Performance and Internal Flow of a Dental Air Turbine Handpiece

1Department of Mechanical Engineering, Ibaraki University, 4-12-1 Nakanarusawa-cho, Hitachi-shi, Ibaraki 316-8511, Japan 2Graduate School of Science and Engineering, Ibaraki University, 4-12-1 Nakanarusawa-cho, Hitachi-shi, Ibaraki 316-8511, Japan 3Yoshida Seiko, Ltd., 660 Yakimaki, Namegata-shi, Ibaraki 311-3506, Japan 4The Yoshida Dental MFG Co., Ltd., 1-3-6 Kotobashi, Sumida-ku, Tokyo 130-8516, Japan


Introduction
An air turbine handpiece is highly valued as a dental abrasive device that rotates at a high speed, and it is an essential device for dental treatment [1].Since its development, many studies have been conducted to measure and evaluate rotation performance [2][3][4][5][6] and measure and evaluate noise [7,8].An air turbine handpiece uses compressed air as the driving force and is characterized by its small size, light weight, and painless abrading at high rotation speed.However, compared to an electric handpiece that uses a motor as the driving force, its torque is small and noise level is high.
As such, improved performance and reduced noise for an air turbine handpiece are desired.Considering that an air turbine handpiece has the equivalent rotation performance as turbine performance, it can be considered as a type of turbomachinery, and the fluid mechanics approach would be effective.In other words, it would be effective to first elucidate the internal flow of an air turbine handpiece and the relation between the performance and the noise characteristics and then control the flow.However, the main component of an air turbine handpiece, the rotor, is small and rotates at high speeds (250,000-400,000 min −1 ); thus, measuring the flow is not easy.In addition, the torque generated by the rotor is extremely small; thus, the measurement of torque is difficult.With the progress of computational fluid dynamics analysis, numerical analysis of internal flow to the head (turbine) of handpiece began recently [9][10][11][12][13], and numerical analysis that models the entire handpiece [14] has also been conducted.However, in these studies, details of internal flow are insufficiently elucidated, and there is no verification of numerical analysis results via experiment.As such, there are few reports on the study of internal flow in an air turbine handpiece.
In this study, as the first step toward improving the performance of air turbine handpiece, we conducted a performance test of an actual handpiece while conducting numerical analysis that models the whole handpiece, and we compared the turbine performances.Furthermore, we examined the torque fluctuation with the rotation of the rotor and examined its relation with the internal flow.

Test Air Turbine Handpiece.
Figure 1 shows the test air turbine handpiece and Table 1 shows its specifications.In addition, Figure 2 shows the schematic of the turbine section.The turbine section, which forms the head section of the handpiece, comprises a nozzle, rotor, and casing and is a single-stage impulse turbine.Figure 3 shows the rotor, while Figure 4 shows its schematic.This air turbine handpiece jets out the compressed air that enters from the entrance through the nozzle, and the air is driven as the jet works on the rotor.The inner diameter of the nozzle is  = 1.3 mm, and there is one nozzle.The outer diameter of the rotor is  1 = 8.8 mm, while the inner diameter is  2 = 3.6 mm and the blade width is  = 3.3 mm, of which there are eight blades.

Experimental Apparatus and Methods.
The rotation performance of the air turbine handpiece is assumed to be equivalent to turbine performance, and there are two methods to measure this value.One is when a test bar is loaded onto a work material at a constant speed, and the other is when the test bar is loaded onto a work material at a constant load [2].Experimental results from the constant speed load method with the descending speed of 1 mm/min are consistent with the constant load method [2].Thus, in this study, we used the constant speed load method, which has a relatively easy mechanism and makes experiments simpler.The experimental apparatus is shown in Figure 5, and its schematic is shown in Figure 6.An air turbine handpiece with a test bar (cemented carbide with radius  = 1 mm) attached to the rotational axis of the rotor is fixed in the movable part and is lowered at a constant speed.Compressed air of 0.22 MPa is injected through the inlet of the handpiece, and when the rotor is turned on, the test bar is rotated.At this time, the pressure was adjusted according to the regulator (SMC Corporation; AW2000) installed at the handpiece inlet, and measured using a pressure gauge (Asahi Gauge Manufacturing Co., Ltd.; 101-F510, accuracy ±1.6% of full scale).The test bar is lowered at a descending speed of 1 mm/min, and the freely rotating test bar is pressed against the work material (cemented carbide) on the support stage.The horizontal force at this time   and rotational speed  were continuously measured with the load cell (Kyowa Electronic Instruments Co., Ltd.; LMB-A-100N, nonlinearity ±0.5% rated output) and fiber sensor (KEYENCE CORPORATION; FU-20/FS-N11N).
The torque  and turbine output  were then obtained with the following equations using the horizontal force   and rotational speed  that were measured: (1)

