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CN113967766A - A method for predicting the grinding force in the grinding process of the inner thread of the planetary roller screw - Google Patents

A method for predicting the grinding force in the grinding process of the inner thread of the planetary roller screw Download PDF

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CN113967766A
CN113967766A CN202111204160.4A CN202111204160A CN113967766A CN 113967766 A CN113967766 A CN 113967766A CN 202111204160 A CN202111204160 A CN 202111204160A CN 113967766 A CN113967766 A CN 113967766A
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grinding
force
internal thread
grinding force
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CN113967766B (en
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佟瑞庭
杜晶涛
刘更
吴宇
王云峰
马尚君
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Northwestern Polytechnical University
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    • 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
    • B23G1/36—Thread cutting; Automatic machines specially designed therefor by grinding

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Abstract

本发明属于行星滚柱丝杠加工制造领域，具体涉及一种内螺纹磨削过程磨削力计算方法，在该方法中先将内螺纹磨削简化为二维平面磨削，得到二维平面磨削过程的磨削力公式；通过对比内螺纹磨削和平面磨削过程的特点，引入磨削修正系数，将二维平面磨削的磨削力公式修正为内螺纹磨削的三维磨削力公式；在Abaqus中建立二维平面磨削模型，进行正交仿真计算，获得磨削力数据，进而求出磨削力经验公式中的修正系数，得到内螺纹磨削过程的磨削力计算公式。这种方法将内螺纹磨削过程简化为二维平面磨削过程，通过修正二维平面磨削力公式得到内螺纹的磨削力计算公式，实现内螺纹磨削加工过程中磨削力的预测，对磨削力的稳定控制和提升磨削质量有重要意义。

Figure 202111204160

The invention belongs to the field of machining and manufacturing of planetary roller screws, and in particular relates to a method for calculating a grinding force in an internal thread grinding process. The grinding force formula of the grinding process; by comparing the characteristics of the internal thread grinding and the surface grinding process, the grinding correction coefficient is introduced, and the grinding force formula of the two-dimensional surface grinding is corrected to the three-dimensional grinding force of the internal thread grinding. formula; establish a two-dimensional surface grinding model in Abaqus, carry out orthogonal simulation calculation, obtain grinding force data, and then obtain the correction coefficient in the grinding force empirical formula, and obtain the grinding force calculation formula of the internal thread grinding process . This method simplifies the internal thread grinding process into a two-dimensional plane grinding process, and obtains the grinding force calculation formula of the internal thread by modifying the two-dimensional plane grinding force formula, so as to realize the prediction of the grinding force during the internal thread grinding process. , which is of great significance to the stable control of grinding force and the improvement of grinding quality.

Figure 202111204160

Description

Grinding force prediction method for planetary roller screw internal thread grinding process
Technical Field
The invention relates to the field of grinding machining of internal threads of planetary roller screws, in particular to a method for calculating grinding force in the process of grinding the internal threads.
Background
The internal thread grinding is different from the traditional internal grinding, and grinding factors such as the rotating speed of a grinding wheel, the feeding speed, the rotating speed of a workpiece, the grinding depth and the like have important influences on material removal, grinding temperature, grinding force of a grinding area, thermal deformation and elastoplastic deformation during grinding, further influence the processing precision and surface quality of parts, and influence the yield and production cost of products. Therefore, a theoretical model of the internal thread high-speed grinding process is established, the influence rule of grinding elements on material removal and grinding force in the grinding process is mastered, the change rule and the prediction formula of the grinding force are obtained, the processing precision and the processing quality of the internal thread of the planetary roller screw are improved, and the method has important significance for stably controlling the grinding force and improving the grinding quality.
The grinding of the internal thread is a complex grinding process, a grinding wheel and a workpiece are not simple planes or cylinders, the internal thread of the planetary roller screw needs to be meshed with the roller to transmit power, and the machining precision requirement is high. Patent CN 108897955 a proposes a high-speed internal thread grinding force calculation method considering a thread lead angle and an abrasive grain overlap coefficient, which is based on the relative motion between a grinding wheel and a workpiece, calculates the contact length between the grinding wheel and the abrasive grain, divides the grinding force into a cutting deformation force and a friction force, and obtains a coefficient in a grinding force model by reverse thrust through experiments. The internal thread shape of the planetary roller screw is complex, and the modeling of the internal thread grinding force with different cutting feed times is still difficult at present, which is the reason and the meaning of the invention.
