WO2023138327A1 - Method for predicting threaded-workpiece surface topography during whirlwind milling - Google Patents

Method for predicting threaded-workpiece surface topography during whirlwind milling Download PDF

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WO2023138327A1
WO2023138327A1 PCT/CN2022/142659 CN2022142659W WO2023138327A1 WO 2023138327 A1 WO2023138327 A1 WO 2023138327A1 CN 2022142659 W CN2022142659 W CN 2022142659W WO 2023138327 A1 WO2023138327 A1 WO 2023138327A1
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tool
workpiece
trajectory
threaded
cutting
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PCT/CN2022/142659
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French (fr)
Chinese (zh)
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刘超
丁浩
黄绍服
黄尊鹏
李君�
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安徽理工大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23G—THREAD CUTTING; WORKING OF SCREWS, BOLT HEADS, OR NUTS, IN CONJUNCTION THEREWITH
    • B23G1/00—Thread cutting; Automatic machines specially designed therefor
    • B23G1/32—Thread cutting; Automatic machines specially designed therefor by milling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]

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  • the invention relates to the technical field of mechanical manufacturing and processing, in particular to a method for predicting the surface topography of threaded workpieces in cyclone milling.
  • the control of the surface topography of the workpiece is an important issue in machining, because it will have an important impact on the final service performance of the machined parts, such as fatigue resistance, surface friction and wear.
  • the surface topography of the workpiece will also affect the contact performance and transmission performance of the threaded parts with the ball during use. Therefore, it is necessary to study the surface morphology of the workpiece during thread dry milling.
  • the thread dry whirling milling process is complex, with complex dynamic cutting characteristics such as multi-blade intermittent forming.
  • the indicators used to evaluate the surface topography of workpieces are relatively wide, mainly including residual height, waviness, roughness and surface texture.
  • the analysis of workpiece surface topography is more intuitive is the residual height and waviness of the workpiece surface, both of which can directly reflect the change of the uniformly distributed concave and convex points on the workpiece surface.
  • the residual height and waviness of the workpiece surface will affect the stress concentration phenomenon of the workpiece during use, which in turn will reduce the service performance and service time of the workpiece, and even reach the level of direct damage to the workpiece.
  • the present invention provides a method for predicting the surface topography of threaded workpieces in cyclone milling.
  • the surface topography of threaded workpieces can be reflected by the residual height and waviness index of the workpiece surface, and the processing parameters can be optimized in advance to achieve the best processing plan, thereby improving the processing quality of cyclone milling.
  • a method for predicting the surface topography of a threaded workpiece in whirl milling specifically comprising the following steps:
  • Step 1 Obtain the cutting process of several tools in the surface forming process of threaded workpiece cutting, according to the contact point between the tool and the workpiece, and add auxiliary lines, construct the tool trajectory model and the tool-workpiece contact trajectory model, and obtain the representation equations for describing the tool trajectory model, each coordinate point of the tool-workpiece contact trajectory model, and the auxiliary lines introduced to facilitate the description of the tool trajectory;
  • Step 11 The process of constructing the tool trajectory model is as follows: let the workpiece be located at the origin of the coordinate system (O, Y, Z), and the center coordinates are (0, 0); the tool trajectory centers of the nth tool and the (n+1)th tool are respectively (m n , n n ) and (m n+1 , n n+1 ); the intersection point of the auxiliary line with the outer circle of the workpiece or different tool trajectory is Pi ;
  • the equation is expressed as:
  • R is the radius of the tool trajectory
  • Step 12 The process of constructing the tool-workpiece contact trajectory model is: introducing auxiliary lines to describe the tool trajectory of the nth tool and the (n+1)th tool, and the introduced auxiliary lines l n+1 and l n are expressed as follows:
  • (z i , y i ) is the coordinate point on the auxiliary line;
  • ⁇ n is the rotation angle of the cutterhead during the cutting process of the nth tool;
  • ⁇ i is the rotation angle of the workpiece when the nth tool starts cutting into the workpiece and the (n+1)th tool starts cutting into the workpiece;
  • intersection point of the auxiliary line l n+1 and the outer circle of the workpiece is P 1
  • the intersection point of the auxiliary line l n+1 and the movement track of the (n+1)th tool is P 2
  • the intersection point of the auxiliary line l n+1 and the tool movement track of the nth tool is P3
  • the intersection point of the auxiliary line l n and the outer circle of the workpiece is P4
  • the intersection point of the auxiliary line l n and the tool movement track of the nth tool is P5 ;
  • ⁇ n is the rotation angle of the cutterhead during the cutting process of the nth tool, expressed as:
  • Step 2 Establish a thread workpiece surface topography prediction model based on the tool trajectory model, tool-workpiece contact trajectory model, and tool coupling, and predict the thread workpiece surface topography in whirlwind milling according to the thread workpiece surface topography prediction model;
  • Step 21 According to the surface contour forming mechanism of the threaded workpiece in the thread dry milling process, and combined with the tool trajectory model during the cutting process, calculate the intersection point of the tool trajectory of the current tool and the next tool.
  • the calculation formula is as follows:
  • the intersection point of the tool trajectory of the nth tool and the (n+1)th tool is (m n ,n n ) and (m n+1 ,n n+1 ) are the center of the tool trajectory of the nth tool and the (n+1)th tool respectively;
  • Step 22 Obtain the surface residual height prediction model for calculating the surface residual height of the workpiece by calculating the distance from the intersection point of the tool trajectory of the current tool and the next tool to the thread raceway surface of the threaded workpiece, the expression is:
  • R th is the residual height of the workpiece surface
  • r is the inner diameter of the thread raceway
  • Step 23 Calculate the tool trajectory center based on the cutting forming motion mechanism, use the tool trajectory center and calculate the intersection point of the tool trajectory of two tools according to the tool trajectory model, and calculate the waviness of the thread raceway surface of the threaded workpiece according to the distance between the intersection points of the two tool trajectory generated by three adjacent tools.
  • the surface waviness prediction model is expressed as:
  • Sh2 (y sh2 , z sh2 ) is the intersection point of the tool trajectory of the (n+1)th tool and the (n+2)th tool; (m n+2 , n n+2 ) is the center of the tool trajectory of the (n+2)th tool; W sh is the waviness; ⁇ is the helix angle of the threaded workpiece.
  • the surface topography of the workpiece is described from two aspects: surface waviness and residual height, so the surface topography prediction model consists of a surface waviness prediction model and a surface residual height prediction model.
  • the present invention discloses a method for predicting the surface morphology of threaded workpieces in whirl milling, which obtains the relative motion relationship between the nth tool and the (n+1)th tool and the threaded workpiece in the thread dry milling process, and completes the analysis of the tool paths of different tools.
  • a prediction model for the residual height of the threaded raceway surface and a prediction model for the surface waviness were established respectively, considering the influence of parameters such as cutting parameters, undeformed chip thickness, inner and outer diameters and helix angles of the thread, the number and geometric size of tools, and the eccentricity between the workpiece and the tool on the surface topography of the threaded raceway, so as to realize the accurate prediction of the surface topography of the threaded workpiece in whirling milling.
  • Fig. 1 is the relative motion analysis schematic diagram of cutter and workpiece in the (n+1) cutter cutting process that the present invention provides;
  • FIG. 2 accompanying drawing is the enlarged schematic diagram of part A of relative motion analysis of tool and workpiece during the (n+1) knife cutting process provided by the present invention
  • FIG. 3 accompanying drawing is the enlarged schematic diagram of part B of relative motion analysis of tool and workpiece during the cutting process of (n+1) knife provided by the present invention
  • Fig. 4 accompanying drawing is the schematic diagram of the surface topography mechanism in the process of thread dry rotary milling provided by the present invention
  • Figure 5 is a partially enlarged schematic diagram of the surface topography mechanism in the process of thread dry rotary milling provided by the present invention
  • Fig. 6 accompanying drawing is the schematic diagram of workpiece surface profile in the front view provided by the present invention.
  • Figure 7 is a schematic diagram of the waviness and residual height of the surface of the workpiece provided by the present invention.
  • FIG. 8 accompanying drawing is the threaded workpiece schematic diagram provided by the present invention.
  • Figure 9 is a schematic diagram of the influence of the cutting speed provided by the present invention on the surface topography of the workpiece
  • Figure 10 is a schematic diagram of the influence of the maximum depth of cut provided by the present invention on the surface topography of the workpiece;
  • Figure 11 is a schematic diagram of the influence of the number of cutting tools provided by the present invention on the surface morphology of the workpiece.
  • the embodiment of the present invention discloses a method for predicting the surface morphology of a threaded workpiece in cyclone milling, and the specific steps are as follows:
  • S1 Analyze the surface topography forming process, and establish the surface topography model of the threaded workpiece; the relative motion analysis between the tool and the workpiece during the surface topography forming process is the basis for modeling the surface topography of the threaded workpiece;
  • Fig. 1 is a schematic diagram of the contact analysis between the tool and the workpiece during the surface forming process of threaded workpiece cutting.
  • Fig. 1 combines the cutting process of the first cutting stage and the second cutting stage; in Fig.
  • the coordinates (0, 0) are the origin of the workpiece coordinate system; (m no ,n no ) and (m n+1 ,n n+1 ) are respectively the center of the tool trajectory of the nth tool and the (n+1)th tool; point P i is the intersection point of the auxiliary line and the outer circle of the workpiece or different tool trajectories; the formation of the surface topography of the workpiece is mainly caused by the joint action of multi-tool intermittent cutting and the relative motion of the tool and the workpiece. Therefore, it is necessary to model the tool trajectory and the tool-workpiece contact motion;
  • the point P1(y 1 , z 1 ) in Figure 2 is the intersection point of the auxiliary line l n+1 and the outer circle of the workpiece.
  • the intersection point can be obtained by equations (6):
  • the point P2(y 2 , z 2 ) in Figure 2 is the intersection point of the auxiliary line l n+1 and the tool movement trajectory of the (n+1)th tool, which can be solved by equations (7):
  • the point P3(y 3 ,z 3 ) in Figure 3 is the intersection point of the auxiliary line l n+1 and the tool movement track of the nth tool, which can be obtained by the equation group (8):
  • the point P4(y 4 , z 4 ) in Fig. 3 is the intersection point of the auxiliary line l n and the outer circle of the workpiece, which can be obtained by the equation group (9):
  • the point P5 (y 5 , z 5 ) in Figure 3 is the intersection point of the auxiliary line l n and the tool movement track of the nth tool, which can be obtained by the equation group (10):
  • ⁇ n is the rotation angle of the cutter head during the cutting process of the nth tool, which can be expressed as:
  • the surface morphology of the workpiece is affected by the surface forming error caused by the geometric motion mechanism of material removal during the cutting process, the tooth shape error caused by the geometric profile of the tool, the material springback error caused by the material properties of the workpiece, and other random errors caused by tool wear and cutting vibration.
