CN114444297A - Method for predicting surface topography of threaded workpiece in cyclone milling - Google Patents

Method for predicting surface topography of threaded workpiece in cyclone milling Download PDF

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CN114444297A
CN114444297A CN202210071975.8A CN202210071975A CN114444297A CN 114444297 A CN114444297 A CN 114444297A CN 202210071975 A CN202210071975 A CN 202210071975A CN 114444297 A CN114444297 A CN 114444297A
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刘超
黄尊鹏
黄绍服
郑娟娟
李君�
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Anhui University of Science and Technology
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Abstract

The invention discloses a method for predicting the surface appearance of a threaded workpiece in cyclone milling, which analyzes the surface appearance characteristics of the workpiece by utilizing the characteristic of a multi-edge intermittent forming process of thread dry milling. According to the forming mechanism of the surface topography of the threaded workpiece, a prediction model of the residual height of the surface of the threaded raceway and a prediction model of the surface waviness are established, and the influence of parameters such as cutting parameters, the thickness of undeformed cuttings, the inner and outer diameters and the helix angle of threads, the number and the geometric dimension of cutters, the eccentricity of the workpiece-cutter and the like on the surface topography of the threaded raceway is considered. According to the prediction model of the surface topography of the workpiece, the machining parameters can be optimized in advance to achieve the optimal machining scheme, and further the cyclone milling machining quality is improved.

Description

Method for predicting surface topography of threaded workpiece in cyclone milling
Technical Field
The invention relates to the technical field of machining, in particular to a method for predicting the surface appearance of a threaded workpiece in cyclone milling.
Background
In metal cutting machining, the control of the surface topography of a workpiece is an important issue in machining, because it has a significant effect on the final service properties of the machined part, such as fatigue resistance, surface friction and wear. In addition, the surface topography of the workpiece can affect the contact performance and transmission performance of the threaded part with the ball during use. Therefore, the surface appearance of the workpiece needs to be studied in the dry-type rotary milling process of the thread.
At present, a part of research is conducted on a method for predicting the surface appearance of a machined workpiece, but research is mainly focused on turning, milling, grinding and the like, a thread dry type cyclone milling process is different from a traditional machining mode, the thread dry type rotary milling cutting process is complex and has complex dynamic cutting characteristics such as multi-edge intermittent forming, and when the surface appearance of the machined threaded workpiece is modeled, the relative motion condition of contact between multiple cutters and the workpiece and the thickness change characteristic of undeformed cuttings caused by cutting of a single cutter need to be considered. At present, indexes for evaluating the surface appearance of a workpiece are wide, and mainly comprise residual height, waviness, roughness, surface texture and the like. The analysis of the surface appearance of the workpiece is more intuitive, namely the residual height and the waviness of the surface of the workpiece, and the residual height and the waviness can directly reflect the change condition of concave and convex points uniformly distributed on the surface of the workpiece. In addition, the residual height and waviness of the surface of the workpiece can affect the stress concentration phenomenon of the workpiece in the using process, and further can reduce the service performance and service time of the workpiece and even reach the degree of directly damaging the workpiece.
Therefore, how to realize the surface topography prediction of the threaded workpiece in the cyclone milling is a problem which needs to be solved by the technical personnel in the field.
