Based on Figs. 5–7, it was observed that in the Region (I), which is considered conventional grinding range (Low-speed grinding), the bone temperature rise (ΔT) has had a direct relationship with the cutting speed (v), and almost at all feed rates, the maximum temperature rise has been achieved at the end of this range of cutting speeds. To analyze this phenomenon, the factors affected by cutting speed would be examined concurrently:
• The mechanism of chip formation and grinding forces: with the increase in the rotational speed, finer cuts are created in the bone, thereby reducing the volumetric material removal per grit. Accordingly, the required deformation energy as well as the grinding forces will decrease. Thus, from the above aspect, an increase in the cutting speed causes reduced temperature rise [8].
• The chip evacuation velocity: upon elevation of the tool rotational speed, the chip evacuation velocity increases, and due to improved heat transfer rate, the temperature rise of the bone decreases slightly [6, 18].
• Friction: upon an increase in the cutting speed of the tool (rotational speed) at a constant feed rate, the number of revolutions of the rotating tool as well as the physical contact of its surface with the bone increase, causing higher friction and intensification of frictional heating. This frictional heating has a direct relationship with cutting speed and causes a further temperature rise of the bone [6].
With the increase in the cutting speed within the Region (I) range, the grinding forces have reached the possible minimum value under conventional machining conditions, and with further elevation of speed, no notable reduction would occur in the amount of machining forces. Further, due to the low thermal conductivity of bone, which is in the range of 0.38–2.3 W.m− 1.K− 1 [15, 16], the share of heat transfer by chips is limited (unlike metal chips during the drilling which are able to evacuate up to 85% of the total heat generated in the process thanks to their high heat capacity and high thermal conductivity coefficient [25]), and application of higher speeds would not improve heat evacuation considerably. On the other hand, the heat generated in response to friction is notable, whose value is directly associated with the cutting speed. All of these factors justify the ascending trend of temperature rise upon elevation of the cutting speed within the Region (I) range.
In Region (II) range, as the cutting speed goes beyond v = 250 m.min− 1, the descending trend of temperature rise begins, and the cutting speed of the bone grinding process has entered the HSC-range; thus, 250 m.min− 1 can be considered as the threshold of the HSC-range (vHSC). The changes occurring in the temperature rise trend within the above range are affected by changes in the nature of the bone chip, formation of powder-shaped chips, facilitation of the chip formation and evacuation conditions, and decline of the machining forces [6, 18]. At the end of HSC-range, the cutting speed reaches its optimal value regarding development of the minimum temperature rise, and upon leaving the HSC-range and entering the Region (III), the bone temperature rise has experienced an ascending trend again. The notable point in Figs. 5–7 is that the HSC-range has begun for all feed rates from vHSC= 250 m.min− 1, though the extent of this range is directly associated with the feed rate, and for higher feed rates, it has involved a more extensive speed range (Table 3). Since the HSC-range threshold speed is essentially dependent on the shear strength of the material and type of machining process, concurrent beginning of the HSC-range at vHSC= 250 m.min− 1 for different feed rates is absolutely predictable, and suggests independence of vHSC from the feed rate [17]. Nevertheless, based on Figs. 5–7 and Table 3, it is evident that the length of the HSC-range has essentially been dependent on the feed rate, and application of higher feed rates has led to the larger magnitude of the HSC-range. The factor causing the low feed rates to have shorter HSC-range is the frictional interaction between the rotating tool and the bone as well as the heat resulting from friction. As mentioned earlier, upon entering the HSC-range and as the cutting speed goes beyond the vHSC, the nature of the bone chip changes, and the incidence of the chip size shrinkage as well as formation of the powder-shaped chip has considerably reduced the grinding forces. All of these factors lead to diminished heat generation in response to the cutting as well as its resulting decreased temperature rise. On the other hand, the elevation of the tool rotational speed will increase its physical contact with the bone surface and frictional heating. Thus, friction is an additional heat source adversely affecting the desired outcomes of speed elevation within HSC-range. Since at low feed rates, the rotating tool crosses over the bone surface at a slower rate, thus the bone surface will be in contact with the rotating tool for a longer time and will undergo greater frictional heating. Accordingly, at low feed rates, the extent of frictional heating will be larger, and the factor of friction overcomes the reduced temperature rise resulting from entering the HSC-range earlier. This causes the range to end more quickly. Conversely, at high feed rates, as the tool crosses over the workpiece surface faster, the frictional heating will be lower and the factor of friction will require a longer time in order to overcome the reduced temperature rise resulting from changes in the chip nature. As a result, ascending the trend of temperature changes will be delayed. After leaving the HSC-range and entering the Region (III), due to the predominance of the effect of friction factor, the ascending trend of frictional heating continues, whereby the bone temperature rise has increased.
