising:
The actual processing radius of any point on S line is obtained according to radius approximating function, the actual processing radius is subtracted into target
Radius of machining obtains the radius correction value of each grinding points, and the S line is bulb sword line.
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