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

Transcription

1 EFFICIENCY CONSIDERATIONS FOR THE PURELY TAPERED INTERFERENCE FIT (TIF) ABUTMENTS USED IN DENTAL IMPLANTS by Dnçer Bozkaya, Graduate Student Snan Müftü 1, Ph.D. Assocate Professor Northeastern Unversty Department of Mechancal Engneerng Boston MA 0115 Submtted n October 003 Revsed n January, 004 Journal of Bomechancal Engneerng, Transactons of the ASME 1 Correspondng author: Northeastern Unversty Department of Mechancal Engneerng, 334 SN Boston, MA 0115 Tel: , Fax: Emal: smuftu@coe.neu.edu 1

2 ABSTRACT A tapered nterference ft provdes a mechancally relable retenton mechansm for the mplant-abutment nterface n a dental mplant. Understandng the mechancal propertes of the tapered nterface wth or wthout a screw at the bottom has been the subject of a consderable amount of studes nvolvng experments and fnte element (FE) analyss. In ths paper, approxmate closed-form formulas are developed to analyze the mechancs of a tapered nterference ft. In partcular the nserton force, the effcency, defned as the rato of the pull-out force to nserton force, and the crtcal nserton depth, whch causes the onset of plastc deformaton, are analyzed. It s shown that the nserton force s a functon of the taper angle, the contact length, the nner and outer rad of the mplant, the statc and the knetc coeffcents of frcton, and the elastc modul of the mplant/abutment materals. The effcency of the tapered nterference ft, whch s defned as the rato of the pull-out force to nserton force, s found to be greater than one, for taper angles that are less than 6 o when the frcton coeffcent s 0.3. A safe range of nserton forces has been shown to exst. The lower end of ths range depends on the maxmum pull-out force that may occur due to occluson n the multple tooth restoratons and the effcency of the system; and the upper end of ths range depends on the plastc deformaton of the abutment and the mplant due to nterference ft. It has been shown that usng a small taper angle and a long contact length wdens the safe range of nserton forces. Keywords: Dental mplant; Tapered nterference ft; Pull-out force; Inserton force, Effcency of the attachment, Implant-abutment nterface

3 INTRODUCTION A dental mplant s a prosthetc devce of alloplastc materal mplanted nto the oral tssues beneath the mucosa and perosteal tssues and nto the jaw bone to support a fxed or removable prosthess. An abutment s the component of the dental mplant system, whch helps the soft tssue heal around t, or serves to support and/or retan the prosthess. Prosthetc abutments can be connected to the mplant mmedately followng surgcal placement or after osseontegraton takes place dependng on the decson of tmng of the loadng. The abutment s retaned n the mplant by employng a mechancal attachment method. Ideally the abutment should stay fxed wth respect to the mplant throughout the lfe of the mplant. In the most common mechancal attachment method, the abutment s secured to the mplant by usng a retanng-screw. In other desgns, a taper-ntegrated screw (TIS) or a purely tapered nterference ft (TIF) are used n order to connect the mplant and the abutment. Relablty of the abutment retenton mechansm s an mportant consderaton for the mplant bomechancs and clncal success, as the nstablty of the mplant-abutment nterface s one of the most commonly observed modes of mplant complcatons [1]. In partcular, n sngle tooth replacements screw loosenng can be a problem. The mechancal desgn of the connecton method, whch s nfluenced by bologcal and clncal factors, has a sgnfcant effect on the relablty of the mplant-abutment nterface, and thus drectly nfluences the long-term success of an mplant system. Occlusal forces on dental abutments act n dfferent drectons and magntudes. The axal component of the occlusal force s predomnantly compressve for a sngle tooth restoraton. However, for multple tooth restoratons supportng a brdge, the axal component of the occlusal force could become tensle wth a magntude as large as 450 N 3

4 []. Desgn of the mplant-abutment nterface should consder these loadng mechansms. In TIF type systems, tensle forces and loosenng torques are the loadng types that could result n abutment loosenng. In systems that rely on screwed-n connectons, compressve forces and loosenng torques could do the same. Approxmately 80% of the mplants sold n the US feature a pure screw-type mplant-abutment (IA) connecton mechansm [3] whch s represented by the desgn by Nobel Bocare (Nobel Bocare AB, Göteborg, Sweden) external hex mplant body n Fg. 1a. Hgh rate (up to 40%) of clncal complcatons related to the screw, such as loosenng and fracture had been encountered wth the screw-retaned abutment connecton mechansm, partcularly n sngle tooth replacements [4,5]. Inadequate screw preload, the msft of the matng components and rotatonal characterstcs of the screws were consdered to be the reasons leadng to screw loosenng or fracture [5]. These problems have been allevated, n part by materal selecton and surface treatment, n the recent versons of ths type of attachment method [6]. Screw loosenng has been less problematc wth the taper-ntegrated screwed-n (TIS) abutments, where the tapered, top end of the screw makes an nterference ft wth the mplant [7-9]. In the TIS abutments, the connecton s secured by the frctonal forces on the screw threads and on the tapered secton. Dependng on the desgn, the contact area and the contact forces on the tapered secton of the abutment are consderably larger as compared to those of the screw threads. Therefore, most of the resstance to loosenng torques occurs n the tapered secton [10]. In the TIS desgns by Ankylos (Degussa Dental, Hanau-Wolfgang, Germany) and ITI (Insttut Straumann AG, Waldenburg, Swtzerland), shown n Fgs 1b and 1c, 4