  • the surface topography prediction model only considers the influence of the relative geometric motion of the tool and workpiece during the forming process of the workpiece material; the influence caused by other factors such as tool vibration and extrusion deformation of the workpiece material is not considered for the time being;
  • Fig. 4 shows the surface topography forming process of the thread raceway of the threaded workpiece.
  • the tool movement trajectory of the tool, the workpiece blank is finally formed into a threaded part during the cutting process of multiple tools, and the surface morphology of the workpiece is also generated; after the current tool and the next tool are cut, a raised sharp point will be generated on the workpiece surface.
  • h1 and S h2 is the intersection point of different tool motion trajectories, where point S h1 is the intersection point of the tool motion trajectory of the nth tool and the (n+1)th tool, point S h2 It is the intersection point of the tool motion trajectory of the (n+1)th tool and the (n+2)th tool, point S h1 or S h2
  • the distance to the surface of the thread raceway is the residual height of the workpiece surface; the value of the residual height of the workpiece depends on the thickness of the undeformed chip when the tool is about to exit the workpiece;
  • Figure 6 shows the front view of the inner ring of the threaded workpiece thread raceway. This figure is the projection of the thread on the axial direction of the workpiece.
  • the surface profile of the thread raceway is composed of many sharp points.
  • the workpiece residual height R th can be obtained by calculating the distance from the point Sh1 to the workpiece surface in the radial direction of the workpiece, and the calculation equation is as follows:
  • r is the inner diameter of the thread raceway
  • the schematic diagram of the surface waviness of the thread raceway of the threaded workpiece is shown in Figure 7; the waviness W sh is the distance from point Sh1 to point Sh2 .
  • the point S h2 (y sh2 , z sh2 ) is the intersection point of the tool motion trajectory of the (n+1)th tool and the (n+2)th tool, which can be obtained by the following equations:
  • the coordinate point (m n+2 ,n n+2 ) represents the center of the tool motion trajectory of the (n+2)th tool; based on the analysis of the cutting and forming motion mechanism, (m n+2 ,n n+2 ) can be expressed as:
  • the workpiece surface waviness W sh can be expressed as:
  • ⁇ is the helix angle of the threaded workpiece.
  • the test verifies that the predicted value of the surface topography (including residual height and waviness) of the workpiece thread raceway in the thread dry milling process under different process parameters is in good agreement with the experimental value.
  • the experimental value of the thread raceway residual height of the threaded workpiece is larger, and the experimental value of the waviness is smaller than the theoretical value.
  • the main reason for this phenomenon is that the newly generated workpiece surface undergoes plastic deformation under the cutting force of the tool. Therefore, after the dry rotary milling process, the convex part of the threaded workpiece increases in the radial direction of the workpiece (increased residual height) and decreases in the tangential direction of the workpiece (reduced waviness).
  • the effectiveness and accuracy of the established surface topography model in the process of thread dry rotary milling can be verified through the comparison results of theoretical values and experimental values and the results of error analysis.
  • the experimental verification of the surface morphology of the threaded workpiece under different process parameters was carried out on the "HJ092 ⁇ 80" CNC rotary milling machine.
  • the material of the workpiece used in the experiment was AISI52100, and the hardness range was 63-65hrc.
  • the geometric parameters of the threaded workpiece are shown in Table 1;
  • Thread workpiece geometric parameters value Axial pitch 10.00mm Outer circle diameter 62.05mm root circle diameter 57.95mm Helix angle 2.50° Thread Workpiece Length 1000mm
  • the schematic diagram of the threaded workpiece after processing is shown in Figure 8.
  • the tool material installed on the cutter head is PCBN; among them, the geometric parameters of the tool used are shown in Table 2.
  • Thread dry spin milling experiments were carried out at cutting speeds of 60m/min, 100m/min, 140m/min, and 180m/min; the number of selected tools was 2, 3, 4, and 6; the maximum cutting depths used were 0.04mm, 0.06mm, 0.08mm, and 0.1mm, respectively.
  • the cutting conditions used in the model verification experiments are shown in Table 3;
  • the depth of cut is the same as the undeformed chip thickness.
  • the cutting depth changes instantaneously, which is reflected by the thickness of undeformed chips; when setting process parameters, generally only the maximum cutting depth needs to be set.
  • the surface morphology of the threaded workpiece was measured by the MFT-5000 multifunctional tribometer produced by Rtec Company.
  • the measuring device integrates a 3D optical profiler and can be used to measure the surface profile of an object.
  • the observation area of the thread raceway of the thread workpiece is magnified by 10 times with a white light interference objective lens.
  • the threaded workpiece is measured at three equidistant positions along the circumference, and the average value of the three measurements is taken as the final experimental result of the residual height and waviness of the workpiece.
  • the results measured by the MFT-5000 multifunctional tribometer are picture information, which needs to be converted into digital information by Gwyddion analysis software, and finally the specific measurement values of residual height and waviness can be obtained.
  • the upper and lower deviations of the residual height measurement values of three equidistant positions along the circumference of the threaded workpiece are within 0.10 and 0.08; the standard deviation is kept within 0.07. From the deviation and standard deviation of the residual height measurement value and the error analysis of the residual height measurement value of the threaded workpiece, it can be seen that the fluctuation of the multiple measurement values of the residual height is small.
  • the upper and lower deviations of the waviness measurement values at three equidistant positions along the circumference of the threaded workpiece are within 0.45 and the downward deviation is within 0.37; the standard deviation is kept within 0.32. From the analysis of the deviation and standard deviation of the waviness measurement value and the error analysis of the waviness measurement value of the threaded workpiece, it can be seen that the fluctuation of the waviness measurement value is small.
  • the prediction error of thread raceway residual height and waviness of threaded workpiece can be calculated by the following formula.
  • ⁇ R and ⁇ W are respectively the relative error of residual height and waviness
  • R th-theoretical are the theoretically calculated values of residual height and waviness, respectively.
  • Fig. 9 The analysis of the effect of cutting speed on the surface topography (including residual height and waviness) of the thread dry milling process is shown in Fig. 9. It can be seen from Figure 9 that the cutting speed has little effect on the residual height and waviness of the workpiece surface; with the change of cutting speed, the residual height and waviness of the workpiece surface basically remain unchanged.
  • the residual height of the workpiece surface is a function of the intersection coordinates of the tool trajectory and the radius of the workpiece
  • the waviness of the workpiece surface is a function of the intersection coordinates of the tool trajectory and the thread helix angle.
  • the only variable parameter is the intersection coordinates of the tool motion trajectory. At this time, the cutting speed and the number of tools have little influence on the tool trajectory, which explains the slight changes in the residual height and waviness of the workpiece surface.
  • FIG. 10 The variation of the workpiece surface residual height and waviness with the maximum depth of cut is shown in Figure 10.
  • the surface topography of the workpiece basically increases linearly with the increase of the maximum depth of cut.
  • the main reason for this phenomenon is that at a lower maximum depth of cut, the continuous notches on the surface of the workpiece caused by the intersection of tool motion trajectories are very close to each other; as the maximum depth of cut increases, the distance between continuous notches begins to increase, and fewer and fewer notches are produced on the workpiece surface.
  • the effect of the number of tools on the residual height and waviness of the workpiece surface during thread dry milling is shown in Figure 11.
  • the influence of the number of cutting tools on the surface morphology of the workpiece is similar to that of the cutting speed on the surface morphology of the workpiece in Figure 10.
  • the residual height and waviness of the workpiece surface basically do not change.
  • the residual height and waviness of the workpiece surface are mainly functions of the tool trajectory, and the change in the number of tools has little effect on the tool trajectory. Therefore, the remaining height and waviness of the workpiece surface only slightly change.
  • the maximum depth of cut is a sensitive parameter affecting the workpiece surface residual height; cutting speed has no significant effect on the workpiece surface residual height; when the number of tools is small, the impact of the number of tools on the workpiece surface residual height is more significant, and the degree of significance decreases with the increase of the number of tools.
  • the ranking order of the degree of influence of process parameters on workpiece surface residual height is as follows: the maximum depth of cut is the largest, the number of tools is small, and the cutting speed is the smallest.
  • the main effect analysis of workpiece surface waviness is similar to the main effect analysis of workpiece surface residual height, and the maximum depth of cut is a sensitive parameter that affects workpiece surface waviness.
  • the number of tools and the depth of cut have no significant effect on the surface waviness of the workpiece.
  • the order of influence of process parameters on workpiece surface waviness is as follows: the maximum cutting depth is the largest, and the number of tools and cutting speed are small. In summary, the maximum depth of cut is the main influencing factor of surface topography.
  • each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other.
  • the description is relatively simple, and for relevant details, please refer to the description of the method part.

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Abstract

Disclosed in the present invention is a method for predicting threaded-workpiece surface topography during whirlwind milling. In the method, the surface topography characteristics of a workpiece are analyzed by using a multi-cutting-edge intermittent forming process characteristic of dry thread milling. According to a surface topography forming mechanism of a threaded workpiece, a thread raceway surface residual height prediction model and a thread raceway surface waviness prediction model are built, and the effects on thread raceway surface topography of parameters such as cutting parameters, an undeformed chip thickness, the minor and major diameters and the helix angle of a thread, the number of cutting tools, the geometric dimensions of the cutting tool, and a workpiece-to-cutting-tool eccentric distance are taken into consideration. By means of a workpiece surface topography prediction model, machining parameters can be optimized in advance, so as to obtain the optimal machining solution, thereby improving the machining quality of whirlwind milling.

Description

一种旋风铣削中螺纹工件表面形貌的预测方法A Prediction Method of Surface Topography of Threaded Workpiece in Whirlwind Milling 技术领域technical field
本发明涉及机械制造加工技术领域，更具体的说是涉及一种旋风铣削中螺纹工件表面形貌的预测方法。The invention relates to the technical field of mechanical manufacturing and processing, in particular to a method for predicting the surface topography of threaded workpieces in cyclone milling.
