EFFICIENCY CONSIDERATIONS FOR THE PURELY TAPERED INTERFERENCE FIT (TIF) ABUTMENTS USED IN DENTAL IMPLANTS

It is shown that the connection strength of the tapered interference fitinterface, characterized by the pull-out force, is a function of the taper angle, the contactlength, the inner and

EFFICIENCY CONSIDERATIONS FOR THE PURELY TAPERED

INTERFERENCE FIT (TIF) ABUTMENTS USED IN DENTAL IMPLANTS

by

Dinçer Bozkaya, Sinan Müftü 1 , Ph.D.

Graduate Student Associate Professor

Northeastern UniversityDepartment of Mechanical Engineering

Boston MA 02115

October 2003

1Corresponding author: Northeastern University

Department of Mechanical Engineering, 334 SN

A tapered interference fit provides a mechanically reliable retention mechanismfor the implant-abutment interface in a dental implant Understanding the mechanicalproperties of the tapered interface with or without a screw at the bottom has been thesubject of a considerable amount of studies involving experiments and finite element(FE) analysis In this paper approximate analytical formulas are presented to investigatethe effects of the parameters affecting the mechanical properties of a pure taperedinterference fit It is shown that the connection strength of the tapered interference fitinterface, characterized by the pull-out force, is a function of the taper angle, the contactlength, the inner and outer radii of the implant, the static and the kinetic coefficients offriction, and the elastic modulii of the implant/abutment materials The efficiency of thetapered interference fit abutment attachment method, which is defined as the ratio of thepull-out force to insertion force, was found to be greater than one, for taper angles thatare less than 6o and when the friction coefficient is greater than 0.2 The magnitude of thepull-out and insertion force depend significantly on the insertion depth, contact length,radii of the implant and elastic modulus of the material

Keywords: Dental implants; Taper lock; Morse taper; Conical interference fit; Tapered

interference fit; Connection mechanism; Pull-out force; Loosening torque

The reliability and the stability of an implant-abutment connection mechanism is

an essential prerequisite for long-term success of dental implants [1] High rate of screwcomplications such as screw loosening has been encountered with screw-type implant-abutment connection mechanism [2,3] Inadequate preload, the misfit of the matingcomponents and rotational characteristics of the screws were considered to be the reasonsleading to screw loosening or fracture [3] A tapered implant-abutment attachment with orwithout a screw is an alternative method to the screw type attachment systems In thispaper an abutment which uses only the tapered interference fit as the connection means is

called a tapered interference fit (TIF), whereas the term taper integrated screwed-in (TIS)

abutment is used to describe an abutment which uses a screw and a tapered fit together.Four commercial implant systems are shown in Fig 1 The design by Nobel Biocare(Nobel Biocare AB, Göteborg, Sweden) uses a screw, the designs by Ankylos (DegussaDental, Hanau-Wolfgang, Germany) and ITI (Institut Straumann AG, Waldenburg,Switzerland) use TIS type abutments; and the design by Bicon (Bicon Inc., Boston, MA,USA) uses the TIF type abutment

The main advantage of the TIS abutment is reducing screw-loosening incidents,attributed to the increased interfacial strength between implant and abutment A highincidence of screw loosening, up to 40%, was found for systems using screw-onlyimplant-abutment connection; whereas, the failure rate for tapered interface implants waslower, as much as 3.6% to 5.3% [4] A retrospective study with 80 implants showed thatTIS connection provides a very low incidence of failure [5] The lack of retrievabilitycould be considered as the disadvantage of a TIS system [6] Clinical studies showing the

success of the TIS type implant-abutment interface encouraged the researchers andimplant companies to focus on understanding and evaluating the mechanical properties ofthe tapered interface.