5 respectvely, a tapered screw s ncorporated to the end of the abutment, thus elmnatng the need to use a thrd component. The market share of mplant sales for the ITI system n the US s approxmately 15% [3]. The prosthetc complcaton rate of 3.6% to 5.3%, for the ITI mplant system s consderably lower than the retenton mechansm usng only a screw [7-9]. Mechancs of the TIS method for the ITI system s analyzed by fnte element method by Merz et al. [7]. TIS type mplants are nvestgated analytcally n [10] where closed-form formulas are developed for estmatng the tghtenng and loosenng torque values. The occlusal forces apply axal and tangental forces, and moments on the mplants, n part due to the geometry of the prosthetc components [11]. Ths complcated loadng mechansm could apply a large enough torque to loosen the abutment. Effcency, defned as the rato of the loosenng torque to tghtenng torque, has been used as an evaluaton metrc for the TIS type IA connecton method. Effcency of the ITI system has been studed expermentally. At clncally relevant torque levels of N-mm, dfferent nvestgators found dfferent effcency ranges; by Norton [1]; Sutter et al. [13], and Squre et al. [14]. The general range of effcency was predcted to be , by Bozkaya and Müftü when the statc coeffcent µ s was vared between 0.1 and 1 and the knetc frcton coeffcent µ k was vared between 70 and 100% of µ s [10]. The authors showed that low effcency was assocated wth low frcton coeffcent and hgh effcency s related to the dfference between the knetc and statc frcton coeffcents. The thrd method of attachment uses a tapered abutment and an mplant wth a tapered recevng hole. The engagement of the abutment wth the mplant s provded by 5

6 an mpact force actng along the longtudnal axs of the abutment. The tapered nterference ft (TIF) desgn by Bcon (Bcon Inc., Boston, MA, USA) s depcted n Fg 1d. The market share of TIF type mplant systems s small compared to the mplants usng the other two connecton methods mentoned above []. For ths system, prosthetc complcatons related to IA connecton mechansm falures were reported to be 0.74 % for sngle tooth replacements [15]. Smlar to the TIS type connecton mechansm, the tapered surface of the TIF abutments create a relatvely large frctonal resstance area, and the nterference ft provdes the necessary large normal forces for frctonal retenton. Prevously, approxmate analytcal solutons for the contact pressure, the pull-out force and the loosenng torque actng n a TIF-type system were developed, by modelng the tapered nterference as a seres of cylndrcal nterferences wth varable rad by O Callaghan et al. [16] and then by Bozkaya and Müftü [17]. These formulas were compared wth non-lnear fnte element analyses for dfferent desgn parameters and the results agreed well [17]. An elastc-plastc fnte element analyss of a TIF mplantabutment nterface, wth dfferent nserton depths, showed that the stresses n the mplant and abutment locally exceed the yeld lmt of the ttanum alloy at the tps of the nterface for an nserton depth of 0.10 mm. The plastc deformaton regon spreaded radally nto the mplant, for nserton depths greater than 0.1 mm. It was also found that the plastc deformaton decreases the ncrease n the pull-out force due to ncreasng nserton depth. The optmum nserton depth was obtaned when the mplant starts to deform plastcally [17]. A complete analytcal soluton of the tapered nterference ft has not yet been reported. The cylndrcal nterference ft formulas, on the other hand, can be found n 6

7 many textbooks ncludng Shgley and Mschke [18]. The elastc-plastc analyss of cylndrcal nterference fts was studed, for example, by Gamer and Müftü [19]. Ths paper extends the dscusson about the tapered nterference ft gven n a prevous study by the authors [17]. In partcular, approxmate closed-form formulas are developed for a) estmatng the nserton force; b) evaluatng the effcency of the TIF abutments; c) estmatng the crtcal nserton depth, whch causes the onset of plastc deformaton; and, d) determnng an nserton force range, whch provdes a safe pull-out force durng occluson and prevents plastc deformaton n the materal. These varables are nvestgated wth respect to dfferent parameters. The equatons developed here, provde a relatvely smple way of assessng the nterdependence of the geometrc and materal propertes of the system; and n one case, presented later, show a reasonably good match wth expermental measurements of O Callaghan et al. [16]. The mportant desgn varables that affect the retenton and ther effects are nvestgated. THEORY Fgure descrbes the geometry of a TIF abutment system. The nserton force F requred to seat a taper lock abutment nto the matchng mplant s typcally appled by tappng. The nterference ft takes place, once the abutment s axally dsplaced by an amount z by tappng. Interference gves rse to contact pressure p () z whose magntude changes along the axal drecton z of the cone [17]. The resultant normal force N (Fgure b), actng normal to the tapered face of the abutment, s obtaned by ntegratng p () z along the length s of the nterference, [17] c c πe zlsnθ N = 3 b r L sn 3r + L sn 6b c ( ab) c θ( ab c θ) (1) 7