背景技术Background technique
金属切削加工过程中，对工件表面形貌的控制是机械加工中的一个重要问题，因为它会对被加工零件的最终服役性能，如抗疲劳、表面摩擦和磨损等产生重要的影响。此外，工件表面形貌还会影响螺纹零件在使用过程中与滚珠的接触性能和传动性能。因此，需要对螺纹干式旋铣加工过程中工件表面形貌进行研究。During the metal cutting process, the control of the surface topography of the workpiece is an important issue in machining, because it will have an important impact on the final service performance of the machined parts, such as fatigue resistance, surface friction and wear. In addition, the surface topography of the workpiece will also affect the contact performance and transmission performance of the threaded parts with the ball during use. Therefore, it is necessary to study the surface morphology of the workpiece during thread dry milling.
目前对于切削加工工件表面形貌预测方法已有部分探索，但是研究主要集中在车削、铣削、磨削等方面，而螺纹干式旋风铣削过程与传统的加工方式有所不同，螺纹干式旋铣切削过程复杂，具有多刃断续成形等复杂动态切削特性，在对其加工的螺纹工件表面形貌建模时，需要考虑多刀具与工件接触的相对运动情况以及单把刀具切削所引起的未变形切屑厚度变化特性。目前用于评价工件表面形貌的指标比较广，主要包括残留高度、波纹度、粗糙度与表面纹理等。对工件表面形貌的分析比较直观的是工件表面残留高度与波纹度，两者能够直接的反应工件表面均匀分布的凹凸点的变化情况。此外，工件表面残留高度与波纹度会对工件在使用过程中的应力集中现象产生影响，进而会降低工件的服役性能与服役时间，甚至达到对工件直接破坏的程度。At present, there have been some explorations on the surface topography prediction methods of machining workpieces, but the research mainly focuses on turning, milling, grinding, etc., and the thread dry whirling milling process is different from the traditional processing method. The thread dry whirling milling process is complex, with complex dynamic cutting characteristics such as multi-blade intermittent forming. When modeling the surface topography of the threaded workpiece processed by it, it is necessary to consider the relative motion of multiple tools in contact with the workpiece and the undeformed chip thickness variation characteristics caused by single tool cutting. At present, the indicators used to evaluate the surface topography of workpieces are relatively wide, mainly including residual height, waviness, roughness and surface texture. The analysis of workpiece surface topography is more intuitive is the residual height and waviness of the workpiece surface, both of which can directly reflect the change of the uniformly distributed concave and convex points on the workpiece surface. In addition, the residual height and waviness of the workpiece surface will affect the stress concentration phenomenon of the workpiece during use, which in turn will reduce the service performance and service time of the workpiece, and even reach the level of direct damage to the workpiece.
因此，如何实现旋风铣削中螺纹工件表面形貌预测是本领域技术人员亟需解决的问题。Therefore, how to realize the prediction of the surface topography of the threaded workpiece in whirl milling is an urgent problem to be solved by those skilled in the art.
发明内容Contents of the invention
有鉴于此，本发明提供了一种旋风铣削中螺纹工件表面形貌的预测方法，通过工件表面残留高度与波纹度指标来反应螺纹工件表面形貌，可以预先对加工参数进行优化以达到最佳的加工方案，进而提高旋风铣削加工质量。In view of this, the present invention provides a method for predicting the surface topography of threaded workpieces in cyclone milling. The surface topography of threaded workpieces can be reflected by the residual height and waviness index of the workpiece surface, and the processing parameters can be optimized in advance to achieve the best processing plan, thereby improving the processing quality of cyclone milling.
为了实现上述目的，本发明采用如下技术方案：In order to achieve the above object, the present invention adopts the following technical solutions:
一种旋风铣削中螺纹工件表面形貌的预测方法，具体包括如下步骤：A method for predicting the surface topography of a threaded workpiece in whirl milling, specifically comprising the following steps:
步骤1：获取螺纹工件切削加工表面成形过程中若干刀具的切削过程，根据刀具和工件的接触点，并增加辅助线，构建刀具运动轨迹模型以及刀具-工件接触运动轨迹模型，分别得到用于描述刀具运动轨迹模型、刀具-工件接触运动轨迹模型的各个坐标点以及便于描述刀具运动轨迹而引入的辅助线的表示方程；Step 1: Obtain the cutting process of several tools in the surface forming process of threaded workpiece cutting, according to the contact point between the tool and the workpiece, and add auxiliary lines, construct the tool trajectory model and the tool-workpiece contact trajectory model, and obtain the representation equations for describing the tool trajectory model, each coordinate point of the tool-workpiece contact trajectory model, and the auxiliary lines introduced to facilitate the description of the tool trajectory;
步骤11：构建所述刀具运动轨迹模型过程为：令工件位于坐标系(O,Y,Z)原点，中心坐标为(0，0)；第n把刀具和第(n+1)把刀具的刀具运动轨迹中心分别为(m n,n n)和(m n+1,n n+1)；辅助线与工件外圆或不同刀具运动轨迹的交点为P i；则第(n+1)把刀具和第n把刀具的刀具运动轨迹中心坐标点方程表示为： Step 11: The process of constructing the tool trajectory model is as follows: let the workpiece be located at the origin of the coordinate system (O, Y, Z), and the center coordinates are (0, 0); the tool trajectory centers of the nth tool and the (n+1)th tool are respectively (m n , n n ) and (m n+1 , n n+1 ); the intersection point of the auxiliary line with the outer circle of the workpiece or different tool trajectory is Pi ; The equation is expressed as:
Figure PCTCN2022142659-appb-000001
Figure PCTCN2022142659-appb-000001
Figure PCTCN2022142659-appb-000002
Figure PCTCN2022142659-appb-000002
式中，e为工件中心到刀具运动轨迹中心的距离；Δ为刀具切削工件的初始角；θ i为从第n把刀具开始切入工件到第(n+1)把刀具开始切入工件时工件旋转的角度；η为第(n+1)把刀具的刀具运动轨迹中心到刀具插入工件初始点的连线与第(n+1)把刀具的刀具运动轨迹中心到工件中心点连线的夹角；其中夹角η通过切削过程中三角函数关系确定，表示为： In the formula, e is the distance from the center of the workpiece to the center of the tool trajectory; Δ is the initial angle at which the tool cuts the workpiece; θi is the rotation angle of the workpiece when the nth tool starts to cut into the workpiece to the (n+1)th tool starts to cut into the workpiece; η is the angle between the line connecting the center of the tool trajectory of the (n+1)th tool to the initial point where the tool is inserted into the workpiece and the line connecting the center of the tool trajectory of the (n+1)th tool to the center point of the workpiece; the included angle η is determined by the trigonometric function relationship in the cutting process, expressed as:
Figure PCTCN2022142659-appb-000003
Figure PCTCN2022142659-appb-000003
式中，R为刀具运动轨迹半径；In the formula, R is the radius of the tool trajectory;
步骤12：构建所述刀具-工件接触运动轨迹模型的过程为：引入辅助线用于描述第n把刀具和第(n+1)把刀具的刀具运动轨迹，引入的辅助线l n+1与l n表示如下： Step 12: The process of constructing the tool-workpiece contact trajectory model is: introducing auxiliary lines to describe the tool trajectory of the nth tool and the (n+1)th tool, and the introduced auxiliary lines l n+1 and l n are expressed as follows:
z i-n n+1＝tan(Δ+θ)·(y i-m n+1)        (4) z i -n n+1 ＝tan(Δ+θ)·(y i -m n+1 ) (4)
z i-n n＝tan(Δ+θ n+θ i)·(y i-m n)         (5) z i -n n ＝tan(Δ+θ n +θ i )·(y i -m n ) (5)
式中，(z i，y i)为辅助线上的坐标点；θ n为第n把刀具切削过程中刀盘旋转角度；θ i为第n把刀具开始切入工件到第(n+1)把刀具开始切入工件时工件旋转的角度； In the formula, (z i , y i ) is the coordinate point on the auxiliary line; θ n is the rotation angle of the cutterhead during the cutting process of the nth tool; θi is the rotation angle of the workpiece when the nth tool starts cutting into the workpiece and the (n+1)th tool starts cutting into the workpiece;
辅助线l n+1与工件外圆的交点为P 1，辅助线l n+1与第(n+1)把刀具的运动轨迹交点为P 2，辅助线l n+1与第n把刀具的刀具运动轨迹交点为P 3，辅助线l n与工件外圆的交点为P 4，辅助线l n与第n把刀具的刀具运动轨迹交点为P 5； The intersection point of the auxiliary line l n+1 and the outer circle of the workpiece is P 1 , the intersection point of the auxiliary line l n+1 and the movement track of the (n+1)th tool is P 2 , the intersection point of the auxiliary line l n+1 and the tool movement track of the nth tool is P3 , the intersection point of the auxiliary line l n and the outer circle of the workpiece is P4 , the intersection point of the auxiliary line l n and the tool movement track of the nth tool is P5 ;
P 1在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 1 in the coordinate system (O, Y, Z) are expressed as:
Figure PCTCN2022142659-appb-000004
Figure PCTCN2022142659-appb-000004
P 2在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 2 in the coordinate system (O, Y, Z) are expressed as:
Figure PCTCN2022142659-appb-000005
Figure PCTCN2022142659-appb-000005
P 3在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 3 in the coordinate system (O, Y, Z) are expressed as:
Figure PCTCN2022142659-appb-000006
Figure PCTCN2022142659-appb-000006
P 4在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 4 in the coordinate system (O, Y, Z) are expressed as:
Figure PCTCN2022142659-appb-000007
Figure PCTCN2022142659-appb-000007
P 5在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 5 in the coordinate system (O, Y, Z) are expressed as:
Figure PCTCN2022142659-appb-000008
Figure PCTCN2022142659-appb-000008
式中，θ n为第n把刀具切削过程中刀盘旋转角度，表示为： In the formula, θ n is the rotation angle of the cutterhead during the cutting process of the nth tool, expressed as:
Figure PCTCN2022142659-appb-000009
Figure PCTCN2022142659-appb-000009
式中，
Figure PCTCN2022142659-appb-000010
为第n把刀具的刀具运动轨迹中心(m n,n n)到点P 1的距离，表示为： In the formula,
Figure PCTCN2022142659-appb-000010
is the distance from the center of the tool movement trajectory (m n , n n ) of the nth tool to point P 1 , expressed as:
Figure PCTCN2022142659-appb-000011
Figure PCTCN2022142659-appb-000011
步骤2：根据刀具运动轨迹模型、刀具-工件接触运动轨迹模型和刀具之间的耦合建立螺纹工件表面形貌预测模型，根据螺纹工件表面形貌预测模型预测旋风铣削中螺纹工件表面形貌；Step 2: Establish a thread workpiece surface topography prediction model based on the tool trajectory model, tool-workpiece contact trajectory model, and tool coupling, and predict the thread workpiece surface topography in whirlwind milling according to the thread workpiece surface topography prediction model;
步骤21：根据螺纹干式旋铣加工过程螺纹工件表面轮廓成形机理，并结合切削过程中刀具运动轨迹模型，计算当前刀具与下一把刀具的刀具运动轨迹的交点，计算公式如下：Step 21: According to the surface contour forming mechanism of the threaded workpiece in the thread dry milling process, and combined with the tool trajectory model during the cutting process, calculate the intersection point of the tool trajectory of the current tool and the next tool. The calculation formula is as follows:
Figure PCTCN2022142659-appb-000012
Figure PCTCN2022142659-appb-000012
其中，第n把刀具与第(n+1)把刀具的刀具运动轨迹的交点为
Figure PCTCN2022142659-appb-000013
(m n,n n)和(m n+1,n n+1)分别为第n把刀具和第(n+1)把刀具的刀具运动轨迹中心； Among them, the intersection point of the tool trajectory of the nth tool and the (n+1)th tool is
Figure PCTCN2022142659-appb-000013
(m n ,n n ) and (m n+1 ,n n+1 ) are the center of the tool trajectory of the nth tool and the (n+1)th tool respectively;
步骤22：通过计算当前刀具与下一把刀具的刀具运动轨迹的交点到螺纹工件的螺纹滚道表面的距离获得计算工件表面残留高度的表面残留高度预测模型，表达式为：Step 22: Obtain the surface residual height prediction model for calculating the surface residual height of the workpiece by calculating the distance from the intersection point of the tool trajectory of the current tool and the next tool to the thread raceway surface of the threaded workpiece, the expression is:
Figure PCTCN2022142659-appb-000014
Figure PCTCN2022142659-appb-000014
其中，R th为工件表面残留高度；r为螺纹滚道内径； Among them, R th is the residual height of the workpiece surface; r is the inner diameter of the thread raceway;
步骤23：基于切削成形运动机理计算刀具运动轨迹中心，利用刀具运动轨迹中心并根据刀具运动轨迹模型计算两把刀具的刀具运动轨迹交点，根据相邻工作的三把刀具产生的两个刀具运动轨迹交点的距离计算螺纹工件的螺纹滚道表面的波纹度，表面波纹度预测模型表示为：Step 23: Calculate the tool trajectory center based on the cutting forming motion mechanism, use the tool trajectory center and calculate the intersection point of the tool trajectory of two tools according to the tool trajectory model, and calculate the waviness of the thread raceway surface of the threaded workpiece according to the distance between the intersection points of the two tool trajectory generated by three adjacent tools. The surface waviness prediction model is expressed as:
Figure PCTCN2022142659-appb-000015
Figure PCTCN2022142659-appb-000015
Figure PCTCN2022142659-appb-000016
Figure PCTCN2022142659-appb-000016
Figure PCTCN2022142659-appb-000017
Figure PCTCN2022142659-appb-000017
其中，S h2(y sh2,z sh2)是第(n+1)把刀具和第(n+2)把刀具的刀具运动轨迹的交点；(m n+2,n n+2)为第(n+2)把刀具的刀具运动轨迹的中心；W sh为波纹度；ψ为螺纹工件的螺旋角。工件表面形貌从工件表面波纹度和残留高度两个方面 进行描述，故表面形貌预测模型由表面波纹度预测模型和表面残留高度预测模型组成。 Among them, Sh2 (y sh2 , z sh2 ) is the intersection point of the tool trajectory of the (n+1)th tool and the (n+2)th tool; (m n+2 , n n+2 ) is the center of the tool trajectory of the (n+2)th tool; W sh is the waviness; ψ is the helix angle of the threaded workpiece. The surface topography of the workpiece is described from two aspects: surface waviness and residual height, so the surface topography prediction model consists of a surface waviness prediction model and a surface residual height prediction model.
经由上述的技术方案可知，与现有技术相比，本发明公开提供了一种旋风铣削中螺纹工件表面形貌的预测方法，获得螺纹干式旋铣加工过程中第n把刀具和第(n+1)把刀具与螺纹工件的相对运动关系，完成了不同刀具走刀路径分析。根据螺纹工件表面形貌成形机理，分别建立了螺纹滚道表面残留高度预测模型与表面波纹度预测模型，考虑了切削参数、未变形切屑厚度、螺纹内外径与螺旋角、刀具个数与几何尺寸以及工件-刀具偏心距等参数对螺纹滚道表面形貌的影响，实现旋风铣削中螺纹工件表面形貌的精确预测。It can be seen from the above-mentioned technical solution that, compared with the prior art, the present invention discloses a method for predicting the surface morphology of threaded workpieces in whirl milling, which obtains the relative motion relationship between the nth tool and the (n+1)th tool and the threaded workpiece in the thread dry milling process, and completes the analysis of the tool paths of different tools. According to the forming mechanism of the surface topography of the threaded workpiece, a prediction model for the residual height of the threaded raceway surface and a prediction model for the surface waviness were established respectively, considering the influence of parameters such as cutting parameters, undeformed chip thickness, inner and outer diameters and helix angles of the thread, the number and geometric size of tools, and the eccentricity between the workpiece and the tool on the surface topography of the threaded raceway, so as to realize the accurate prediction of the surface topography of the threaded workpiece in whirling milling.
附图说明Description of drawings
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据提供的附图获得其他的附图。In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the accompanying drawings required in the description of the embodiments or prior art. Obviously, the accompanying drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other accompanying drawings can also be obtained according to the provided drawings without creative work.
图1附图为本发明提供的第(n+1)刀切削过程中刀具与工件相对运动分析示意图；Accompanying drawing of Fig. 1 is the relative motion analysis schematic diagram of cutter and workpiece in the (n+1) cutter cutting process that the present invention provides;
图2附图为本发明提供的第(n+1)刀切削过程中刀具与工件相对运动分析局部A放大示意图；Fig. 2 accompanying drawing is the enlarged schematic diagram of part A of relative motion analysis of tool and workpiece during the (n+1) knife cutting process provided by the present invention;
图3附图为本发明提供的第(n+1)刀切削过程中刀具与工件相对运动分析局部B放大示意图；Fig. 3 accompanying drawing is the enlarged schematic diagram of part B of relative motion analysis of tool and workpiece during the cutting process of (n+1) knife provided by the present invention;
图4附图为本发明提供的螺纹干式旋铣加工过程中表面形貌机理示意图；Fig. 4 accompanying drawing is the schematic diagram of the surface topography mechanism in the process of thread dry rotary milling provided by the present invention;
图5附图为本发明提供的螺纹干式旋铣加工过程中表面形貌机理局部放大示意图；Figure 5 is a partially enlarged schematic diagram of the surface topography mechanism in the process of thread dry rotary milling provided by the present invention;
图6附图为本发明提供的主视图中工件表面廓形示意图；Fig. 6 accompanying drawing is the schematic diagram of workpiece surface profile in the front view provided by the present invention;
图7附图为本发明提供的工件表面波纹度与残留高度示意图；Figure 7 is a schematic diagram of the waviness and residual height of the surface of the workpiece provided by the present invention;
图8附图为本发明提供的螺纹工件示意图；Fig. 8 accompanying drawing is the threaded workpiece schematic diagram provided by the present invention;
图9附图为本发明提供的切削速度对工件表面形貌的影响示意图；Figure 9 is a schematic diagram of the influence of the cutting speed provided by the present invention on the surface topography of the workpiece;
图10附图为本发明提供的最大切深对工件表面形貌的影响示意图；Figure 10 is a schematic diagram of the influence of the maximum depth of cut provided by the present invention on the surface topography of the workpiece;
图11附图为本发明提供的刀具个数对工件表面形貌的影响示意图。Figure 11 is a schematic diagram of the influence of the number of cutting tools provided by the present invention on the surface morphology of the workpiece.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.
