_____________________________________________________________________________ 1

THIN-WALLED HOLLOW BOLTS

Experimental and numerical study

Teixeira, C. D. S.

Department of Mechanical Engineering,

Instituto Superior Técnico,

Av. Rovisco Pais, 1049-001, Lisbon, Portugal, 2010

Abstract

This work aims to evaluate an innovative concept for the manufacture of thin-walled hollow

bolts. To achieve this, it was necessary to design, develop and manufacture one tool for this purpose and

analyze the manufacturing feasibility of these screws exclusively for metal forming.

The main objectives of the work presented here are to design, develop and manufacture a tool to

obtain thin-walled hollow bolts and verify the applicability of this new method of manufacture thin-

walled hollow bolts only using metalforming.

To analyze this manufacturing method feasibility, we used numerical simulation and

experimental analysis.

To obtain results on the numerical simulation, the material used as raw material, steel S460MC

had to be characterized, after that we used the finite element programs I_Form2 and I_Form3, developed

at Instituto Superior Técnico.

To perform the experimental analysis it was necessary to make a tool and run several tests to

obtain results for comparison with the results obtained by numerical simulation.

The numerical and experimental results showed that this innovative method to obtain thin-walled

hollow bolts proposed is feasible.

It is important to refer that the correlation numerical-experimental was very satisfactory.

Keywords:

Thin-walled hollow bolts; Tools design, development and manufacture; Numerical and experimental

analysis; Clean production

_____________________________________________________________________________ 2

1. INTRODUCTION

The bolt is an element used to fix two or more objects. It is a cylindrical or conical shaft, which around

develops a helical geometry appropriate to its use. Generally, it has a head on one end which

simultaneously serves as a stop and allows the use of an appropriate tool to cause the rotational movement

responsible for fixing the bolt. One of the advantages associated with this component, when compared

with other fixation techniques such as the preaching, riveting or welding, is that it can be used repeatedly

without losing its efficiency.

There are trillions of copies currently in worldwide service. There will also be many thousands, if not

millions bolts manufactured daily. If the manufacture of each one bolt could save a minimum amount of

material, this global savings would be enormous, not only in terms of material, but also in energy terms

for the process. If we think that many of these bolts are used in transportation, environmental and

economic benefits from the use of lighter structures would be enormous.

It is precisely in this context that the idea to design, develop and manufacture a prototype tool that allows

the manufacture bolts lighter, with similar mechanical properties and whose processing requires lower

power consumption.

For the hollow bolts manufacture, pre-departure form are conventional bolts internally machined until

obtain desired wall thickness. At this step we have much material and energy waste. The time factor also

comes in these wastes because it takes longer to manufacture a hollow bolt than the conventional bolt.

Based on the know-how acquired in recent years by the “Secção de Tecnologia Mecânica do IST” group

in mechanical tubes processing, has ocurred the concept of "thin-walled hollow bolt", a process that

developed and presented in this paper.

2. EXPERIMENTAL BACKGROUND Commercial S460MC (carbon steel) welded tubes in the form of 32 mm diameter and 1.5 mm thickness

were utilized in the „as-received‟ condition. The mechanical characterization tests and the tube end

forming experiments were performed at room temperature on a universal testing machine with a cross-

head speed equal to 100 mm/min (1.7 mm/s).

2.1 Mechanical behavior and Timoshenko curves Tensile and compression tests were performed in order to obtain the true stress-strain behaviour of

S460MC. The specimens utilized in the tensile tests were machined from the supplied tube stock while

the specimens utilized in the compression tests were assembled by pilling up circular discs cut from the

tube stock by a hole saw. The stress-strain curve to characterize the material mechanical behavior and

Timoshenko (blue curve) intersection are given in figure 1. Timoshenko curve was necessary to obtain

the critical instability load, crP , analytically using the next equation:

(1)

where Et = dσ /dε, h is the tube high and r is the interior tube radius. So, we can obtain σcr easily by the

intersection of the two curves on figure 1.

_____________________________________________________________________________ 3

Figure 1 - True stress-strain behaviour of S460MC welded tubes.

525,82 MPa

525,82 x π x (16.22 – 14.4

2) = 90988N

2.2 Critical instability load

The critical instability load crP for the occurrence of local buckling in S460MC welded tubes subjected

to axial loading was experimentally determined by compressing tubular specimens between flat dies.

Figure 2 shows the load recorded during the experiments as a function of the displacement of the upper

flat die.

Figure 2 - Load-displacement curve for the axial compression of S460MC welded tubes.