Disclosure of Invention
In view of the above, the invention provides a method for predicting the surface morphology of a threaded workpiece in cyclone milling, which reflects the surface morphology of the threaded workpiece through the residual height and waviness index of the workpiece surface, and can optimize the processing parameters in advance to achieve an optimal processing scheme, thereby improving the processing quality of the cyclone milling.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for predicting the surface topography of a threaded workpiece in cyclone milling specifically comprises the following steps:
step 1: the method comprises the steps of obtaining the cutting process of a plurality of cutters in the cutting processing surface forming process of the threaded workpiece, building a cutter movement track model and a cutter-workpiece contact movement track model according to contact points of the cutters and the workpiece and adding auxiliary lines, and respectively obtaining representation equations of the auxiliary lines introduced for describing each coordinate point of the cutter movement track model and the cutter-workpiece contact movement track model and conveniently describing the cutter movement track;
step 11: the process of constructing the cutter motion trail model comprises the following steps: the workpiece is positioned at the origin of a coordinate system (O, Y, Z), and the central coordinate is (0, 0); the motion track centers of the nth cutter and the (n +1) th cutter are respectively (m)n,nn) And (m)n+1,nn+1) (ii) a The intersection point of the auxiliary line and the excircle of the workpiece or the motion tracks of different cutters is Pi(ii) a Then (n +1) th represents the tool and the tool motion track center coordinate point equation of the tool of the nth term as follows:
Figure BDA0003482566310000021
Figure BDA0003482566310000022
in the formula, e is the distance from the center of the workpiece to the center of the motion track of the cutter; delta is the initial angle of the cutter cutting workpiece; thetaiThe angle of rotation of the workpiece from the nth time the tool begins to cut into the workpiece to the (n +1) th time the tool begins to cut into the workpiece; eta is an included angle between a connecting line from the cutter motion track center of the (n +1) th cutter to the initial point of inserting the cutter into the workpiece and a connecting line from the cutter motion track center of the (n +1) th cutter to the central point of the workpiece; the included angle eta is determined by trigonometric function relation in the cutting process and is expressed as:
Figure BDA0003482566310000023
in the formula, R is the radius of the motion track of the cutter;
step 12: the process of constructing the tool-workpiece contact motion trail model comprises the following steps: introducing auxiliary lines for describing the motion tracks of the nth tool and the (n +1) th tool, and introducing auxiliary lines ln+1And lnIs represented as follows:
zi-nn+1＝tan(Δ+θ)·(yi-mn+1) (4)
zi-nn＝tan(Δ+θn+θi)·(yi-mn) (5)
wherein (z)i，yi) Coordinate points on the auxiliary line; thetanRotating the cutter in the cutting process of the nth cutter by an angle; thetaiThe angle of rotation of the workpiece from the nth time the tool begins to cut into the workpiece to the (n +1) th time the tool begins to cut into the workpiece;
auxiliary line ln+1The point of intersection with the excircle of the workpiece is P1Auxiliary line ln+1The intersection point of the motion track of the (n +1) th cutting tool and the motion track of the (n +1) th cutting tool is P2Auxiliary line ln+1The intersection point of the motion tracks of the tool and the nth tool is P3Auxiliary line lnThe point of intersection with the excircle of the workpiece is P4Auxiliary line lnThe intersection point of the motion tracks of the tool and the nth tool is P5；
P1The coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure BDA0003482566310000031
P2the coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure BDA0003482566310000032
P3the coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure BDA0003482566310000033
P4the coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure BDA0003482566310000034
P5the coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure BDA0003482566310000035
in the formula, thetanFor the nth tool rotation angle during cutting, the value is expressed as:
Figure BDA0003482566310000036
in the formula (I), the compound is shown in the specification,
Figure BDA0003482566310000037
is the tool motion track center (m) of the nth tooln,nn) To point P1Is represented as:
Figure BDA0003482566310000038
step 2: establishing a threaded workpiece surface appearance prediction model according to the coupling among the cutter motion track model, the cutter-workpiece contact motion track model and the cutter, and predicting the surface appearance of the threaded workpiece in the cyclone milling according to the threaded workpiece surface appearance prediction model;
step 21: according to a forming mechanism of the surface profile of a threaded workpiece in the thread dry-type rotary milling process and by combining a cutter motion track model in the cutting process, the intersection point of the cutter motion tracks of the current cutter and the next cutter is calculated, and the calculation formula is as follows:
Figure BDA0003482566310000041
wherein the intersection point of the tool motion tracks of the nth tool and the (n +1) th tool is
Figure BDA0003482566310000042
(mn,nn) And (m)n+1,nn+1) The motion track centers of the nth cutter and the (n +1) th cutter are respectively;
step 22: the surface residual height prediction model for calculating the residual height of the workpiece surface is obtained by calculating the distance from the intersection point of the tool motion tracks of the current tool and the next tool to the surface of the thread raceway of the threaded workpiece, and the expression is as follows:
Figure BDA0003482566310000043
wherein R isthThe residual height of the surface of the workpiece is obtained; r is the inner diameter of the thread roller path;
step 23: calculating the center of a tool motion track based on a cutting forming motion mechanism, calculating the intersection point of the tool motion tracks of two tools by using the center of the tool motion track and according to a tool motion track model, calculating the waviness of the surface of a thread raceway of a threaded workpiece according to the distance between the intersection points of the two tool motion tracks generated by three adjacent tools, wherein a surface waviness prediction model is expressed as follows:
Figure BDA0003482566310000044
Figure BDA0003482566310000045
Figure BDA0003482566310000046
wherein S ish2(ysh2,zsh2) Is the intersection point of the tool motion tracks of the (n +1) th tool and the (n +2) th tool; (m)n+2,nn+2) The center of the tool motion track of the (n +2) th tool; wshIs waviness; psi is the helix angle of the threaded workpiece. The surface topography of the workpiece is described from two aspects of the waviness and the residual height of the surface of the workpiece, so that the surface topography prediction model consists of a surface waviness prediction model and a surface residual height prediction model.
