CN113486474A - Method for designing shape of grinding wheel for grinding complex curved surface part - Google Patents
Method for designing shape of grinding wheel for grinding complex curved surface part Download PDFInfo
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Abstract
The invention provides a method for designing the shape of a grinding wheel for grinding a complex curved surface part. The invention comprises the following steps: the method comprises the steps of obtaining the curvature of a target complex curved surface sample piece, determining the basic radius of a grinding wheel and the maximum gradient of the whole domain of a curved surface based on the curvature of the complex curved surface, and determining the lifting angle range of the grinding wheel based on the maximum gradient of the whole domain of the curved surface; determining the basic form and the minimum radius of the grinding wheel based on the processing ultra-precision processing grinder style of the target complex curved surface sample piece and the grinding process parameters; determining the minimum lifting angle of the grinding wheel according to the effective processing area of the grinding wheel; and finally determining the shape and parameters of the grinding wheel for grinding the complex curved surface part by comprehensively considering the characteristics of the processed curved surface, the processing parameters and the processing conditions. The grinding wheel for complex curved surface grinding is oriented to the processing requirements of complex curved surface parts, has strong practicability, convenient operation and short time consumption, can be effectively applied to the grinding processing of various complex curved surfaces, provides guarantee for improving the production efficiency and the processing precision of the complex curved surfaces, and has important theoretical significance and use value for obtaining the grinding wheel suitable for the grinding processing of the complex curved surfaces.
Description
Technical Field
The invention relates to the field of grinding wheel design for precision grinding, in particular to a method for designing the shape of a grinding wheel for grinding a complex curved surface part.
Background
With the development of society and the progress of science and technology, in order to ensure the competitive power of products in increasingly competitive markets, the development cycle and the production cycle of the products are gradually shortened, industrial products are gradually changed into flexible production of multiple varieties and small batches, meanwhile, in order to meet the requirements of service performance and appearance modeling, more and more products with complex curved surfaces are obtained, and the products are widely applied to the aspects of household appliances, molds, energy sources, aerospace and the like. But these products with complex curved surfaces also present processing challenges.
Besides conventional spherical surfaces, industrially commonly used curved surfaces include complex curved surfaces such as ellipsoids, hyperboloids, paraboloids, combined curved surfaces thereof, off-axis curved surfaces and the like on which concave-convex characteristics are superimposed, and free curved surfaces under the constraint of more complex parameters. In order to realize high-quality and high-efficiency machining of complex curved surfaces, grinding is often adopted as a finish machining or final machining process, but parameters, shapes and the like of a grinding tool are often selected by experience, a large amount of working hours are consumed, the influence of the shape and the parameters of the selected grinding tool on machining conditions is not considered, the optimal machining efficiency and machining quality are not achieved, and the finally selected grinding tool generally has further optimization space. But the research and exploration of the grinding wheel design method at home and abroad are less, a systematic design method is lacked, and the application of grinding in the complex curved surface machining is severely restricted.
Disclosure of Invention
The invention aims to overcome the technical defects and shortcomings that curved surface characteristics and processing conditions are not considered in the existing complex curved surface grinding processing, a definite grinding wheel shape design method is not available, a large amount of time and energy are often consumed for selecting a grinding wheel with a proper shape and parameters, the problem of shape selection of the grinding wheel corresponding to a complex curved surface is considered, and on the premise of considering the complex curved surface parameters, the research of a parameter optimization method for grinding wheel constraint by curved surface geometric parameters, processing process parameters and processing conditions is carried out, so that the invention provides the grinding wheel shape design method for grinding complex curved surface parts. The method is oriented to the machining requirements of parts with complex curved surfaces, has strong practicability, convenient operation and short time consumption, can be effectively applied to the grinding machining of various complex curved surfaces, provides guarantee for improving the production efficiency and the machining precision of the complex curved surfaces, and has important theoretical significance and use value for obtaining the grinding wheel suitable for the grinding machining of the complex curved surfaces. The technical means adopted by the invention are as follows:
a method for designing the shape of a grinding wheel for grinding a complex curved surface part comprises the following steps:
step 2, determining the basic form and the minimum radius of the grinding wheel based on the model of the machining ultra-precision machining grinding machine of the target complex curved surface sample piece and the grinding technological parameters;
step 3, determining the minimum lifting angle of the grinding wheel according to the effective processing area of the grinding wheel;
and 4, comprehensively considering the characteristics of the machined curved surface, the machining parameters and the machining conditions to finally determine the shape and the parameters of the grinding wheel for grinding the complex curved surface part.