A considerable amount of experimental and finite element studies were performed

on understanding the mechanical properties of the tapered implant-abutment interfacewith or without screw [2] The mechanics of a TIF type implant was first explainedanalytically by O’Callaghan et al [9] and then by Bozkaya and Müftü [7] Approximateanalytical solutions for the contact pressure, the pull-out force and loosening torqueacting in a tapered interference were developed by modeling the tapered interference as aseries of cylindrical interferences with variable radii These formulas were verified bynon-linear finite element analyses for different design parameters [7] TIS type implantsare investigated analytically in [10]; closed-form formulas are developed for estimatingthe tightening and loosening torque values and to evaluate the efficiency of the implant-abutment interface

An elastic-plastic finite element analysis of a TIF implant-abutment interface,with different insertion depths, showed that the stresses in the implant and abutmentlocally exceeds the yield limit of the titanium alloy at the tips of the interface for aninsertion depth of 0.10 mm The plastic deformation region spreads radially into implant,for insertion depths greater than 0.1 mm It was also found that the plastic deformationdecreases the increase in the pull-out force due to increasing insertion depth Theoptimum insertion depth is obtained when the implant starts to deform plastically [7]

A similar interface to the tapered implant-abutment exists between the sleeve andthe bone in total hip prosthesis where the tapered cone is press-fit to the sleeve drilled to

a mating tapered shape Pennock et al investigated the influence of the dryness of thetaper components, impaction force, number of impacts required to assemble the taper andthe taper angle on the pull-out force [8] The pull-out force was found to be linearlyproportional to the insertion force The experiments with successive impactions showedthat pull-out force gained from the multiple impactions is equal to the pull-out forcegained from the single largest impaction

In this paper, approximate closed-form formulas are developed for a) estimatingthe insertion force and b) evaluating the efficiency of the TIF abutments The implant isassumed to be a cylinder, and the taper of the abutment is modeled as a stack ofcylindrical interference fits with variable radius as in [7] Commercially availableimplants are not cylindrical; they typically have a variable outer radius profile This issuehas been addressed in the authors' previous work [7] The equations developed here,provide a relatively simple way of assessing the interdependence of the geometric andmaterial properties of the system; and in one case, presented later, show a reasonablygood match with experimental measurements

THEORY

Figure 2 describes the geometry of a TIF abutment system The insertion force F i

required to seat a taper lock abutment into the matching implant is typically applied bytapping The interference fit takes place, once the abutment is axially displaced by anamount ∆z by tapping Interference gives rise to contact pressure p z whose magnitude c( )

changes along the axial direction z of the cone [7] The resultant normal force N (Figure

2b), acting normal to the tapered face of the abutment, is obtained by integrating p z c( )

along the length s of the interference, [7]

2 2

where L c is the contact length, b 2 is the outer radius of the implant, r ab is the bottom radius

of the abutment, θ is the taper angle as shown in Figure 2, and, E is the elastic modulus of

the implant and abutment, assumed to be made from the same material

An average value for the insertion force F i can be found from the energy balance,

where the work done by the insertion force W i is equal to the sum of the work done

against friction W f and the strain energy U t stored in the abutment and the implant This isexpressed as,

W =F z W∆ = +U (0)The work done against friction W f by sliding a tangential force µk N along the side

s of the taper, by a distance ∆s, is found from,

2

2 2

During the insertion of the abutment, some portion of the work done by theinsertion force is stored in the abutment and the implant as strain energy The total strain

energy U t of the system is given by,

where the radial and tangential stresses are σ rr and σ θθ and the radial and tangential strains

are ε rr and ε θθ , and the superscripts ‘a’ and ‘i’ refer to the abutment and the implant, respectively The radius of the abutment b 1 varies along the axial direction z as

tan 1 2

tan 1

1 2

The total strain energy U t of the system is calculated by using Eqns (5)-(9) Once U t is

evaluated, the insertion force F i can be found in closed form, from Eqns (2) and (4) Thisexpression is not given here in order to conserve space However, its results are presentedlater in the paper