According to the technical scheme, compared with the prior art, the invention discloses a method for predicting the surface topography of a threaded workpiece in cyclone milling, obtains the relative motion relationship between the nth cutter and the (n +1) th cutter and the threaded workpiece in the dry-type rotary milling process of the thread, and completes analysis of different cutter feed paths. According to the forming mechanism of the surface topography of the threaded workpiece, a prediction model of the residual height of the surface of the threaded raceway and a prediction model of the surface waviness are respectively established, and the influence of parameters such as cutting parameters, the thickness of undeformed cuttings, the inner and outer diameters and the helix angle of threads, the number and the geometric dimension of cutters, the eccentricity of the workpiece and the cutters and the like on the surface topography of the threaded raceway is considered, so that the accurate prediction of the surface topography of the threaded workpiece in the cyclone milling is realized.
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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 used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic diagram illustrating the analysis of the relative movement between the tool and the workpiece during the cutting process of the (n +1) th tool provided by the present invention;
FIG. 2 is an enlarged view of a part A of the analysis of the relative movement between the tool and the workpiece during the cutting process of the (n +1) th tool provided by the present invention;
FIG. 3 is an enlarged view of a part B of the analysis of the relative movement between the tool and the workpiece during the cutting process of the (n +1) th tool provided by the present invention;
FIG. 4 is a schematic diagram of a surface topography mechanism in a thread dry-type rotary milling process according to the present invention;
FIG. 5 is a partially enlarged schematic view of a surface morphology mechanism in the process of dry-type rotary milling of threads according to the present invention;
FIG. 6 is a schematic representation of the surface profile of a workpiece in a front view provided by the present invention;
FIG. 7 is a schematic view of the waviness and residual height of a workpiece provided by the present invention;
FIG. 8 is a schematic view of a threaded workpiece provided by the present invention;
FIG. 9 is a schematic representation of the effect of cutting speed on the surface topography of a workpiece according to the present invention;
FIG. 10 is a schematic illustration of the effect of the maximum cut depth provided by the present invention on the surface topography of a workpiece;
FIG. 11 is a schematic diagram illustrating the influence of the number of tools on the surface topography of a workpiece according to the present invention.
Detailed Description
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 only a part of the embodiments of the present invention, and not all of the embodiments. 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.
The embodiment of the invention discloses a method for predicting the surface topography of a threaded workpiece in cyclone milling, which comprises the following specific steps:
s1: analyzing the surface appearance forming process, and establishing a thread workpiece surface appearance model; the analysis of the relative motion of the cutter and the workpiece in the surface appearance forming process is the basis of the modeling of the surface appearance of the threaded workpiece;
FIG. 1 is a schematic view showing the analysis of the contact between a tool and a workpiece during the formation of a machined surface of a threaded workpiece, and in order to facilitate the analysis of the contact point between the tool and the workpiece, FIG. 1 shows the first embodimentCombining the cutting processes of the first cutting stage and the second cutting stage; in fig. 1, coordinates (0, 0) are the origin of the workpiece coordinate system; (m)n,nn) And (m)n+1,nn+1) The centers of the motion tracks of the nth cutter and the (n +1) th cutter are respectively; point PiIs the intersection point of the auxiliary line and the excircle of the workpiece or different cutter tracks; the formation of the surface topography of the workpiece is mainly caused by the combined action of multi-tool interrupted cutting and tool-workpiece relative motion, so that the tool motion trajectory and tool-workpiece contact motion need to be modeled;
the equation of the coordinate point of the center of the motion track of the tool of the (n +1) th tool and the tool of the nth tool is as follows:
Figure BDA0003482566310000061
Figure BDA0003482566310000062
wherein e is the distance (eccentricity) from the center of the workpiece to the center of the tool path; delta is the initial angle of the cutter cutting workpiece; thetaiThe angle of rotation of the workpiece from the nth time the tool begins to cut into the workpiece to the (n +1) th time the tool begins to cut into the workpiece; eta is an included angle between a connecting line from the center of the cutter motion track of the (n +1) th cutter to the initial point of inserting the cutter into the workpiece and a connecting line from the center of the cutter motion track of the (n +1) th cutter to the central point of the workpiece, wherein the included angle eta can be determined by a trigonometric function relationship in the cutting process and satisfies the following equation:
Figure BDA0003482566310000071
auxiliary line l introduced in FIG. 1n+1And lnIs represented as follows:
zi-nn+1＝tan(Δ+θ)·(yi-mn+1) (4)
zi-nn＝tan(Δ+θn+θi)·(yi-mn) (5)
point P1 (y) in FIG. 21,z1) As an auxiliary line ln+1The intersection with the outer circle of the workpiece, which can be determined in the coordinate system (O, Y, Z) by the system of equations (6):
Figure BDA0003482566310000072
point P2 (y) in FIG. 22,z2) As an auxiliary line ln+1The intersection point with the tool motion trajectory of the (n +1) th tool can be solved by equation set (7):