Numerical Analysis Method and Conditions
In this study, we performed a 3D compressible unsteady flow analysis by modeling the whole air turbine handpiece.
For the analysis, we used general-purpose thermal fluid analysis software, ANSYS CFX14.5 (ANSYS, Inc.), and the working fluid was air.The governing equations were the mass conservation equation, momentum conservation equation, energy conservation equation, and ideal gas law [15], which were solved with the finite volume method.Furthermore, we used the Shear Stress Transport (SST) model [16] as the turbulence model.Figure 7 shows the computational model for the whole air turbine handpiece, and Figure 8 shows the turbine section region.The calculation regions are inlet flow region, turbine section region, and outlet flow region.The numbers of computational elements were approximately 391,000, 1,127,000, and 783,000 for the inlet flow region, the turbine section region, and the outlet flow region, respectively, corresponding to a total number of elements of approximately 2,301,000.Boundary conditions were a total pressure of 0.22 MPa and static temperature of 25 ∘ C for the inlet boundary and static pressure of 0 Pa for the outlet boundary.In addition, we provided arbitrary rotation speed to the rotor region, and the wall surface had adiabatic and nonslip conditions.The boundary between the rotational region and static region was attached using the Transient Rotor-Stator [17].Time step size was determined the rotor rotates once with 120 steps at any speed.Calculations were continued until fluctuations in the torque stabilized.In terms of grid dependency, the number of computational elements was increased approximately 1.52 times, and it was analyzed with a rotation rate of  = 250,000 min −1 .The result was that this decreased by approximately 2.2% in relation to the torque in this paper, and it was confirmed that the effect of the number of computational elements was comparatively small.For the coordinate system, we defined and -axes as in Figure 5.For the blade phase angle  * , the position at which the front surface of the reference Blade A is parallel to the -axis (the position in Figure 5) is set as  * = 0 ∘ , and the counterclockwise direction was set as positive.Furthermore, we defined the blade ahead of Blade A as Blade B. The cross-section at 3.7 mm from the rotation center in the perpendicular direction to the front surface of Blades A and B was defined as cross-section a-a, and the cross-section at 4.1 mm was defined as cross-section b-b.

Results and Discussion
4.1.Turbine Performance.Figure 9 shows the relation between torque  and rotational speed , while Figure 10 shows the relation between turbine output  and rotational speed .Figures 9 and 10 show that calculated  and  are slightly higher than the experimental values, but both  and  are consistent.Considering that calculated  and  ignore the loss of mechanical friction on the bearing, these analytical results are valid.Experimental and calculated  decreased with increase in rotational speed, and calculated  showed the maximum value at  = 250,000 min −1 (L = 12.1 W).
Next, to search the locations where loss inside of the handpiece is high, we created a measurement surface in seven locations, as shown in Figure 11, and obtained entropy  for each measurement surface.Figure 12 shows the entropy  on each measurement surface for the handpiece when the maximum output rotational speed was  = 250,000 min −1 .Figure 12 shows that  demonstrated the highest increase in locations that are equivalent to the rotor region inside of F4-F5   casing among measurement surfaces.Therefore, in terms of the loss inside of the handpiece, the loss in the rotor region is the most dominant.However, E increased slightly in F1-F4 inlet flow and F6-F7 outlet flow; thus, the loss in the inlet and outlet flows cannot be ignored.
We obtained adiabatic efficiency  ad of the turbine section and the whole handpiece with the following equations: where ṁ is the mass flow rate and  is the specific heat ratio (1.4). 1 ,  1 , and V 1 are fluid density, static pressure, and absolute velocity at the inlet, respectively.To calculate  ad of the turbine section, we used the value from the turbine section inlet (F2); to calculate  ad of the whole handpiece, we used the value from the handpiece inlet (F1). 2 and V 2 are static pressure and absolute velocity at the outlet, respectively, and to calculate  ad of the turbine section we used the value from the turbine section outlet (F6), and to calculate  ad of the whole handpiece, we used the value from the handpiece outlet (F7).
Figure 13 shows the relation between adiabatic efficiency  ad and rotational speed  of the turbine section and the whole handpiece.Figure 13 shows that  ad of the turbine section and the whole handpiece present the maximum value when  = 250,000 min −1 , which is similar to the maximum value of the turbine output, and they show a major drop at high rotational speed.The maximum  ad of the turbine section was quite low at 0.185.The maximum  ad of the whole handpiece was 0.086, and this is approximately 46% less than the maximum  ad of the turbine section.minimum value presents a negative value.When torque fluctuation increases, it lowers workability of the air turbine headpiece and causes fluid noise; thus, suppression of these issues is a challenge.Since torque fluctuates, periodically to the number of blades, torque fluctuation for one blade pitch is shown in Figure 15. Figure 15 shows that when the blade phase angle is around  * = 36 ∘ ,  becomes a minimum.Subsequently,  increases rapidly and after reaching the maximum around  * = 48 ∘ , it gradually decreases.