Disclosure of Invention
The invention aims to provide a three-dimensional grinding force calculation method for a planetary roller screw internal thread grinding process, which can realize accurate calculation and prediction of grinding force in a grinding area, can be applied to the prediction of the grinding force of different grinding parameters and feed times, and has important significance for grinding mechanism research, stable control of the grinding force and improvement of grinding quality.
The practical problems solved by the invention are as follows: according to the grinding force prediction formula, grinding force numerical values under different grinding parameters (grinding wheel rotating speed, workpiece feeding speed and grinding depth) and feeding times can be obtained through calculation, the influence of factors such as vibration and grinding heat on the internal thread machining quality caused by the change of the grinding force in the internal thread grinding process of the planetary roller screw is reduced by controlling the change of the grinding force, the internal thread grinding precision of the planetary roller screw is improved, and the grinding force prediction formula has guiding significance for the control of the grinding force in the grinding process and the analysis of the internal thread grinding mechanism.
Starting from the research and control of the thread grinding process, a grinding process analysis model which accords with the high-speed grinding characteristics of the internal thread is established, the internal thread grinding process is theoretically analyzed based on a generalized finite element model analysis method, the internal thread grinding process is simplified into a plane grinding process, and a plane grinding process grinding force formula of primary feed is obtained. Based on a single abrasive grain grinding force model, according to the characteristics of the internal thread grinding process, considering the removal volume change of the internal thread grinding process converted from the two-dimensional plane grinding process and the difference between the ith removal volume and the first removal volume, and converting the grinding force of the two-dimensional plane grinding process into the grinding force of the internal thread grinding process by introducing a correction coefficient to obtain the grinding force prediction formula of the ith feed.
The technical scheme of the invention is as follows: a grinding force prediction method in a planetary roller screw internal thread grinding process comprises the following steps:
step 1: the grinding process is simplified: the grinding process of the internal thread of the planetary roller screw is simplified into a two-dimensional plane grinding process;
step 2: correcting the grinding force: the conversion from two-dimensional plane grinding force to three-dimensional internal thread grinding force is realized by introducing an internal thread grinding correction coefficient, and a three-dimensional grinding force formula in the internal thread grinding process is obtained;
and step 3: calculating the grinding correction coefficient of the internal thread, obtaining grinding force data through orthogonal finite element simulation calculation, calculating the correction coefficient of the internal thread grinding by using a control variable method, obtaining a grinding force prediction formula in the internal thread grinding process, and finally predicting the grinding force in the internal thread grinding process.
The further technical scheme of the invention is as follows: the specific content in the step 2 is as follows: the three-dimensional grinding force formula is as follows:
Figure BDA0003306234940000031
Figure BDA0003306234940000032
Fa,i＝Fn,itanλ (3)
in the formula, vsIs the rotational speed v of the grinding wheelwIs the feed speed, apIs the grinding depth; fiTotal grinding force for ith feed, Fn,i、Ft,iAnd Fa,iNormal grinding force, tangential grinding force and axial grinding force of the ith feed are respectively; k is a radical ofnAnd ktNormal and radial grinding force coefficients, respectively, of positive value, b1、b2、b3、c1、c2、c3Is an index related to the rotation speed, feed speed and grinding depth of the grinding wheel, the numerical values are positive numbers, lambda is a lead angle, K1,iThe correlation coefficient of the ratio of the ith feed removal volume to the 1 st feed removal volume, K2,iRemoving a correlation coefficient of a volume ratio of the ith feed internal thread grinding to the plane grinding;
the further technical scheme of the invention is as follows: the grinding force prediction formula in the step 3 is as follows:
Figure BDA0003306234940000033
Figure BDA0003306234940000034
Figure BDA0003306234940000035
Figure BDA0003306234940000036
wherein v issIs the rotational speed of the grinding wheel, vwFor the feed rate, apTo grind depth, knAnd ktIs a coefficient of grinding force, which is constant, K1,iThe correlation coefficient of the ratio of the ith feed removal volume to the 1 st feed removal volume, K2,iAnd lambda is a thread lead angle, and is a correlation coefficient of the volume ratio of the ith feed internal thread grinding to the planar grinding removal.