Figure BDA0003482566310000073
point P3 (y) in FIG. 33,z3) As an auxiliary line ln+1The intersection point with the tool motion trajectory of the nth tool can be obtained by equation (8):
Figure BDA0003482566310000074
point P4 (y) in FIG. 34,z4) As an auxiliary line lnThe intersection point with the outer circle of the workpiece can be obtained by equation set (9):
Figure BDA0003482566310000075
point P5 (y) in FIG. 35,z5) As an auxiliary line lnThe intersection point with the tool motion trajectory of the nth tool can be obtained by equation (10):
Figure BDA0003482566310000076
in the above equation set, θnFor cutting the nth toolThe angle of rotation of the cutter during the process can be expressed as:
Figure BDA0003482566310000077
in the formula (I), the compound is shown in the specification,
Figure BDA0003482566310000078
is the tool motion track center (m) of the nth tooln,nn) The distance to point P1 is represented by the following equation:
Figure BDA0003482566310000079
s2: carrying out surface topography prediction modeling;
in the metal cutting process, the surface appearance of a workpiece is influenced by surface forming errors caused by a material removal geometric motion mechanism in the cutting process, tooth profile errors caused by the geometric profile of a cutter, material rebound errors caused by the material property of the workpiece, other random errors caused by cutter abrasion and cutting vibration and the like, but in the cutting process, errors caused by the relative geometric forming motion of the cutter and the workpiece in the material removal process are the most main and basic factors of the surface appearance of the workpiece, and the geometric forming errors caused in the material removal process must be analyzed firstly, so that the established thread workpiece surface appearance prediction model formed by thread dry rotary milling only considers the influence of the relative geometric motion of the cutter and the workpiece in the material forming process of the workpiece; the influence caused by other factors such as cutter vibration, extrusion deformation of workpiece materials and the like is temporarily not considered;
in the process of thread dry-type rotary milling, because the convex part (forming the surface appearance of the thread workpiece) on the workpiece is caused by multi-edge cutting, the relative contact movement between a cutter and the workpiece and the coupling between multiple cutters need to be considered in the process of modeling the surface appearance prediction model of the thread workpiece; FIG. 4 shows the surface topography of the thread path of a threaded workpiece, wherein the surface topography of the thread path is primarily formed in the second cutThe machining process is generated when the machining stage is finished, the dotted line circumferences in the drawing show the movement tracks of the (n-1) th, n, (n +1) th and (n +2) th cutters, a workpiece blank finally forms a threaded part in the machining process of the plurality of cutters, and meanwhile, the surface appearance of the workpiece is generated; after the current tool and the next tool have finished cutting, a raised sharp point is generated on the surface of the workpiece, and the generation of the sharp point is caused by different tool feed paths and undeformed chip geometric characteristics, in fig. 4, a point Sh1And Sh2Is the intersection of the motion paths of different tools, wherein the point Sh1Is the intersection point of the tool motion paths of the nth tool and the (n +1) th tool, point Sh2Is the intersection point of the tool motion paths of the (n +1) th tool and the (n +2) th tool, point Sh1Or Sh2The distance from the surface of the thread roller path is the residual height of the surface of the workpiece; the value of the residual height of the workpiece depends on the thickness of undeformed chips when the cutter is about to exit the workpiece;
the distribution of the surface topography of the thread raceway of the threaded workpiece is shown in FIG. 6, FIG. 6 is a front view of the inner ring of the thread raceway of the threaded workpiece, the view is a projection of the thread on the axial direction of the workpiece, the surface profile of the thread raceway consists of a plurality of sharp points, and the raised sharp points are redundant parts of the threaded workpiece generated by the motion tracks of two adjacent cutters; under an ideal state, the projection of the threaded raceway surface of the threaded workpiece on the axial direction of the workpiece is a circle; the raised sharp points on the surface of the thread roller path are uniformly distributed on the circumference;
according to the surface contour forming mechanism of a threaded workpiece in the thread dry-type rotary milling process, combining the movement track of a cutter in the cutting process; intersection point of tool motion tracks of the nth tool and the (n +1) th tool
Figure BDA0003482566310000081
This can be obtained by the following system of equations:
Figure BDA0003482566310000091
therefore, the workpiece residual height RthCan be calculated by calculating the point Sh1The distance to the surface of the workpiece in the radial direction of the workpiece is obtained, and the calculation equation is as follows:
Figure BDA0003482566310000092
in the formula, r is the inner diameter of the thread roller path;
the corrugation degree of the thread raceway surface of the threaded workpiece is schematically shown in FIG. 7; waviness WshIs a slave point Sh1To point Sh2The distance of (c). Point Sh2(ysh2,zsh2) Is the intersection point of the tool motion tracks of the (n +1) th tool and the (n +2) th tool, and can be obtained by the following equation system:
Figure BDA0003482566310000093
in the formula, coordinate point (m)n+2,nn+2) The center of the tool motion track of the (n +2) th tool is shown; based on the analysis of the movement mechanism of the cutting forming, (m)n+2,nn+2) Can be expressed as:
Figure BDA0003482566310000094
waviness W of workpiece surfaceshCan be expressed as:
Figure BDA0003482566310000095
where ψ is the helix angle of the threaded workpiece.