Further, before the curvature of the target complex curved surface sample is obtained in the step 1, the following steps are also included: and (3) constructing a complex curved surface sample, and constructing a digital model of a product by curve and curved surface reconstruction by combining a computer aided geometric modeling method, or obtaining an equation expression of the superposed curved surface by mathematical solution of the target complex curved surface.
Further, the step 1 specifically includes the following steps:
step 11, writing the curved surface parameter equation obtained by deconstruction into a vector function form:
wherein P (u, v) is a point on the curved surface;
step 12, solving any curve and corresponding curvature of a point P on the curved surface:
wherein s is a natural parameter, alpha is a tangent vector of the curve, beta is a principal normal vector of the curve, and k is the curvature of the curve at the point P;
step 13, obtaining the basic radius R of the grinding wheel:
wherein k ismin conFor minimum curvature, R, at the pits of complex curved surfacesmaxMaximum radius value obtainable for grinding wheel
Step 14, obtaining the P point gradient θ, specifically:
solving a tangent equation of a point P on the curve:
spatial mid-sole plane equation:
Ax+By+Cz+D＝0 (24)；
wherein, A, B, C and D are equation parameters corresponding to the plane;
p-point steepness θ:
wherein n is a normal vector of a plane, and t is a vector of a tangential direction
The lifting angle range of the grinding wheel meets the following requirements:
Δαmin＝θmax (26)。
further, the step 2 specifically includes the following steps:
step 21, obtaining the minimum grinding speed V used by the grinding wheelmin；
Step 22, obtaining the minimum allowable spherical radius r of the grinding wheel according to the minimum grinding speedmin：
Wherein n is the rotating speed of the grinding shaft of the machine tool.
Further, the step 22 further comprises the following steps:
step 23, judging the relation between the minimum allowable spherical radius and the basic radius of the grinding wheel obtained in the step 1 except the grinding wheel with the basic spherical profile, and if the minimum allowable spherical radius is larger than the relation of the basic radius of the grinding wheel, introducing an eccentric amount e to bias the spherical area of the grinding wheel into a toroidal area;
step 24, based on the introduced eccentricity e, reconsidering the limitation of the curvature of the curved surface pit to the basic radius of the grinding wheel:
wherein R' is the radius of the torus region circle;
step 25, solving the height H and the maximum lift angle alpha of the spherical grinding area under the constraint of the grinding speedmax
Step 26, calculating the surface area of the grinding wheel corresponding to the shape of the grinding wheel:
wherein f (x) is the grinding wheel profile curve, and f (x) is not less than 0.
Further, the step 3 specifically includes the following steps:
step 31, in order to meet the requirement of grinding processing, the allowable grinding wheel wear volume is ensured to be larger than the wear volume of the grinding material:
in the formula VmaterialRemoving the volume of a material in the service life of the grinding wheel, wherein G is the grinding ratio of the corresponding grinding wheel, delta is the effective abrasive layer thickness of the grinding wheel, the value is related to the material attribute under the same processing condition, and S is the surface area of a grinding area of the grinding wheel;
step 32, obtaining the surface area of the grinding wheel grinding area:
wherein, the curve of the grinding wheel outline surface is an excircle taking the basic radius obtained in the step 1 as the radius,
step 33, considering the allowable grinding wheel wear volume, the combined type (10), (11) and (14) obtains the minimum raising angle alpha of the grinding wheelmin：
Further, when the spherical area of the grinding wheel is offset to be a toroidal area, or the minimum raising angle alpha of the grinding wheel obtained by the methodminThe lift angle range delta alpha is less than that obtained in the step 1minIn the step 32, the surface area of the grinding wheel is as follows:
further, the grinding wheel shape and parameters determined in step 4 are as follows:
wherein D is1Is the diameter of the grinding wheel spindle, which satisfies
D1＝R (37)；
α1The elevation angle is shown on the basis of the superposition of the lifting angle of the grinding wheel.