The further technical scheme of the invention is as follows: the solving process of the grinding force prediction formula is as follows:
according to the geometrical relationship of internal thread grinding processing, the following results are obtained:
Figure BDA0003306234940000041
Figure BDA0003306234940000042
Figure BDA0003306234940000043
wherein R is the radius of the grinding wheel is a known quantity, R is the inner diameter of the workpiece to be processed is a known quantity, and thetaRFor the angle theta corresponding to the arc length of the grinding wheel cutting into the workpiecerFor the arc length of work to be cut intoD is the length of the line segment corresponding to the arc length, apA known amount for the total grinding depth; according to the formula, the angle theta corresponding to the arc length of the grinding wheel cut into the workpiece is obtainedRAngle theta corresponding to arc length of cut into workpiecerThe length d of the line segment corresponding to the arc length;
from the geometric relationship, the area S can be obtainedRAnd SrIn which S isRAnd SrThe areas respectively comprise the arc length of the grinding wheel cut-in workpiece and the cut-in arc length of the workpiece and a line segment d, and the difference value of the two areas is the i-th axial section removal area delta Si(i＝1， 2，3……)。
Figure BDA0003306234940000044
Figure BDA0003306234940000045
Figure BDA0003306234940000046
Then the ith removal volume:
Figure BDA0003306234940000047
the 1 st removal volume was:
Figure BDA0003306234940000051
obtaining:
Figure BDA0003306234940000052
flat grinding for the ith removal of volume:
Vi＝ap×d×iap (13)
obtaining:
Figure BDA0003306234940000053
and finally obtaining a planetary roller screw internal thread grinding force prediction formula.
Effects of the invention
The invention has the technical effects that: 1) because the internal thread machining precision requirement of the planetary roller screw nut is high, the grinding process can be completed only by feeding for many times, and the defect that the conventional internal thread grinding force formula cannot calculate the grinding force of feeding for many times is overcome, the grinding force prediction formula obtained by the invention can accurately calculate the grinding force of the internal thread grinding process of feeding for many times, and a specific grinding force value can be calculated only by setting specific grinding wheel and workpiece size parameters, the grinding wheel rotating speed, the feeding speed, the grinding depth and the feeding times; 2) grinding parameters such as the influence rule of the grinding wheel rotating speed, the feeding speed and the grinding depth on the grinding force can be explored according to the grinding force prediction formula obtained by the invention, and an internal thread grinding mechanism is further explored.
Drawings
FIG. 1 is a flow chart of a method provided by an embodiment of the present invention;
FIG. 2 is an exploded view of the grinding force of the internal thread grinding process;
FIG. 3 is a schematic representation of axial force versus radial force;
FIG. 4 is a tangential schematic view of the internal thread grinding process;
FIG. 5 is an axial schematic view of the internal thread grinding process;
fig. 6 is a two-dimensional grinding model of a multi-abrasive grain grinding wheel built in Abaqus.
Detailed Description
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations and positional relationships based on those shown in the drawings, and are used only for convenience of description and simplicity of description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be considered as limiting the present invention.
Referring to fig. 1 to 6, the grinding force calculating method for the internal thread grinding process of the present invention comprises the steps of:
s1, simplifying the internal thread grinding process into a two-dimensional plane grinding process. FIG. 2 is a schematic diagram showing the decomposition of the grinding force during the grinding of internal threads, which can be decomposed into three components perpendicular to each other, i.e., a normal grinding force F along the radial direction of the grinding wheelnTangential grinding force F in the tangential direction of the grinding wheeltAnd axial grinding force F in the direction of the axis of rotation of the grinding wheela. The grinding process of the internal thread is complex, and the grinding process of the internal thread of the planetary roller screw can be simplified into a two-dimensional plane grinding process to obtain a two-dimensional plane grinding force formula in consideration of the fact that in the actual grinding process, the lead angle of the planetary roller screw is small and the axial force in the grinding process is small. The grinding force of two-dimensional plane grinding is composed of two parts, normal grinding force FnAnd tangential grinding force Ft，
Figure BDA0003306234940000061
Wherein v issIs the rotational speed of the grinding wheel, vwFor the feed rate, apTo grind depth, knAnd ktTwo grinding force coefficients, which are constants.
FIG. 3 is a schematic diagram of the relationship between axial force and normal force during the internal thread grinding process, which can be obtained from the geometric relationship between axial force and normal force:
tanλ＝L/S＝L/πdw (2)
wherein, lambda is a lead angle of the screw thread, L is a lead of the nut, S is an inner circumference of the nut, and dwIs the inner diameter of the nut.