σ= 616.4ε0.0563

σ= 34.689ε-0.947

0

100

200

300

400

500

600

700

0 0.2 0.4 0.6 0.8 1

Tru

e S

tre

ss

(M

Pa

)

True Strain

S460MC

0

20

40

60

80

100

120

0 5 10 15 20 25 30

Lo

ad

(k

N)

Displacement (mm)

S460MC

Instability (S460MC)

_____________________________________________________________________________ 4

As we can see, the load increases sharply from zero and local buckling occurs upon reaching a critical

experimental value 91crP kN. Subsequent deformation of the tubular specimens results in additional

folds, additional instability waves with circular shape in case of S460MC tubes, and to the development

of a cyclic peak-to-peak load-displacement evolution.

2.3 Thin-walled hollow bolts forming tool

The prototype tool presented in this paper was conceived to allow the tube forming into thin-walled

hollow bolts. For the study presented here, the process was divided in two different steps. The first step

was the Bolt head and stop forming and the second step was the screw thread forming.

2.3.1 Bolt head and stop forming

Next figure shows the Bolt head and stop forming dies:

Figure 3 – Tube and Bolt head and stop forming dies.

On the left image, it is represented the inferior die and the tube inside of that. On the center and right

image it is represented, respectively, the die set and raw material at the process beginning and at the end

of process.

The next figure presents the geometry at the forming process beginning and at the process end.

Figure 4 – Tube geometry before and after Bolt head and stop forming.

_____________________________________________________________________________ 5

2.3.2 Bolt screw thread forming

Next figure shows the Bolt screw thread forming dies:

Figure 5 – Thread forming dies.

The first image, on top, shows the screw thread forming die. On bottom, left image shows the screw

thread die and the bolt inside of that. The figure in the center presents the die set and raw material without

the punch at the process beginning, the figure on the right presents the complete set ready to start the

screw thread forming process.

The final screw thread obtained after that process is showed on 4.Results and discussion.

3. FINITE ELEMENT BACKGROUND

Because the experiments in cold end forming of welded steel tubes were performed under a quasi-static

constant displacement rate of the upper-table of the press, no inertial effects on forming mechanisms are

likely to occur and therefore no dynamic effects in deformation mechanics are needed to be taken into

account. These operating conditions allowed numerical modelling of the process to be performed with the

finite element flow formulation and enabled the authors to use the in-house computer program I_Form2

and I_Form3 that have been extensively validated against experimental measurements of metal forming

processes since the end of the 80‟s (Alves et al., 2003).

_____________________________________________________________________________ 6

The finite element flow formulation giving support to the computer program I_Form is built upon the

following variational statement,

dSdudSuTdVKdV

f

r

T S

|u|

rf

V

i

S

iv

V

0

2

21

((2)

where, K is a large positive constant enforcing the incompressibility constraint and V is the control

volume limited by the surfaces US and TS , where velocity and traction are prescribed, respectively.

Friction at the contact interface fS between workpiece and tooling is assumed to be a traction boundary

condition and the additional power consumption term is modelled through the utilization of the law of

constant friction mkf .

Convergence studies with varying arrangements of quadrilateral elements in the thickness direction

showed that the utilization of tree elements was adequate for modelling the distribution of the major field

variables and for getting a proper evolution of the load-displacement curve. The contours of the dies were

discretized by means of contact-friction linear elements. No intermediate remeshing operations were

utilized and, therefore, no influence of field variable recovery techniques on the final results needed to be

taken into account.

The bolt head and stop case, was performed by means of a standard discretization procedure based on the

utilization of eight-node hexahedral elements and in order to ensure the incompressibility requirements of

the plastic deformation of metals, both complete and reduced Gauss point integration schemes where

utilized.

The 3 dimensional finite element computer models were set-up, in order to reproduce material flow in a

tool system equipped with an upper and lower die (figure 3) and on account of symmetry the

discretization was simplified and restricted to a quarter of the initial perform (figure 6).

The numerical integration of the friction boundary integral in (2) is performed by means of a five Gauss

point quadrature and the active tool components (dies) were discretized by means of contact-friction

spatial linear triangular elements (figure 6).

The numerical simulations were also accomplished through a succession of displacement increments each

one modeling approximately 0.1% of the initial perform length. The convergence of the numerical

simulations was stable in an analysis containing 5600 elements.

Figure 6 – Bolt head and stop finite element model. Tube (left image). Tube and dies (right image)

_____________________________________________________________________________ 7

For the screw thread simulation, the numerical evaluation of the volume integrals included in equation (2)

is performed by means of a standard discretization procedure that, on account of the rotational symmetry

of the forming process and because no anisotropy effects due to material or welding seam were taken into

consideration, consisted on the discretization of the initial cross section of the tubular pre-forms by means

of four-node axisymmetric quadrilateral elements (Figure 7).

