A New Binding Model Based on Classical Friction

Objective: Binding is an important component of resistance to sliding during orthodontic treatment.  Extensive experimental binding results have been published in the literature.  This study is aimed at providing a fundamental understanding of the relationship between binding and classical friction.  A binding model based on classical friction will be constructed.

Methods: Binding is modeled as the resultant frictional force when the deformed archwire applies "normal forces" on bracket's archwire slot.  The coefficient of friction that is used in this binding model is the same as that of classical friction measured when the archwire is passive in the slot.  Since these "normal forces" are very difficult to measure, Finite Element Analysis (FEA) was used to model binding mechanics.  Experimental data from different archwire and bracket systems was used to verify the model.

Results:  FEA can be used to predict binding forces when the coefficient of classical friction and angulation are known.  This model was applied to stainless steel and alumina brackets coupled with stainless steel and nickel titanium wires. The resultant binding forces from the model were comparable to those that were measured experimentally. For instance, the following table shows a close correlation between the experimental result (calculated from a linear regression with r²=0.93) and FEA result for an 0.022" Clarity™ bracket, a polycrystalline alumina bracket, and an 0.019x0.025" stainless steel archwire. 

Angulation (degrees)	Calculated Experimental Binding Force (cN)	Binding Force from FEA (cN)
3	19	13
5	120	57
7	221	223
9	322	322
11	423	411

 

Conclusion:  The proposed binding model provides a better understanding of binding based on first principle mechanics.  The results from this study establish a framework for more comprehensive modeling and prediction of the frictional behavior of a full orthodontic system.