8 where L c s the contact length, b s the outer radus of the mplant, r ab s the bottom radus of the abutment, θ s the taper angle as shown n Fgure, and, E s the elastc modulus of the mplant and abutment, assumed to be made from the same materal. An average value for the nserton force F can be found from the energy balance, where the work done by the nserton force W s equal to the sum of the work done aganst frcton W f and the stran energy U t stored n the abutment and the mplant. Ths s expressed as, W = F z= Wf + Ut. () The work done aganst frcton W f by sldng a tangental force µ k N along the sde s of the taper, by a dstance s, s found from, s z dz Wf = µ k Nds= µ k N 0 0 cosθ (3) where µ k s the knetc coeffcent of frcton, and the geometrc relaton s = z/cosθ s used. Note that, n ths equaton the knetc frcton coeffcent s used, as abutment nserton s a dynamc process. The work done aganst frcton s calculated from Eqns (1) and (3) as, πµ ke z Lcsnθ f = ab c ab + c 6b ( ) θ( θ) W 3 b r L sn 3r L sn. (4) Durng the nserton of the abutment, some porton of the work done by the nserton force s stored as stran energy n the abutment and the mplant. The total stran energy U t of the system s gven by, Lc cosθ b1 L cosθ b c a a a a ( θθ θθ ) ( θθ θθ ) U = πr σ ε + σ ε drdz+ πr σ ε + σ ε drdz, (5) t rr rr rr rr b1 8

9 where the radal and tangent al stresses are σ rr and σ θθ, and the radal and tangental strans are ε rr and ε θθ, and the superscrpts a and refer to the abutment and the mplant, respectvely. The radus of the abutment b 1 vares along the axal drecton z as b () z = r + ( L cos θ z)tanθ. The stresses and strans for a TIF connecton can be 1 ab c approxmated as follows [17], σ ε σ a rr a rr rr 1 ( ) a E ztanθ b z = σθθ = 1 b1( z) b ( ν) ( ) 1 ( ) a ztanθ 1 b z = εθθ = 1 b1 z b ( ) tanθ b ( ) E zb1 z E zb1 z tanθ b = 1 ; σ 1 θθ b r = + b r ( ) b1 z ztanθ b b1 z ztanθ b εrr = ( 1+ ν) ( 1 ν) ; εθθ ( 1 ν) ( 1 ν) b r + = + + b r ( ) (6) (7) (8) (9) where ν s the Posson s rato. The total stran energy U t of the system s calculated by usng Eqns (5)-(9). Once U t s evaluated, the nserton force F can be found n closed form, from Eqns () and (4). Ths expresson s not gven here n order to conserve space. However, ts results are presented later n the paper. Effcency of a Tapered Interference Ft Abutment The effcency η of a TIF type abutment system s defned here as the rato of the pull-out force F p to the nserton force F, 9

10 F p η =. (10) F An approxmate relaton for the effcency can be obtaned by notng that n Eqns (1)-(9) the stran energy U t of the system s small as compared to the work done aganst frcton. For example, the stran energy U t of the system s approxmately 6% of the total work done W for a 5 mm mplant-abutment system, usng the parameters gven n Table 1. Wth ths assumpton the nserton force can be approxmated by consderng only the work done aganst frcton ( W W ) as, f k c ab c ab c 6b E zl sn F πµ θ = 3( b r ) L snθ[ 3r + L snθ]. (11) The pull-out force of the tapered nterference was gven by Bozkaya and Müftü as [17], π E zl F = 3 b r L snθ 3r + L sn θ ( µ cosθ sn θ)cos θ ( ) [ ] c p ab c ab c s 3b (1) where the statc coeffcent of frcton µ s s used, as the pull-out force s appled on the ntally statonary mplant. The followng smplfed effcency ' η formula for the TIF type abutment s obtaned by usng Eqns (11) and (1), Fp cosθ η ' = = µ s cosθ snθ F µ k ( ). (13) The relatve error ε nvolved n usng Eqn (11) to fnd the nserton force s evaluated as, Crtcal Inserton Depth ( ) ( f t) W + U z W z f t f U W t f ε = = = 1 W + U z W + U W + U f t f t. (14) 10

11 The nterference ft results n a stress varaton n the mplant and the abutment as predcted by Eqns (6)-(9). Typcal crcumferental σ θθ and radal σ rr stress varaton along the radal drecton (r/r ab ) n the abutment and the mplant, as predcted by these formulas, s presented n Fgure 3, for dfferent locatons (z) along the contact length L c. Ths fgure shows that the maxmum stresses occur n the mplant, at locaton z = L c cosθ, where the abutment radus s b 1 = r ab. It s clear, from Eqns (6)-(9), that both radal and crcumferental stresses are lnearly proportonal to the nserton depth z. Thus a crtcal nserton depth value exsts, whch causes plastc deformaton of the mplant materal. The von Mses stress yeld crteron s used to determne the onset of yeldng. The equvalent von Mses stress s defned as, (( ) ( ) ( ) ) 1/ σ = σ σ + σ σ + σ σ (15) where the prncpal stresses σ 1, σ and σ 3 are σ θθ, 0 and σ rr respectvely. Then by evaluatng σ θθ and σ rr at z = L c cosθ and b 1 = r ab from Eqns (8a) and 8(b), the followng relaton for the crtcal nserton depth z p, whch causes the onset of plastc deformaton can be obtaned from Eqn (15), σ r r b 1 Y ab ab zp = Rc E + tanθ b rab where σ Y s the yeld strength of the mplant materal obtaned from unaxal tenson test, 1/ (16) and R c s a stress concentraton factor. It should be noted that the plan stress elastcty approach used here provdes only approxmate answers. One drawback, of ths approach s that t does not capture the stress concentratons at the ends of the contact regon[17]. The stress concentraton factor R c, whch should have a value greater than one, could be used to take ths effect nto account. 11