Further, said α is1Satisfies the following conditions:
α1＝3°～10° (38)。
the method has the obvious effects and benefits that the method for designing the shape of the grinding wheel for grinding the complex curved surface part is provided aiming at the technical defects and shortcomings that a definite grinding wheel shape design method is not provided for different grinding processing requirements of the complex curved surface part, and a large amount of time and energy are consumed for selecting a proper shape and parameter grinding wheel. Starting from the geometrical parameters of the curved surface, primarily determining the basic radius and the lifting angle range of the grinding wheel, determining the minimum radius and the basic form of the grinding wheel through grinding process parameters, determining the maximum elevation angle and the basic form of the grinding wheel through grinding wheel abrasion, and finally, comprehensively considering the characteristics of the machined curved surface, the machining parameters and the machining conditions to finally determine the shape and the parameters of the grinding wheel for grinding the complex curved surface part, thereby conveniently and effectively determining the shape of the grinding wheel for grinding the complex curved surface part. The method is oriented to the machining requirements of parts with complex curved surfaces, has strong practicability, convenient operation and short time consumption, can be effectively applied to the grinding machining of various complex curved surfaces, provides guarantee for improving the production efficiency and the machining precision of the complex curved surfaces, and has important theoretical significance and use value for obtaining the grinding wheel suitable for the grinding machining of the complex curved surfaces.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the method for designing the shape of the grinding wheel for grinding complex curved surface parts according to the invention.
FIG. 2 is a schematic diagram of a paraboloid of revolution and its processing trajectory in an embodiment of the present invention, wherein (a) is a schematic diagram of a paraboloid of revolution; (b) is a schematic diagram of a processing track.
Fig. 3 is a complex curved surface of an embodiment of the present invention in which a paraboloid of revolution is superimposed with normally offset dimples, and fig. 3(c) 1, 2, 3, and 4 respectively represent four superimposed dimples.
FIG. 4 is a schematic view of an unbiased grinding wheel shape in an embodiment of the invention.
FIG. 5 is a schematic view of an offset wheel shape according to an embodiment of the present invention.
Fig. 6 shows the final design wheel shape in an embodiment of the present invention.
Fig. 7 is a schematic diagram of complex curved surface grinding in the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in figure 1, the invention discloses a method for designing the shape of a grinding wheel for grinding a complex curved surface part, which comprises the following steps:
specifically, before the curvature of the target complex curved surface sample is obtained in step 1, the following steps are further included: constructing a complex curved surface sample with high gradient, frequency unevenness, circumferential fluctuation and even non-continuity characteristics, and constructing a digital model of a product by curve and curved surface reconstruction by combining a computer-aided geometric modeling method, or obtaining an equation expression of a superposed curved surface by mathematical solution of a target complex curved surface. The grinding point of the grinding wheel can completely cover the whole complex curved surface profile, so the complex curved surface has certain requirements on the basic size of the grinding wheel. By analyzing the characteristics of the target complex curved surface, the overall gradient of the target complex curved surface and the maximum curvature radius of the curved surface near the pit are focused, and then the basic radius R and the minimum lift angle of the grinding wheel are determined.
Step 11, writing the curved surface parameter equation obtained by deconstruction into a vector function form:
wherein P (u, v) is a point on the curved surface;
step 12, solving any curve (C) and corresponding curvature of a point P on the curved surface:
wherein s is a natural parameter, alpha is a tangent vector of the curve, beta is a principal normal vector of the curve, and k is the curvature of the curve at the point P;
step 13, obtaining the basic radius R of the grinding wheel:
wherein k ismin conFor minimum curvature, R, at the pits of complex curved surfacesmaxMaximum radius value obtainable for grinding wheel
Step 14, obtaining the P point gradient θ, specifically:
solving a tangent equation of a point P on the curve:
spatial mid-sole plane equation:
Ax+By+Cz+D＝0 (43)；
wherein, A, B, C and D are equation parameters corresponding to the plane;
p-point steepness θ:
wherein n is a normal vector of a plane, and t is a vector of a tangential direction
In complicated curved surface grinding process, can both process to for guaranteeing the curved surface, then the emery wheel lift angle range should be guaranteed to be greater than the global maximum steepness of curved surface, as shown in fig. 4, emery wheel lift angle range satisfies promptly:
Δαmin＝θmax (45)；
the equation shows that the minimum value min of the lifting angle range of the grinding wheel is equal to the maximum gradient max of the whole surface of the curved surface.
