Pavel V.Bol'shakov*et al. /International Journal of Pharmacy & Technology
IJPT| Dec-2016 | Vol. 8 | Issue No.4 | 24242-24251 Page 24242
ISSN: 0975-766X
CODEN: IJPTFI
Available Online through Research Article
www.ijptonline.com
EVALUATION OF THE STRENGTH OF ROTARY ORTHOPEDIC EXTERNAL
FIXATION DEVICE Pavel V.Bol'shakov
1, Ruslan F.Khasanov
2, Petr S. Andreyev
2, Aleksey D.Lustin
3, Oskar A. Sachenkov
1,3
1Kazan Federal University, 18, Kremlyovskaya St., Kazan, (420008) Russia.
2Republican clinical hospital, 138, Orenburg tract, Kazan, Russia.
3Kazan National Research Technical University, 10, K. Marksa st., Kazan, Russia.
Email: [email protected]
Received on 14-08-2016 Accepted on 20-09-2016
Abstract:
This paper presents the calculation results of the strength and stiffness of external fixation device used within the
framework of the concept of three-plane spatial correction of pathological orientation of the proximal femur subject
to the disease stage, localization of a degenerative-dystrophic process and its severity. We have created a three-
dimensional parametric model of the device and performed its finite element sampling with the use of quad-nodal
tetrahedral finite element with linear approximation and the quad-nodal hexagonal hub finite element with linear
approximation. We have determined the stress-strain state of the structure in a linear position based on the method of
finite elements for different turn values of a swivel bracket. We have also determined the stress localization areas and
dangerous zones of junctions of the threaded joints. We have calculated the values of maximum shear stress and
stress intensity for different states of the structure under the influence of elementary forces in different directions.
Based on these data, we have determined the directed maximum operating loads, which were 160 N and 7,000 Nm.
Structural plasticity envelope carries loads depending on their direction. The results obtained allowed us to evaluate
structural integrity upon exposure to the elementary forces, which will ensure a more detailed analysis of the
structure.
Keywords: Biomechanics, rotational osteotomy, external fixation device, strength.
Introduction
High incidence of the hip joint disease in children determines the medical and social significance of the problem.
Among the hip joint diseases in childhood, the Perthes disease was noted in 25-30% of cases.Treating the Perthes
disease in case of severe lesion of the pineal gland leads in 89.5% to the residual deformation of the femoral head and
the acetabulum, and the development of coxarthrosis. Objective of this research is to study and calculate the strength
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of the external fixation device used for medical rehabilitation of children and adolescents [1-4], As well as to
determine the stress-strain state of the external fixation device at different angles between the rotary and supporting
parts, and evaluate external force action on the structural strength. This paper describes an external fixation device
used within the framework of the concept of three-plane spatial correction of pathological orientation of the proximal
femur subject to the disease stage, localization of a degenerative-dystrophic process and its severity. As part of
treatment, an intertrochanteric femoral osteotomy is performed along the lower contour of the femoral neck, parallel
to its longitudinal axis, outwards. A bone wedge is resected from the distal fragment of the femur at an angle equal to
the difference between the neck-shaft angle (NSA) on both the affected and the healthy limb segments. The base of
the bone wedge is turned inward, performing a “slant” behind to the angle of an excessive femoral torsion (FT) with
respect to the first osteotomy so that when joining together the bone fragments there would be a complete correction
of the FT and NS angles [3, 4]. Two intraosseous rods are placed into the femoral neck [5, 6]. The rods are fixed in
the neck support, which is connected to the device applied on the thigh and the iliac bone in the FT and NS correction
position. The affected area is released from load by turning the neck support by gradual rotation of the femoral neck.
This method provides a correction of biomechanical angles of the proximal femur, prevention of the development of
the hip joint contracture after rotating the femoral neck, and stable fixation of the femur fragments in the adjusted
position [3, 4, 6, 7]. Loads arising in the joint after the performed osteotomy are primarily transferred to the external
fixing device, which should provide sufficient strength, otherwise, the action of muscle forces may lead to flexion
and reverse rotation in the joint followed by degradation in the quality of treatment, and even by dislocation [5, 8-10].
Methods: The external fixation device is a three-dimensional structure with the rods serving as the support and
interconnected with brackets and pins (see Fig. 1). Structurally, the device can be divided into two parts: rotating
(part L in Fig. 1) and supporting (part R in Fig. 1). The angle between these parts can be varied depending on the
disease localization and surgical approach. All structural components are interconnected by a threaded joint, which
reliability is subject to the basic requirements.