Efficiency of a Tapered Interference Fit Abutment

The efficiency ηc of a TIF type abutment system is defined here as the ratio of the pull-out force F p to the insertion force F i,

p c i

F F

η = (0)

An approximate relation for the efficiency can be obtained by noting that in Eqns (1)-(9)

the strain energy U t of the system is small as compared to the work done against friction

For example, the strain energy U t of the system is approximately 6% of the total work

done W i for a 5 mm implant-abutment system, using the parameters given in Table 1.With this assumption the insertion force can be approximated by considering only thework done against friction (W i ≅W f) as,

2 2

Critical Insertion Depth

The interference fit results in a stress variation in the implant and the abutment aspredicted by equations (6)-(9) Typical circumferential σθθand radial σrr stress variation

along the radial direction (r/r ab) in the abutment and the implant, as predicted by these

formulas, is presented in Figure 3, for different locations (z) along the contact length L c.

This figure shows that the maximum stresses occur in the implant at location z = L ccosθ ,

where the abutment radius is b 1 = r ab It is clear, from equations (6)-(9), that both radialand circumferential stresses are linearly proportional to the insertion depth ∆z Thus a

critical insertion depth value exists which causes plastic deformation of the implantmaterial The von Mises stress yield criterion is used to determine the onset of yielding.The equivalent von Mises stress is defined as,

12

σ = σ σ− + σ σ− + σ σ− (0)

where the principal stresses σ1, σ2 and σ3 are σθθ, 0 and σrr respectively Then thefollowing relation for the critical insertion depth ∆z p, which causes the onset of plasticdeformation is obtained,

1/ 2 2 2

and R c is a stress concentration factor It should be noted that the plain stress elasticityapproach used here provides only approximate answers One drawback, of this approach

is that it does not capture the stress concentrations at the ends of the contact region [7]

The stress concentration factor R c, which has a value greater than one,is an attempt totake this effect into account.

RESULTS

The parameters of the implant-abutment system, given in Table 1, were taken asbase values to investigate the mechanics of the TIF type abutments

Checking the Insertion Depth Formula

In Figure 4 the insertion depth ∆z is plotted as a function of work done during insertion W i (= F i ∆z) The solid lines indicate the predictions based on the formulas

developed here, and the circles indicate the curve fit to the experimental results ofO’Callaghan et al [9] The curve fit, which is valid in the range 10-3 ≤ ∆z ≤ 6×10-3

inches, is given as ∆z = 1.9×10-3W i0.579, where the units of ∆z and W i are “inch” and W i

“oz.in,” respectively On the other hand, by considering, for example, the simplified

insertion force formula F i given in equation (11), the insertion depth ∆z is found to be proportional to W i 0.5 The error between the experimental curve fit formula and this work

is plotted as broken lines in Figure 4, and is seen to be less than 20% The discrepancy islargely due to the plastic deformation of the implant which is predicted to start around ∆z

= 0.13 mm and occupy a wider area at deeper ∆z values Therefore, it is concluded that equation (11) provides a fairly good estimate of the insertion force F I, when the materialremains elastic

Critical Insertion Depth

Figure 5a shows the effect of the bottom radius of the abutment r ab on the criticalinsertion depth ∆z p (Eqn (16)) for different taper angles θ This figure demonstrates that if

a design has small radius r ab and a large taper angle θ, then onset of plastic deformation

occurs at a lower insertion-depth value ∆z Figure 5b shows the variation of the critical

insertion depth ∆z p with the outer radius b 2 of the implant for different abutment radii r ab.This figure indicates that the critical insertion depth decreases with increasing implantradius This result may seem counter intuitive at first, but it can be explained by noting

that the contact pressure also increases with b 2 at the tip of the abutment[7] Therefore,

the stress levels rise with increasing (b 2 − r ab) distance On the other hand, for a fixed

value of implant radius b 2 , increasing the abutment radius r ab has the effect of increasingthe value of the critical insertion depth

