Finite element analysis of the hottest spiral cutt

2022-10-23
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Finite element analysis in spiral cutting tool CAD

Abstract: the finite element analysis method is introduced into the strength and deformation calculation of spiral cutting tool CAD, the lattice division, element node setting and stress condition of spiral groove of fried dough twist drill are analyzed, and the influence of the change of main parameters of fried dough twist drill with different diameters on the torsional stiffness is calculated

due to the complex structure of the spiral blade tool, the traditional design method cannot carry out accurate strength, stiffness and stress analysis of the tool. In the spiral cutting tool CAD, we use the finite element method to analyze and calculate the tool, and study the rationality of the geometric parameters of the tool from the point of view of stiffness, strength and stress. On the premise of meeting the cutting conditions, with the minimum deformation and the maximum stiffness as the goal, we can obtain the best geometric parameters of the tool, so as to improve its cutting performance. The spiral cutting tools we analyze include fried dough twist drills, end mills, reamers and various non-standard tools. This paper takes fried dough twist drills as an example to introduce the finite element analysis process

I. structural characteristics and stress condition of fried dough twist drill

1 Structural characteristics of fried dough twist drill

ordinary fried dough twist drill is the most commonly used spiral cutting tool, and its structure and geometric parameters are shown in Figure 1. The linear main cutting edge of fried dough twist drill is very long, almost extending to the center of the drill; The number of cutter teeth is small, only 2, and the two main cutting edges are connected by horizontal edges; The two chip holding grooves are spiral to facilitate chip removal; The two flanks are part of the conical surface or spiral surface. The main geometric parameters of fried dough twist drill: diameter D, working part length L (including cutting part length l0 and guide part length L1), helix angle Q, vertex angle 2F, cross edge angle y, back angle A and drill core diameter D

Figure 1 Structure and geometric parameters of fried dough twist drill

2 Stress of fried dough twist drill

the stress of fried dough twist drill during cutting is complex. During drilling, the force on the fried dough twist drill mainly includes the deformation resistance of the workpiece material and the force on the fried dough twist drill. The friction between the twist drill and the hole wall and the chip will be affected by the three cutting forces FX, FY and FZ on each cutting edge, as shown in figure 2. Ideally, FX is basically balanced with each other, and the remaining forces are axial and circumferential forces. The circumferential force constitutes the torque and consumes the main power. The fried dough twist drill produces transverse bending, longitudinal bending and torsional deformation under the action of cutting force, among which the torsional deformation is the most significant. The torque is mainly generated by the cutting force on the main cutting edge, accounting for about 80% of the total torque; The length of the transverse blade is short, and the torque generated accounts for about 10%. The axial force is mainly generated by the transverse blade, accounting for about 50% - 60%; The axial force on the main cutting edge accounts for about 40%

Figure 2 fried dough twist drill cutting

II. Finite element analysis

we use SAP5P software developed by the Department of mechanics of Peking University to analyze and calculate the deformation of twist drill cutting in a new factory producing PPS (polyphenylene sulfide) composites in the Hungarian production base

1. Selection of isoparametric elements

sap5p program provides a variety of unit types. Since the fried dough twist drill is a three-dimensional solid structure, eight types of three-dimensional isoparametric elements with variable number of nodes are selected, and 8 ~ 21 nodes are selected for each element according to the needs

2. Division of unit

the cutting cone of fried dough twist drill is the main force bearing body, and the load mainly acts on the main cutting edge. Therefore, when dividing the unit, the cutting cone can be divided into finer parts, while the guide part can be divided into thicker parts, and gradually from the connection between the cone and the guide part to sparse. The unit division of fried dough twist drill is shown in Figure 3

Figure 3 also participated in the optimization and improvement of key parts of the car body; In the high-end pure electric car run jointly produced with great wall Huaguan, the unit division diagram of fried dough twist drill

because the cutting cone is similar to a cone, and the transverse edge is only a straight line, there must be a problem of transitional connection between units. As shown in Figure 4, a node (node 28) is constructed in the middle of the cone, and a hexahedron is constructed through this node and the cross edge, two flanks and two grooves. This hexahedron is divided into 8 units. If there is a need to replace the gasket, a cross section is made at the connection between the cone and the guide part, and 8 units are constructed between this cross section and the hexahedron, so that the cutting cone is divided into 16 units

Figure 4 cutting cone unit division figure

the guide part is a cylinder with two spiral grooves. Solid segments with different heights are intercepted along the axis, and each segment is divided into 8 20 node elements. According to the computer capacity and the cutting length of fried dough twist drill, the corresponding number of solid segments and units are selected