12 RESULTS The desgn formulas developed above are used to evaluate the effects of varous desgn parameters on the connecton stablty of a TIF system. The desgn parameters are appled n a relatvely wde range around the base values, taken from a Bcon mplant, whch s the most wdely used TIF type mplant system, albet wth a small share of the US market []. The geometrc and materal propertes of ths system are gven n Table 1, along wth the propertes of the tapered secton of the ITI and Ankylos systems. Ths table shows that the geometrc parameters are smlar between these systems, wth the excepton of the taper angle where the TIF system has the smallest taper angle. The geometrc parameters of the TIF system are vared n the neghborhood of ts base parameters. In selectng the appled ranges, ndcated n Table 1, practcal mplant sze and values of the Ankylos and ITI systems were consdered. Checkng the Inserton Depth Formula In the nserton depth z s plotted as a functon of work done durng nserton W (= F z). The sold lnes ndcate the predctons based on the formulas developed here, and the crcles ndcate the curve ft to the expermental results of O Callaghan et al. [16]. The curve ft, whch s vald n the range 0.05 z 0.15 mm, s gven by O Callaghan et al. as z = W 0.579, where the unts of z and W are mm and N-mm, respectvely. On the other hand, by consderng, for example, the smplfed nserton force formula F gven n Eqn (11), the nserton depth z s found to be proportonal to W 0.5. The error between the expermental curve ft formula and ths work s plotted as 1

13 broken lnes n, and s seen to be less than 0%. The dscrepancy s largely due to the plastc deformaton of the mplant, whch s predcted to start around z = 0.13 mm and occupy a wder area at deeper z values. Therefore, t s concluded that Eqn (11) provdes a farly good estmate of the nserton force F, when the materal remans elastc. Crtcal Inserton Depth Fgure 5a shows the effect of the bottom radus of the abutment r ab on the crtcal nserton depth z p (Eqn (16)) for dfferent taper angles θ. Ths fgure demonstrates that f a desgn has small radus r ab and a large taper angle θ, then onset of plastc deformaton occurs at a lower nserton-depth value z. Fgure 5b shows the varaton of the crtcal nserton depth z p wth the outer radus b of the mplant for dfferent abutment rad r ab. Ths fgure ndcates that the crtcal nserton depth decreases wth ncreasng mplant outer radus. Ths result may seem counter ntutve at frst, but t can be explaned by notng that the contact pressure also ncreases wth b at the tp of the abutment [17]. Therefore, the stress levels rse wth ncreasng (b r ab ) dstance. On the other hand, for a fxed value of mplant radus b, ncreasng the abutment radus r ab has the effect of ncreasng the value of the crtcal nserton depth. Effects of System Parameters on Effcency The effect of the desgn parameters on the effcency η of the system s nvestgated for the TIF nterface n Fgure 6, usng Eqns (10) and (13) wth complete ( F ) and smplfed ( F ) nserton force formulas. Investgaton of Eqn (13) shows that the effcency of the nterface η ' depends on the knetc and statc coeffcents of frcton 13

14 µ, and taper angle θ. In Fgure 6, both the complete η and smplfed η ' effcency relatons are plotted for dfferent taper angles θ n the range 1-10 o, coeffcent of frcton µ ( = µ = µ ) n the range and the knetc coeffcent of frcton as a k s fracton of statc coeffcent of frcton µ / µ n the range for µ s = 0.5. Fgure 6a k and Fgure 6c show that ncreasng θ and µ / µ results n effcency reducton, whereas Fgure 6b shows that ncreasng µ ( = µ = µ ) results n effcency ncrease. For θ smaller k s than 5.8 o, one fndsη > 1. For large taper angles, such as θ = 10 o, the effcency of the nterface s around 0.5. Increasng coeffcent of frcton from 0.1 to 0. ncreases the effcency from 1.4 to A further ncrease n the coeffcent of frcton results n an ncrease n the effcency wth decreasng slope as shown n Fgure 6b. As the dfference between statc and knetc coeffcent of frcton s ncreased by takng the statc frcton coeffcent larger, the effcency of the system ncreases. A dfference of 30% of the statc frcton coeffcent results n an effcency of.6. s k s The relatve error ε between usng F and F s defned by Eqn (14). The accuracy of the smplfed nserton force F formula (Eqn (11)), whch gves an nsght to nterdependence of the desgn parameters, s also nvestgated n Fgure 6. In general, t s seen that Eqn (13) overestmates the effcency of the attachment. The relatve error ntroduced by usng F ncreases wth ncreasng θ and decreasng µ. The smplfed formula can be used wth less than 10% relatve error for the followng ranges, 0. µ 0.9 and 1 o θ.4 o. 14