本发明实施例公开了一种旋风铣削中螺纹工件表面形貌的预测方法，具体步骤如下：The embodiment of the present invention discloses a method for predicting the surface morphology of a threaded workpiece in cyclone milling, and the specific steps are as follows:
S1：对表面形貌成形过程进行分析，建立螺纹工件表面形貌模型；表面形貌成形过程中刀具与工件的相对运动分析是螺纹工件表面形貌建模的基础；S1: Analyze the surface topography forming process, and establish the surface topography model of the threaded workpiece; the relative motion analysis between the tool and the workpiece during the surface topography forming process is the basis for modeling the surface topography of the threaded workpiece;
图1所示为螺纹工件切削加工表面成形过程中刀具与工件接触分析示意图，为了便于对刀具和工件接触点的分析，图1将第一切削阶段与第二切削阶段切削过程进行合并；图1中，坐标(0，0)为工件坐标系原点；(m n,n n)和(m n+1,n n+1)分别为第n把刀具和第(n+1)把刀具的刀具运动轨迹圆心；点P i为辅助线与工件外圆或不同刀具轨迹的交点；工件表面形貌的形成主要由多刀具断续切削以及刀具-工件相对运动共同作用所导致，因此，需要对刀具运动轨迹以及刀具-工件接触运动进行建模； Fig. 1 is a schematic diagram of the contact analysis between the tool and the workpiece during the surface forming process of threaded workpiece cutting. In order to facilitate the analysis of the contact point between the tool and the workpiece, Fig. 1 combines the cutting process of the first cutting stage and the second cutting stage; in Fig. 1, the coordinates (0, 0) are the origin of the workpiece coordinate system; (m no,n no) and (m n+1,n n+1) are respectively the center of the tool trajectory of the nth tool and the (n+1)th tool; point P iis the intersection point of the auxiliary line and the outer circle of the workpiece or different tool trajectories; the formation of the surface topography of the workpiece is mainly caused by the joint action of multi-tool intermittent cutting and the relative motion of the tool and the workpiece. Therefore, it is necessary to model the tool trajectory and the tool-workpiece contact motion;
第(n+1)把刀具和第n把刀具的刀具运动轨迹中心坐标点方程如下所示：The equations of the (n+1)th tool and the center coordinate point of the tool movement track of the nth tool are as follows:
Figure PCTCN2022142659-appb-000018
Figure PCTCN2022142659-appb-000018
Figure PCTCN2022142659-appb-000019
Figure PCTCN2022142659-appb-000019
式中，e为工件中心到刀具轨迹中心的距离(偏心距)；Δ为刀具切削工件的初始角；θ i为从第n把刀具开始切入工件到第(n+1)把刀具开始切入工件时工件旋转的角度；η为第(n+1)把刀具的刀具运动轨迹中心到刀具插入工件初始点的连线与第(n+1)把刀具的刀具运动轨迹中心到工件中心点连线的夹角，其中夹角η可通过切削过程中三角函数关系确定，满足以下方程： In the formula, e is the distance (eccentricity) from the center of the workpiece to the center of the tool track; Δ is the initial angle at which the tool cuts the workpiece; θi is the angle of rotation of the workpiece when the nth tool starts to cut into the workpiece to the (n+1)th tool starts to cut into the workpiece; η is the angle between the line from the center of the tool’s trajectory of the (n+1)th tool to the initial point where the tool is inserted into the workpiece and the line from the center of the tool’s trajectory of the (n+1)th tool to the center point of the workpiece, wherein the included angle η can be determined through the relationship of trigonometric functions in the cutting process, satisfy the following equation:
Figure PCTCN2022142659-appb-000020
Figure PCTCN2022142659-appb-000020
图1中引入的辅助线l n+1与l n表示如下： The auxiliary lines l n+1 and l n introduced in Figure 1 are expressed as follows:
z i-n n+1＝tan(Δ+θ)·(y i-m n+1)        (4) z i -n n+1 ＝tan(Δ+θ)·(y i -m n+1 ) (4)
z i-n n＝tan(Δ+θ n+θ i)·(y i-m n)        (5) z i -n n ＝tan(Δ+θ n +θ i )·(y i -m n ) (5)
图2中点P1(y 1,z 1)为辅助线l n+1与工件外圆的交点，在坐标系(O,Y,Z)中，该交点可通过方程组(6)求出： The point P1(y 1 , z 1 ) in Figure 2 is the intersection point of the auxiliary line l n+1 and the outer circle of the workpiece. In the coordinate system (O, Y, Z), the intersection point can be obtained by equations (6):
Figure PCTCN2022142659-appb-000021
Figure PCTCN2022142659-appb-000021
图2中点P2(y 2,z 2)为辅助线l n+1与第(n+1)把刀具的刀具运动轨迹的交点，可由方程组(7)进行求解： The point P2(y 2 , z 2 ) in Figure 2 is the intersection point of the auxiliary line l n+1 and the tool movement trajectory of the (n+1)th tool, which can be solved by equations (7):
Figure PCTCN2022142659-appb-000022
Figure PCTCN2022142659-appb-000022
图3中点P3(y 3,z 3)为辅助线l n+1与第n把刀具的刀具运动轨迹的交点，可由方程组(8)进行求出： The point P3(y 3 ,z 3 ) in Figure 3 is the intersection point of the auxiliary line l n+1 and the tool movement track of the nth tool, which can be obtained by the equation group (8):
Figure PCTCN2022142659-appb-000023
Figure PCTCN2022142659-appb-000023
图3中点P4(y 4,z 4)为辅助线l n与工件外圆的交点，可由方程组(9)求出： The point P4(y 4 , z 4 ) in Fig. 3 is the intersection point of the auxiliary line l n and the outer circle of the workpiece, which can be obtained by the equation group (9):
Figure PCTCN2022142659-appb-000024
Figure PCTCN2022142659-appb-000024
图3中点P5(y 5,z 5)为辅助线l n与第n把刀具的刀具运动轨迹的交点，可由方程组(10)求出： The point P5 (y 5 , z 5 ) in Figure 3 is the intersection point of the auxiliary line l n and the tool movement track of the nth tool, which can be obtained by the equation group (10):
Figure PCTCN2022142659-appb-000025
Figure PCTCN2022142659-appb-000025
上述方程组中，θ n为第n把刀具切削过程中刀盘旋转角度，可表示为： In the above equations, θ n is the rotation angle of the cutter head during the cutting process of the nth tool, which can be expressed as:
Figure PCTCN2022142659-appb-000026
Figure PCTCN2022142659-appb-000026
式中，
Figure PCTCN2022142659-appb-000027
为第n把刀具的刀具运动轨迹中心(m n,n n)到点P1的距离，通过以下方程表示： In the formula,
Figure PCTCN2022142659-appb-000027
It is the distance from the center of the tool movement track (m n , n n ) of the nth tool to point P1, expressed by the following equation:
Figure PCTCN2022142659-appb-000028
Figure PCTCN2022142659-appb-000028
S2：进行表面形貌预测建模；S2: Perform surface topography prediction modeling;
在金属切削加工过程中，工件表面形貌受切削加工过程中材料去除几何运动机理引起的表面成形误差、刀具几何廓形引起的齿形误差、工件材料属性引起的材料回弹误差以及刀具磨损和切削振动引起的其它随机误差等影响，但在切削加工过程中，由材料去除过程刀具-工件相对几何成形运动引起的误差是工件表面形貌最主要与最基本的因素，必须先对材料去除过程引起的几何成形误差进行分析，因此，建立的螺纹干式旋铣形成的螺纹工件表面形貌预测模型仅考虑工件材料成形过程中刀具工件相对几何运动的影响；对由刀具振动和工件材料所发生的挤压变形等其它因素造成的影响暂不考虑；In the process of metal cutting, the surface morphology of the workpiece is affected by the surface forming error caused by the geometric motion mechanism of material removal during the cutting process, the tooth shape error caused by the geometric profile of the tool, the material springback error caused by the material properties of the workpiece, and other random errors caused by tool wear and cutting vibration. The surface topography prediction model only considers the influence of the relative geometric motion of the tool and workpiece during the forming process of the workpiece material; the influence caused by other factors such as tool vibration and extrusion deformation of the workpiece material is not considered for the time being;
在螺纹干式旋铣加工过程中，由于工件上的凸起部分(构成螺纹工件表面形貌)是由多刃切削所导致，因此，在螺纹工件表面形貌预测模型建模过程中需要考虑刀具与工件的相对接触运动以及多刀具之间的耦合；图4所示为螺纹工件的螺纹滚道表面形貌成形过程，螺纹滚道表面形貌成形过程主要在第二切削阶段快结束的时候产生，图中虚线圆周表示第(n-1)、n、(n+1)和(n+2)把刀具的刀具运动轨迹，工件毛坯在多把刀具的切削加工过程中最终形成螺纹零件，同时也产生了工件表面形貌；当前刀具与下一把刀具在切削完成后，会在工件表面产生一个凸起的尖点，这些尖点的产生是由不同刀具走刀路径与未变形切屑几何特性所引起的，图4中，点S h1和S h2为不同刀具运动轨迹的交点，其中，点S h1为第n把刀具与第(n+1)把刀具的刀具运动轨迹的交点，点S h2为第(n+1)把刀具与第(n+2)把刀具的刀具运动轨迹的交点，点S h1或S h2到螺纹滚道表面的距离为工件表面残留高度；工件残留高度的值取决于刀具即将退出工件时未变形切屑厚度的大小； In the thread dry milling process, since the convex part on the workpiece (constituting the surface topography of the threaded workpiece) is caused by multi-edge cutting, the relative contact motion between the tool and the workpiece and the coupling between multiple tools need to be considered in the modeling process of the surface topography prediction model of the threaded workpiece; Fig. 4 shows the surface topography forming process of the thread raceway of the threaded workpiece. The tool movement trajectory of the tool, the workpiece blank is finally formed into a threaded part during the cutting process of multiple tools, and the surface morphology of the workpiece is also generated; after the current tool and the next tool are cut, a raised sharp point will be generated on the workpiece surface. The generation of these sharp points is caused by different tool paths and undeformed chip geometry. h1and S h2is the intersection point of different tool motion trajectories, where point S h1is the intersection point of the tool motion trajectory of the nth tool and the (n+1)th tool, point S h2It is the intersection point of the tool motion trajectory of the (n+1)th tool and the (n+2)th tool, point S h1or S h2The distance to the surface of the thread raceway is the residual height of the workpiece surface; the value of the residual height of the workpiece depends on the thickness of the undeformed chip when the tool is about to exit the workpiece;
螺纹工件螺纹滚道表面形貌的分布如图6所示，图6所示为螺纹工件螺纹滚道内圈主视图，该图为螺纹在工件轴向上的投影，螺纹滚道表面轮廓由许多尖点组成，这些凸起的尖点为螺纹工件由于两把相邻刀具的运动轨迹而产生的多余部分；在理想状态下，螺纹工件螺纹滚道表面在工件轴向上的投影为一个圆形；螺纹滚道表面上这些凸起的尖点在圆周上均匀分布；The distribution of the surface morphology of the thread raceway of the threaded workpiece is shown in Figure 6. Figure 6 shows the front view of the inner ring of the threaded workpiece thread raceway. This figure is the projection of the thread on the axial direction of the workpiece. The surface profile of the thread raceway is composed of many sharp points.
根据螺纹干式旋铣加工过程螺纹工件表面轮廓成形机理，并结合切削过程中刀具运动轨迹；第n把刀具与第(n+1)把刀具的刀具运动轨迹交点
Figure PCTCN2022142659-appb-000029
可以通过以下方程组获取： According to the surface contour forming mechanism of the threaded workpiece in the thread dry milling process, combined with the tool movement trajectory during the cutting process; the intersection point of the tool movement trajectory of the nth tool and the (n+1)th tool
Figure PCTCN2022142659-appb-000029
It can be obtained by the following equations:
Figure PCTCN2022142659-appb-000030
Figure PCTCN2022142659-appb-000030
因此，工件残留高度R th可以通过计算点S h1到工件表面在工件径向方向上的距离获取，计算方程如下： Therefore, the workpiece residual height R th can be obtained by calculating the distance from the point Sh1 to the workpiece surface in the radial direction of the workpiece, and the calculation equation is as follows:
Figure PCTCN2022142659-appb-000031
Figure PCTCN2022142659-appb-000031
式中，r为螺纹滚道内径；In the formula, r is the inner diameter of the thread raceway;
螺纹工件的螺纹滚道表面波纹度示意图如图7所示；波纹度W sh为从点S h1到点S h2的距离。点S h2(y sh2,z sh2)是第(n+1)把刀具和第(n+2)把刀具的刀具运动轨迹的交点，可通过以下方程组获得： The schematic diagram of the surface waviness of the thread raceway of the threaded workpiece is shown in Figure 7; the waviness W sh is the distance from point Sh1 to point Sh2 . The point S h2 (y sh2 , z sh2 ) is the intersection point of the tool motion trajectory of the (n+1)th tool and the (n+2)th tool, which can be obtained by the following equations:
Figure PCTCN2022142659-appb-000032
Figure PCTCN2022142659-appb-000032
式中，坐标点(m n+2,n n+2)表示第(n+2)把刀具的刀具运动轨迹的中心；基于切削成形运动机理的分析，(m n+2,n n+2)可表示为： In the formula, the coordinate point (m n+2 ,n n+2 ) represents the center of the tool motion trajectory of the (n+2)th tool; based on the analysis of the cutting and forming motion mechanism, (m n+2 ,n n+2 ) can be expressed as:
Figure PCTCN2022142659-appb-000033
Figure PCTCN2022142659-appb-000033
工件表面波纹度W sh可以表示为： The workpiece surface waviness W sh can be expressed as:
Figure PCTCN2022142659-appb-000034
Figure PCTCN2022142659-appb-000034
式中，ψ为螺纹工件的螺旋角。In the formula, ψ is the helix angle of the threaded workpiece.
