CN106886635B - Milling cutter's helix angle design method based on minimum cutting force peak value - Google Patents
Milling cutter's helix angle design method based on minimum cutting force peak value Download PDFInfo
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Abstract
The invention discloses a kind of milling cutter's helix angle design method based on minimum cutting force peak value, for solving the technical problem of existing milling cutter's helix angle design method design helical angle poor accuracy.Technical scheme is first against milling mode and the incision of radial cutting depth calculation, cuts out angle size.The arc-tangent value of radially and tangentially the ratio between Milling force parameter is calculated according to the radially and tangentially Milling force parameter calibrated.Then whether the number of teeth according to selected by judging the arc-tangent value for cutting, cutting out the ratio between angle and Cutting Force Coefficient meets the applicable elements of this method.When number of teeth meets decision condition, the number of degrees of milling cutter's helix angle according to corresponding to axial cutting depth, milling cutter radius and number of teeth calculate minimum Milling Force peak value.Compared with background technology, without being tested or finite element simulation is with regard to that can obtain the milling cutter's helix angle under minimum cutting force peak value condition, easy to operate and accuracy is high.
Description
Technical Field
The invention relates to a milling cutter helical angle design method, in particular to a milling cutter helical angle design method based on a minimum cutting force peak value.
Background
In cutting machining, low cutting force plays an important role in reducing cutting deformation, reducing tool abrasion and prolonging the service life of the tool. Typically, reducing the cutting force is done by choosing more conservative process parameters, but this comes at the expense of machining efficiency. Therefore, optimizing the milling cutter geometry to reduce the milling forces is an alternative, and the helix angle is one of the important geometry parameters. Obtaining the optimal helix angle corresponding to the lowest milling force peak value under different cutting parameters has important significance.
Document 1, a. Hosokawa, n.high, t.ueda, t.Furumoto, high-quality machining of CFRP with high helix end mill, annals of the CIRP 63 (2014) 89-92, "discloses a method of designing a large helix angle suitable for high quality processing of carbon fiber reinforced plastics. Hosokawa et al, based on experimental results, indicate that a larger helix angle of the cutter can significantly reduce tangential and normal cutting forces. They only qualitatively analyze the change rule of the milling force under a large helical angle, and do not provide a milling cutter helical angle selection strategy under different cutting parameters.
Document 2"A.H.Li, J.ZHao, Z.Q.Pei, N.B.Zhu, simulation-based solid carbide end mill design and geometry optimization, international Journal of Advanced Manufacturing Technology 71 (2014) 1889-1900" discloses a method for selecting an end mill helix angle based on finite element simulation. By finite element simulation analysis of milling forces at 6 different helix angles, li et al found that a lowest point, namely the optimized helix angle position, occurred during the variation of the peak value of the resultant force of the milling forces with the helix angle. They do not give an accurate spiral angle calculation method.
The technical problems of the above documents are: when the helix angle is selected based on the minimum cutting force peak, the approximate position of the helix angle under specific cutting conditions is obtained from only a limited set of experimental data or finite element simulation results, and the accurate value of the optimum helix angle cannot be obtained.
Disclosure of Invention
In order to overcome the defect that the design accuracy of the helical angle of the traditional milling cutter helical angle design method is poor, the invention provides a milling cutter helical angle design method based on the minimum cutting force peak value. The method firstly calculates the sizes of the cut-in angle and the cut-out angle according to the milling mode and the radial cutting depth. Calculating the arctangent value of the ratio of the radial and tangential milling force coefficients according to the calibrated radial and tangential milling force coefficients. And then judging whether the selected number of the cutter teeth meets the applicable condition of the method or not according to the arctangent value of the ratio of the cutting-in angle, the cutting-out angle and the cutting force coefficient. And when the number of the cutter teeth meets the judgment condition, calculating the degree of the spiral angle of the milling cutter corresponding to the minimum milling force peak value according to the axial cutting depth, the radius of the milling cutter and the number of the cutter teeth. Because the size of the cut-in angle and the cut-out angle is calculated through the cutting parameters, then the arctangent value of the ratio of the cutting force coefficients is obtained based on the radial cutting force coefficient and the tangential cutting force coefficient, whether the tooth number of the milling cutter meets the applicable condition of the method is further judged, and finally the degree of the optimal spiral angle corresponding to the minimum cutting force peak value is obtained. Compared with the prior art, the milling cutter helix angle under the condition of the minimum cutting force peak can be obtained without experiments or finite element simulation, and the operation is simple and convenient and the accuracy is high.