Fig. 1.Structural scheme of the external fixation device.a – side view, b – top view, с – view at rotation. 1 – rod,
2 – brackets, 3 – stud, 4 – supports.
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Turning the bracket (2L in Fig. 1) at a certain angle results in shift in relation to the bracket (2R in Fig. 1) of one of
the studs (3 in Fig. 1) down, the second, respectively, raises up in relation to the same bracket, with simultaneous
rotation of the fasteners, which connect the bracket (2L in Fig. 1) and studs (3 in Fig. 1).
As part of the study, we have created a three-dimensional parametric model of the external fixation device to conduct
the rotational osteotomy [3, 5]. To build the model, we selected different locations between the rotating and
supporting parts, namely angles of 5, 10, 15 and 20, and applied forces to the structure: Pz=10 N, Px=10 N, Py=10
N and the moments: Mz=100Н∙mm , Mx=100 N∙mm, My=100 N∙mmto the center of the rods (1L in Fig. 1)(see Fig.
2). Rods (1R in Fig. 1) are rigidly fixed [8].
For these positions the finite element sampling was conducted: brackets (2L and 2R in Fig. 1) and rods (1 in Fig. 1)
were separated with 8-node hexagonal finite element, and the supports (4 in Fig. 1), rods (3 in Fig. 1) and fasteners
that connect the bracket (2L in Fig. 1) and studs (3 in Fig. 1) – with 4-node tetrahedral finite element [8, 9, 10-13].
Node-to-node couplings were applied on all the rods (1 in Fig. 1) connected with the supports (4 in Fig. 1), on the
studs (3 in Fig. 1) fixed to the bracket (2R in Fig. 1), and between the fasteners that connect the studs (3 in Fig. 1) and
the bracket (2L in Fig. 1).
Constructing conditions for the additional one-dimensional binding grid were used as a central connection between
rods (1L in Fig. 1) for the application of forces [11-13]. The coordinate system, to which the forces have been
applied, is at the point where the additional one-dimensional binding grid was plotted [14-17]. The Z axis goes along
the rods (1L in Fig. 1), the Y axis goes along the rod 3 from right to left (see Fig. 1), the X axis is perpendicular to the
OZ plane so as to create a right-sided triplet of vectors.
Maximum power was derived from the formula:
[ ]T
Max
Max
F F
(1.1)
whereF is force applied.
Results and discussions
These results were obtained for the external fixation device with the arrangement between a rotating and supporting
parts in 10.
The structure is made of steel 12Х18Н10Т, with mechanical characteristics:
, . ,[ ] ,[ ]T cpE GPa MPa MPa 200 0 3 600 140
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Fig. 3. Mises stress.
а – Pzapplication, b – Pxapplication, c – Pyapplication, d– Mz application, e – Mx application, f – My
application
We can conclude from these calculations that the maximum Mises stress of the whole structure, at a rotation angle of
10, is caused by Pz and Px loads, and by Mz and Mx moments (see Fig. 3). It follows from the formula (1.1) that
maximum load Pz must be not more than 160 N, and Px – not more than 165 N. The stress will not exceed the yield
point at the moment Mz = 20,000 N∙mm, and at Mx = 18,600 N∙mm.
a
b
c
d
e
f
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We shall consider the junction graphics of right and left mounting bolts, right and left fasteners with a stud at a load
Pz = 10 N, Px = 10 N, Py = 10 N, and the moment Mz = 100 N∙mm, Mx = 100 N∙mm, My = 100 N∙mm with respect to
angle variation.
Fig. 4. Diagram of the left bolt load-caused Mises stress (MPa)
Load Px causes maximum stress in the left bolt in the interval 5-20. Loads Pzand Pyat rotation angle of 5 and 20
result in approximately the same stress. However, load Py causes substantially greater stress at 10-15. Load Px is the
most “undesirable” for the left bolt in the entire interval, the greatest stress of 10.6 MPa occurs at an angle of
10.Minimum stress-strain state of 2.4 MPa occurs at an angle of 15 with Pz.
Fig. 5. Diagram of the right bolt load-caused Mises stress (MPa)
Among all loads, load Px causes maximum stress in the right bolt in the entire range. Maximum stress of 10.9 MPa
occurs at an angle of 10 between the rotating and supporting parts. Load Py causes stress equal to 4 N in the entire
range. While load Pz causes stress in the interval of 3.1-6.43 Ma. Minimum stress equal to 3.1 MPa occurs at 10 with
Pz.
