Experimental modal analysis of hand-held burs for biomedical applications

Abstract

Surgical bur micro-burs commonly used in orthopaedics, neurology and otolaryngology procedures cut into bone structures at high rotational speeds. These tools can produce large amplitude vibrations during cutting, potentially causing instability and overheating that may damage surrounding tissues. It is thus vital to understand their vibrational characteristics to mitigate such occurrences. This research investigates micro-bur dynamics through experimental modal analysis. Traditional methods of modal analysis, typically used for analysis of macro-structures, are found to be unsuitable for the small and complex geometry of micro-tools. Thus, implementation of alternative excitation and measurement techniques are examined, including the use of high-speed cameras and flexible piezoelectric sensors. A comparative study of two different micro-burs is conducted to examine their dynamic characteristics, which may contribute to increased control and safety of the burs. The effect of rotational speed and effective bur length on the natural frequencies of the bur are investigated, through experimentation and finite element modelling. The effect of fixture position on the dynamic measurements taken from the bur is examined to understand the impact of surgeons grip position. With a better understanding of the dynamics of high-speed micro-burs, their design can be improved to minimise instability while cutting, ultimately enhancing the safety of surgeries and improving patient outcomes.

1. Introduction

High-speed micro-burs are used for precision surgical procedures on small areas of bone across many surgical specialties. It is vital that a reasonable degree of control over the motion of the bur is maintained during the burring operation to avoid harming the patient (Jamshidi et al., 2022). However, the high rotational speeds of the bur of up to 75000 rpm can potentially lead to large amplitude vibrations in the bur (Kusins et al., 2018). These large-amplitude events, known as chatter, are likely to cause instability in the bur, leading to uneven cuts on the bone surface or deviation from the intended cut trajectory. This could lead to an increased risk of damaging the surrounding tissues (Noordin et al., 2015). Vibrations can also have a significant effect on the surgeon’s hands, leading to loss of sensation in the fingertips that inhibits tactile feedback from the bur (Ghasemloonia et al., 2016). Long-term exposure to vibration from handheld tools can cause Hand-Arm Vibration Syndrome (HAVS), which can result in permanent loss of hand function and sensation (Gerger et al., 2023; Pendleton et al., 2024). Therefore, it is crucial to design and characterise the vibrational dynamics of these burs to protect both the patient and the surgeon.

Numerical (Mustapha and Zhong, 2013) and analytical models (Wang et al., 2011) are often used to theoretically obtain the modal characteristics of micro-tools without the need for complex experimental setups. However, these methods rely on simplified models and assumptions about model parameters. It is therefore important to validate results through experimental approaches. A high-speed bur is composed of a spherical bur head fixed to a shank which is driven by a motorised hand-piece. The burs can range from 0.5 mm to 10 mm in diameter. Due to the small and complex shape of the bur, accurately identifying its dynamic characteristics through traditional experimental modal analysis techniques poses some challenges (Chou and Wang, 2001). Traditional impact excitation methods can only excite a low frequency bandwidth and they also risk damaging the bur, while measurement instruments, such as accelerometers, would add significant mass to the system, thus altering the dynamics of the micro-tool (Filiz and Ozdoganlar, 2010). Alternative methods of measuring micro-bur dynamics are therefore necessary. Filiz and Ozdoganlar (2010) employed a laser Doppler vibrometer (LDV) and a piezoelectric actuator to analyse the dynamics of fluted micro-drills. However, the study was not performed under operational conditions.

Bediz et al. (2014) developed an impact excitation system in which a small instrumented impact tip was attached to a flexure cantilever with an automated magnetised release system. However, this method requires the manufacturing of repeated design iterations of the system to acquire the desired excitation forces. Shekhar et al. (2023) used this impact excitation system with a Laser Doppler vibrometer (LDV) for measurement, to examine the effect of rotational speed on ultra-high-speed spindles. This technique accurately measured frequencies up to 15 kHz and speeds of up to 120000 rpm.

The difficulty with this type of impaction and measurement system for micro-tools is the need for it to be very precisely positioned to produce reliable results. Filho and Melotti (2022) developed a system of automating the position of the LDV and the execution of the impact tests for modal analysis of micro-mills. This minimises the effect of human error on the results of the experiments.

Wiederkehr et al. (2020) used shooting bearing balls as excitations to examine micro-milling tools while they rotated, exciting a frequency range of 100 kHz. High-speed cameras and finite element analysis (FEA) were used to calculate impaction force. Gupta et al. (2021) used low and high-speed cameras for modal analysis of a boring bar, endmill and grooving blade. The shape of the tool was used to register motion using image tracking algorithms. Modal parameters found using this method were shown to agree with parameters extracted with a more traditional measurement approach using contact accelerometers.