The axial force is:
Fa＝Fntanλ (3)
the actual grinding force in the grinding process is
Figure BDA0003306234940000071
And S2, converting the grinding force in the two-dimensional plane grinding process into the grinding force in the internal thread grinding process by introducing a correction coefficient. Because only the removal area is calculated in the two-dimensional plane grinding process, the removal volume in the real grinding process cannot be calculated, the influence of the removal volume on the grinding force and the change of the removal volume caused by different feed times are ignored, and only the rotating speed v of the grinding wheel is consideredsA feeding speed vwAnd grinding depth apInfluence on grinding force. According to a plane grinding force formula, comparing the characteristics of the internal thread grinding process and the two-dimensional plane grinding process, considering the removal volume change converted from the two-dimensional plane grinding process to the internal thread grinding process, and introducing a grinding depth coefficient K by removing the volume change at different feed times of the internal thread grinding1,iAnd K2,iThe grinding force formula is corrected, under the condition of the same grinding wheel rotating speed, feeding speed and grinding depth, the grinding force is different due to different removal volumes of different cutting times, the grinding force formula of two-dimensional plane grinding is converted into the grinding force formula of three-dimensional internal thread grinding, and the three-dimensional grinding force formula of the internal thread grinding process is obtained,
Figure BDA0003306234940000072
Figure BDA0003306234940000073
Fa,i＝Fn,itanλ (7)
in the formula, vsIs the rotational speed v of the grinding wheelwThe feed rate is,apIs the grinding depth; fiTotal grinding force for ith feed, Fn,i、Ft,iAnd Fa,iNormal grinding force, tangential grinding force and axial grinding force of the ith feed are respectively; k is a radical ofnAnd ktNormal and radial grinding force coefficients, respectively, of positive value, b1、b2、b3、c1、c2、c3The numerical values of the indexes related to the rotation speed, the feeding speed and the grinding depth of the grinding wheel are positive numbers, and lambda is a lead angle.
In order to ensure the grinding precision of the internal thread of the planetary roller screw, the internal thread grinding needs to be finished by feeding for many times, and the same grinding depth is ensured by feeding every time. Finite element simulation studies the grinding process of the first feed. K1,iThe correlation coefficient of the ratio of the ith feed removal volume to the 1 st feed removal volume, K2,iAnd removing the correlation coefficient of the volume ratio of the internal thread grinding and the plane grinding for the ith feed.
S3, establishing a finite element model of the plane grinding process, obtaining data of normal grinding force and tangential grinding force of the grinding process through orthogonal finite element simulation calculation, and solving a coefficient k by using a control variable methodn、kt、K1,i、K2,i、b1、b2、 b3、c1、c2、c3To obtain the normal grinding force Fn,iAnd tangential grinding force Ft,iPrediction formula given corresponding grinding wheel speed vsA feeding speed vwGrinding depth apThe normal grinding force F can be obtained by the feed times in,iAnd tangential grinding force Ft,iIs calculated to calculate the axial grinding force Fa,iAnd total grinding force Fi。
(1) Further, the coefficient k in the plane grinding force formula is solved in the step S3n、ktAnd index b1、b2、 b3、c1、c2、c3The specific method comprises the following steps:
①b1、c1and kn、ktIs calculated byThe method comprises the following steps:
due to b1And c1Is related to the rotational speed v of the grinding wheelsRelated index, thus maintaining the feed speed vwAnd grinding depth apFor constant value, by taking different values of the rotational speed v of the grinding wheelsTo obtain the values of the normal grinding force and the tangential grinding force of the 1 st feed, in this case, it is considered that
Figure BDA0003306234940000081
Wherein d issIs the diameter of the grinding wheel, vsIs the rotational speed of a grinding wheel, k'1And k ″)1Substituting the data into a formula (8) for curve fitting to obtain a fitted curve of the radial grinding force and the tangential grinding force along with the change of the rotating speed of the grinding wheel, and obtaining b1And c1The numerical value of (c). During this calculation, multiple sets of k 'are available'1And k ″)1The calculated values of (1) are respectively taken as a plurality of groups of k'1And k ″)1The average of the values is kn、ktThe value of (c).
②b2And c2The calculating method of (2):
due to b2And c2Is related to the feed speed vwRelative index, thus maintaining the grinding wheel speed vsAnd grinding depth apFor constant value, by taking different values of the feed speed vwTo obtain the values of the normal grinding force and the tangential grinding force of the 1 st feed, in this case, it is considered that
Figure BDA0003306234940000091
Wherein v iswIs feed speed, k'2And k ″)2Substituting the data into formula (9) for fitting curve to obtain fitted curve of radial grinding force and tangential grinding force varying with the rotation speed of the grinding wheel, and calculating b2And c2The numerical value of (c).
