An Accurate Modeling Method of Body-thread of Penetration Fuze in FEM

To address the issue that the influence of body-thread on the acceleration signal characteristics in penetration fuze is ambiguous, an accurate modeling method of body-thread is proposed in the finite element method (FEM). The body-thread element segments are obtained by the three-dimensional entity thread model, the initial layer nodes set and elements on the outer surface of the thread are established, and the initial layer elements are copied, rotated, and translated. Repeat this transformation, and get a complete thread model. This method is applied to simulation analysis of a warhead penetrating 4-layer concrete plates, and the influence of thread connection on acceleration signal characteristics in penetration fuze is studied. By comparing the acceleration signal and frequency spectrum of the proposed thread model with that of the simplified thread model, the amplitude of the acceleration signal of the proposed one is smaller than that of the simplified one in some certain frequency spectrum. It shows that the thread connection structure has with damping effect and effectively reduces the high-frequency interference of acceleration signal in penetration fuze.


Introduction
Body thread is a typical connection of warhead and fuze in penetration weapons.When the warhead penetrates the hard plate, the warhead is suffering from a high-shock overload, the teeth and groove of thread will crash and apart irregularly.The influence of thread on acceleration in penetration fuze is ambiguous.
The analytical study of the influence of thread on acceleration in penetration fuze is difficult, for the elastic-plastic deformation and nonlinear force distribution of thread are complicated.While finite element method (FEM) is a useful way to do this kind of analysis.
The traditional way of modeling a body-thread is axial symmetry with tetrahedron and hexahedron in FEM.The lift angle of thread screw is ignored in axial symmetry model.Calculation precision of arbitrary tetrahedron model is low.And calculation precision of the strict hexahedron model is high, but it is difficult to describe a mold like a thread accurately [1].
An accurate modeling method of body-thread in penetration fuze is proposed in this paper, this modeling method of hexahedron is easy to achieve.And it is a way to analyze the influence of thread on acceleration characteristics in penetration fuze.

Accurate Modeling Method of Body-thread Connection
There are two traditional ways to model a body-thread.
The first one: the three-dimensional solid model is established, and the solid model is accurately divided into elements.The precision of finite elements is depended on the solid model and division strategy.The action of division is complex, and it comes with a heavy workload [2].
The other one of modeling a body thread is the contour math function, every coordination and serial number of nodes on thread teeth contour is assembled and calculated in Matlab.The calculated coordination and serial number of nodes are used to establish the model [1].
The contour of the thread is from the rotation of a slice of thread teeth, and the contour is the same in every layer.The contour of the thread is from the projection of teeth rotation.Fig. 1 is a diagram of a cross-section of thread teeth.In the extent thread pitch of P/2, the thread teeth are segmented into three parts: crest, flack, and root [1].Similarly, with ignorance of curve of thread root, R means the expression of distance of internal thread contour to axial, as it is listed below: ) D is inner diameter of body-thread, D1 is outer diameter of body-thread.The rest parameter is as same as equation 1.

Math Theoretical Foundation of Thread Model
The contour line is extracted from solid body, and nodes of thread is extracted from the contour line.And the outer surface elements are created by the nodes set.Transformation of duplication, rotation and translation is used to born the whole external surface.The elements of whole body-thread are supplemented by the outer surface of surface elements.And the completed modeling is set.This method need not fine segments of solid body, and need not the complex program to calculate the coordination and serial number.In this modeling method, along extant of one thread pitch, the hexahedron element number in layer and hexahedron element number in contour is correlative.The length of fuze thread pitch is P, and it is segmented in n layers.n is integer number, the adjacent layer rotation degree is 360/n.Make sure the nodes set of adjacent layers are aligned, every layer of thread should be segmented in k*n element.k is an integer number too.
The thread model is established in NX, in aiming at establishing the surface element of thread easily, a cylinder is segmented from the model.The surface thread model is translated into ANSYS/LS-DYNA, and three-dimensional model is deleted, the surface and contour of external thread have remained in model shown in Fig. 2(a), and the nodes set of external thread element shown in Fig. 2(b).
Duplicate the nodes set of first lateral layer, move this set P/n along the axis, and rotate the set 360/n, shown in Fig. 2(d).These nodes set of two layers are framework case of the element.Every adjacent eight nodes are the eight point of a hexahedron element, as it is shown in Fig. 2(e).the nodes of inner cylinder are as same as the adjacent thread inner contour, and inner cylinder and thread have merged into a part of body-thread layer, as it is shown in Fig. 2(f).And the layer is one of n layer, the whole model of body-thread is shown in Fig. 3    The modeling method of internal thread of warhead case is as same as body-thread.Threedimensional entity model is established to get the nodes set of one layer, and same transformation to get the whole part of body-thread and internal thread.The proposed modeling method of body-thread of fuze and internal thread of warhead case is based on the situation of tight-fitted, surface-coatingfree and preload-free.