Such studies highlight both the necessity and effectiveness of unconventional excitation and measurement techniques for assessing micro-tool vibrations. However, the described excitation methods are challenging to manufacture and deploy. The following studies make use of operational analysis to measure vibrations in surgical burs by utilising the bur’s own motor for excitation.

Loushin et al. (2022) evaluated the exposure levels neurosurgeons had to HAVs from surgical drills. While this study analysed the amplitude of vibration at the grip of the drill and didn’t find the modal characteristics, it demonstrated the necessity of minimising vibration levels in these drills to a safe level.

Ghasemloonia et al. (2016) evaluated the vibrational accuracy of virtual reality (VR) haptic controllers compared to real surgical bur drills, by measuring hand-piece vibrations with an accelerometer. VR simulations are an increasingly popular method of surgical training, as the surgeon can gain familiarity with complicated surgeries without putting a real patient at risk (Evans and Schenarts, 2016). The accuracy of vibro-tactile feedback from the surgical tools in these simulations is paramount to help the surgeon develop their skills appropriately (Huang et al., 2020).

Kusins et al. (2018) examined the effect bur geometry and setup had on the cutting forces, bone temperature and vibration of the tool. A linear actuator advanced the tool through a synthetic bone mounted on a load cell to measure cutting forces, while a piezoelectric accelerometer on the hand-piece measured vibration across a 1−10000 Hz range. High rotational speeds significantly increased vibration amplitude, though the measured forces were relatively low, under 3N.

Due to the small size, noise inadvertently arises in their vibrations while cutting due to the effects of material impurities of the tool, manufacturing tolerances and tool-tissue interactions. Vibration control methods could address such challenges (Yang, 2025).

Danda et al. (2017) assessed dynamic forces on burs during bone cutting using a dynamometer, focusing on bur angle and feed direction. The observed vibrations primarily showed a significant frequency component related to rotational speed, with no other notable frequencies due to the dynamometer’s limited frequency range.

While cutting forces, heat generation and grip vibration amplitude are well-studied, there exists a significant gap in literature regarding the identification of modal features of surgical micro-burs. This study aims to address this gap by identifying these dynamic characteristics through operational modal analysis techniques, measuring the bur vibrations with the use of a flexible piezoelectric sensor and high-speed cameras. The high-speed camera allows the capture of vibrations by non-contact means, and the lightweight piezoelectric sensor avoids altering the bur’s dynamics through mass loading effects. Furthermore, a comparative analysis of two representative cases of micro-burs has been performed to assess their dynamic characteristics for improved control and safety.

The significance of this research lies in characterising bur vibrations and analysing natural frequencies to design more stable and controllable surgical burs. Understanding bur vibrations also helps tailor surgical burs to surgeons’ preferences and contributes to the development of precise surgical robots and training simulators. In this study, two burs are examined, uncovering why one is preferred over the other and quantifying the differences in their reported “feel.”

The paper is organised as follows. In the next section, the experimental methods are outlined. This is followed by the results from these experiments. The implications of these studies are discussed in the Discussions section and finally, the key insights in the paper are summarised in the conclusions section.

2. Proposed methodology

The effect of rotational speed, effective bur length and fixture positioning on the dynamics of the drill of two representative burs was investigated. Initial modal estimates were obtained with the help of high-fidelity numerical simulations, by replicating the key features of the geometry, materials and boundary conditions of the two bur designs. The results provided an initial estimation of natural frequencies.

This was followed by an experimental investigation by mounting the bur in the hand-held piece and providing it with controlled excitation. The burs were first excited using an impact hammer, which demonstrated the limitations of traditional methods for the modal analysis of a micro-bur. Further experiments therefore excited the burs using operational analysis by using the drills own motor to rotate the bur at high speeds in free-air. This provided an understanding of the burs dynamics under real-world conditions while exciting a high range of frequencies. Further investigation of the bur’s dynamics under real operating conditions was done by measuring the vibrations of the bur while it cut through a synthetic bone replica.

A high-speed camera was used as a non-contacting measurement technique for the bur in the impulse and free-air operational experiment, while a flexible piezoelectric sensor was used for measurement at the hand-piece grip in both operational experiments. These measurement techniques avoided the effect of mass loading that would have occurred by using the more traditional accelerometer approach. A comprehensive description of the methods and experimental setup are discussed in the following paragraphs.