实施例Example
试验验证不同工艺参数下螺纹干式旋铣加工过程中工件螺纹滚道表面形貌(包括残留高度和波纹度)预测值与实验值有较好的一致性。The test verifies that the predicted value of the surface topography (including residual height and waviness) of the workpiece thread raceway in the thread dry milling process under different process parameters is in good agreement with the experimental value.
螺纹工件螺纹滚道残留高度的实验值与理论值相比偏大，波纹度的实验值比理论值小。出现这种现象的主要原因是新生成的工件表面在刀具的切削力作用下发生塑性变形。因此，螺纹工件上凸起部分经过干式旋铣加工处理后，在工件径向方向上增加(残留高度增加)而在工件切向方向上减小(波纹度减小)。通过理论值与实验值的对比结果与误差分析结果，能够验证建立的螺纹干式旋铣加工过程中表面形貌模型的有效性与准确性。Compared with the theoretical value, the experimental value of the thread raceway residual height of the threaded workpiece is larger, and the experimental value of the waviness is smaller than the theoretical value. The main reason for this phenomenon is that the newly generated workpiece surface undergoes plastic deformation under the cutting force of the tool. Therefore, after the dry rotary milling process, the convex part of the threaded workpiece increases in the radial direction of the workpiece (increased residual height) and decreases in the tangential direction of the workpiece (reduced waviness). The effectiveness and accuracy of the established surface topography model in the process of thread dry rotary milling can be verified through the comparison results of theoretical values and experimental values and the results of error analysis.
不同工艺参数下螺纹工件表面形貌的实验验证在“HJ092×80”型数控旋铣机床上进行，实验所采用工件材料为AISI52100，硬度范围为63～65hrc；螺纹工件几何参数如表1所示；The experimental verification of the surface morphology of the threaded workpiece under different process parameters was carried out on the "HJ092×80" CNC rotary milling machine. The material of the workpiece used in the experiment was AISI52100, and the hardness range was 63-65hrc. The geometric parameters of the threaded workpiece are shown in Table 1;
表1 工件几何参数Table 1 Workpiece geometric parameters
螺纹工件几何参数Thread workpiece geometric parameters 数值value
轴向节距Axial pitch 10.00mm10.00mm
外圆直径Outer circle diameter 62.05mm62.05mm
齿根圆直径root circle diameter 57.95mm57.95mm
螺旋角Helix angle 2.50°2.50°
螺纹工件长度Thread Workpiece Length 1000mm1000mm
加工后的螺纹工件示意图如图8所示。安装在刀盘上的刀具材料为PCBN；其中，所采用的刀具几何参数如表2所示。The schematic diagram of the threaded workpiece after processing is shown in Figure 8. The tool material installed on the cutter head is PCBN; among them, the geometric parameters of the tool used are shown in Table 2.
表2 刀具几何参数Table 2 Tool geometry parameters
几何参数Geometric parameters 数值value
前角 front angle 0°0°
后角Rear angle 9°9°
倒角Chamfer 25°*1.50mm25°*1.50mm
刀尖圆角半径Corner Radius 3.30mm3.30mm
此外，为了消除刀具磨损对实验值的影响，在每一组切削条件下使用了新刀具。在加工参数为60m/min、100m/min、140m/min、180m/min的切削速度下进行了螺纹干式旋铣加工实验；所选择的刀具数为2、3、4、6把；采用的最大切削深度分别为0.04mm、0.06mm、0.08mm和0.1mm。模型验证实验所采用的切削条件如表3所示；Furthermore, in order to eliminate the influence of tool wear on the experimental values, new tools were used in each set of cutting conditions. Thread dry spin milling experiments were carried out at cutting speeds of 60m/min, 100m/min, 140m/min, and 180m/min; the number of selected tools was 2, 3, 4, and 6; the maximum cutting depths used were 0.04mm, 0.06mm, 0.08mm, and 0.1mm, respectively. The cutting conditions used in the model verification experiments are shown in Table 3;
表3 螺纹干式旋铣实验的切削条件Table 3 Cutting conditions of thread dry milling experiment
NO.No. 切削速度(m/min)Cutting speed (m/min) 刀具个数Number of tools 最大切深depth of cut
11 6060 33 0.060.06
22 100100 33 0.060.06
33 140140 33 0.060.06
44 180180 33 0.060.06
55 140140 22 0.060.06
66 140140 33 0.060.06
77 140140 44 0.060.06
88 140140 66 0.060.06
99 140140 33 0.040.04
1010 140140 33 0.060.06
1111 140140 33 0.080.08
1212 140140 33 0.100.10
其中，切削深度与未变形切屑厚度相同。在螺纹工件断续切削加工过程中，切削深度瞬时变化，通过未变形切屑厚度体现；在工艺参数设置时，一般只需要设置最大切削深度即可。Among them, the depth of cut is the same as the undeformed chip thickness. During the intermittent cutting process of threaded workpieces, the cutting depth changes instantaneously, which is reflected by the thickness of undeformed chips; when setting process parameters, generally only the maximum cutting depth needs to be set.
螺纹工件表面形貌(包括工件表面残留高度和波纹度)采用Rtec公司生产的MFT-5000型多功能摩擦仪进行测量。该测量设备集成了三维光学轮廓仪，可用于测量物体表面轮廓。在测量螺纹工件螺纹滚道形貌时，用白光干涉物镜将螺纹工件螺纹滚道观察区域放大10倍。对螺纹工件沿周向3个等间距位置进行测量，并将3次测量值的平均值作为工件残留高度和波纹度的最终实验结果。通过MFT-5000型多功能摩擦仪测量的结果为图片信息，需要采用Gwyddion分析软件将图片信息转化为数字信息，最终获取残留高度与波纹度的具体测量数值。The surface morphology of the threaded workpiece (including the residual height and waviness on the surface of the workpiece) was measured by the MFT-5000 multifunctional tribometer produced by Rtec Company. The measuring device integrates a 3D optical profiler and can be used to measure the surface profile of an object. When measuring the shape of the thread raceway of the thread workpiece, the observation area of the thread raceway of the thread workpiece is magnified by 10 times with a white light interference objective lens. The threaded workpiece is measured at three equidistant positions along the circumference, and the average value of the three measurements is taken as the final experimental result of the residual height and waviness of the workpiece. The results measured by the MFT-5000 multifunctional tribometer are picture information, which needs to be converted into digital information by Gwyddion analysis software, and finally the specific measurement values of residual height and waviness can be obtained.
螺纹工件沿周向3个等间距位置的残留高度测量值上偏差在0.10以内，下偏差在0.08以内；标准差保持在0.07以内。由残留高度测量值的偏差与标准差和螺纹工件残留高度测量值误差分析可知，残留高度的多次测量值波动较小。The upper and lower deviations of the residual height measurement values of three equidistant positions along the circumference of the threaded workpiece are within 0.10 and 0.08; the standard deviation is kept within 0.07. From the deviation and standard deviation of the residual height measurement value and the error analysis of the residual height measurement value of the threaded workpiece, it can be seen that the fluctuation of the multiple measurement values of the residual height is small.
螺纹工件沿周向3个等间距位置的波纹度测量值上偏差在0.45以内，下偏差在0.37以内；标准差保持在0.32以内。由波纹度测量值的偏差与标准差和螺纹工件波纹度测量值误差分析可知，波纹度的多次测量值波动较小。The upper and lower deviations of the waviness measurement values at three equidistant positions along the circumference of the threaded workpiece are within 0.45 and the downward deviation is within 0.37; the standard deviation is kept within 0.32. From the analysis of the deviation and standard deviation of the waviness measurement value and the error analysis of the waviness measurement value of the threaded workpiece, it can be seen that the fluctuation of the waviness measurement value is small.
通过对3个测量点的残留高度与波纹度分别取平均值，最终获得工件表面形貌实验值。不同工艺参数下螺纹干式旋铣加工过程中工件螺纹滚道表面形貌(包括残留高度和波纹度)预测值与实验值如表4所示。By taking the average value of the residual height and waviness of the three measurement points, the experimental value of the surface topography of the workpiece is finally obtained. The predicted and experimental values of the surface morphology (including residual height and waviness) of the workpiece thread raceway during thread dry milling under different process parameters are shown in Table 4.
表4 工件表面残留高度与波纹度的理论值与实验值Table 4 Theoretical and experimental values of residual height and waviness on workpiece surface
Figure PCTCN2022142659-appb-000035
Figure PCTCN2022142659-appb-000035
螺纹工件螺纹滚道残留高度和波纹度的预测误差可以通过以下公式进行计算。其中，η R与η W分别为残留高度与波纹度的相对误差；R th-experimental与
Figure PCTCN2022142659-appb-000036
分别为残留高度与波纹度的实验值R th-theoretical与
Figure PCTCN2022142659-appb-000037
分别为残留高度与波纹度的理论计算值。 The prediction error of thread raceway residual height and waviness of threaded workpiece can be calculated by the following formula. Wherein, η R and η W are respectively the relative error of residual height and waviness; R th-experimental and
Figure PCTCN2022142659-appb-000036
are the experimental values of residual height and waviness R th-theoretical and
Figure PCTCN2022142659-appb-000037
are the theoretically calculated values of residual height and waviness, respectively.