The technical scheme adopted by the invention for solving the technical problems is as follows: a milling cutter helix angle design method based on minimum cutting force peak is characterized by comprising the following steps:
step one, calculating the size of an entry angle and an exit angle according to the selected milling mode, the radial cutting depth and the radius of the milling cutter. The cut-in angle and the cut-out angle during the forward milling are calculated by adopting the following formula:
φ ex ＝π
the cutting-in angle and the cutting-out angle during the back milling are calculated by adopting the following formula:
φ st ＝0
in the formula, phi st Is the angle of entry, phi ex Is the cutting corner, R is the radius of the milling cutter, a e Is the radial depth of cut.
Step two, calculating the coefficient of cutting force by adopting the following formula:
in the formula, τ s Is the shear stress, phi n Is shear angle, beta n Is the normal friction angle, α n Is the normal rake angle, beta is the milling cutter helix angle, eta is the chip flow angle, K r 、K t Respectively radial and tangential cutting force coefficient, alpha n Beta is a cutter parameter.
Step three, calculating the arc tangent value of the ratio of the cutting force coefficients by adopting the following formula:
and step four, judging whether the number of teeth of the milling cutter meets the judgment condition. The conditions for determination during forward milling are as follows:
the condition for judging the reverse milling is as follows:
a)sin(φ ex -theta) is less than or equal to 0, the number of the cutter teeth is true for any cutter teeth;
b)sin(φ ex -θ)&and gt, 0, the number of cutter teeth satisfies the following formula:
in the formula, N is the number of teeth of the milling cutter, and int represents rounding down the operation result.
Step five, when the condition of the step four is met, calculating the optimal spiral angle corresponding to the lowest milling force peak value by the following formula:
in the formula, a p Is the axial depth of cut.
The invention has the beneficial effects that: the method firstly calculates the sizes of the cut-in angle and the cut-out angle according to the milling mode and the radial cutting depth. Calculating an arctangent value of a ratio of the radial and tangential milling force coefficients based on the calibrated radial and tangential milling force coefficients. And then judging whether the selected number of the cutter teeth meets the applicable condition of the method or not according to the arctangent value of the ratio of the cutting-in angle, the cutting-out angle and the cutting force coefficient. And when the number of the cutter teeth meets the judgment condition, calculating the degree of the spiral angle of the milling cutter corresponding to the minimum milling force peak value according to the axial cutting depth, the radius of the milling cutter and the number of the cutter teeth. Because the sizes of the cut-in angle and the cut-out angle are calculated through cutting parameters, then the arctangent value of the ratio of the cutting force coefficients is obtained based on the radial cutting force coefficient and the tangential cutting force coefficient, whether the tooth number of the milling cutter meets the applicable condition of the method is further judged, and finally the degree of the optimal spiral angle corresponding to the minimum cutting force peak value is obtained. Compared with the prior art, the milling cutter helix angle under the condition of the minimum cutting force peak can be obtained without experiments or finite element simulation, and the operation is simple and convenient and the accuracy is high.
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Drawings
Fig. 1 is a milling cutter helix angle design method based on the minimum cutting force peak value of the present invention, in example 2, the milling cutter helix angle is a cutting force peak value curve at 30 °, 40 °, 50 ° and 55 °, the cutting parameters are axial cutting depth of 8mm, radial cutting depth of 1.5mm, and feeding per tooth of 0.1mm.
Detailed Description
The following examples refer to fig. 1.
Example 1:
(1) Selecting a 4-tooth flat-bottom spiral end mill with the diameter of 12mm, and processing by adopting a forward milling mode of axial cutting depth of 5mm, radial cutting depth of 4mm and feeding of 0.05mm per tooth, wherein the cut-in angle and the cut-out angle are calculated by adopting the following formula:
φ ex ＝π
wherein R =6mm, a e ＝4mm；
(2) The physical parameter φ 34-45 is determined by reference to the database disclosed in "M.Kaymakci, Z.M.Kilic, Y.Altatitas, unified cutting for model for turning, ringing, drilling and milling operations, international Journal of Machine Tools and Manual 54-55 (2012) 34-45 n ，β n And τ s . The geometrical parameters and the physical parameters of the material of the milling cutter are substituted into the following formula to calculate the coefficient of cutting force:
(3) The arctangent value of the ratio of the cutting force coefficients was calculated using the following formula:
(4) The number of cutter teeth N =4, and the following determination condition is satisfied:
(5) Calculating the optimal helix angle corresponding to the minimum cutting force peak value by adopting the following formula:
example 2:
(1) Selecting a 4-tooth flat-bottom spiral end mill with the diameter of 12mm, and processing by adopting a down-milling mode of axial cutting depth of 8mm, radial cutting depth of 1.5mm and feeding of 0.1mm per tooth, wherein a cutting-in angle and a cutting-out angle are calculated by adopting the following formula:
φ ex ＝π
wherein R =6mm, a e ＝1.5mm；
(2) The physical parameter φ of the material is determined by reference to a database disclosed in "M.Kaymakci, Z.M.Kilic, Y.Altints, unified cutting for model for turning, ringing, drilling and milling operations, international Journal of Machine Tools and Manual 54-55 (2012) 34-45 n ，β n And τ s . The geometrical parameters and the physical parameters of the material of the milling cutter are substituted into the following formula to calculate the coefficient of cutting force:
(3) The arctangent value of the ratio of the cutting force coefficients was calculated using the following formula:
(4) The number of cutter teeth N =4, and the following determination condition is satisfied:
(5) Calculating the optimal helix angle corresponding to the minimum cutting force peak value by adopting the following formula:
as can be seen from the graph 1, the milling force peak value is lowest when the helix angle is measured to be 50 degrees through experiments, and the phenomenon accords with the optimization result, so that the accuracy of the design method is proved.