2.1. Numerical modal analysis

To obtain numerical estimates of the modal characteristics of the burs, 3D FEA models replicating the essential features and geometry of the burs were created in Autodesk Fusion v.16.9.1.2222 and analysed using Ansys Discovery 2024 R1. The two bur designs are similar but have different geometry at the clamping end; see Figure 1. The S2 bur (2010 version) possesses an axisymmetric cross section with a diameter comparable to the rest of the shaft. The Signature-2 bur has an asymmetric cross section with a smaller diameter around the shank. To simplify the model, the bur head is represented as a sphere without flutes. M42 high-speed steel alloy properties were assigned, and a tetrahedral mesh with 12,387 elements and 20,672 nodes was created, as shown in Figure 1. A mesh convergence study was carried out and fixed boundary condition was applied to the end of each bur where they are clamped into the bur hand-piece. The first ten modal frequencies and mode shapes were simulated for both burs.

Figure 1.

(a) The cross sections of the S2 drive bur (top) and Signature-2 bur (top) near the clamped end. (b) The corresponding FEA models with applied tetrahedral mesh.

2.2. Experiments with impulse excitation

Impulse excitation was provided to the burs with the steel-tipped Kistler 2000N Quartz Impulse Hammer at the impaction point shown in Figure 2. A Phantom high-speed camera measured the displacement of the bur tip during the experiment. The hand-piece was clamped in a vice, with the camera positioned perpendicularly. A floodlight was necessary to accommodate the camera’s short exposure time. The bur’s small size renders it unsuitable for direct impaction, so the attachment was impacted at the position shown in Figure 2, exciting the bur through its connection. The force imparted by the impact hammer was observed with a Diligent Analog Discovery 2 oscilloscope at a 5 kHz sampling frequency. The camera recorded the resulting vibrations at 5000fps, with a resolution of 0.016 mm/pixel. The footage was analysed with Phantom Camera Control (PCC) software and points along the bur were tracked as it vibrated, shown in Figure 2. The impact and vibration measurements were processed in MATLAB R2023b. A third order Butterworth high-pass filter removed noise below 5 Hz. The signal was zero-padded to twice its length and a Hanning window was applied to reduce the effects of leakage. The power spectral density (PSD) of the signal was then computed and averaged across ten repetitions to reduce the amplitude of random noise. The ratio between excitation and response was calculated to analyse the resulting frequency spectrum. It was observed that the band of frequencies excited by the modal hammer were limited in range and noisy, necessitating alternative techniques of excitation for further analysis of the bur’s dynamic characteristics.

Figure 2.

(a) Impaction point. (b) Points on the bur tracked for displacement measurements.

2.3. Rotating bur experiments

The burs were examined under operational conditions to measure vibrations that closely mimic real surgical scenarios. The burs were driven by a motor in the hand-piece, rotating at high speeds exceeding 50000 r/min. Such high rotational speeds excited a broader frequency bandwidth than was achievable with a modal hammer. The burs were tested with a free boundary condition on their bur ends to understand their dynamical behaviour without the influence of cutting forces. Figure 3 presents the schematic of the experimental setup.

Figure 3.

Experimental setup with bur rotating in free air. The bur is lit from behind with a floodlight, while a high-speed camera and piezo-sensor measure the vibrations at the bur and bur grip.

A custom 3D-printed fixture was clamped around the bur hand-piece to secure it to the workbench. A Leanstar flexible piezoelectric sensor, sampling at 20 kHz, was taped to the grip of the hand-piece to measure the vibrations experienced by a surgeon. The Stryker CORE 2 Console, powered the bur and controlled its speed, acceleration, torque and braking, while a foot pedal was used for activation. A Phantom high-speed camera, recording at 20000fps with a resolution of 0.041 mm/pixel, was positioned orthogonal to the bur to provide a clear visualisation of the bur. The PCC tracking software was used to track points along the length of the bur as it vibrated.

A third order high-pass Butterworth filter was applied to the vibrational measurements to remove noise below 70 Hz, while a Hanning window and zero-padding reduced leakage effects and improved resolution. Dominant frequencies were identified by calculating the PSD of the signal. The PSD was then averaged across fifteen readings of the piezoelectric sensor, and across five readings of three measured points on the high speed camera, to reduce the occurrence of random noise.

These experiments were carried out for several rotational speeds, effective lengths and fixture positions to understand their effect on the dynamics of the bur. Three speed levels of 75000 rpm, 60000 rpm and 50000 rpm were examined. The effective length was varied between clamping positions five (80 mm), three (85 mm) and one (70 mm) as marked on the bur shaft. Two fixture positions were analysed to understand the vibrations experienced at different positions of gripping.

2.4. Cutting experiments

This experiment analysed the effect of cutting processes on the bur dynamics at different speeds. The boundary conditions of the bur change when cutting, as force is exerted on the distal end of the bur by the bone. This force varies as a function of cut depth, rotational speed, feed rate, cut angle and material characteristics (Danda et al., 2017). It is crucial to investigate the bur under cutting conditions since it is the most representative of a real surgical scenario. The setup for this experiment is shown in Figure 4.