Step 2, determining the basic form and the minimum radius of the grinding wheel based on the model of the machining ultra-precision machining grinding machine of the target complex curved surface sample piece and the grinding technological parameters;
specifically, most of the ultraprecise grinding machines used for machining the complex curved surface contour are four-shaft ultraprecise grinding machines with a Z shaft, an X shaft, a main shaft/C shaft and a B shaft, in addition to rotation of the main shaft/C shaft of the grinding machine, traversal grinding of the complex curved surface contour is realized through interpolation motion of the Z shaft and the X shaft in the machining process, and meanwhile, control of a grinding point of a grinding wheel of a grinding shaft is realized through rotation motion of the B shaft, namely a working area where the surface of the grinding wheel contour participates in grinding can be controlled.
Based on the four-axis ultra-precision grinding machine, the interference problem of a grinding wheel machine tool in the complex curved surface machining process is considered, so that the shape of the grinding wheel base body is selected to be a hemispherical grinding wheel. In addition, in the actual grinding process, the smaller the grinding wheel is, the better the grinding wheel is, the size of the grinding wheel is obvious by the grinding parameters, particularly the grinding speed, when the grinding speed is too small, the processing capacity of the grinding wheel abrasive particles cannot be exerted, meanwhile, the grinding quality is deteriorated, and the grinding wheel is worn. Therefore, grinding parameters of the grinding wheel also have certain requirements on basic shape and manufacture of the grinding wheel.
Step 21, obtaining the minimum grinding speed V used by the grinding wheel according to a process parameter experiment and the likeminAccording to the rotary profile grinding wheel, the minimum grinding speed V can be achieved only by ensuring the minimum grinding wheel radius]That is, it is also found that when the grinding speed is 0, the grinding wheel grinding region does not have the machining capability, and therefore, the grinding wheel grinding region having no machining capability does not need to be considered. In summary, the grinding wheel is composed of a region with good grinding capability, and the rest region increases the load of the spindle, which brings difficulty to the dressing of the grinding wheel and the adjustment of dynamic balance, so that this region needs to be removed, and the grinding region of the truncated hemispherical grinding wheel can be represented as a spherical region with a height H and a raise angle α. The size of this area is determined in accordance with the grinding parameters.
Step 22, obtaining the minimum allowable spherical radius r of the grinding wheel according to the minimum grinding speedmin：
In the formula, n is the rotating speed of a grinding shaft of the machine tool; and V is the minimum speed selectable by the process parameters, and Vmin is the designed minimum grinding speed determined by considering the minimum speed selectable by the process parameters in the grinding wheel design process, so that the Vmin is ensured to be more than or equal to V.
Besides the grinding wheel with the basic spherical profile, when the minimum allowable spherical radius is larger than the basic radius of the grinding wheel obtained in the step one, the introduction of the eccentricity e can be considered, and the spherical area of the grinding wheel is offset into a toroidal area. The method can also be used as a measure for further increasing the minimum machining speed for grinding. If the eccentricity e is introduced, the limitation of the curvature at the curved surface pit on the basic radius of the grinding wheel needs to be considered again, as shown in fig. 5, that is:
wherein R' is the radius of the torus region circle;
obtaining the height H and the maximum lifting angle alpha of the spherical grinding area under the constraint of the grinding speedmax
It is noted that the smaller the lift angle of the grinding wheel is, the better the lift angle of the grinding wheel is, the smaller the effective grinding area is, the wear resistance of the grinding wheel cannot be guaranteed, and the service life of the grinding wheel is directly influenced. The influence of the machining conditions, i.e. the life of the grinding wheel, on the lifting angle of the grinding wheel therefore needs to be taken into account.
The service life of the grinding wheel is related to the wear volume of the grinding wheel. The grinding wheel grinding area can be guaranteed to be used under the same material four-shaft ultra-precision grinding machine processing condition, and therefore the size of the grinding wheel grinding area is determined.
Calculating the surface area of the grinding wheel grinding area corresponding to the shape of the grinding wheel:
wherein f (x) is the grinding wheel profile curve, and f (x) is not less than 0.