Table 3
HSC-rang for various feed rates.
Feed rate, f (mm.min− 1)
|
HSC-rang, v (m.min− 1)
|
20
|
250–400
|
30
|
250–500
|
40
|
250–650
|
Another notable point regarding the results in Figs. 5–7 is the direct relationship between temperature rise and the feed rate. In this regard, with elevation of the feed rate, the tool’s penetration volume into the bone increases, which requires greater shear energy for chip formation, thus causing higher grinding forces. According to the theory of machining mechanics, application of larger forces would lead to greater heating and elevation of temperature rise [8].
In order to verify the results of the present research, Fig. 8 compares them with the findings obtained by Shakouri and Mirfallah, obtained using air pencil grinder tool [6] (under the same conditions regarding cutting speed and depth of cut). Figure 8 indicates that changes in the temperature rise have followed a similar trend for both studies. Further, the slight difference between the results of these two studies at various feed rates is due to application of a bur with a larger diameter in the present research, causing increased chip removal volume, increased grinding forces, and more heating.
Based on the results of the present research, it can be deduced that the cutting speed vHSC= 250 m.min− 1 has been the HSC-range threshold for the bone grinding operation, and by applying the optimal cutting speed, lying at the end of the above-mentioned range, the minimum temperature rise can be achieved during surgery, thereby significantly reducing the risk of thermal damages. Hence, as a recommendation for orthopedic surgery and neurosurgery, the values presented in Table 4 are proposed. Note that since application of a bur with an approximate diameter of 4 mm is common in neurosurgical bone grinding, the rotational speed suitable for diameter of 4 mm has been calculated in order to achieve the desired cutting speed, and presented in the above table. Concerning the direct relationship between temperature rise and depth of cut [6], and as grinding tests in the present research have been performed with the depth of cut d = 0.75 mm, which is larger than the average prevalent depth of cut during the neurosurgical bone grinding, it can be ensured that in case of applying a smaller depth of cut under the optimal cutting conditions proposed in Table 4, the bone temperature rise would not exceed the allowable range, thereby minimizing the incidence of thermal damages. Further, the authors state that one of the limitations of the present research was the complexity of conducting experimental test on the human skull bone and use of a similar bone (bovine femur). Definitely, running high-speed grinding tests on the human skull bone would lead to more accurate results.
Table 4
Optimal grinding conditions in order to obtain minimum thermal damage (Depth of cut, d = 0.75 mm).
Rank
|
Feed rate, f (mm.min− 1)
|
Cutting speed, v (m.min− 1)
|
Rotational speed, N (r.min− 1)
|
Temperature rise, ΔT (°C)
|
Recommended rotational speed for bur with a diameter of 4.21 mm, N (r.min− 1)
|
1
|
20
|
350–425
|
9100–11000
|
4.8–8.5
|
26500–32150
|
2
|
30
|
500–550
|
13000–14300
|
7.2–9.3
|
37800–41600
|
3
|
40
|
650–675
|
16900–17500
|
10-12.5
|
49150–51000
|