15 Effects of System Parameters on Forces In ths work the mplant s assumed to be a cylnder. Commercally avalable mplants are not cylndrcal; they typcally have a varable outer radus profle. Ths ssue has been addressed n the authors' prevous work, where t was shown that ths condton ntroduces a small effect [17]. Eqns (11) and (1) provde a relatvely smple way of assessng the nterdependence of the geometrc and materal propertes of the system. For example, the magntudes of the nserton F and the pull-out F p forces, found n Eqns (11) and (1), depend on the parameters z, E, µ lnearly; on the parameters b, r ab parabolcally; on the parameter L c n a cubc manner; and, on the parameter θ trgonometrcally. The detals of these functonal dependence are nvestgated next. Effect of Taper Angle Fgure 7a shows the effect of taper angle θ on the nserton F and pull-out forces F p. In evaluatng ths fgure, the nterference δ = z tanθ was kept constant at 4 µm for θ = 1.5 o and z = mm. Keepng the δ value constant mples that the nserton force s kept approxmately constant as the taper angle vares n the range 1 o - 10 o. In fact Fgure 7a shows ths asserton to be correct for the most part. The magntude of the pullout force F p, on the other hand, decreases from 1750 N to 500 N n the same range. The pull-out force becomes less than the nserton force for taper angles greater than 5.8 o. Ths fgure n general shows that larger taper angles reduce the pull-out force; ths s a stuaton, whch should be avoded for the long term stablty of the nterface. 15

16 Effect of the Contact Length The pull-out and nserton forces ncrease wth the cube of the contact length L c as shown n Eqns () and (1). However, n the regon of nterest for dental mplants, 1 < L c 5 mm, ths dependence appears lnear, as shown n Fgure 7b. Increasng the contact length causes nserton force F to ncrease 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 vares between 90 N and 150 N. Effect of Frcton The coeffcent of frcton, despte ts sgnfcant effects on the nserton and pullout processes, s dffcult to determne exactly. Frst, a dstncton must be made between the statc and knetc coeffcent of frcton values; typcally the statc coeffcent of frcton µ s s greater than the knetc coeffcent of frcton µ k [0]. Second, the value of the coeffcent of frcton could be affected by the presence of salva, whch acts as a lubrcant n the contact nterface. The frcton coeffcent could also depend on the surface roughness and treatment [1]. Wth many factors affectng ts value, t s mportant to understand the effect of a relatvely wde range of frcton coeffcents, on the mechancs of the connecton. The dependence of the nserton force F on the knetc frcton coeffcent µ k, and the pull-out force F p on the statc frcton coeffcent µ s are shown to be lnear n Eqns () and (1). Fgure 7c demonstrates the effect of coeffcent of frcton when µ k = µ s. Ths fgure shows that the pull-out force F p s more adversely affected by the reducton of coeffcent of frcton. For example, at µ = 0.1 the pull-out force s equal to the nserton force (00 N), but at µ = 0.7 the pull-out force (000 N) s nearly twce as much as the 16

17 nserton force (1000 N). Ths behavor s also evdent n the smplfed effcency formula, gven n Eqn (13), and plotted n Fgure 6b. Close nspecton of ths formula shows that when µ k = µ s, and for nfnte frcton (µ ) the smplfed effcency of the system behaves as η ' cos θ. The complete and smplfed effcency formulas approach ths lmt n Fgure 6b, whch has the value of for θ = 1.5 o. Fgure 7d shows the effect of the knetc coeffcent of frcton on the nserton force F by varyng the rato µ k /µ s n the range for µ s = 0.5. Ths fgure shows that the nserton force vares lnearly n ths range from 580 N to 800 N. Range of Inserton Forces Two factors lmt the magntude of the nserton force F to be appled to the abutment. Frst, F should be suffcently large to seat the abutment securely, and hence provde enough frctonal resstance to pull-out forces. Second, excessve plastc deformaton of the mplant and the abutment due to nterference-ft should be avoded. The mnmum admssble nserton force mn F should be based on the maxmum pull-out force F p whch could occur durng occluson. Brunsk states ths value to be 450 N []. Then, for a gven desgn, the admssble nserton force (16) and t s found as descrbed n Eqn (). mn F value can be found from Eqn (10). The maxmum max F depends on the crtcal nserton depth z p gven by Eqn Next the effects of the taper angle θ and the contact length L c on the nserton force F are nvestgated. Arguably, θ and L c are two of the many desgn parameters whch could be changed wthout much mpact on the bomechancs of the system. A relaton between the nserton force and the pull-out force can be obtaned from Eqns () 17