③b3And c3The calculating method of (2):
due to b3And c3Is related to the grinding depth apRelative index, thus maintaining the grinding wheel speed vsAnd a feed speed vwFor constant value, by taking different values of grinding depth apTo obtain the values of the normal grinding force and the tangential grinding force of the 1 st feed, in this case, it is considered that
Figure BDA0003306234940000092
Wherein a ispIs grinding depth, k'3And k ″)3Substituting the data into a formula (10) for curve fitting to obtain a fitted curve of the radial grinding force and the tangential grinding force along with the change of the rotating speed of the grinding wheel, and solving b3And c3The value of (c).
(2) Solving the grinding depth coefficient in the plane grinding force formula in the step S3
Figure BDA0003306234940000094
And
Figure BDA0003306234940000093
the solution process of (2) is as follows:
FIG. 4 is a schematic tangential view of the grinding process of the internal thread, where R is the radius of the grinding wheel, R is the inner diameter of the workpiece to be machined, and θ isRFor the angle theta corresponding to the arc length of the grinding wheel cutting into the workpiecerThe angle corresponding to the arc length of the cut workpiece, d is the length of the line segment corresponding to the arc length, apIs the grinding depth.
According to the geometrical relationship, the following are obtained:
Figure BDA0003306234940000101
Figure BDA0003306234940000102
Figure BDA0003306234940000103
the radius R of the grinding wheel, the radius R of the workpiece to be processed and the grinding depth apAll the known quantities are known, the simultaneous equations (11) - (13) can solve the angle theta corresponding to the arc length of the grinding wheel cutting into the workpieceRAngle theta corresponding to arc length of cut into workpiecerAnd the length d of the line segment corresponding to the arc length.
Further, the area S can be obtained from the geometric relationshipRAnd SrIn which S isRAnd SrThe areas respectively comprise the arc length of the grinding wheel cut-in workpiece and the cut-in arc length of the workpiece and a line segment d, and the difference value of the two areas is the i-th axial section removal area delta Si(i＝1，2，3……)。
Figure BDA0003306234940000104
Figure BDA0003306234940000105
Figure BDA0003306234940000106
Then the ith removal volume:
Figure BDA0003306234940000107
the 1 st removal volume was:
Figure BDA0003306234940000108
obtaining:
Figure BDA0003306234940000111
fig. 5 is an axial schematic diagram of internal thread grinding, and the volume is removed in the ith time of flat grinding:
Vi＝ap×d×iap (20)
obtaining:
Figure BDA0003306234940000112
therefore, the final internal thread grinding force prediction formula is as follows:
Figure BDA0003306234940000113
Figure BDA0003306234940000114
Figure BDA0003306234940000115
Figure BDA0003306234940000116
wherein v issIs the rotational speed of the grinding wheel, vwFor the feed rate, apTo grind depth, knAnd ktIs a coefficient of grinding force, which is constant, K1,iThe correlation coefficient of the ratio of the ith feed removal volume to the 1 st feed removal volume, K2,iAnd lambda is a thread lead angle, and is a correlation coefficient of the volume ratio of the ith feed internal thread grinding to the planar grinding removal.
The invention is illustrated below with reference to specific examples:
the invention comprises three steps, the grinding process is simplified, the grinding force is decomposed, the high-speed grinding of the internal thread is simplified into two-dimensional plane grinding, and the two-dimensional plane is obtainedAn empirical formula of grinding force for face grinding; according to the characteristics of internal thread grinding and two-dimensional plane grinding, the conversion from two-dimensional plane grinding force to three-dimensional internal thread grinding force is realized by introducing a correction coefficient, and a three-dimensional grinding force formula of the internal thread in the high-speed grinding process is obtained; the coefficient k is obtained by the grinding force obtained by orthogonal finite element simulation calculation and the control variable methodn、kt、K1,i、K2,i、b1、b2、b3、c1、c2、c3And further obtaining a grinding force prediction formula.
A two-dimensional plane grinding model of a plurality of abrasive grains was created in Abaqus, and as shown in fig. 5, the grinding force at the 1 st feed was studied, the maximum rotation speed of the grinding wheel spindle was 30000rpm, the grinding wheel was a diamond grinding wheel, and the radius R was 15 mm. The workpiece material is GCr15, the radius of the inner circle is r-20 mm, and the diameter of the outer circle is dw50mm, length of workpiece lw80 mm. The internal thread model is M42 x 3, and the lead angle is lambda equal to 2 degrees 48'.