Effects of System Parameters on Efficiency

The effect of the design parameters on the efficiency ηc of the system isinvestigated for the TIF interface in Figure 6, using Eqns (10) and (13) with complete and

approximate insertion force F i formulas Investigation of Eqn (13) shows that theefficiency of the interface η%c depends on the kinetic and static coefficients of friction μ,

and taper angle θ In Figure 6, both the exact ηc and approximate η%c efficiency relations

are plotted for different taper angles θ in the range 1-10o, coefficient of friction μ

( =µk =µs) in the range 0.1-0.9 and the kinetic coefficient of friction as a fraction of staticcoefficient of friction µk s/ in the range 0.7-1 for μ s = 0.5 Figure 6a and Figure 6c show

that increasing θ and µk s/ results in efficiency reduction, whereas Figure 6b shows that

increasing μ results in efficiency increase For θ smaller than 5.8o, the efficiency of theinterface is larger than 1 For high taper angles such as 10o, the efficiency of the interface

is around 0.5 Increasing coefficient of friction from 0.1 to 0.2 increases the efficiency

from 1.24 to 1.56 A further increase in the coefficient of friction results in an increase inthe efficiency with decreasing slope as shown in Figure 6b As the difference betweenstatic and kinetic coefficient of friction is increased by taking the static frictioncoefficient larger, the efficiency of the system increases A difference of 30% of the staticfriction coefficient results in an efficiency of 2.6

The accuracy of the simplified insertion force F i formula in Eqn (11), is alsoinvestigated in Figure 6 In general, it is seen that Eqn (11) overestimates the efficiency

of the attachment The error introduced by the use of this equation increases with

increasing θ and decreasing μ The simplified formula can be used with less than 10%

error for the following ranges, 0.2 ≤ μ ≤ 0.9 and 1o≤ θ ≤ 2.4o

Effects of System Parameters on Forces

In this work the implant is assumed to be a cylinder Commercially availableimplants are not cylindrical; they typically have a variable outer radius profile This issuehas been addressed in the authors' previous work [7] Eqns (11) and (12) provide arelatively simple way of assessing the interdependence of the geometric and material

properties of the system For example, the magnitudes of the pull-out F p and insertion

forces F i , found in Eqns (11) and (12), depend on the parameters ∆z, E, μ k , μ s linearly; on the parameters b 2 , r ab parabolically; on the parameter L c in a cubic manner; and, on the

parameter θ trigonometrically The details of these functional dependence are given next.

Effect of Taper Angle

Figure 7a shows the effect of taper angle θ on the insertion and pull-out forces, F i

and F p given by Eqns (11) and (12), respectively In evaluating this figure, theinterference δ = ∆z tanθ was kept constant at 4 µm for θ = 1.5o and ∆z = 0.1524 mm.

Keeping the δ value constant implies that the insertion force is kept approximatelyconstant as the taper angle varies in the range 1o - 10o In fact Figure 7a shows this

assertion to be correct for the most part The magnitude of the pull out force F p, on theother hand decreases from 1750 N to 500 N in the same range The pull-out forcebecomes less than the insertion force for taper angles greater than 5.8o This figure ingeneral shows that larger taper angles reduce the pull-out force; situation which should beavoided for the long term stability of the interface

Effect of the Contact Length

The pull-out and insertion forces increase with the cube of the contact length L c asshown in Eqns (11) and (12) However, in the region of interest for dental implants, 1 <

L c≤ 5 mm, this dependence appears linear, as shown in Figure 7b Increasing the contact

length causes insertion force F i to increase from 150 N at L c = 1 mm to 700 N at L c = 5

mm; In the same L c range the pull-out force F p varies between 290 N and 1250 N

Effect of Friction

The coefficient of friction, despite its significant effects on the insertion and out processes, is difficult to determine exactly First, a distinction must be made betweenthe static and kinetic coefficient of friction values; typically the static coefficient offriction µs is greater than the kinetic coefficient of friction µk Second, the value of the