18 and (1); as both the nserton force F and the pull-out force F p depend on nserton depth z n a lnear fashon, ther nterdependence s also lnear. Note that ths lnear dependence was also shown n an expermental work presented n reference []. The varaton of the pull-out force F p wth respect to the nserton force F s plotted n Fgure 8 for θ = 1.5 o, 3 o and 4.5 o. The pull-out force s taken as 400 N. The maxmum nserton force max F s evaluated for dfferent contact lengths of L c =.5, 3.5, and 4 mm for θ = 1.5 o, as descrbed above, and marked on the fgure. Ths fgure shows that as the contact length L c decreases, the maxmum admssble nserton force mn max F also decreases. In fact, there exsts a crtcal contact length where F = F. It max s, therefore, concluded that, n order to allow a wde range of nserton force F for the clncan, a relatvely long contact length L c s necessary. The admssble range of nserton forces F for taper angle values of θ = 1.5 o, 3 o and 4 o and contact length values of L c =.5, 3.5 and 4 mm are presented n Table. Ths table shows that usng a large taper angle θ has an adverse effect on the desgn; as the taper angle ncreases from 1.5 o to 4.5 o t s seen that the mnmum nserton force ncreases, the admssble nserton force range narrows and the maxmum pull-out force becomes lower. SUMMARY AND CONCLUSIONS There may be sgnfcant dfferences n load magntudes and drectons actng on the abutment of a sngle tooth restoraton, as compared to that of a multple tooth restoraton. In a sngle tooth restoraton, the abutment could be subjected to a compressve axal load, a loosenng torque and a bendng moment. Therefore, pull-out s not expected to be a problem for a TIF type system. However, t has been shown that 18

19 tensle axal forces may act on the abutments supportng multple tooth restoratons. Ths, along wth the loosenng torque, s the man load component that could cause abutment loosenng n the TIF mplants. The effects of loosenng torques have been nvestgated n [17]. In ths paper, the pull-out force s consdered, along wth nserton force, nserton effcency and plastc deformaton of the materals. The tensle (pull-out, F p ) force value at whch a TIF type abutment becomes loose s an ndcaton of the stablty of the mplant-abutment connecton. The present study showed that F p s lnearly proportonal to the nserton force F and to the nserton depth z. The nserton force, whch s provded by an mpact, could be dffcult to control and could vary between clncans. A safe range of nserton forces has been shown to exst. The lower end mn F of ths range s determned by the maxmum pull-out force appled by occluson and the effcency of the system. The upper end max F of ths range s determned by the plastc deformaton of the abutment and the mplant due to nterference ft. The effects of taper angle θ and contact length L c on mn F and max F have been nvestgated. It has been shown that small taper angle and long contact length mproves the safe range of nserton forces. It should be noted that n determnng the safe-range of nserton forces, the other system parameters such as r ab, b, E, µ k, and µ s could also be vared. However, often, there are practcal constrants on these parameters. For example, E s constraned by the elastc modulus of the mplant materal, b s constraned by the avalable bone space and the stresses transferred to the bone, and r ab s constraned by b and θ. Precse control of both of the frcton coeffcent values µ s and µ k s nearly mpossble. Therefore, emphass has been placed on varyng the taper angle θ and the contact length L c. 19

20 The effcency η, whch s defned as the rato of the pull-out force to the nserton force s another sgnfcant parameter n evaluatng the stablty of the attachment. The taper angle θ and frcton coeffcent are determned to be the parameters that have the most sgnfcant nfluences on the effcency. Surprsngly, contact length L c, mplant radus b and elastc modulus E have no sgnfcant effect on η. A large frcton coeffcent mproves the effcency of the nterface. However, the frcton coeffcent could be subject to large uncertantes, due to varous factors such as presence of salva, surface fnsh of the matng components, etc. Therefore, use of a small taper angle n the desgns ensures relatvely hgh effcency of the TIF type connecton mechansm. Ths study provdes an nsght nto the effect of varous parameters on the stablty of the TIF type attachment method used n dental mplants. Approxmate closed form formulas are presented to evaluate the effcency of the mplant-abutment nterface, as well as to suggest safe ranges of nserton forces. Future studes should nclude expermental determnaton of frcton coeffcents n dental mplants under varous loadng and bologcal condtons. ACKNOWLEDGMENTS The authors gratefully acknowledge the dscussons they had wth Mr. Fred Weekley (Unted Ttanum, Wooster, OH) and the partal support of Bcon Implants (Bcon Inc., Boston, MA) for ths work. The help of Dr. Al Müftü (Tufts Unversty, Boston, MA) durng all stages of ths work s also gratefully acknowledged. 0