Examples
Tests prove that the predicted value of the surface appearance (including residual height and waviness) of the threaded raceway of the workpiece in the thread dry-type rotary milling process under different process parameters is better consistent with the experimental value.
The experimental value of the residual height of the thread roller path of the thread workpiece is larger than the theoretical value, and the experimental value of the waviness is smaller than the theoretical value. The main reason for this is that the newly created workpiece surface is plastically deformed by the cutting force of the tool. Therefore, the raised portion on the threaded workpiece increases in the radial direction of the workpiece (the residual height increases) and decreases in the tangential direction of the workpiece (the waviness decreases) after the dry-type rotary milling process. The effectiveness and the accuracy of the established surface appearance model in the thread dry-type rotary milling machining process can be verified through a comparison result and an error analysis result of a theoretical value and an experimental value.
The experimental verification of the surface appearance of the threaded workpiece under different process parameters is carried out on an HJ 092X 80 type numerical control rotary milling machine, the workpiece material adopted by the experiment is AISI52100, and the hardness range is 63-65 hrc; the geometric parameters of the threaded workpiece are shown in table 1;
TABLE 1 workpiece geometry parameters
Geometric parameters of threaded workpieces Numerical value
Axial pitch 10.00mm
Diameter of outer circle 62.05mm
Root diameter 57.95mm
Helix angle 2.50°
Length of threaded workpiece 1000mm
A schematic view of the threaded workpiece after machining is shown in fig. 8. The cutter material arranged on the cutter head is PCBN; the geometrical parameters of the tool used are shown in table 2.
TABLE 2 tool geometry parameters
Geometric parameters Numerical value
Front angle 0°
Relief angle 9°
Chamfering 25°*1.50mm
Radius of nose fillet 3.30mm
In addition, to eliminate the effect of tool wear on the experimental values, a new tool was used under each set of cutting conditions. Performing a thread dry-type rotary milling experiment at cutting speeds of 60m/min, 100m/min, 140m/min and 180 m/min; the number of the selected cutters is 2, 3, 4 and 6; the maximum cutting depths used were 0.04mm, 0.06mm, 0.08mm and 0.1mm, respectively. Cutting conditions adopted in the model verification experiment are shown in table 3;
TABLE 3 cutting conditions for thread Dry-type milling experiments
Figure BDA0003482566310000101
Figure BDA0003482566310000111
Wherein the depth of cut is the same as the undeformed chip thickness. In the interrupted cutting process of the threaded workpiece, the cutting depth is instantaneously changed and reflected by the thickness of undeformed cuttings; when setting the process parameters, only the maximum cutting depth is generally required to be set.
The surface topography of the threaded workpiece (including the residual height of the workpiece surface and waviness) was measured using a MFT-5000 multifunction tribometer manufactured by Rtec corporation. The measuring device integrates a three-dimensional optical profiler and can be used for measuring the surface profile of an object. When the appearance of the thread roller path of the thread workpiece is measured, a white light interference objective lens is used for amplifying the observation area of the thread roller path of the thread workpiece by 10 times. And measuring 3 equally-spaced positions of the threaded workpiece along the circumferential direction, and taking the average value of the 3 measured values as the final experimental result of the residual height and the waviness of the workpiece. The result measured by the MFT-5000 type multifunctional tribometer is picture information, the picture information needs to be converted into digital information by adopting Gwyddion analysis software, and the specific measurement values of the residual height and the waviness are finally obtained.