Figure PCTCN2022142659-appb-000038
Figure PCTCN2022142659-appb-000038
Figure PCTCN2022142659-appb-000039
Figure PCTCN2022142659-appb-000039
通过相对误差计算结果表明(如表4所示)，残留高度和波纹度的理论预测值与实验值有较好的一致性。在12组切削加工参数下，残留高度理论预测值的相对误差最小为0.86％，最大为10.73％；波纹度理论预测值的相对误差最小为1.70％，最大为6.54％。残留高度与波纹度理论预测值的相对误差分别控制在11％与7％以内。理论值与实验值的对比结果与误差分析结果，验证了建立的螺纹干式旋铣加工过程中的螺纹工件表面形貌预测模型的有效性与准确性。由表4可知，螺纹工件螺纹滚道残留高度的实验值与理论值相比偏 大，波纹度的实验值比理论值小。出现这种现象的主要原因是新生成的工件表面在刀具的切削力作用下发生塑性变形。因此，螺纹工件上凸起部分经过干式旋铣加工处理后，在工件径向方向上增加(残留高度增加)而在工件切向方向上减小(波纹度减小)。The results of relative error calculations (as shown in Table 4) show that the theoretical prediction values of the residual height and waviness are in good agreement with the experimental values. Under 12 sets of cutting parameters, the relative error of theoretical prediction value of residual height is minimum 0.86% and maximum is 10.73%; relative error of theoretical prediction value of waviness is minimum 1.70% and maximum is 6.54%. The relative errors of residual height and waviness theoretical prediction are controlled within 11% and 7%, respectively. The comparison results of theoretical values and experimental values and the results of error analysis verify the validity and accuracy of the established model for predicting the surface topography of threaded workpieces in the process of thread dry-rotary milling. It can be seen from Table 4 that the experimental value of the thread raceway residual height 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 phenomenon is that the newly generated workpiece surface undergoes plastic deformation under the cutting force of the tool. Therefore, after the dry rotary milling process, the convex part of the threaded workpiece increases in the radial direction of the workpiece (increased residual height) and decreases in the tangential direction of the workpiece (reduced waviness).
表面形貌影响因素分析：Analysis of influencing factors of surface topography:
螺纹干式旋铣加工过程切削速度对工件表面形貌(包括残留高度与波纹度)影响分析如图9所示。由图9可知，切削速度对工件表面残留高度与波纹度影响不大；随着切削速度的变化，工件表面残留高度与波纹度基本保持不变。由螺纹工件表面形貌预测模型可知，工件表面残留高度是刀具运动轨迹与工件半径相交坐标的函数，工件表面波纹度是刀具运动轨迹与螺纹螺旋角相交坐标的函数。在工件半径与螺纹螺旋角为固定值的情况下，唯一变化的参数是刀具运动轨迹的交点坐标。此时，切削速度和刀具个数对刀具运动轨迹的影响较小，解释了工件表面残留高度与波纹度只是产生了微小的变化。The analysis of the effect of cutting speed on the surface topography (including residual height and waviness) of the thread dry milling process is shown in Fig. 9. It can be seen from Figure 9 that the cutting speed has little effect on the residual height and waviness of the workpiece surface; with the change of cutting speed, the residual height and waviness of the workpiece surface basically remain unchanged. According to the surface topography prediction model of the threaded workpiece, the residual height of the workpiece surface is a function of the intersection coordinates of the tool trajectory and the radius of the workpiece, and the waviness of the workpiece surface is a function of the intersection coordinates of the tool trajectory and the thread helix angle. When the workpiece radius and thread helix angle are fixed values, the only variable parameter is the intersection coordinates of the tool motion trajectory. At this time, the cutting speed and the number of tools have little influence on the tool trajectory, which explains the slight changes in the residual height and waviness of the workpiece surface.
工件表面残留高度与波纹度随着最大切深的变化情况如图10所示。由图10所示，工件表面形貌基本上随着最大切深的增加呈线性增加的趋势。这种现象的主要原因是在较低的最大切削深度下，工件表面由刀具运动轨迹相交引起的连续刻痕彼此非常接近；随着最大切削深度的增加，连续刻痕之间的距离开始增大，在工件表面上产生的刻痕会越来越少。从图10可以看出，当最大切深为0.04mm时，工件表面残留高度和波纹度的值分别为10.26×10-4mm和13.36×10-2mm；而当最大切深为0.1mm时，这些值分别达到了13.17×10-4mm和46.96×10-2mm。这种现象表明随着最大切深的增加，工件表面波纹度的增长率高于工件表面波纹度的增长率。The variation of the workpiece surface residual height and waviness with the maximum depth of cut is shown in Figure 10. As shown in Figure 10, the surface topography of the workpiece basically increases linearly with the increase of the maximum depth of cut. The main reason for this phenomenon is that at a lower maximum depth of cut, the continuous notches on the surface of the workpiece caused by the intersection of tool motion trajectories are very close to each other; as the maximum depth of cut increases, the distance between continuous notches begins to increase, and fewer and fewer notches are produced on the workpiece surface. It can be seen from Figure 10 that when the maximum depth of cut is 0.04mm, the residual height and waviness of the workpiece surface are 10.26×10-4mm and 13.36×10-2mm respectively; and when the maximum depth of cut is 0.1mm, these values reach 13.17×10-4mm and 46.96×10-2mm respectively. This phenomenon shows that with the increase of the maximum depth of cut, the growth rate of the workpiece surface waviness is higher than that of the workpiece surface waviness.
螺纹干式旋铣加工过程刀具个数对工件表面残留高度与波纹度的影响如图11所示。刀具个数对工件表面形貌的影响规律与图10中切削速度对工件表面形貌的影响规律类似。随着刀具个数的改变，工件表面残留高度与波纹度基本不发生变化。工件表面残留高度与波纹度主要是刀具运动轨迹的函数，刀具个数发生变化对刀具运动轨迹影响较小。因此，工件表面残留高度与波纹度只产生微小的变化。The effect of the number of tools on the residual height and waviness of the workpiece surface during thread dry milling is shown in Figure 11. The influence of the number of cutting tools on the surface morphology of the workpiece is similar to that of the cutting speed on the surface morphology of the workpiece in Figure 10. With the change of the number of tools, the residual height and waviness of the workpiece surface basically do not change. The residual height and waviness of the workpiece surface are mainly functions of the tool trajectory, and the change in the number of tools has little effect on the tool trajectory. Therefore, the remaining height and waviness of the workpiece surface only slightly change.
由上述分析可知，在螺纹干式旋铣加工过程中，切削速度、最大切深与刀具个数对工件表面形貌与工件表面残余应力的影响程度是不同的。通过主 效应分析方式对工件表面残留高度与波纹度进行灵敏度分析，探寻影响工件表面形貌的敏感因素。From the above analysis, it can be seen that in the process of dry thread rotary milling, the cutting speed, maximum depth of cut and number of tools have different influences on the surface morphology and residual stress of the workpiece. Through the main effect analysis method, the sensitivity analysis of the residual height and waviness on the surface of the workpiece is carried out, and the sensitive factors affecting the surface morphology of the workpiece are explored.
由工件表面残留高度主效应影响分析可以得出，最大切深是影响工件表面残留高度的敏感参数；切削速度对工件表面残留高度的影响不显著；当刀具个数较少时，刀具个数对工件表面残留高度的影响较为显著，随着刀具个数的增加，显著程度降低。工艺参数对工件表面残留高度影响程度大小排序依次为：最大切深最大，刀具个数较小，切削速度最小。From the main effect analysis of workpiece surface residual height, it can be concluded that the maximum depth of cut is a sensitive parameter affecting the workpiece surface residual height; cutting speed has no significant effect on the workpiece surface residual height; when the number of tools is small, the impact of the number of tools on the workpiece surface residual height is more significant, and the degree of significance decreases with the increase of the number of tools. The ranking order of the degree of influence of process parameters on workpiece surface residual height is as follows: the maximum depth of cut is the largest, the number of tools is small, and the cutting speed is the smallest.
工件表面波纹度主效应影响分析与工件表面残留高度主效应影响分析类似，最大切深为影响工件表面波纹度的敏感参数。此外，刀具个数与切削深度对工件表面波纹度的影响不显著。工艺参数对工件表面波纹度影响程度大小排序依次为：最大切深最大，刀具个数与切削速度较小。综上，最大切削深度为表面形貌的主要影响因素。The main effect analysis of workpiece surface waviness is similar to the main effect analysis of workpiece surface residual height, and the maximum depth of cut is a sensitive parameter that affects workpiece surface waviness. In addition, the number of tools and the depth of cut have no significant effect on the surface waviness of the workpiece. The order of influence of process parameters on workpiece surface waviness is as follows: the maximum cutting depth is the largest, and the number of tools and cutting speed are small. In summary, the maximum depth of cut is the main influencing factor of surface topography.
本说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同相似部分互相参见即可。对于实施例公开的装置而言，由于其与实施例公开的方法相对应，所以描述的比较简单，相关之处参见方法部分说明即可。Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other. As for the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and for relevant details, please refer to the description of the method part.
对所公开的实施例的上述说明，使本领域专业技术人员能够实现或使用本发明。对这些实施例的多种修改对本领域的专业技术人员来说将是显而易见的，本文中所定义的一般原理可以在不脱离本发明的精神或范围的情况下，在其它实施例中实现。因此，本发明将不会被限制于本文所示的这些实施例，而是要符合与本文所公开的原理和新颖特点相一致的最宽的范围。The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention will not 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. 一种旋风铣削中螺纹工件表面形貌的预测方法，其特征在于，具体包括如下步骤：A method for predicting the surface topography of a threaded workpiece in whirl milling, characterized in that it specifically includes the following steps:
    步骤1：获取螺纹工件切削加工表面成形过程中若干刀具的切削过程，根据刀具和工件的接触点，并增加辅助线，构建刀具运动轨迹模型以及刀具-工件接触运动轨迹模型；Step 1: Obtain the cutting process of several tools in the surface forming process of threaded workpiece cutting, according to the contact point between the tool and the workpiece, and add auxiliary lines, construct the tool trajectory model and the tool-workpiece contact trajectory model;
    步骤2：根据刀具运动轨迹模型、刀具-工件接触运动轨迹模型和刀具之间的耦合建立螺纹工件表面形貌预测模型；Step 2: According to the tool trajectory model, the tool-workpiece contact trajectory model and the coupling between the tools, a threaded workpiece surface topography prediction model is established;
    步骤3：获取相关切削参数，根据螺纹工件表面形貌预测模型获得工件表面残留高度和波纹度，实现旋风铣削中螺纹工件表面形貌预测。Step 3: Obtain relevant cutting parameters, obtain the residual height and waviness of the surface of the workpiece according to the prediction model of the surface topography of the threaded workpiece, and realize the prediction of the surface topography of the threaded workpiece in whirl milling.