21 REFERENCES 1. Scacch, M., Merz, B.R. and Schär, A.R. (000), "The development of the ITI Dental Implant System," Cln Oral Imp Res 11, pp Brunsk, J. B. (1999), In vvo bone response to bomechancal loadng at the bone/dental-mplant nterface, Adv Dent Res, 13, pp Anonyomous, (001), U.S. Markets for Dental Implants 001: Executve Summary, Implant Dentstry, 10:4, Geng, J., Tan, K. and Lu, G., (001), "Applcaton of fnte element analyss n mplant dentstry: A revew of the lterature," J Prosthet Dent, 85, pp Schwarz, M.S., (000), "Mechancal complcatons of dental mplants," Cln Oral Impl Res, 11, pp Martn, W. C., Woody, R.D., Mller B.H., Mller A.W. (001), Implant abutment screw rotatons and preloads for four dfferent screw materals and surfaces, J Prosthet Dent, 86, pp Merz, B.R., Hunenbart, S. and Belser, U.C., (000), "Mechancs of the mplantabutment connecton: An 8-degree taper compared to a butt jont connecton," Int J Oral Maxllofac Implants, 15, pp Levne R.A., Clem D.S., Wlson T.G. Jr., Hggnbottom F., Solnt G., (1997), Multcenter retrospectve analyss of the ITI mplant system used for sngle-tooth replacements: Prelmnary results at 6 or more months of loadng, Int J Oral Maxllofacal Implants, 1, Levne R.A., Clem D.S., Wlson T.G. Jr., Hggnbottom F., Saunders S.L., (1999), A multcenter retrospectve analyss of the ITI mplant system used for sngle- 1

22 tooth replacements: Results of loadng for or more years, Int J Oral Maxllofacal Implants, 14, pp Bozkaya, D. and Müftü, S. (004) "Mechancs of the Taper Integrated Screwed-In (TIS) Abutments Used Dental Implants," accepted for publcaton J Bomech. 11. Warren Bdez, M. and Msch C.E. (1999), Clncal bomechancs n mplant dentstry, n Implant Dentstry, second edton, ed. Msch C.E., Mosby, St. Lous, MO, pp Norton M.R., (1999), Assessment of cold weldng of the nternal concal nterface of two commercally avalable mplant systems, J Prosthet Dent, 81, pp Sutter F., Weber H.P., Sorensen J., Belser U., (1993) The new restoratve concept of the ITI Dental Implant System: Desgn and engneerng, Int J Perodont Rest Dent, 13, pp Squer, R.S., Psoter, W.J. and Taylor, T.D., (00), "Removal torques of concal, tapered mplant abutments: The effects of anodzaton and reducton of surface area," Int J Oral Maxllofac Implants, 17, pp Müftü, A., Chapman R.J., (1998), Replacng posteror teeth wth freestandng mplants: four year prosthodontc results of a prospectve study, J Am Dent Assoc, 19, pp O'Callaghan, J., Goddard, T., Brch, R., Jagodnk, J.J. and Westbrook, S., (00), "Abutment hammerng tool for dental mplants," Amercan Socety of Mechancal Engneers, IMECE-00 Proceedngs Vol., Nov , 00, Paper No. DE- 511.

23 17. Bozkaya, D. and Müftü, S., (003) "Mechancs of the tapered nterference ft n dental mplants," J Bomech, 36:11, pp Shgley, J.E. and Mschke, C.R. (001) Mechancal Engneerng Desgn, McGraw Hll, Boston, MA. 19. Gamer, U., Müftü, S., (1990) On the elastc-plastc shrnk ft wth supercrtcal nterference, ZAMM 70:11, pp Rabnowcz, E. (1995), Frcton and Wear of Materals, John Wley and Sons, NY. 1. Adams G.G., Müftü S., Mohd Azar N., (003), A Scale-Dependent Model for Mult-Asperty Model for Contact and Frcton, Journal of Trbology, 15, pp Pennock, A.T., Schmdt, A.H. and Bourgeault, C.A., (00), "Morse-type tapers: Factors that may nfluence taper strength durng total hp arthroplasty," The Journal of Arthroplasty, 17, pp

24 Lst of Fgures Fgure 1 Varous mplant-abutment attachment methods are used n commercally avalable dental mplants. a) screw only; b) and c) TIS; d) TIF type attachment methods Fgure a) Defnton of the desgn parameters of the tapered nterface. b) The free body dagram of the tapered abutment depctng the force balance durng nserton. Fgure 3 The dstrbuton of the radal and crcumferental stresses n the abutment and the mplant at dfferent axal (z) locatons. Fgure 4 The nserton depth as a functon of work of nserton. Expermental results of O'Callaghan et al. [16] represented by the curve ft formula, z = W are compared wth the results of ths work calculated for the base parameters of Bcon system. Fgure 5 The crtcal nserton depth z p, whch causes onset of plastc deformaton as a functon of a) bottom radus of the abutment r ab for dfferent taper angles θ, and b) mplant outer radus b for dfferent r ab values. The other parameters, whch are fxed, are reported n Table 1. Fgure 6 The varaton of the effcency of the attachment wth respect to dfferent parameters. θ, µ and µ / µ are the sgnfcant parameters affectng the effcency of the k s attachment. The other parameters, whch are fxed, are reported n Table 1. Fgure 7 Varaton of pull-out F p and nserton F force wth a) taper angle θ, b) contact length L c, c) coeffcent of frcton, d) rato of knetc to statc frcton coeffcent; and e) varaton of the pull-out force vs. nserton force. The other parameters, whch are held fxed, are reported n Table 1. Fgure 8 The pull-out force F p as a functon of nserton force F, for dfferent contact lengths L c and taper angles θ. 4