The deviation of the measured values of the residual heights of the threaded workpiece at 3 equally spaced positions along the circumferential direction is within 0.10, and the lower deviation is within 0.08; the standard deviation remains within 0.07. The deviation and the standard deviation of the residual height measurement value and the error analysis of the residual height measurement value of the threaded workpiece show that the fluctuation of multiple measurement values of the residual height is small.
The upper deviation of the waviness measured values of 3 equidistant positions of the threaded workpiece along the circumferential direction is within 0.45, and the lower deviation is within 0.37; the standard deviation remains within 0.32. The fluctuation of the measured value of the waviness is small as can be seen from the deviation and the standard deviation of the measured value of the waviness and the error analysis of the measured value of the waviness of the threaded workpiece.
And finally, obtaining the experimental value of the surface topography of the workpiece by respectively averaging the residual heights and the waviness of the 3 measurement points. The predicted values and experimental values of the surface topography (including residual height and waviness) of the threaded raceway of the workpiece in the dry-type rotary milling process of the threads under different process parameters are shown in table 4.
TABLE 4 theoretical and experimental values of residual height and waviness of workpiece surface
Figure BDA0003482566310000121
The prediction error of the residual height and the waviness of the thread raceway of the threaded workpiece can be calculated by the following formula. Wherein etaRAnd ηWRelative errors of residual height and waviness are respectively; rth-experimentalAnd
Figure BDA0003482566310000122
the experimental values R of the residual height and waviness respectivelyth-theoreticalAnd
Figure BDA0003482566310000123
respectively, the theoretical calculation values of the residual height and the waviness are obtained.
Figure BDA0003482566310000124
Figure BDA0003482566310000125
The results of the relative error calculation (as shown in table 4) show that the theoretical predicted values of the residual height and waviness are in good agreement with the experimental values. Under 12 groups of cutting processing parameters, the relative error of the theoretical predicted value of the residual height is 0.86 percent at minimum and 10.73 percent at maximum; the relative error of the theoretical prediction value of the waviness is 1.70 percent at minimum and 6.54 percent at maximum. The relative error between the residual height and the theoretical prediction value of waviness is controlled within 11% and 7%, respectively. And the effectiveness and the accuracy of the established prediction model of the surface topography of the thread workpiece in the thread dry-type rotary milling process are verified by the comparison result of the theoretical value and the experimental value and the error analysis result. As can be seen from Table 4, the experimental value of the residual height of the threaded raceway of the threaded workpiece is larger than the theoretical value, and the experimental value of the waviness is smaller than the theoretical value. The main reason for this is that the newly created workpiece surface is plastically deformed by the cutting force of the tool. Therefore, the raised portion on the threaded workpiece increases in the radial direction of the workpiece (the residual height increases) and decreases in the tangential direction of the workpiece (the waviness decreases) after the dry-type rotary milling process.
Analyzing influence factors of surface morphology:
the analysis of the influence of the cutting speed on the surface topography (including residual height and waviness) of the workpiece during the dry-type rotary milling process of the thread is shown in fig. 9. As can be seen from fig. 9, the cutting speed has little influence on the remaining height and waviness of the workpiece surface; the residual height and the waviness of the surface of the workpiece are basically kept unchanged along with the change of the cutting speed. According to the prediction model of the surface topography of the threaded workpiece, the residual height of the surface of the workpiece is a function of the intersection coordinate of the motion track of the cutter and the radius of the workpiece, and the waviness of the surface of the workpiece is a function of the intersection coordinate of the motion track of the cutter and the helix angle of the thread. In the case of fixed values for the workpiece radius and thread helix angle, the only parameter that varies is the intersection coordinates of the tool motion trajectories. At this time, the influence of the cutting speed and the number of the cutters on the movement track of the cutters is small, and the reason is that the residual height and the waviness of the surface of the workpiece are only slightly changed.
The variation of the residual height and waviness of the workpiece surface with the maximum cutting depth is shown in fig. 10. As shown in fig. 10, the surface topography of the workpiece increases substantially linearly with increasing maximum cut depth. The main reason for this phenomenon is that at lower maximum cutting depths, the successive scores of the workpiece surface caused by the intersection of the tool motion trajectories are very close to each other; as the maximum depth of cut increases, the distance between successive scores begins to increase, resulting in fewer and fewer scores on the surface of the workpiece. As can be seen from FIG. 10, when the maximum cut depth is 0.04mm, the values of the residual height of the surface of the workpiece and the waviness are 10.26X 10-4mm and 13.36X 10-2mm, respectively; while when the maximum cutting depth is 0.1mm, these values reach 13.17X 10-4mm and 46.96X 10-2mm, respectively. This phenomenon indicates that the rate of increase in waviness of the surface of the workpiece is higher than that of the surface of the workpiece with an increase in maximum cutting depth.