3. Establishment of node mathematical model

calculate the node coordinates according to the actual structure of the cutting cone of the fried dough twist drill

the outer diameter of the guide part is basically the same, except that the upper layer of the solid section rotates a certain angle along the helix relative to the lower layer. Let the lower node coordinates of any unit be x (I), y (I), Z (I); The upper node coordinates are x (J), y (J), Z (J), then

x (J) =x (I) cosf - Y (I) sinf

y (J) =x (I) cosf + y (I) sinf

z (J) =z (I) +h

where f = (h/r) TGW, h is the thickness of the unit (i.e. the height of the solid segment), R is the radius of the outer circle of the drill head, W is the spiral angle, and ﹤ is the rotation angle of the lower node of the unit along the spiral line

4. Simplification and calculation of load

the stress condition of fried dough twist drill is complex, so the load can be simplified. The following two loading methods are used for calculation

the load acts on the outermost end of the main cutting edge in the form of a concentrated force. Assuming that the fried dough twist drill is only affected by torque, assuming that the torque is m (n · mm) and the maximum outer diameter of the fried dough twist drill is d (mm), the force F acting on the outermost end of the main cutting edge is f = m/d

the load acts on the corresponding node of the main cutting edge according to the actual situation, as shown in Figure 5

Fig. 5 load distribution diagram of main cutting edge

set P as the load of unit radius length, then

tangential force Pt = 9.81hbf/2

normal force PN = (0.5 ~ 1.0) Pt

radial force PR = pncos φ

axial force PA = pnsin φ

where Hb is the hardness of the workpiece material to be processed, and F is the drilling feed (mm/r). Then the load distributed by the corresponding node of the main cutting edge is approximately

p1 = pr/6

p2 = 4pr/6

p3 = pr/6

5 Constraints

when using SAP5P program to analyze and calculate the fried dough twist drill, only the cutting part and the guide part are calculated, and the influence of the handle is ignored. Therefore, in the overall analysis, the fixed end constraints should be added to the nodes at the connection between the handle and the guide part to limit their degrees of freedom in six directions; Other nodes are given translational degrees of freedom in the X, y, and Z directions to limit the severe oil leakage of the X, y, and Z oil pressure systems. Oil leakage in the oil circuit system usually appears in the rotational degrees of freedom at the joints of buffer valves, oil return valves, oil delivery valves, oil pumps, and pipelines

6. Preprocessing general interface program

we have written the preprocessing general interface program in Borland C language. Users only need to input the main geometric parameters of fried dough twist drill. By running the preprocessing program, they can automatically divide the lattice and automatically generate data files for SAP5P to run. The finite element calculation process is shown in Figure 6

Figure 6 finite element calculation flow chart

III. calculation results

select three groups of fried dough twist drill parameters as shown in Table 1 for calculation. Modulus of elasticity e = 2.15 × 105/mm2, shear modulus of elasticity g = 8.05 × 104n/mm2, Poisson coefficient = 0.25, load calculation takes HB = 200, f = 2.5mm/r, PN = 0.75pt. Table 1 three groups of fried dough twist drill parameters

serial number diameter d

(mm) drill core d

(mm) working length

l (mm) spiral angle

w transverse blade angle

y vertex angle

2f rear angle

a1142.010830 ° 55 ° 118 ° 11 ° 2202 0160

input three groups of parameters into the pre-processing program, generate data files for SAP5P operation, and enter SAP5P for calculation. See Figure 7 for the deformation diagram of fried dough twist drill. According to the output displacement and deformation diagram, the maximum deformation occurs at the outermost end of the main cutting edge, that is, at node 32 (56)

Fig. 7 deformation diagram of fried dough twist drill

take the fried dough twist drill with diameter d = 20mm as an example, change the core thickness and spiral angle respectively, and other parameters remain unchanged. Enter SAP5P for calculation, and the results are shown in Table 2. Figure 8 shows d0-d change curve, and Figure 9 shows d0- ω Change curve. Table 2 stiffness value of fried dough twist drill with different core thickness and spiral angle

core thickness

d (mm) stiffness d0

(nm/rad) spiral angle

w stiffness d0

(nm/rad) 2.67.625 × 10420°5.941 × 1042.97.917 × 10430°7.917 × 1043.08.493 × 10440°1.014 × 1053.59.022 × 10450°1.222 × 105

figure 8 d0-d change curve figure 9 D0- ω Change curve

IV. conclusion

taking fried dough twist drill as an example, this paper analyzes the influence of the change of the main geometric parameters of the spiral blade cutter on the torsional stiffness by using the finite element method. It can be seen from the calculation results that the deformation and stiffness values of fried dough twist drills are different with different geometric parameters; With the increase of drill core diameter and helix angle, the deformation decreases and the stiffness increases gradually, so the geometric parameters of the tool with the minimum deformation and the maximum stiffness can be optimized, so as to improve the cutting performance of the tool. (end)

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