Figure 4.

Experimental setup with bur cutting into a synthetic bone medium. The bone medium is advanced by a slide rail at a consistent feed rate towards the bur. The piezoelectric sensor records the vibrations at the grip of the bur.

Sawbone 40PCF, a synthetic cortical bone medium was used for the cutting experiments to ensure a consistent cutting surface. This medium was advanced towards the bur using a slide rail which maintained a consistent feed rate for each test. The slide rail was inclined so that the medium fell under the weight of gravity, at a mean feed rate of 30 mm/s. The bur was clamped adjacent to the slide rail and aligned to maintain a consistent cut depth. The flexible piezoelectric sensor, sampling at 20 kHz, was again used to measure vibrations at the grip of the bur during the cutting process. The high-speed camera was unsuitable due to dust around the cut site obscuring the view of the bur. The measured vibration signal was processed similarly to the rotational experiment above and dominant frequencies and dynamic characteristics were extracted from the resulting frequency spectrum.

3. Results

The results from the conducted numerical and experimental tests are detailed in the following section.

3.1. Finite element analysis

The first ten modal frequencies for the S2 and Signature-2 burs are shown in Table 1. Since the S2 bur is axisymmetric along its length, the natural frequencies for the bending mode shapes are arranged in pairs, corresponding to the bur bending along each plane. The Signature-2 bur is asymmetric and therefore has two different natural frequencies corresponding with each plane of motion. The motor used in both cases is a π-drive motor. Therefore, the only differences arise from the clamping arrangements and the geometry of the burs. The mode shapes for both burs are shown in Figure 5, with the corresponding natural frequencies in Table 1.

Table 1.

Numerically obtained Bending (B) and Torsional (T) modal frequencies using Finite Element simulations.

Mode	S2(Hz)	Signature-2(Hz)
B1	224	95.7
B2	224	122
B3	1520	1210
B4	1520	1290
B5	4430	3600
B6	4430	3790
T1	7450	4360
B7	8820	7610
B8	8820	7860
B9	14600	11800

Figure 5.

Mode shapes obtained using dynamic analysis in FEA for the (a) S2 bur and (b) Signature-2 bur.

The modal frequencies for S2 are observed to be consistently higher than those of the Signature-2 bur, which may be attributed to differences in their geometry and stiffness. The first bending mode of the S2 bur occurs at 224 Hz, while it occurs at a lower frequency of 96 Hz in Signature-2. The first torsional mode occurs at a significantly higher frequency of 7450 Hz for the S2, than the Signature-2 bur, at a frequency of 4360 Hz. These differences highlight the impact that structural characteristics can have on the dynamic behaviour of the bur.

3.2. Modal hammer tests

Frequency response function (FRF) plots were obtained from the modal hammer tests to identify the natural frequencies of the burs. Since the excitation bandwidth of the hammer was limited to 1000 Hz, only the first two natural frequencies could be extracted. These are identified as points in the FRFs where there is a pronounced peak in amplitude. The first natural frequency for the S2 bur appears at 244 Hz, while in the Signature-2 lower frequencies of 86 Hz and 152 Hz are found, as seen in Figure 6(a) and 6(b). Due to the small geometry of the bur it had to be excited through the attachment point of the hand-piece instead of direct impaction. This caused the natural frequencies of the hand-piece and attachment to interfere with those of the bur. Smaller vibration amplitudes due to indirect impaction meant short measurement times. It was therefore difficult to identify the natural frequencies in the FRF plot. For this reason, along with the low frequency range of excitation, alternative methods of excitation were explored.

Figure 6.

FRF of vibrations recorded by high-speed camera of (a) S2 bur and (b) Signature-2 bur, excited by impact hammer.

It is worth noting the difference in FRF amplitude between the two drills. The internal structure of the hand-pieces had an effect on the amplitude of force transmitted to the bur. The Signature-2 bur is clamped within the top part of the drill, so when this part was impacted by the hammer, a larger proportion of force was transmitted to the bur, compared to the S2 bur which is clamped within the base of the hand-piece, and therefore received less of the impaction force.

3.3. Free air operational experiments

The responses obtained from these experiments included the natural frequency components from both the bur as well as the hand-piece, in addition to a prominent frequency associated with the bur’s rotational speed (F₁) and its superharmonics (2F₁, 3F₁, etc.).

3.3.1. Varying rotational speed

The natural frequencies of both burs found at each speed and measurement type are described in Tables 2 and 3. The PSD plots at top speed of 75000 rpm are shown as representative cases for both the burs in Figures 7 and 8. The natural frequencies of each bur remain somewhat consistent across different rotational speeds for both the piezo sensors and the high speed camera, as demonstrated by the plots depicting natural frequencies as a function of the corresponding rotational speeds, in Figure 9.