Fig. 11 shows the influence of the number of cutters on the residual height and waviness of the surface of the workpiece in the dry-type rotary milling process of the thread. The rule of the influence of the number of the cutters on the surface appearance of the workpiece is similar to the rule of the influence of the cutting speed on the surface appearance of the workpiece in fig. 10. Along with the change of the number of the cutters, the residual height and the waviness of the surface of the workpiece are basically unchanged. The residual height and waviness of the surface of the workpiece are mainly functions of the movement track of the cutter, and the influence of the change of the number of the cutters on the movement track of the cutter is small. Therefore, the residual height and waviness of the workpiece surface are only slightly changed.
From the above analysis, it can be known that the influence degrees of the cutting speed, the maximum cutting depth and the number of the cutters on the surface appearance of the workpiece and the residual stress of the surface of the workpiece are different in the thread dry-type rotary milling process. Sensitivity analysis is carried out on the residual height and the waviness of the surface of the workpiece in a main effect analysis mode, and sensitive factors influencing the surface appearance of the workpiece are searched.
The main effect influence analysis of the residual height on the surface of the workpiece can obtain the maximum cutting depth which is a sensitive parameter influencing the residual height on the surface of the workpiece; the influence of the cutting speed on the residual height of the surface of the workpiece is not obvious; when the number of the cutters is small, the influence of the number of the cutters on the residual height of the surface of the workpiece is obvious, and the obvious degree is reduced along with the increase of the number of the cutters. The sequencing of the influence degree of the process parameters on the residual height on the surface of the workpiece is as follows: the maximum cutting depth is maximum, the number of cutters is small, and the cutting speed is minimum.
The main effect influence analysis of the waviness of the surface of the workpiece is similar to the main effect influence analysis of the residual height of the surface of the workpiece, and the maximum cutting depth is a sensitive parameter influencing the waviness of the surface of the workpiece. In addition, the influence of the number of cutters and the cutting depth on the surface waviness of the workpiece is not obvious. The sequence of the influence degrees of the process parameters on the surface waviness of the workpiece is as follows: the maximum cutting depth is the largest, and the number of cutters and the cutting speed are small. In summary, the maximum depth of cut is the main factor affecting the surface topography.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (3)

1. A method for predicting the surface topography of a threaded workpiece in cyclone milling is characterized by comprising the following steps:
step 1: acquiring cutting processes of a plurality of cutters in the forming process of the cutting processing surface of the threaded workpiece, and constructing a cutter motion trail model and a cutter-workpiece contact motion trail model according to contact points of the cutters and the workpiece and adding auxiliary lines;
step 2: establishing a threaded workpiece surface appearance prediction model according to the coupling among the cutter motion track model, the cutter-workpiece contact motion track model and the cutter;
and step 3: and acquiring related cutting parameters, and acquiring the residual height and waviness of the surface of the workpiece according to the prediction model of the surface topography of the threaded workpiece, so as to realize the surface topography prediction of the threaded workpiece in the cyclone milling.