Step 3, determining the minimum lifting angle of the grinding wheel according to the effective processing area of the grinding wheel;
specifically, in step 31, in order to meet the requirement of grinding processing, it is required to ensure that the allowable grinding wheel wear volume is larger than the wear volume of the grinding material:
in the formula VmaterialRemoving the volume of a material in the service life of the grinding wheel, wherein G is the grinding ratio of the corresponding grinding wheel, delta is the effective abrasive layer thickness of the grinding wheel, the value is related to the material attribute under the same processing condition, and S is the surface area of a grinding area of the grinding wheel;
step 32, obtaining the surface area of the grinding wheel grinding area:
wherein, the curve of the grinding wheel outline surface is an excircle taking the basic radius obtained in the step 1 as the radius,
step 33, considering the allowable grinding wheel wear volume, the combined type (10), (11) and (14) obtains the minimum raising angle alpha of the grinding wheelmin：
If the spherical area of the grinding wheel is offset to be the torus area in the step two, or the minimum raising angle alpha of the grinding wheel obtained in the step twominThe lift angle range delta alpha is less than that obtained in the step oneminWhen the grinding wheel is used, the spherical area of the grinding wheel needs to be offset into the torus area to meet the conditions, and the surface area of the grinding wheel and the minimum lifting angle alpha of the grinding wheel at the momentminComprises the following steps:
the minimum grinding speed of the grinding wheel is also improved through the offset of the spherical area of the grinding wheel.
The minimum lifting angle alpha under the bias of the spherical area of the grinding wheel can be obtained by the same principlemin
And 4, comprehensively considering the characteristics of the machined curved surface, the machining parameters and the machining conditions to finally determine the shape and the parameters of the grinding wheel for grinding the complex curved surface part.
The grinding wheel shape control parameters determined according to the steps one to three are as follows:
in addition, additional parameters of the grinding wheel are determined according to actual grinding conditions, wherein the thickness D of the grinding wheel rod and the raising angle alpha of the grinding wheel are mainly considered1：
The thickness of the grinding wheel rod determines the overall rigidity of the grinding wheel and is related to the material of the grinding wheel rod, the grinding force in the grinding process and other factors. It is proposed that the grinding wheel be made of cemented carbide or tungsten steel, and the diameter of the grinding wheel is half of the basic diameter of the grinding wheel, i.e. the grinding wheel is made of tungsten steel
D1＝R (56)
In addition, considering that the grinding condition of the sharp angle of the grinding wheel is poor in the actual grinding process, the base elevation angle alpha needs to be superposed on the lifting angle of the grinding wheel1The value is mainly related to factors such as interference in the grinding process. It is proposed herein to take
α1＝3°～10° (57)
Therefore, the method determines the final grinding wheel shape and parameters as follows:
example 1
First step, determining the basic radius and the lifting angle range of the grinding wheel
Firstly, the parameter characteristics of the curved surface to be processed are determined. The shape of the grinding wheel is designed by taking a revolution paraboloid structure as a main body and overlapping a complex curved surface sample formed by concave features formed by means of the upward bias. Before calculation and analysis, specific geometric parameters are specified for the characteristics of the complex surface sample piece model. Let C be 0.042, k be-1, and r be the maximum caliber of the paraboloidmax50 as shown in figure 2. The ideal processing track is a spiral line taking the top point of the complex curved surface sample piece model as the center of a circle, and the axis of the machine tool X, Y, Z enables a grinding point to move along a spiral tool path around the curved surface through interpolation motion so as to carry out enveloping grinding on the curved surface.
On rotatingOn the basis of a paraboloid, four concave features of 1, 2, 3 and 4 are superposed, the amplitude of a concave pit is A-3, and the position coefficients of the four concave features on the curved surface are a1＝9.5，b1＝14.6，a2＝15.9，b2＝15.9，a3＝-27.5，b3＝16，a4＝-14，b4-30.5; the size of the affected area and the effect coefficient of the four concave features on the curved surface are respectively c1＝29.1，c2＝28.4，c3＝30.5，c431.5; the concavity coefficient in the four concave features is: d1＝d2＝d3＝d4Is-1. The model of the complex curved surface sample part with four concave features superimposed is shown in figure 3.
Considering the constraint of the minimum curvature at the pit of the complex curved surface to the radius of the grinding wheel, and solving the basic radius 2R of the grinding wheel based on the formula (3)maxNot more than 46.36mm, considering the restraint of the maximum gradient of the universe of the complex curved surface to the lifting angle range of the grinding wheel, and obtaining the lifting angle range delta alpha of the grinding wheel based on the formula (6)min≥60°。
Here, R is 23mm, and Δ α is 60 °.