  2. 根据权利要求1所述的一种旋风铣削中螺纹工件表面形貌的预测方法，其特征在于，所述步骤1的具体实现过程为：A method for predicting surface topography of threaded workpieces in whirl milling according to claim 1, characterized in that the specific implementation process of said step 1 is:
    步骤11：构建所述刀具运动轨迹模型过程为：令工件位于坐标系(O,Y,Z)原点，中心坐标为(0，0)；第n把刀具和第(n+1)把刀具的刀具运动轨迹中心分别为(m n,n n)和(m n+1,n n+1)；辅助线与工件外圆或不同刀具运动轨迹的交点为P i；则第(n+1)把刀具和第n把刀具的刀具运动轨迹中心坐标点方程表示为： Step 11: The process of constructing the tool trajectory model is as follows: let the workpiece be located at the origin of the coordinate system (O, Y, Z), and the center coordinates are (0, 0); the tool trajectory centers of the nth tool and the (n+1)th tool are respectively (m n , n n ) and (m n+1 , n n+1 ); the intersection point of the auxiliary line with the outer circle of the workpiece or different tool trajectory is Pi ; The equation is expressed as:
    Figure PCTCN2022142659-appb-100001
    Figure PCTCN2022142659-appb-100001
    式中，e为工件中心到刀具运动轨迹中心的距离；Δ为刀具切削工件的初始角；θ i为从第n把刀具开始切入工件到第(n+1)把刀具开始切入工件时工件旋转的角度；η为第(n+1)把刀具的刀具运动轨迹中心到刀具插入工件初始点的连线与第(n+1)把刀具的刀具运动轨迹中心到工件中心点连线的夹角；其中夹角η通过切削过程中三角函数关系确定，表示为： In the formula, e is the distance from the center of the workpiece to the center of the tool trajectory; Δ is the initial angle of the tool cutting the workpiece; θi is the angle of rotation of the workpiece from the nth tool cutting into the workpiece to the (n+1)th tool starting to cut into the workpiece; η is the included angle between the line connecting the (n+1)th tool’s tool trajectory center to the tool’s initial point inserted into the workpiece and the (n+1)th tool’s tool trajectory center to the workpiece center point; wherein the included angle η is determined by the trigonometric function relationship in the cutting process, expressed as:
    Figure PCTCN2022142659-appb-100002
    Figure PCTCN2022142659-appb-100002
    式中，R为刀具运动轨迹半径；In the formula, R is the radius of the tool trajectory;
    步骤12：构建所述刀具-工件接触运动轨迹模型的过程为：引入辅助线用于描述第n把刀具和第(n+1)把刀具的刀具运动轨迹，引入的辅助线l n+1与l n表示如下： Step 12: The process of constructing the tool-workpiece contact trajectory model is: introducing auxiliary lines to describe the tool trajectory of the nth tool and the (n+1)th tool, and the introduced auxiliary lines l n+1 and l n are expressed as follows:
    z i-n n+1＝tan(Δ+θ)·(y i-m n+1)  (4) z i -n n+1 ＝tan(Δ+θ)·(y i -m n+1 ) (4)
    z i-n n＝tan(Δ+θ n+θ i)·(y i-m n)  (5)； z i -n n =tan(Δ+θ n +θ i )·(y i -m n ) (5);
    式中，(z i，y i)为辅助线上的点的坐标；θ n为第n把刀具切削过程中刀盘旋转角度；θ i为第n把刀具开始切入工件到第(n+1)把刀具开始切入工件时工件旋转的角度； In the formula, (z i , y i ) are the coordinates of the points on the auxiliary line; θ n is the rotation angle of the cutterhead during the cutting process of the nth tool; θi is the rotation angle of the workpiece when the nth tool starts cutting into the workpiece and the (n+1)th tool starts cutting into the workpiece;
    辅助线l n+1与工件外圆的交点为P 1，辅助线l n+1与第(n+1)把刀具的运动轨迹交点为P 2，辅助线l n+1与第n把刀具的刀具运动轨迹交点为P 3，辅助线l n与工件外圆的交点为P 4，辅助线l n与第n把刀具的刀具运动轨迹交点为P 5； The intersection point of the auxiliary line l n+1 and the outer circle of the workpiece is P 1 , the intersection point of the auxiliary line l n+1 and the movement track of the (n+1)th tool is P 2 , the intersection point of the auxiliary line l n+1 and the tool movement track of the nth tool is P3 , the intersection point of the auxiliary line l n and the outer circle of the workpiece is P4 , the intersection point of the auxiliary line l n and the tool movement track of the nth tool is P5 ;
    P 1在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 1 in the coordinate system (O, Y, Z) are expressed as:
    Figure PCTCN2022142659-appb-100003
    Figure PCTCN2022142659-appb-100003
    P 2在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 2 in the coordinate system (O, Y, Z) are expressed as:
    Figure PCTCN2022142659-appb-100004
    Figure PCTCN2022142659-appb-100004
    P 3在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 3 in the coordinate system (O, Y, Z) are expressed as:
    Figure PCTCN2022142659-appb-100005
    Figure PCTCN2022142659-appb-100005
    P 4在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 4 in the coordinate system (O, Y, Z) are expressed as:
    Figure PCTCN2022142659-appb-100006
    Figure PCTCN2022142659-appb-100006
    P 5在坐标系(O,Y,Z)中坐标表示为： The coordinates of P 5 in the coordinate system (O, Y, Z) are expressed as:
    Figure PCTCN2022142659-appb-100007
    Figure PCTCN2022142659-appb-100007
    式中，θ n为第n把刀具切削过程中刀盘旋转角度，表示为： In the formula, θ n is the rotation angle of the cutterhead during the cutting process of the nth tool, expressed as:
    Figure PCTCN2022142659-appb-100008
    Figure PCTCN2022142659-appb-100008
    式中，
    Figure PCTCN2022142659-appb-100009
    为第n把刀具的刀具运动轨迹中心(m n,n n)到点P 1的距离，表示为：     In the formula,
    Figure PCTCN2022142659-appb-100009
    is the distance from the center (m n , n n ) of the tool movement track of the nth tool to point P 1 , expressed as:
    Figure PCTCN2022142659-appb-100010
    Figure PCTCN2022142659-appb-100010
  3. 根据权利要求1所述的一种旋风铣削中螺纹工件表面形貌的预测方法，其特征在于，所述螺纹工件表面形貌预测模型由螺纹工件螺纹滚道的表面残留高度预测模型和表面波纹度预测模型构成，所述步骤2的具体实现过程为：A method for predicting the surface topography of threaded workpieces in whirlwind milling according to claim 1, wherein the surface topography prediction model of the threaded workpieces is composed of a surface residual height prediction model and a surface waviness prediction model of the thread raceway of the threaded workpiece, and the specific implementation process of the step 2 is:
    步骤21：根据螺纹干式旋铣加工过程螺纹工件表面轮廓成形机理，并结合切削过程中刀具运动轨迹模型，计算当前刀具与下一把刀具的刀具运动轨迹的交点，计算公式如下：Step 21: According to the surface contour forming mechanism of the threaded workpiece in the thread dry milling process, and combined with the tool trajectory model during the cutting process, calculate the intersection point of the tool trajectory of the current tool and the next tool. The calculation formula is as follows:
    Figure PCTCN2022142659-appb-100011
    Figure PCTCN2022142659-appb-100011
    其中，第n把刀具与第(n+1)把刀具的刀具运动轨迹的交点为
    Figure PCTCN2022142659-appb-100012
    (m n,n n)和(m n+1,n n+1)分别为第n把刀具和第(n+1)把刀具的刀具运动轨迹中心；R为刀具运动轨迹半径；     Among them, the intersection point of the tool trajectory of the nth tool and the (n+1)th tool is
    Figure PCTCN2022142659-appb-100012
    (m n ,n n ) and (m n+1 ,n n+1 ) are the center of the tool trajectory of the nth tool and the (n+1)th tool respectively; R is the radius of the tool trajectory;
    步骤22：通过计算当前刀具与下一把刀具的刀具运动轨迹的交点到螺纹工件的螺纹滚道表面的距离获得工件表面残留高度，则表面残留高度预测模型表达式为：Step 22: Obtain the surface residual height of the workpiece by calculating the distance from the intersection point of the tool trajectory of the current tool and the next tool to the thread raceway surface of the threaded workpiece, then the surface residual height prediction model expression is:
    Figure PCTCN2022142659-appb-100013
    Figure PCTCN2022142659-appb-100013
    其中，R th为工件表面残留高度；r为螺纹滚道内径； Among them, R th is the residual height of the workpiece surface; r is the inner diameter of the thread raceway;
    步骤23：基于切削成形运动机理计算刀具运动轨迹中心，利用刀具运动轨迹中心并根据刀具运动轨迹模型计算两把刀具的刀具运动轨迹交点，根据相邻工作的三把刀具产生的两个刀具运动轨迹交点的距离计算螺纹工件的螺纹滚道表面的波纹度，表面波纹度预测模型表示为：Step 23: Calculate the tool trajectory center based on the cutting forming motion mechanism, use the tool trajectory center and calculate the intersection point of the tool trajectory of two tools according to the tool trajectory model, and calculate the waviness of the thread raceway surface of the threaded workpiece according to the distance between the intersection points of the two tool trajectory generated by the three adjacent tools. The surface waviness prediction model is expressed as:
    Figure PCTCN2022142659-appb-100014
    Figure PCTCN2022142659-appb-100014
    Figure PCTCN2022142659-appb-100015
    Figure PCTCN2022142659-appb-100015
    Figure PCTCN2022142659-appb-100016
    Figure PCTCN2022142659-appb-100016
    其中，S h2(y sh2,z sh2)是第(n+1)把刀具和第(n+2)把刀具的刀具运动轨迹的交点；(m n+2,n n+2)为第(n+2)把刀具的刀具运动轨迹的中心；W sh为波纹度；ψ为螺纹工件的螺旋角；e为工件中心到刀具运动轨迹中心的距离；Δ为刀具切削工件的初始角；θ i为从第n把刀具开始切入工件到第(n+1)把刀具开始切入工件时工件旋转的角度。 Among them, Sh2 (y sh2 , z sh2 ) is the intersection point of the tool trajectory of the (n+1)th tool and the (n+2)th tool; (m n+2 , n n+2 ) is the center of the tool trajectory of the (n+2)th tool; W sh is the waviness; ψ is the helix angle of the threaded workpiece; e is the distance from the center of the workpiece to the center of the tool trajectory; The rotation angle of the workpiece when the (n+1)th tool starts cutting into the workpiece.
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CN108262648A (en) * 2018-01-30 2018-07-10 上海理工大学 Axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method
CN113704928A (en) * 2021-09-15 2021-11-26 上海交通大学 Inclined milling surface appearance creation method based on processing physical process
CN114444297A (en) * 2022-01-21 2022-05-06 安徽理工大学 Method for predicting surface topography of threaded workpiece in cyclone milling

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