Four groups of different feeding speeds are set for the grinding wheel in the Abaqus, wherein the four different feeding speeds are 10000r/min, 12000r/min, 13000r/min and 20000r/min respectively, the grinding depth is set to be 0.03mm, the feeding speed is 30mm/s, the negative rake angle of the abrasive particles is-45 degrees, and the number of the abrasive particles is 9. The average grinding force values at the respective rotational speeds were obtained as shown in table 1.
TABLE 1 mean value of grinding force corresponding to each rotation speed
Rotating speed (r/min) 10000 12000 13000 20000
Tangential force (N) 3.12 2.56 2.35 1.513
Radial force (N) 4.57 3.75 3.44 2.42
Importing the data into MATLAB to fit a curve according to a formula (8) to obtain a nonlinear parameter b1＝-1.082， c1＝-0.9833。
Five groups of different feeding speeds are set in the Abaqus, the feeding speeds are respectively 40mm/s, 60mm/s, 80mm/s, 90mm/s and 100mm/s, the grinding depth is set to be 0.03mm, the rotating speed of the grinding wheel is 10000r/min, the negative rake angle of the abrasive particles is-45 degrees, and the number of the abrasive particles is 9. The average values of the grinding forces at different feed rates are shown in table 2.
TABLE 2 grinding force corresponding to different feed rates
Figure BDA0003306234940000121
Figure BDA0003306234940000131
Importing the data into MATLAB to fit a curve according to a formula (9) to obtain a nonlinear parameter b2＝1.493，c2＝2.268。
Three groups of different grinding depths are set in the Abaqus, the grinding depths are respectively 0.01mm, 0.02mm and 0.03mm, the feeding speed is set to be 100mm/s, the rotating speed of the grinding wheel is 10000r/min, the negative rake angle of the abrasive grains is-45 degrees, the number of the abrasive grains is 9, and the average values of the grinding forces under the different grinding depths are obtained and are shown in the table 3.
TABLE 3 mean value of grinding force peak value applied to each cutting depth
Grinding depth/(mm) Radial force/(N) Tangential force/(N)
0.01 2.39 2.11
0.02 4.57 3.12
0.03 7.06 4.92
Importing the data into MATLAB to fit a curve according to a formula (10) to obtain a nonlinear parameter b3＝0.8243， c3＝0.5107。
The above calculations are all grinding forces for the 1 st feed, so the formula for obtaining the two-dimensional plane grinding force is
Figure BDA0003306234940000132
The feed rate is 30mm/s, the cutting depth is 0.03mm, and the rotating speed is 1000, 12000, 13000,The grinding force value of 20000r/min is introduced into the formula (26) to obtain knHas an average value of 6.918 × 10-2，ktHas an average value of 9.782 × 10-4And the grinding force formula of the finally obtained plane grinding process is as follows:
Figure BDA0003306234940000133
according to a plane grinding force formula, the characteristics of the internal thread grinding process and the plane grinding process are compared, the change of the removal volume caused by different cutting times is considered, and the grinding depth coefficient K is introduced by the difference between the internal thread grinding process and the plane grinding process1,iAnd K2,iCorrecting the grinding force formula, converting the grinding force formula of the plane grinding into the grinding force formula of the internal thread grinding to obtain a three-dimensional grinding force formula of the internal thread in the high-speed grinding process, wherein the grinding force formula is
Figure BDA0003306234940000141
In the research, the grinding of the internal thread of the planetary roller screw nut needs to be finished by five times of feed, each time of feed is 0.02mm, and the total cutting depth of the five times of feed is 0.1 mm.
The i-th cut removal volume of the internal thread grinding calculated from equations (11) to (18) is shown in table 4.