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Fig. 6. Diagram of the left bolt moment-caused Mises stress (MPa)
The most critical moment for the left bolt is My. It causes maximum Mises stress equal to 0.584 MPa at an angle of 5
and 15.The minimum stress equal to 0.125 MPa is caused by the moment Mz at 10. This moment also causes
minimum stress in the left bolt at any angles being considered in this study.
Fig. 7. Diagram of the right bolt moment-caused Mises stress (MPa)
Similar to the left bolt, the same loads cause maximum Mises stress of 0.701 MPa and minimum 0.06 MPa in the
right bolt in the entire range of intervals. Unlike the left bolt, the moment My causes stress-strain state of 0.7 MPa at
angles of 5 and 20.Minimum stress equal to 0.06 MPa occurs at an angle of 15 and moment Mz.
Analyzing the Figures 4-7, we can conclude that the largest contribution to the stress of the left and right mounting
bolts is caused by load Px and the moment My. It is also obvious that the left and right bolts experience a state of
maximum load stress at an angle between the rotating and supporting parts equal to 10.However, the same angle for
the moments will be 5. Almost in every interval, all minimum stresses were caused by loads in the OZ direction.
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Fig. 8. Diagram of the load-caused Mises stress (MPa) in the junction of the left stud and the fastener
Load Px causes maximum stress at an angle of 20. When the angle between the supporting and rotating parts is 15,
each of three loads causes the same stress in the junction of the left stud and the fastener. Stress in the interval of 5-
15 at loads Pzand Pxoccurs with little difference. The minimum stress occurs at load Pz.
Fig. 9. Diagram of the load-caused Mises stress (MPa) in the junction of the right stud and the fastener
Analyzing the load-caused Mises stresses in the junction of the right stud and the fastener we can note that loads Px
and Py cause roughly the same stresses in the entire interval of 5-15 degrees. Load Pz causes maximum stress-strain
state of 14 MPa at 20. We can also note that the stress charts have two intersections, which is due to the fact that
each of the loads causes the same stress at these angles.
Fig. 10. Diagram of the moment-caused Mises stress (MPa) in the junction of the left stud and the
fastener
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The most critical moment for the junction of the left stud and the fastener is Mx. It causes maximum Mises stress
equal to 1.058 MPa at an angle of 15.The minimum Mises stress equal to 0.141 MPa is caused by the moment Mz at
10. This moment also causes minimum stress in the left bolt at any angles being considered in this study.
Fig. 11. Diagram of the moment-caused Mises stress (MPa) in the junction of the right stud and the
fastener
Similar to the left junction, the same loads cause maximum and minimum Mises stresses in the junction of the right
stud and the fastener in the entire range of intervals. However, unlike the left junction, the moment Mx causes stress
equal to 1.1 MPa at an angle of 15.Minimum stress equal to 0.102 MPa occurs at an angle of 20 and moment Mz.
Considering the Figures 10-11 we can see that the maximum stress occurs at the moment Mx. A more interesting case
can be seen in Figures 8-9, as at different rotation angles the maximum stress depends on various loads. Having
analyzed the Figure 7, we loads Px and Py cause nearly the same stress at angles of 5 and 10, but when an angle is
15, each of three loads equally contributes to the maximum stress. Load Px causes maximum stress in the interval of
15-20.
Diagram of the load-caused Mises stress in the junction of the right stud and the fastener (see Fig. 8) shows similar
stress caused by loads Pxand Py at an angle of 10, while Pz causes maximum stress at angles of 5, 15, and 20.
Summary
For the external fixation device, we have performed assembly, finite element sampling and calculations at different
rotation angles of 5, 10, 15, and 20 degrees with the use of Siemens NX package. We have determined the loads
occurring at these positions that cause the maximum stress-strained state. It follows from the analysis that the
maximum stress at any rotation angle both in the right and left bolt occurs under the influence of OX-directed load
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(Px) and the moment (My) about OY-axis. We have also noted that the most “undesirable" loads for stress-strain state
at an angle between the rotating and the supporting parts of 5-15 degrees in the stud-fastener junction are Px, Py, and a
moment Mx. While at an angle of 20 degrees, the maximum stress in the left junction occurs under the influence of
Px, and in the right – Pz. It follows from the formula (1.1) that maximum load Pz must be not more than 160 N, and Px
– not more than 165 N. The stress will not exceed the yield point at the moment Mz = 20,000 N∙mm, and at Mx =
18,600 N∙mm; the maximum shear stress occurs at the moment Mz, which must not exceed 8216.49 N∙mm, and My
must not exceed 7777.77 N∙mm.
Acknowledgements
The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal
University and the work was partially supported by the Russian Foundation for Basic Research within scientific
projects No. 14-01-31291, 15-31-20602.
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