Table 2.

Natural frequencies of S2 bur rotating at three different speeds in free air.

Method	Speed(Hz)	B1&2(Hz)	B3&4(Hz)	B5&6(Hz)	T1(Hz)	B7&8(Hz)
FEA		224	1520	4430	7450	8820
Piezo	75	246	1561	4375	7510	8816
Camera	75	251	1524	4656	7512	9033
Piezo	60	255	1502	4493	7493	8968
Camera	60	223	1496	4509	7505	8740
Piezo	50	255	1460	4367	7485	8858
Camera	50	214	1401	4526	7496	8332

Table 3.

Natural frequencies (Hz) of Signature-2 bur rotating at three different speeds in free air.

Method	Speed(krpm)	B1(Hz)	B2(Hz)	B3(Hz)	B4(Hz)	B5(Hz)	B6(Hz)	T1(Hz)	B7(Hz)	B8(Hz)
FEA	-	96	122	1210	1290	3600	3790	4360	7610	7860
Piezo	75 krpm	106	154	1175	1323	3643	3906	4331	7413	7771
Camera	75 rpm	107	-	1180	1359	3644	3871	4321	7436	8076
Piezo	60 krpm	100	155	1105	1284	3286	3809	4308	7498	8038
Camera	60 krpm	110	162	1200	1294	3553	3793	4210	7497	7994
Piezo	50 krpm	100	155	1084	-	3252	-	4264	7684	7987
Camera	50 krpm	-	128	1204	1277	3502	3836	4342	7415	8041

Figure 7.

FFT of vibrations recorded by (a) piezo-sensor and (b) camera of S2 bur rotating at 75000 rpm in free air.

Figure 8.

FFT of vibrations of Signature-2 bur rotating at 75000 r/min in free air from data recorded by (a) the piezo-sensor and (b) camera.

Figure 9.

Campbell diagrams for the Signature-2 drill for three rotational speeds as recorded by the (a) piezo-sensor and (b) high speed camera.

The time histories corresponding to each rotational speed, as recorded by the piezo-sensor, are presented in Figure 10. The corresponding root-mean-squared (rms) amplitudes are detailed in Table 4. It is intuitive that larger amplitudes of vibration occur at faster speeds. At the grip of the bur, as measured by the piezoelectric sensor, the amplitude of vibration is 1.6 to 3.4 times higher in the Signature-2 bur than the S2 bur. However at the body of the bur, as measured by the high-speed camera, the amplitude of vibration is higher in the S2 bur at speeds of 60000 rpm and 70000 rpm. Atypical behaviour was observed in the Signature-2 bur rotating at 50000 rpm, as shown in Figure 10(c), with larger amplitudes of vibration occurring for the first 50 milliseconds after the bur is set into operation. The intensity of vibrations reduces significantly after this period, but the amplitudes remain greater than the faster speed of 60000 rpm. This behaviour may be due to internal resonance occurring in the motor, hand-piece or bur when operating at this speed. The observation of more intense vibrations during the first 50 milliseconds suggests transient resonance effects as the bur accelerates to its operational speed, and needs to be investigated further.

Figure 10.

Time domain vibrations of (a) S2 bur and (b) Signature-2 bur rotating at three different speeds in free air, as measured by the piezoelectric sensor. (c) Atypical behaviour of Signature-2 bur when rotated at 50000 rpm in free air.

Table 4.

Amplitude (rms) of vibrations experienced at bur (Camera) and hand-piece grip (piezo-sensor).

Speed (krpm)	S2 bur		Signature-2 bur
	Piezo	Camera	Piezo	Camera
	(g)	(mm)	(g)	(mm)
75	3.137	0.0393	5.123	0.0165
60	1.247	0.0190	2.589	0.0143
50	0.959	0.0167	3.233	0.0187

3.3.2. Method comparison

The results of both the piezoelectric sensor and the high speed camera are compared against the FEA model and tabulated in Tables 2 and 3. Experimental measurements show higher first natural frequency for the S2 bur and second natural frequency for the Signature-2 bur than predicted by the model. These discrepancies arise due to minor structural differences between the simplified FEA model and the actual tool. Overall, experimental results closely match the FEA predictions, with an average of 4% relative error, providing a certain degree of confidence in both the methods.