TABLE 4 ith feed removal volume
Number of feeds 1 st time 2 nd time 3 rd time 4 th time 5 th time
Volume removed (mm)3) 0.000532 0.0025 0.0053 0.0081 0.0126
The ith removal volume V can be obtained by flat grinding from the formulae (11) to (13) and (20)1＝0.0238mm3，V2＝0.0476mm3， V3＝0.0714mm3，V4＝0.0952mm3，V5＝0.119mm3。
From the equations (19) and (21), the grinding depth correction coefficients are obtained as:
Figure BDA0003306234940000142
Figure BDA0003306234940000143
Figure BDA0003306234940000144
Figure BDA0003306234940000145
Figure BDA0003306234940000146
Figure BDA0003306234940000147
Figure BDA0003306234940000151
Figure BDA0003306234940000152
Figure BDA0003306234940000153
Figure BDA0003306234940000154
therefore, the formula of the corrected 1 st feed grinding force is as follows:
Figure BDA0003306234940000155
the formula of the grinding force of the 2 nd feed is as follows:
Figure BDA0003306234940000156
the formula of the 3 rd feed grinding force is as follows:
Figure BDA0003306234940000157
the formula of the grinding force of the 4 th feed is as follows:
Figure BDA0003306234940000158
the formula of the 5 th feed grinding force is as follows:
Figure BDA0003306234940000159
wherein v issIs the grinding wheel rotation speed (r/min), vwFor the feed rate (mm/min), apIs the grinding depth (mm).

Claims (4)

1.一种行星滚柱丝杠内螺纹磨削过程磨削力预测方法，其特征在于：包括以下步骤：1. a method for predicting the grinding force in the grinding process of the inner thread of the planetary roller screw, is characterized in that: comprise the following steps: 步骤1：磨削过程简化：将行星滚柱丝杠内螺纹磨削过程简化为二维平面磨削过程；Step 1: Simplify the grinding process: simplify the grinding process of the inner thread of the planetary roller screw into a two-dimensional surface grinding process; 步骤2：磨削力修正：通过引入内螺纹磨削修正系数来实现二维平面磨削力向三维内螺纹磨削力的转变，得到内螺纹磨削过程的三维磨削力公式；Step 2: Grinding force correction: The transformation of the two-dimensional plane grinding force to the three-dimensional internal thread grinding force is realized by introducing the internal thread grinding correction coefficient, and the three-dimensional grinding force formula of the internal thread grinding process is obtained; 步骤3：计算内螺纹磨削修正系数，通过正交有限元仿真计算得到磨削力数据，运用控制变量法计算内螺纹磨削的修正系数，得到内螺纹磨削过程的磨削力预测公式，最终预测内螺纹磨削过程的磨削力。Step 3: Calculate the correction coefficient of internal thread grinding, obtain the grinding force data through orthogonal finite element simulation calculation, use the control variable method to calculate the correction coefficient of internal thread grinding, and obtain the grinding force prediction formula of the internal thread grinding process, The final prediction of the grinding force of the internal thread grinding process. 2.如权利要求1所述的一种行星滚柱丝杠内螺纹磨削过程磨削力预测方法，其特征在于，所述步骤2中的具体内容为：三维磨削力公式为：2. the method for predicting the grinding force of the inner thread grinding process of a planetary roller screw as claimed in claim 1, wherein the specific content in the step 2 is: the three-dimensional grinding force formula is:
Figure FDA0003306234930000011
Figure FDA0003306234930000011
Figure FDA0003306234930000012
Figure FDA0003306234930000012
 Fa,i＝Fn,itanλ (3)F a,i =F n,i tanλ (3) 式中，vs为砂轮转速、vw为进给速度、ap为磨削深度；Fi为第i次进刀的总磨削力，Fn,i、Ft,i和Fa,i分别为第i次进刀的法向磨削力、切向磨削力和轴向磨削力；kn和kt分别为法向和径向磨削力系数，其值为正数，b1、b2、b3、c1、c2、c3为与砂轮转速、进给速度、磨削深度相关的指数，其数值均为正数，λ为螺纹升角，K1,i为第i次进刀去除体积与第1次进刀去除体积比的相关系数，K2,i为第i次进刀内螺纹磨削与平面磨削去除体积比的相关系数。In the formula, v s is the rotational speed of the grinding wheel, v w is the feed speed, and a p is the grinding depth; F i is the total grinding force of the i-th infeed, F n,i , F t,i and F a, i is the normal grinding force, tangential grinding force and axial grinding force of the i-th infeed, respectively; k n and k t are the normal and radial grinding force coefficients, respectively, and their values are positive numbers, b 1 , b 2 , b 3 , c 1 , c 2 , and c 3 are indices related to the grinding wheel speed, feed rate, and grinding depth, all of which are positive numbers, λ is the thread lead angle, K 1,i is the correlation coefficient between the volume ratio of the i-th infeed and the volume ratio of the first in-feed, K 2,i is the correlation coefficient between the i-th in-feed internal thread grinding and the surface grinding removal volume ratio. 3.如权利要求1所述的一种行星滚柱丝杠内螺纹磨削过程磨削力预测方法，其特征在于，所述步骤3中的磨削力预测公式为：3. the method for predicting the grinding force of a planetary roller screw internal thread grinding process as claimed in claim 1, wherein the grinding force prediction formula in the step 3 is:
Figure FDA0003306234930000021
Figure FDA0003306234930000021
Figure FDA0003306234930000022
Figure FDA0003306234930000022
Figure FDA0003306234930000023
Figure FDA0003306234930000023
Figure FDA0003306234930000024
Figure FDA0003306234930000024
 其中，vs为砂轮转速，vw为进给速度，ap为磨削深度，kn和kt为磨削力系数，其为常数，K1,i为第i次进刀去除体积与第1次进刀去除体积比的相关系数，K2,i为第i次进刀内螺纹磨削与平面磨削去除体积比的相关系数，λ为螺纹升角。Among them, v s is the grinding wheel speed, v w is the feed rate, a p is the grinding depth, k n and k t are the grinding force coefficients, which are constants, and K 1,i is the i-th infeed removal volume and The correlation coefficient of the volume ratio removed by the first feed, K 2,i is the correlation coefficient of the volume ratio removed by the i-th feed of internal thread grinding and surface grinding, and λ is the thread lift angle. 4.如权利要求3所述的一种行星滚柱丝杠内螺纹磨削过程磨削力预测方法，其特征在于，所述磨削力预测公式的求解过程如下：4. the method for predicting the grinding force of the inner thread grinding process of a planetary roller screw as claimed in claim 3, wherein the solution process of the said grinding force prediction formula is as follows: 根据内螺纹磨削加工的几何关系得到：According to the geometric relationship of internal thread grinding, we get:
Figure FDA0003306234930000025
Figure FDA0003306234930000025
Figure FDA0003306234930000026
Figure FDA0003306234930000026
Figure FDA0003306234930000027
Figure FDA0003306234930000027
 其中R为砂轮半径为已知量，r为被加工工件的内径为已知量，θR为砂轮切入工件弧长对应的角度，θr为工件被切入弧长对应的角度，d为弧长对应的线段长度，ap为总磨削深度为已知量；根据上式求出砂轮切入工件弧长对应的角度θR，工件被切入弧长对应的角度θr，弧长对应的线段长度d；Where R is the known value of the grinding wheel radius, r is the known value of the inner diameter of the workpiece to be machined, θ R is the angle corresponding to the arc length of the grinding wheel cutting into the workpiece, θ r is the angle corresponding to the arc length of the workpiece being cut into, and d is the arc length Corresponding line segment length, a p is the total grinding depth and is a known value; according to the above formula, the angle θ R corresponding to the arc length of the grinding wheel cutting into the workpiece is obtained, the angle θ r corresponding to the arc length of the workpiece is cut into the workpiece, and the line segment length corresponding to the arc length is obtained. d; 由几何关系就能求出面积SR和Sr，其中SR和Sr分别为砂轮切入工件弧长和工件被切入弧长与线段d组成的面积，两个面积的差值即为第i次轴截面去除面积ΔSi(i＝1，2，3……)。The areas S R and S r can be obtained from the geometric relationship, where S R and S r are the area composed of the arc length of the grinding wheel cutting into the workpiece and the arc length of the workpiece being cut into the line segment d, and the difference between the two areas is the i-th Minor axis section removed area ΔS i (i=1, 2, 3...).
Figure FDA0003306234930000031
Figure FDA0003306234930000031
Figure FDA0003306234930000032
Figure FDA0003306234930000032
Figure FDA0003306234930000033
Figure FDA0003306234930000033
 则第i次去除体积：Then the i-th volume is removed:
Figure FDA0003306234930000034
Figure FDA0003306234930000034
 第1次去除体积为：The first removal volume is:
Figure FDA0003306234930000035
Figure FDA0003306234930000035
 求得：Get:
Figure FDA0003306234930000036
Figure FDA0003306234930000036
 平磨第i次去除体积：The ith removal volume of flat grinding: Vi＝ap×d×iap (13) Vi = a p ×d × ia p (13) 求得：Get:
Figure FDA0003306234930000037
Figure FDA0003306234930000037
 最终得到行星滚柱丝杠内螺纹磨削力预测公式。Finally, the prediction formula of the internal thread grinding force of the planetary roller screw is obtained.
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