Claims (1)
1. A milling cutter helix angle design method based on minimum cutting force peak is characterized by comprising the following steps:
step one, calculating the size of an entry angle and a cut-out angle according to the selected milling mode, the radial cutting depth and the radius of the milling cutter; the cut-in angle and the cut-out angle during the forward milling are calculated by adopting the following formula:
φ ex ＝π
the cut-in angle and the cut-out angle during reverse milling are calculated by adopting the following formula:
φ st ＝0
in the formula, phi st Is the angle of entry, phi ex Is the cutting angle, R is the radius of the milling cutter, a e Is the radial depth of cut;
step two, calculating the coefficient of cutting force by adopting the following formula:
in the formula, τ s Is the shear stress, phi n Is the shear angle, beta n Is the normal friction angle, alpha n Is the normal rake angle, beta is the milling cutter helix angle, eta is the chip flow angle, K r 、K t Respectively radial and tangential cutting force coefficient, alpha n Beta is a cutter parameter;
step three, calculating the arctangent value of the ratio of the cutting force coefficients by adopting the following formula:
judging whether the number of teeth of the milling cutter meets a judgment condition; the conditions for determination during forward milling are as follows:
the condition for judging the reverse milling is as follows:
a)sin(φ ex -theta) is less than or equal to 0, the number of the cutter teeth is true for any cutter teeth;
b)sin(φ ex - θ) > 0, the number of cutter teeth satisfies the following equation:
in the formula, N is the number of teeth of the milling cutter, and int represents that the operation result is rounded downwards;
step five, when the condition that the milling force peak value is the lowest is judged to be met, the milling cutter spiral angle corresponding to the milling force peak value is calculated according to the following formula:
in the formula, a p Is axialThe depth of cut.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102136021A (en) * | 2011-04-21 | 2011-07-27 | 西北工业大学 | Milling force modeling method for titanium alloy TC18 milling process |
| CN102436527A (en) * | 2011-11-10 | 2012-05-02 | 西北工业大学 | Milling force modeling method of milling process of countersinking vertical milling cutter |
| CN105364151A (en) * | 2015-10-05 | 2016-03-02 | 唐山学院 | Non-linear screw-blade cylindrical end mill |
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- 2017-01-20 CN CN201710045787.7A patent/CN106886635B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102136021A (en) * | 2011-04-21 | 2011-07-27 | 西北工业大学 | Milling force modeling method for titanium alloy TC18 milling process |
| CN102436527A (en) * | 2011-11-10 | 2012-05-02 | 西北工业大学 | Milling force modeling method of milling process of countersinking vertical milling cutter |
| CN105364151A (en) * | 2015-10-05 | 2016-03-02 | 唐山学院 | Non-linear screw-blade cylindrical end mill |
Non-Patent Citations (4)
| Title |
|---|
| High-quality machining of CFRP with high helix end mill;Akira Hosokawa et.al.;《CIRP Annals-Manufacturing Technology》;20141212;第89-92页 * |
| Simulation-based solid carbide end mill design;Anhai Li et.al.;《Int J Adv Manuf Technol》;20141212(第71期);第1889-1900页 * |
| The Machinability of CFRP with Cutting Movement of End-milling;Takashi Inoue et.al.;《Key Engineering Materials》;20150723;第391-397页 * |
| Unified cuttingforcemodelforturning,boring,drillingand;M. Kaymakci et.al.;<InternationalJournalofMachineTools&Manufacture>;20121212;第34-45页 * |
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