3.3.3. Varying effective length

The natural frequencies estimated at each effective length are shown in Tables 5 and 6, with the associated PSD for one of the burs presented in Figure 11. As the effective length decreases, the natural frequencies for all modes (bending and torsional) increase. In the S2 bur, the first mode shifts from 246 Hz at 80 mm to 331 Hz at 70 mm, while the Signature-2 increases from 106 Hz to 200 Hz. At higher modes, the frequency increase is pronounced, with differences exceeding 1000 Hz between the shortest and longest lengths. This trend aligns with Euler–Bernoulli beam theory, which predicts an inverse-square relationship between natural frequency and length. Linear fitting yields proportionality constants k_FEA ≈ 2174027 Hz ⋅mm² and k_Piezo ≈ 1810713 Hz ⋅mm², indicating that FEA data shows a slightly steeper frequency increase with decreasing length compared to piezo data, though both exhibit a linear correlation with the inverse square of length.

Table 5.

Natural frequencies of S2 bur clamped at three effective lengths (L_e).

Method	Le(mm)	B1&2(Hz)	B3&4(Hz)	B5&6(Hz)	T1(Hz)	B7&8(Hz)
FEA	80	224	1520	4430	7450	8820
Piezo	80	246	1561	4375	7510	8816
FEA	75	271	1810	5230	8080	10400
Piezo	75	260	1736	5444	7940	-
FEA	70	328	2170	6220	8730	12300
Piezo	70	331	2197	6244	8740	-

Table 6.

Natural Frequencies (Hz) of Signature-2 bur at three effective lengths (L_e).

Method	Le(mm)	B1(Hz)	B2(Hz)	B3(Hz)	B4(Hz)	B5(Hz)	B6(Hz)	T1(Hz)	B7(Hz)	B8(Hz)
FEA	80	96	122	1210	1290	3600	3790	4360	7610	7860
Piezo	80	106	154	1175	1323	3643	3906	4331	7413	7771
FEA	75	120	145	1380	1460	4130	4360	4990	8460	8750
Piezo	75	115	-	1366	1449	4094	4320	4997	8534	8750
FEA	70	178	178	1660	1660	5070	5070	6070	10100	10100
Piezo	70	200	200	1613	1613	4986	4986	6022	-	-

Figure 11.

FFT of vibrations recorded by piezo-sensor on S2 bur clamped at the effective length of (a) 80 mm, (b) 85 mm and (c) 70 mm from the free end in free air experiment.

3.3.4. Varying fixture position

The variation in the placement of the handheld device on the fixture mimics the variations in the bur’s position as held by a surgeon. Differences in clamping positions significantly affect observed vibrations, particularly in the Signature-2 bur. When clamped in the upper position, the fixture secures the bur’s attachment, while in the lower position, the attachment is free to move in response to vibrations transmitted through the hand-piece. Rotational artefacts are more pronounced in the lower position, likely due to the play in the attachment; see Figure 12. Nevertheless, since the boundary conditions between the bur and hand-piece remain unchanged, peaks with lower power in the signal were consistently observed at the same frequencies in both clamping positions.

Figure 12.

FFT of vibrations recorded by piezo-sensor on Signature-2 bur with fixture at (a) upper and (b) lower clamped position.

3.3.5. Acceleration at start

Figure 13 shows the vibrational behaviour of the bur as it accelerates from stationary condition to full speed and then decelerates back to a stop. The amplitude of vibration of the Signature-2 bur is much higher than the S2 bur, with peak accelerations measuring 40g and 6g, respectively, reflecting a sharp jerk being experienced by the surgeon in the former case, which might potentially cause discomfort. The S2 bur’s dominant frequency components increase and decrease gradually, while the Signature-2 bur ramps up quickly with large amplitude vibrations that subside after 0.1 seconds. The wavelet transform of this time signal, shown in Figure 13(d), depicts the presence of a dominant high amplitude frequency, which relates to the rotational frequency. The contribution from this frequency component is higher in the Signature-2 as it accelerates from rest, compared to the S2 bur.

Figure 13.

Time histories showing acceleration to attainable speed of 75000 r/min in free air and eventual deceleration behaviour of (a) S2 bur and (b) Signature-2 bur. The corresponding wavelet transforms for (c) S2 and (d) Signature-2 bur responses.

3.4. Cutting experiments

While cutting into bone medium, the bur experiences resistive forces from the bone medium, as modelled by Danda et al. (2017). The boundary conditions, and therefore the natural frequencies of the bur thus change. Since this resistive force acts against the rotation of the bur, the speed of the bur varies during the cut, and the rotational artefact is therefore diminished. Additionally, the noise in these experiments is higher due to variability in the cutting material. The overall amplitude of vibrations is also orders of magnitude higher than the free-air experiments.