The Influence of Accurate Modeling of Body-thread on Acceleration Signal
The simulation situation of warhead penetrating 4-layer concrete plates is established in ANSYS/LS-DYNA. the comparison of accurate thread model and simplified one is to demonstrate the difference of acceleration [3,[5][6][7].
In simulation model, the diameter and length of warhead is 170mm and 950mm, respectively.The diameter and length of fuze is 94mm and 109mm.the thickness of first plate is 300mm and thickness of other three is 180mm, the spacing of every adjacent plates is 2m, the initial velocity of penetrating is 800m/s.the material of warhead case, fuze case and fuze shell is 35CrMnSiA, the constructive model of 35CrMnSiA is JOHNSON_COOK, the material of shim in fuze is aluminium-2A12, the constructive model is JOHNSON_COOK too, the constructive model of concrete is JOHNSON_HOLMQUIST_CONCRETE [4,8,9].
The parameter of constructive model is shown in Table 1.The simulation model of penetrating is shown in Fig. 5. Hexahedron is as the main way of element in this model.The size of element of tip in egg-ship is smaller the rest part of this model.By the comparison of characteristics in time-domain and frequency-domain, the tendency of two model is similar in time-domain, the characteristics of penetrating multi-layer plate are both obvious, but layer characteristic of the proposed model is sort of obvious than simplified one.The FFT is used to get the frequency spectrum of acceleration of proposed and simplified one.There are three typical frequency characters: 2979Hz, 5762Hz and 8984Hz, shown in Fig. 7.In Table 2, the amplitude difference of 2979Hz and 5762Hz is within 6db.but the amplitude difference of 8984Hz is higher than 20db, and the amplitude of the frequency more than 15kHz, the proposed model method is higher than the simplified one.The Fig. 8 is the short-term FFT of two acceleration signals, the color represents the amplitude of specific time and frequency, the color is lighter, the amplitude is higher.At most frequency of signal along the penetrating, the proposed model method is lighter than the simplified one, especially when the warhead flying between two plates, it means the thread have the damping effect on the acceleration signal in fuze.And it makes a contribution to identify the character of multi-layer in acceleration signal.

Conclusion
This paper proposed an accurate modeling method of body-thread in FEM.The nodes set on the contour of three-dimensional in one layer is the initial set, the transformation of duplication, rotation, and translation of the initial set is used to get the whole part of the body thread.The analysis simulation of a warhead penetrating 4-layer concrete plates is to demonstrate the difference between the proposed method and the simplified one.It shows that the thread connection structure has with damping effect and effectively reduces the high-frequency interference of acceleration signal in penetration fuze.
nominal diameter of external thread contour to axial. 1 d is minor diameter.H is triangle height of thread,  is diameter of thread root.P is thread pitch.
(a) Lateral three-dimensional model of external thread (b) Lateral curve of external thread (c) external thread element nodes set of one layer (d) external thread element nodes set of two layers (e)Outer surface mesh grid of one pitch external thread (f)A pitch mesh grid of external thread

Figure 2 .
Figure 2. The modeling process of one layer in FEM.

Figure 3 .
Figure 3. Complete mesh grid of external thread.

Fig. 4 (
a) is cross section of entity model of warhead and fuze.Fig.4(b) is cross section of model of them, body-thread and internal thread in FEM, the cylinder part and contour surface of thread in fuze is clear in Fig.4(b).

Figure 4 .
Figure 4. Cross section of thread connection position of penetration fuse and it in FEM.

Figure 5 .Figure 6 .
Figure 5. Simulation model of penetration projectile penetrating 4-layer target.The acceleration signal of sensor in the accurate thread and the simplified one is shown in Fig.6(a) and Fig.6(c).

Figure 7 .
Figure 7.The frequency spectrum comparison of proposed and simplified one.

Figure 8 .
Figure 8.The short-term FFT of the acceleration signal of proposed thread model method and simplified one.

Table 1 .
Constructive model parameters of the penetration simulation (cm-g-s)  .

Table 2 .
The amplitude of the spectrum of the acceleration signal.