Second step of determining minimum radius and basic form of grinding wheel
The ultra-precision machining grinding machine adopted for machining the complex curved surface contour is mostly a four-shaft ultra-precision grinding machine with a Z shaft, an X shaft, a main shaft/C shaft and a B shaft, in addition to the rotation of the main shaft/C shaft of the grinding machine, the traversing grinding of the complex curved surface contour is realized through the interpolation motion of the Z shaft and the X shaft in the machining process, meanwhile, the rotation motion of the B shaft also enables the control of a grinding point of a grinding wheel of a grinding shaft to be realized, namely, the working area of the grinding wheel contour surface participating in the grinding can be controlled.
The grinding process parameters directly influence the pitch and processing speed of the spiral tool path. The influence of the minimum grinding speed on the grinding wheel radius is taken into account here. From the results of the earlier experiments, the minimum allowable grinding speed of the material can be determined, which for this example is the minimum allowable grinding speed V]15m/s, the rotating speed of the machine tool ranges from 9000 to 12000r/min, the rotating speed n is 11000r/min during grinding, and r is obtained based on the formula (8)minNot less than 13.02 mm. Obtaining alpha based on the formula (10)maxNot more than 55.52 degrees, and Hmax is 18.96mm。
Note that here, α is obtainedmaxAnd (4) the lifting angle range (delta alpha is 60 degrees) of the grinding wheel obtained in the step one is smaller, namely the condition of the step one is not met. Therefore, the offset of the spherical area of the grinding wheel needs to be considered, and alpha is takenmaxWhen the offset e is determined from equation (9) to be 60 °, e is 3.04mm, R' is 19.96mm, and Hmax is 17.29 mm.
Thirdly, determining the minimum lifting angle alpha of the grinding wheelmin
The minimum lifting angle alpha of the grinding wheel can be determined by the constraint of the machining conditions on the grinding wheel abrasionminAnd comparing with the first two calculation results. In this example, the working material was tungsten alloy, and the material removal volume was 350mm3According to the prior process test, the ideal grinding ratio of the grinding wheel is 30, the radial abrasion delta of the grinding wheel is controlled within 5 mu m, and therefore the minimum raising angle alpha which is required to be met by the corresponding grinding ratio and the grinding condition of the grinding wheel is obtained according to the formula (17)min＝52.44°。
The fourth step: determining final wheel shape and parameters
The grinding wheel shape control parameters obtained in the first three steps are integrated as follows:
and further determining the diameter of the grinding wheel rod and the final lifting angle range of the grinding wheel:
at this time, the grinding wheel had a surface area of 2567.79mm as shown in FIG. 62The curved surface grinding schematic diagram is shown in fig. 7, and analysis on the complex curved surface grinding schematic diagram shown in fig. 7 shows that the grinding wheel shape obtained by the grinding wheel shape design method can better meet the complex curved surface grinding requirement.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A method for designing the shape of a grinding wheel for grinding a complex curved surface part is characterized by comprising the following steps:
step 1, obtaining the curvature of a target complex curved surface sample piece, determining the basic radius of a grinding wheel and the global maximum gradient of a curved surface based on the curvature of the complex curved surface, and determining the lifting angle range of the grinding wheel based on the global maximum gradient of the curved surface, wherein the lifting angle range of the grinding wheel is greater than the global maximum gradient of the curved surface;
step 2, determining the basic form and the minimum radius of the grinding wheel based on the model of the machining ultra-precision machining grinding machine of the target complex curved surface sample piece and the grinding technological parameters;
step 3, determining the minimum lifting angle of the grinding wheel according to the effective processing area of the grinding wheel;
and 4, comprehensively considering the characteristics of the machined curved surface, the machining parameters and the machining conditions to finally determine the shape and the parameters of the grinding wheel for grinding the complex curved surface part.
2. The method for designing the shape of the grinding wheel for grinding a complex curved surface part according to claim 1, wherein the step 1 of obtaining the curvature of the target complex curved surface sample further comprises the following steps: and (3) constructing a complex curved surface sample, and constructing a digital model of a product by curve and curved surface reconstruction by combining a computer aided geometric modeling method, or obtaining an equation expression of the superposed curved surface by mathematical solution of the target complex curved surface.