3.4.1. Varying rotational speed

The natural frequencies remained somewhat consistent across each speed, with some variation introduced due to the cutting conditions. The first natural frequency appears between 650 Hz and 800 Hz for the S2 bur, and between 280 Hz and 410 Hz for the Signature-2 bur, reinforcing the findings from the free-air experiments which found that the Signature-2 bur had lower natural frequencies than the S2 bur. The largest amplitude vibrations occur between 1600 Hz to 1950 Hz in the S2 bur and between 1400 Hz and 1880 Hz in the Signature-2 bur, as shown in Figure 14. Further peaks remain consistent across each rotational speed, as detailed in Tables 7 and 8.

Table 7.

Experimentally obtained natural frequencies of the S2 bur cutting at different rotational speeds.

Speed (krpm)	M1(mm)	M2(Hz)	M3(Hz)	M4(Hz)	M5(Hz)	M6(Hz)
75	793	1622	3238	4963	6668	8154
60	656	1916	3423	5429	7312	-
50	772	1950	3669	5456	7388	8613

Table 8.

Experimentally obtained natural frequencies of Signature-2 bur cutting at different rotational speeds.

Speed (krpm)	M1(mm)	M2(Hz)	M3(Hz)	M4(Hz)	M5(Hz)	M6(Hz)	M7(Hz)
75	382	690	1409	2868	4299	5751	7196
60	410	725	1423	1882	3806	5662	7477
50	286	704	1416	2806	4272	-	7203

Figure 14.

FFT of vibrations measured by piezo-sensor on (a) S2 bur and (b) Signature-2 bur cutting at 75000 rpm.

4. Discussions

4.1. Measurement techniques

The impact hammer test revealed that the limited frequency range and the hammer’s large size relative to the bur resulted in the identification of only two natural frequencies and a low amplitude of excitation, thus necessitating the use of non-contact methods for modal testing. However, the results from this test, followed by the free-air operational experiments, verified the effectiveness of the high-speed camera in capturing bur vibrations. The small complex geometry of the bur lent itself to this measurement technique since the camera could zoom in close to the bur, resulting in a high millimetre to pixel ratio, while the tracking algorithm was able to identify the burs unique shape across each frame, enhancing tracking precision. This method was less effective during cutting due to dust particles surrounding the bur, which could be mitigated with proper ventilation. The use of the high-speed camera for measurement is a simpler method than the LDV, with no requirement for precise positioning of optical microscopes (Filiz and Ozdoganlar, 2010) or mirrors (Filho and Melotti, 2022). This enhances the accessibility of modal analysis of micro-tools to those with less expertise in the field.

Exciting the bur through operational use allowed the measurement of higher natural frequencies than possible through traditional modal analysis techniques. It also precluded the need to manufacture complex excitation systems such as those conceived by Bediz et al. (2014) and Wiederkehr et al. (2020). However since the input force was unknown, it wasn’t possible to measure the mode shapes and damping of the structure. The measurement of the bur during operational use also allowed for the analysis of the dynamics of the bur when activated for normal surgical use. This included analysis of the amplitudes of vibration, the dynamics of the bur as it accelerated from rest and the effect of rotational speed on the bur.

Additionally, the flexible piezoelectric sensor proved effective for measuring both the bur’s natural frequencies and the vibrations experienced at the bur’s grip. The low mass of the sensor relative to the bur meant it had negligible effect on its dynamics, unlike a traditional accelerometer. The flexibility of the sensor allowed it to wrap around the grip of the bur without the need for additional fixation structures.

There is a lack of established method of experimentally determining modal characteristics of high-speed surgical micro-burs. Traditional modal analysis techniques are unsuitable due to their small and complex geometry. Commercially used FEA to simulate tool dynamics is susceptible to modelling limitations and geometrical or numerical simplifications. The methods described in this paper offer a foundation for development of future approaches to accurately determine and verifying dynamic characteristics.

4.2. Comparison of the burs

Surveyed otological surgeons have indicated their preference for the S2 bur over the Signature-2 bur. The dynamic differences identified in this study between the burs may explain the reason for this, as well as inform design considerations for future surgical micro-burs.

The frequency range of human tactile sensation lies between 5Hz–400 Hz, with higher levels of sensation at lower frequencies (Ryun et al., 2017). Vibration occurring in this range are therefore of particular interest since they will have the most significant impact on the tactile sensation of the surgeon. Since the natural frequencies of the Signature-2 bur are lower than those of the S2 bur, surgeons will likely have a stronger sense of its vibrations.

In addition, the amplitude of vibrations is significantly different between the two burs, with the Signature-2 having a 1.6 to 3.4 times higher amplitude than the S2 bur at the grip. Since large amplitudes of vibration can reduce control over the bur and make it more difficult to sense tactile feedback through the bur, it is important that it is minimised as much as possible. It is also important to reduce the surgeons exposure to large vibrations to reduce the risk of HAVS (Gerger et al., 2023).