Torque Fluctuation and Internal Flow.
Therefore, we focused on these blade phase angles and examined the internal flow.First, we present static pressure distribution and absolute velocity vectors for the center crosssection of the blade width for each blade phase angle ( * = 36 ∘ , 48 ∘ ) at the maximum output rotational speed of  = 250,000 min −1 (Figures 16(a At  * = 36 ∘ , where  becomes minimum, Figure 16(a) shows that with Blade A the jet from the nozzle does not enter the front surface of the blade, but it collides with the back surface of the blade.Therefore, as shown in Figures 17(a) and 17(b), static pressure increases on the back surface of the blade.Especially on the cross-section b-b with a large radius, static pressure increased more than the static pressure on the cross-section a-a.Thus, there was a large negative torque on the Blade A. With Blade B, jet flows facing the front surface of the blade.The larger shift in the flow from entering to exiting the blade causes the torque to also increase more.However, since the distance between the nozzle and blades is large, the jet decreases its speed and spreads in the width direction of the blade.Therefore, as shown in Figures 18(a  and 18(b), the flow does not exit along the blade in both crosssections, and the shift in the flow is small.Therefore, although static pressure on the front surface of the blade on the crosssection a-a increases considerably, static pressure on the back surface of the blade is also large; moreover, as it is near the center of the blade with a small radius, it does not sufficiently contribute to the torque.Based on the above, torque near  * = 36 ∘ presented the minimum value.
In contrast, at  * = 48 ∘ where  becomes maximum, as shown in Figure 16(b), the blade tip of Blade A is positioned near the center of the nozzle, and the jet from the nozzle flows to the tip of the Blade A at a close distance where the jet does not lose its speed.Therefore, as shown in Figure 19(b), the flow that entered the front surface of the blade on crosssection b-b flowed out along the blade and static pressure at the front surface of the blade increased, while static pressure on the back surface of the blade decreased.The pressure difference between the front and back surfaces of this blade tip with a large radius is greatly contributing to the torque.As shown in Figure 19(a), since cross-section a-a represents the moment just before Blade A reaches the nozzle, static pressure increase on the front surface of the blade was slightly lower.With Blade B, the distance between the nozzle and blade is larger, and the jet is prevented by Blade A. Therefore, as shown in Figures 20(a  to the blade width direction, and flow that entered the front surface of the blade flows out along the blade.Therefore, the shift in the flow increases, and as shown in Figure 14, at  = 150,000 min −1 , torque increased.
On the contrary, Figures 22(a

Conclusions
We examined performance and internal flow of a dental air turbine handpiece through experiments and numerical analysis and obtained the following findings: (1) Experimental and calculated values of torque and turbine output were consistent in the constant speed load method with a descending speed of 1 mm/min.
(2) Loss in the rotor region is dominant in the loss inside of the handpiece.
(3) The maximum value of adiabatic efficiency in the turbine section was approximately 0.185, which is quite low.Adiabatic efficiency of the whole handpiece decreased approximately 46% compared to the efficiency in the turbine section.
(4) With an increase in the rotational speed, the torque decreases but its fluctuation increases.
(5) When the blade tip is located near the center of the nozzle, the torque attains its maximum value.This is because the jet enters the tip of the blade at a close enough distance to not reduce its speed and then it flows out along the blade.

Figure 10 :
Figure 10: Correlation between rotational speed and turbine output.
Figure 14  shows the torque fluctuation during one rotor rotation for each rotational speed .
) and 16(b)).Figures 17-24 show static pressure distribution and absolute velocity vectors of cross-sections a-a and b-b for each blade (Blade A and Blade B). )

Table 1 :
Specifications of turbine section.