Figure 7 – Screw thread finite element model. Initial tube (left). Tube and dies (center). Tube at the simulation end (right)

The numerical modelling of the screw thread process was accomplished through a succession of

displacement increments each of one modelling approximately 0.01% of the initial tube length. The

convergence of the numerical simulation was very stable and contained a total number of 3500 elements.

4. RESULTS AND DISCUSSION

Next figure shows the forming bolt head and stop characteristic behavior and the deformed mesh along

the process:

Figure 8 – Bolt head and stop forming process characteristic behavior.

_____________________________________________________________________________ 8

When the forming bolt head and stop process start, the load goes up gradually and steady until reaching

the first peak. This is caused by the passage of the conical part of the die, used to obtain the bolt head,

through the tube end, which causes the load to increase to a maximum. After the conical part has passed,

the load decreases and almost reaches a steady state. Then it grows lightly because the contact area

between the tube and the tool increases as the die moves up to 20mm, which corresponds to the die depth.

At the end of this displacement, 20mm, the tube is completely constrained vertically which will cause the

occurrence of local buckling. In the chart this corresponds to the second peak load. After buckling, the

load decreases gradually as expected. After 27mm of die displacement, the load stabilizes and then begins

to rise again as the crushing of the wrinkled surface, caused by the tube instability, starts.

Next figure presents the comparison of numerical and experimental results.

Figure 9 – Bolt head and stop forming process characteristic behavior (experimental vs numerical results)

Regarding the results obtained for the bolt head and stop forming process, it can be said that they were

very satisfactory. The finite element program I_Form3 provided results very close to the experimental

case. As we can see, both by the deformed mesh images along the process and by the results represented

in the Load-Displacement chart (figure 9).

Figure 10 – Bolt screw thread forming process characteristic behavior (experimental vs numerical results)

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35

Lo

ad

(k

N)

Displacement (mm)

NUMERICAL

EXPERIMENTAL

0

5

10

15

20

25

30

35

0 5 10 15 20

Lo

ad

(k

N)

Displacement (mm)

EXPERIMENTAL

NUMERICAL

_____________________________________________________________________________ 9

Regarding the results obtained for the screw thread process, there was some discrepancy between the

numerical results provided by the finite element program I_Form2 and the experimental results. This

discrepancy was encountered at the steady state regime in which the screw thread formation process

enters. Since the beginning until the full passage of the punch through the tube inside the thread die, the

numerical and experimental results are very similar. This discrepancy is, probably, due to the finite

element model used, in which a perfectly axisymmetric tube was modeled, when in reality it is not. The

real tube has an interior welding line which was not taken into account in the simulation.

As for the experimental and numerical screw thread forming processes, whose behavior is presented in

figure 10, the load presents a constant evolution as the conical section of the punch enters the tube in the

beginning of the process. After the conical section of the punch passes the extremity of the tube, the load

on the simulation case, enters in stationary regime until the final displacement. On the other hand, in the

experimental case, the load takes longer to achieve a stationary regime, being it achieved 8 mm later in

the stoke.

Figure 11 –Bolt head and stop (left and center image) and screw thread (right image) obtained.

5. CONCLUSIONS

The present work is aimed mainly at assessing the applicability of an innovative method for

manufacturing thin-walled hollow bolts. This new method consists in obtaining thin-walled hollow bolts

exclusively through metal forming, instead of forging followed by machining. In order to achieve this

goal, a prototype tool was designed and built to carry out an experimental analysis.

In the experimental ambit, tests were also conducted to examine the feasibility of the proposed method of

manufacture and for mechanical characterization of the material used, steel S460MC, to enable a

reproduction of the experiments using a finite element simulation.

In the ambit of the numerical simulation, after the input files, corresponding to dies and raw material,

were introduced in I_Form2 for the case of the thread, and I_Form3 for the head and die stop, the stated

simulation was performed in order to compare its results with the experiments, and so, validate them.

After comparing and analyzing the experimental and numerical results, it was concluded that the finite

element programs I_Form2 and I_Form3 reproduced reliably and satisfactorily the experimental cold

forming case. However the main conclusion to be retained from this work is that it is indeed possible to

fabricate thin wall hollow bolts recurring only to metalforming with simple dies and raw materials easily

found on the marketplace.

_____________________________________________________________________________

10

REFERENCES

[1] Martins, P. and Rodrigues, J., “Tecnologia Mecânica - Tecnologia de Deformação Plástica Vol.1”,

Escolar Editora, 2ª edição (2010).

[2] Martins, P. and Rodrigues, J., “Tecnologia Mecânica - Tecnologia de Deformação Plástica Vol.2”,

Escolar Editora, 2ª edição (2010).

[3] Alves, L.M., Martins, P.A.F., “Forming of thin-walled hollow spheres using sacrificial polymer

mandrels”, Int. Jour. Of Machine Tools & Manufacture, 521-529, 49, (2009)