The behaviour of the two burs is also distinct during the acceleration phase after being activated. The S2 bur has a smooth acceleration phase with the vibrations slowly increasing in amplitude over time as the speed of the bur increases. The Signature-2 bur has a much faster acceleration phase which reaches large amplitudes of vibration within the first 10 ms, before decreasing to steady state amplitudes. This behaviour may cause the bur to jerk in the surgeon’s hands when turned on, causing discomfort and less control over the bur.

Identifying and controlling natural frequencies is crucial to avoid resonant high-amplitude vibrations that can make the bur difficult to control and lead to fatigue and failure. From the operational experiments, it is evident that rotational speed causes excitation at the corresponding frequency. Thus, it’s essential to ensure that common speeds do not overlap with the bur’s natural frequencies. At 75000 rpm, a frequency of 1250 Hz is excited. The S2 bur’s closest natural frequency is 250 Hz away, minimising resonance risk. However, the Signature-2 bur’s closest natural frequency is at 1290 Hz, which could potentially cause resonance at this speed.

Bur geometry can be designed to reduce the likelihood of resonance through several factors. An asymmetrical cross-section like the Signature-2 bur may introduce multiple natural frequencies for each mode, increasing the risk of resonance. Since bur length significantly affects natural frequency range, slightly altering the bur length can shift its natural frequencies away from potential resonant frequencies. This approach offers a practical design modification to reduce resonance risk.

Previous studies have been limited to measuring forces at the burs or amplitudes of vibration at the hand-piece (Ghasemloonia et al., 2016; Kusins et al., 2018; Loushin et al., 2022), and have not measured tip vibrations. Studies on modal characterisation are also few and frequency ranges identified are often limited to those within the range of human tactile perception $(<400Hz)$ (Ghasemloonia et al., 2016), which does not allow for the identification and study of implications of the higher natural frequencies, which has been taken up in this study. This study underscores the need for thorough dynamic testing of surgical micro-burs to minimise operating at regimes that could lead to large amplitude vibrations. Considering dimensional, rotational and cutting factors is essential to avoid resonance. The experimental methods outlined here could potentially inform vibrational testing of micro-burs, benefiting both otolaryngological patients and surgeons.

5. Conclusions

This manuscript investigates the dynamic properties of two almost-identical high-speed micro-burs, in order to shed light on the surgical preference of one over the other. Traditional methods of experimental modal analysis were ineffective for this tool due to its small size and high range of natural frequencies. Instead, operational excitation combined with piezoelectric sensors and high-speed cameras was used to measure vibrations. While the bone chips caused instantaneous hindrances in tracking points along the bur, both the methods consistently matched dynamic FEA predictions, with an average of 4% relative error between experimental and FEA results, validating their effectiveness as both excitation and measurement methods. Analysis at three speeds and effective lengths revealed that the S2 bur comparatively had higher natural frequencies (224 Hz−8820 Hz vs 96 Hz−7860 Hz), while the Signature-2 bur exhibited higher vibration amplitudes at the hand-piece grip (5.12 g vs 3.14 g). Notably, one of the Signature-2 bur’s natural frequencies was within a 3.2% deviation to a commonly used rotational speed, posing a risk of resonance and high-amplitude vibrations. To reduce resonance risk and improve tactile feedback, burs should be designed with natural frequencies well-separated from operational speeds. Additionally, higher natural frequencies are preferable to reduce their impact on surgeon’s tactile sensation.

Furthermore, the impact of effective length on the natural frequencies of the burs is shown to be considerable, with natural frequencies increasing between 16 and 89% from the longest to shortest lengths. This provides an avenue of shifting natural frequencies away from instabilities through small changes in length. The shape of the bur was also shown to have an effect on the natural frequencies, with asymmetrical cross sections resulting in different natural frequencies for each mode shape. The acceleration and deceleration of the bur on start-off and shutting down also significantly impact on the vibrations experienced at the grip of the bur.

The present work can be extended to examine the dynamics of the hand-piece without the bur to isolate its dynamic behaviour from that of the bur attachment. The bur could be isolated and studied under free–free boundary conditions. Analytical coupling techniques could then be explored to provide further understanding of the complete assembled system. Contact mechanics of the bone and the serrated bur edges could be appropriately modelled. By isolating and studying each component’s dynamics separately, improvements can be made on the testing procedures of the diverse range of available burs, without the requirement for individual testing. Further analysis could be done to assess the effects of cut depth, angle, feed rate and various bone or tissue medium properties.

High amplitude vibrations in micro-burs are detrimental, with implications for the success of surgical procedures, as well as the exposure of surgeons to vibrations that can cause long-term health impacts. By analysing the dynamic characteristics of micro-burs, this study provides insights into enhancing the stability of bone burring processes, with a potential to improving surgical outcomes.