A Bezier Profiled Horn for Reducing Penetration Force with

Applications in Surgery

Dung-An WANG and Hai-Dang Tam NGUYEN

Graduate Institute of Precision Engineering, National Chung Hsing

UniversityTaiwan, ROC

2

Motivation Reduced strain for patient’s pain reliefIncreased precision of cutting tissueReduce necrosis of patient’s tissue

Liao et al., 2012.

3

Market for hard tissue removal

Millennium Research Group, 2010

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Industrial and medical interests Decrease cutting force (penetration force) Decrease thermal effects: temperature may

depend on Ultrasonic frequency Penetration force Cutting speed Geometry of cutting blade

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Aims Design of an ultrasonic horn with a new profile

To increase in tool-tip vibration amplitude, allowing a significant amount of material to be removed

To decrease the penetration force, reducing tissue necrosis

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Design Working frequency, 28.0 kHz

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Bézier profile Parametric curve based geometry is flexible

enough to give a much better control over the profile of horns for design purpose.

The profile of the horn is based on a cubic Bézier curve.

Four-point Bézier polygon Q0 Q1 Q2 Q3

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Parametric cubic Bézier curve

10)1(3)1(3)1()(

3

2

1

0

3223

t

P

P

P

P

tttttttP

Q

Q

Q

Q

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Design

The profile of the horn is optimized by allowing points Q1 and Q2 to move in the design space

0

3

0

Q

Q

u

uMMax

ffMin

Specify W120mm, W2=1.5mm, L=94mm. Thickness 1.2 mmf = 28.0 kHz

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Design Finite element analysis to obtain f0 and M of

the horn Material: SS41

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Optimized Bézier horn

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Comparison Catenoidal horn: same back and front end

widths and length as those of the proposed horn.

Stepped and linear horn: same back and front end widths of the proposed horn. The length of the stepped/linear horn is calculated to have the same working frequency of 28.0 kHz as the proposed horn.

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Comparison Normalized displacements along the

normalized length of the horns based on finite element computations

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Comparison The stepped horn: highest displacement

amplification, but high stress concentration at the step discontinuity

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Experiments A Bézier horn and a catenoidal horn are

fabricated by a laser cutting process from a stainless steel SS41

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Experiments Investigate the effects of ultrasound and horn

types on the penetration force of ultrasonic cutting

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Specimens A tissue stimulant, raw potato, as

representative for soft material A polymethylmethacrylate (PMMA) material as

representative for hard material Specimen: 70 mm x 35 mm x 5 mm

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Results Penetration speed 0.25 mm/s Five repeated trials Penetration force by the Bézier horn is 75% of

that of the catenoidal horn

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Results Penetration force as a function of penetration

speed Use Bezier horn Penetration depths: the tissue stimulant 2

mm, PMMA material 3 mm

Tissue stimulant PMMA material

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Mechanics Reduced penetration force is an effective

measure for increasing the critical cutting depth in ultrasonic cutting, and below the critical cutting depth, material can be removed plastically (Zhou et al., 2002).

When the plastic deformation is the predominant mode of deformation, a very smooth and fine surface can be obtained.

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Conclusions A planar Bézier horn with high displacement

amplification and low stress concentration is developed.

The displacement amplification of the Bézier horn is 30% higher than that of the traditional catenoidal horn with the same length and end surface widths

The penetration force by the Bézier horn is 75% of that by the catenoidal horn with a penetration speed of 0.25 mm/s during cutting of the tissue stimulant.