25 Lst of Tables Table 1 The parameters of the tapered nterface n three commercally avalable systems (mplant: ; abutment: ; ITI mplant: S and the matchng ITI-abutment: ; and Ankylos part number ). The parameters of Bcon were taken as the base and the ranges of varables were tested usng the developed relatons. mn max Table Mnmum F and maxmum F nserton forces and the correspondng pullout forces F p are lsted for dfferent taper angles θ and contact lengths L c. * denotes the crtcal contact length when the mnmum requred nserton force s equal to the maxmum nserton force. 5

26 Base Values Range of Parameters ITI Ankylos Bcon Used for TIF System θ ( o ) µ * µ k /µ s , 0.9, 1 L c (mm) b (mm) z (µm) r ab (mm) E (GPa) σ Y (MPa) 950 R c 1 * µ s the frcton coeffcent when t s assumed that µs = µ k. Table 1 The parameters of the tapered nterface n three commercally avalable systems (mplant: ; abutment: ; ITI mplant: S and the matchng ITIabutment: ; and Ankylos part number ). The parameters of Bcon were taken as the base and the ranges of varables were tested usng the developed relatons. 6

27 θ [ o ] L c [mm] η mn max mn max F - F [N] Fp - F p [N] * * * mn max Table Mnmum F and maxmum F nserton forces and the correspondng pull-out forces F p are lsted for dfferent taper angles θ and contact lengths L c. * denotes the crtcal contact length when the mnmum requred nserton force s equal to the maxmum nserton force. 7

28 a) Nobel Bocare b) Ankylos c) ITI d) Bcon Fgure 1 Varous mplant-abutment attachment methods are used n commercally avalable dental mplants. a) screw only; b) and c) TIS; d) TIF type attachment methods. 8

29 abutment z F r θ s z F r µn δ b 1 (z) L c θ N r ab b mplant a) b) Fgure a) Defnton of the desgn parameters of the tapered nterface. b) The free body dagram of the tapered abutment depctng the force balance, durng nserton. 9

30 3.0x10-03 Non-dmensonal stress σ/e.0x x x x10-03 z=0 z=l c cosθ/ z=l c cosθ σ θθ σ rr -.0x10-03 σ θθ a = σ rr a = -P c -3.0x Radal drecton, r/r ab Fgure 3 The dstrbuton of the radal and crcumferental stresses n the abutment and the mplant at dfferent axal (z) locatons. 30

31 Inserton depth, z [mm] Ths work Expermental Data (O'Callaghan et al.) Error Error Inserton work, W [N-mm] Fgure 4 The nserton depth as a functon of work of nserton. Expermental results of O'Callaghan et al. [16] represented by the curve ft formula, z = W are compared wth the results of ths work calculated for the base parameters of Bcon system. 31

32 Crtcal nserton depth, z p (mm) θ = 1.5 o θ = 3.0 o θ = 4.5 o b = 1.50 mm L c = 3.5 mm Crtcal nserton depth, z p (mm) r ab = 0.5 mm r ab = 1.0 mm r ab = 1.5 mm θ = 1.5 o L c = 3.5 mm Abutment bottom radus, r ab (mm) Implant outer radus, b (mm) a) b) Fgure 5 The crtcal nserton depth z p, whch causes onset of plastc deformaton as a functon of a) bottom radus of the abutment r ab for dfferent taper angles θ, and b) mplant outer radus b for dfferent r ab values. The other parameters, whch are fxed, are reported n Table 1. 3

33 Effcency Complete η(eqn (10)) Smplfed η' (Eqn (13)) Relatve Error, ε (Eqn (14)) Relatve Error, ε Effcency Complete η (Eqn (10)) Smplfed η' (Eqn (13)) Relatve Error ε (Eqn (14)) Relatve Error, ε Taper Angle, θ Coeffcent of Frcton, µ (= µ s = µ k ) a) b) Effcency Complete η (Eqn (10)) Smplfed η' (Eqn(13)) Relatve Error ε (Eqn (14)) Relatve Error, ε Rato of Knetc to Statc Frcton Coeffcent, µ k / µ s c) Fgure 6 The varaton of the effcency of the attachment wth respect to dfferent parameters. θ, µ and µ / µ are the sgnfcant parameters affectng the effcency of the k s attachment. The other parameters, whch are fxed are reported n Table 1. 33

34 3000 a) b) F p 000 F p F 000 F Force (N) 1500 Force (N) Taper Angle, θ Contact Length, L c (mm) 3000 c) d) F p 500 F p 000 F 000 F Force (N) 1500 Force (N) Coeffcent of Frcton, µ (= µ s = µ k ) Rato of Knetc to Statc Frcton Coeffcent, µ k / µ s Fgure 7 Varaton of pull-out F p and nserton F force wth a) taper angle θ, b) contact length L c, c) coeffcent of frcton, d) rato of knetc to statc frcton coeffcent; and e) varaton of the pull-out force vs. nserton force. The other parameters, whch are held fxed, are reported n Table 1. 34

35 θ = 1.5 o θ = 3 o θ = 4.5 o Pull-out Force, F p (N) max F for L c = 4 mm max F for L c = 3.5 mm max F for L c =.5 mm F = mn max mm F for L c = 1.94* Inserton Force, F (N) Fgure 8 The pull-out force F p as a functon of nserton force F, for dfferent contact lengths L c and taper angles θ. 35