2. The method for predicting the surface topography of the threaded workpiece in the cyclone milling process as claimed in claim 1, wherein the specific implementation process of the step 1 is as follows:
step 11: the process of constructing the cutter motion trail model comprises the following steps: the workpiece is positioned at the origin of a coordinate system (O, Y, Z), and the central coordinate is (0, 0); the motion track centers of the nth cutter and the (n +1) th cutter are respectively (m)n,nn) And (m)n+1,nn+1) (ii) a The intersection point of the auxiliary line and the excircle of the workpiece or the motion tracks of different cutters is Pi(ii) a Then (n +1) th represents the tool and the tool motion track center coordinate point equation of the tool of the nth term as follows:
Figure FDA0003482566300000011
Figure FDA0003482566300000012
in the formula, e is the distance from the center of the workpiece to the center of the motion track of the cutter; delta is the initial angle of the cutter cutting workpiece; thetaiThe angle of rotation of the workpiece from the nth time the tool begins to cut into the workpiece to the (n +1) th time the tool begins to cut into the workpiece; eta is an included angle between a connecting line from the cutter motion track center of the (n +1) th cutter to the initial point of inserting the cutter into the workpiece and a connecting line from the cutter motion track center of the (n +1) th cutter to the central point of the workpiece; the included angle eta is determined by trigonometric function relation in the cutting process and is expressed as:
Figure FDA0003482566300000013
in the formula, R is the radius of the motion track of the cutter;
step 12: the process of constructing the tool-workpiece contact motion trail model comprises the following steps: introducing auxiliary lines for describing the motion tracks of the nth tool and the (n +1) th tool, and introducing auxiliary lines ln+1And lnIs represented as follows:
zi-nn+1＝tan(Δ+θ)·(yi-mn+1) (4)
zi-nn＝tan(Δ+θn+θi)·(yi-mn) (5)；
wherein (z)i，yi) Coordinates of points on the auxiliary line; thetanRotating the cutter in the cutting process of the nth cutter by an angle; thetaiThe angle of rotation of the workpiece from the start of the cutting of the tool into the workpiece for the nth to the start of the cutting of the tool into the workpiece for the (n +1) th;
auxiliary line ln+1The point of intersection with the excircle of the workpiece is P1Auxiliary line ln+1The intersection point of the motion track of the (n +1) th cutting tool and the motion track of the (n +1) th cutting tool is P2Auxiliary line ln+1The intersection point of the motion tracks of the tool and the nth tool is P3Auxiliary line lnThe point of intersection with the excircle of the workpiece is P4Auxiliary line lnThe intersection point of the motion track of the nth cutter and the motion track of the nth cutter is P5；
P1The coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure FDA0003482566300000021
P2the coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure FDA0003482566300000022
P3the coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure FDA0003482566300000023
P4the coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure FDA0003482566300000024
P5the coordinates in the coordinate system (O, Y, Z) are expressed as:
Figure FDA0003482566300000025
in the formula, thetanFor the nth tool rotation angle during cutting, the value is expressed as:
Figure FDA0003482566300000026
in the formula (I), the compound is shown in the specification,
Figure FDA0003482566300000027
is the tool motion track center (m) of the nth tooln,nn) To point P1Is represented as:
Figure FDA0003482566300000031
3. the method for predicting the surface topography of the threaded workpiece in the cyclone milling process as claimed in claim 1, wherein the model for predicting the surface topography of the threaded workpiece is composed of a model for predicting the residual height of the surface of the threaded raceway of the threaded workpiece and a model for predicting the waviness of the surface, and the step 2 is realized by the following steps:
step 21: according to a forming mechanism of the surface profile of a threaded workpiece in the thread dry-type rotary milling process and by combining a cutter motion track model in the cutting process, the intersection point of the cutter motion tracks of the current cutter and the next cutter is calculated, and the calculation formula is as follows:
Figure FDA0003482566300000032
wherein the nth tool and the (n +1) th toolHaving an intersection point of the motion trajectories of
Figure FDA0003482566300000033
(mn,nn) And (m)n+1,nn+1) The motion track centers of the nth cutter and the (n +1) th cutter are respectively; r is the radius of the motion track of the cutter;
step 22: and calculating the distance from the intersection point of the tool motion tracks of the current tool and the next tool to the surface of the thread raceway of the threaded workpiece to obtain the residual height of the surface of the workpiece, wherein the surface residual height prediction model expression is as follows:
Figure FDA0003482566300000034
wherein R isthThe residual height of the surface of the workpiece; r is the inner diameter of the thread roller path;
step 23: calculating the center of a tool motion track based on a cutting forming motion mechanism, calculating the intersection point of the tool motion tracks of two tools by using the center of the tool motion track and according to a tool motion track model, calculating the waviness of the surface of a thread raceway of a threaded workpiece according to the distance between the intersection points of the two tool motion tracks generated by three adjacent tools, wherein a surface waviness prediction model is expressed as follows:
Figure FDA0003482566300000035
Figure FDA0003482566300000036
Figure FDA0003482566300000037
wherein S ish2(ysh2,zsh2) Is the (n +1) th tool and the (n +2) th toolThe intersection point of the tool motion trajectories; (m)n+2,nn+2) The center of the tool motion track of the (n +2) th tool; wshIs waviness; psi is the helix angle of the threaded workpiece; e is the distance from the center of the workpiece to the center of the motion track of the cutter; delta is the initial angle of the cutter cutting workpiece; thetaiThe angle of rotation of the workpiece from the time the tool begins to cut into the workpiece at the nth to the time the tool begins to cut into the workpiece at (n +1) th.
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