3. The method for designing the shape of the grinding wheel for grinding the complex curved surface part according to claim 2, wherein the step 1 specifically comprises the following steps:
step 11, writing the curved surface parameter equation obtained by deconstruction into a vector function form:
wherein P (u, v) is a point on the curved surface;
step 12, solving any curve and corresponding curvature of a point P on the curved surface:
wherein s is a natural parameter, alpha is a tangent vector of the curve, beta is a principal normal vector of the curve, and k is the curvature of the curve at the point P;
step 13, obtaining the basic radius R of the grinding wheel:
wherein k ismin conFor minimum curvature, R, at the pits of complex curved surfacesmaxMaximum radius value obtainable for grinding wheel
Step 14, obtaining the P point gradient θ, specifically:
solving a tangent equation of a point P on the curve:
spatial mid-sole plane equation:
Ax+By+Cz+D＝0 (5)；
wherein, A, B, C and D are equation parameters corresponding to the plane;
p-point steepness θ:
wherein n is a normal vector of a plane, and t is a vector of a tangential direction
The lifting angle range of the grinding wheel meets the following requirements:
Δαmin＝θmax (7)。
4. the method for designing the shape of the grinding wheel for grinding the complex curved surface part according to claim 3, wherein the step 2 specifically comprises the following steps:
step 21, obtaining the minimum grinding speed V used by the grinding wheelmin；
Step 22, obtaining the minimum allowable spherical radius r of the grinding wheel according to the minimum grinding speedmin：
Wherein n is the rotating speed of the grinding shaft of the machine tool.
5. The method for designing the shape of the grinding wheel for grinding a complex curved surface part according to claim 4, further comprising the following step after the step 22:
step 23, judging the relation between the minimum allowable spherical radius and the basic radius of the grinding wheel obtained in the step 1 except the grinding wheel with the basic spherical profile, and if the minimum allowable spherical radius is larger than the relation of the basic radius of the grinding wheel, introducing an eccentric amount e to bias the spherical area of the grinding wheel into a toroidal area;
step 24, based on the introduced eccentricity e, reconsidering the limitation of the curvature of the curved surface pit to the basic radius of the grinding wheel:
wherein R' is the radius of the torus region circle;
step 25, solving the height H and the maximum lift angle alpha of the spherical grinding area under the constraint of the grinding speedmax
Step 26, calculating the surface area of the grinding wheel corresponding to the shape of the grinding wheel:
wherein f (x) is the grinding wheel profile curve, and f (x) is not less than 0.
6. The method for designing the shape of the grinding wheel for grinding the complex curved surface part according to claim 5, wherein the step 3 specifically comprises the following steps:
step 31, in order to meet the requirement of grinding processing, the allowable grinding wheel wear volume is ensured to be larger than the wear volume of the grinding material:
in the formula VmaterialRemoving the volume of a material in the service life of the grinding wheel, wherein G is the grinding ratio of the corresponding grinding wheel, delta is the effective abrasive layer thickness of the grinding wheel, the value is related to the material attribute under the same processing condition, and S is the surface area of a grinding area of the grinding wheel;
step 32, obtaining the surface area of the grinding wheel grinding area:
wherein, the curve of the grinding wheel outline surface is an excircle taking the basic radius obtained in the step 1 as the radius,
step 33, considering the allowable grinding wheel wear volume, the combined type (10), (11) and (14) obtains the minimum raising angle alpha of the grinding wheelmin：
7. The method of claim 6, wherein the minimum angle α of the grinding wheel is determined when the spherical area of the grinding wheel is offset to the toroidal area or when the minimum angle α of the grinding wheel is determinedminThe lift angle range delta alpha is less than that obtained in the step 1minIn the step 32, the surface area of the grinding wheel is as follows:
8. the method for designing the shape of the grinding wheel for grinding a complex curved surface part according to claim 7, wherein the shape and parameters of the grinding wheel determined in the step 4 are as follows:
wherein D is1Is the diameter of the grinding wheel spindle, which satisfies
D1＝R (18)；
α1The elevation angle is shown on the basis of the superposition of the lifting angle of the grinding wheel.
9. The method of designing a grinding wheel for grinding a complex curved surface part according to claim 8, wherein α is1Satisfies the following conditions:
α1＝3°～10° (19)。
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