Micro Drill Resistance Instrument Measurements at Different Feed Speeds: Novel Conversion Algorithm for Enhanced Accuracy

Drill feed speed significantly affects the measurement accuracy and efficiency of the micro drill resistance instrument. Generally, different speeds are set according to the density of the wood to be drilled. It is necessary to convert the resistance data measured at different drill feed speeds into resistance data at a uniform speed to properly analyze resistance data. In this study, drill resistance data for a Paulownia wood block was measured with a self-made micro drill resistance instrument at different drill feed speeds. We found that the drill resistance is positively correlated with changes in its feed speed and the natural logarithm of change times for feed speed. We developed a conversion algorithm for the micro drill resistance instrument measurements at different feed speeds. The accuracy of the conversion algorithm is up to 95%. The algorithm can be used to convert the drill resistance of Paulownia wood measured at different drill feed speeds; it has reference value for the mutual conversion of other tree species’ drill resistance data measured at different feed speeds. This work may provide a feasible solution to improving micro drill resistance instrument accuracy when drill feed speed error is high.


Introduction
The micro drill resistance instrument a precision tool which uses a motor to control a drill needle into a wood substrate at constant speed while measuring resistance in real time [1][2][3][4].During the measurement process, the relative drill resistance and drill position can be recorded continuously in the drilling path [5].The width of the drill cutter is 3 mm and its shank diameter is 1.5 mm; because the width of the cutter is twice the diameter of the shank, resistance is mainly concentrated on the cutter [1].Resistance increases as the density of wood to be drilled increases, and vice versa [1,2].As the drill penetrates the trees with annual structures along the radial direction, it alternately drills into layers of earlywood and latewood.Latewood is denser than earlywood, so the drill resistance changes alternately.So micro drill resistance instrument can be used to measure the age and rings of the trees with annual structures [6,7]; any rotted portions of the tree can also be measured, as these are portions where drill resistance sharply declines [8][9][10].Similarly, resistance will drop to a value close to the no-load resistance when the drill enters a hole or crack in the wood and can be measured accordingly [11,12].The drill cutter is only 3 mm wide, which is much smaller than the diameter of the increment core, a traditional tool for measuring tree density, tree rings, and defects.At present, although the measurement accuracy of micro drill resistance instrument is lower than that of increment core, some scholars still used micro drill resistance meters to measure living tree wood density [13][14][15][16][17][18][19], living tree age [20], living tree rings [21,22], living tree internal defects [23], ancient wood building health condition [24,25], and so on.If the measurement accuracy of micro drill resistance instrument is further improved, the application of micro drill resistance instrument will become more widely.
The drill resistance, as discussed above, is positively correlated with wood density [1][2][3][4].Meanwhile, the drill resistance is also related to the thickness of the wood cut by the drill.The thicker the cut wood, the greater the drill resistance.The thickness of the cut wood is controlled by the rotation speed and feed speed of the drill.When the rotation speed is the same, the faster the feed speed, the thicker the cut wood.When the feed speed is the same, the slower the rotation speed, the thicker the cut wood.Most micro drill resistance instruments have two motors to control the drill speed.A motor controls the rotation speed of the drill and another motor controls the feed speed of the drill [26][27][28][29][30].When using a micro drill resistance instrument, it is necessary to set an appropriate drill feed speed according to the wood density.When the wood density is low, a higher drill feed speed can be set to improve the efficiency of the instrument.When the wood density is high, a lower drill feed speed can be set to prevent failure of the instrument.If the feed speed of the drill is too low, however, the efficiency of the instrument declines and the measurement cost increases.Conversely, if the feed speed of the drill is too fast, excessive resistance causes vibration or sticking of the needle, even to the point of damaging the equipment.Different feed speeds may be necessary even across the same measured tree species.Sometimes different feed speed of the drill may be set even if the measured tree species are the same [19].Therefore, it is necessary to study conversion algorithm to convert the resistance data measured by different feed speeds into the resistance data of the same feed speed.
In addition, the control accuracy of the drill feed speed significantly influences the resistance measurement accuracy of the micro drill resistance instrument.If the drilled wood density is invariant, then drill resistance increases with feed speed and vice versa.Due to the phenomenon out-of-step, the real-time rotating speed of the step motor has a certain error.So, the real time feed speed of the drill has a certain error.If the error rate of real-time feed speed is high, then drill resistance does not accurately reflect changes in the drilled wood density and the measurement accuracy of the instrument is low.To minimize this error, it is possible to transform the drill resistance of different real-time drill feed speeds into the resistance of a consistent drill feed speed.This requires comprehensive knowledge of the relationship between drill resistance and feed speed.
In this study, a self-made micro drill resistance instrument was used to drill into a Paulownia wood block at different feed speeds.The relationship between drill resistance and feed speed was analyzed to develop an interconversion method among the resistance data measured by the different drill feed speeds.

Test Material
The micro drill resistance instrument can drill into Paulownia tomentosa (Thunb.)Steud.wood safely even at fast feed speeds due to its low density, which allows for a wide range of feed speeds.We sought to determine the variation law of drill resistance over a wide range of feed speed changes with Paulownia wood as experimental material.In November 2020, we cut down a Paulownia tree blown down by the wind in the natural secondary forest of Xinyang Normal University.The tree has diameter at breast height of 42.6 cm.The trunk was intercepted at the stem height from 1.5 to 2.1 m.We removed the bark from the trunk, then processed it into 3.0 cm * 3.0 cm * 3.0 cm wood blocks, then selected 60 of the blocks without decay, knots, or obvious defects as test materials.The moisture content of wood blocks ranges from 80.5 to 84.3%.The absolute dry density of wood blocks ranges from 291.988 to 350.403 kg/m 3 .The wood blocks were stored in a sealed plastic bag to ensure that the moisture content of the wood remains unchanged.

Test Instrument
The primary component we used in this test is a micro drill resistance instrument developed in our laboratory.The mechanical transmission structure of micro drill resistance instrument is shown in Fig. 1 [30].
The drill needle is connected with the DC motor shaft with a clip.The drill needle and DC motor have the same speed.The screw rod is coupled with the step motor shaft, so they also have the same speed.There is a threaded hole in the center of the screw slider, which is installed on the screw rod and can move as the screw rod rotates.The DC motor is installed on the screw slider.The step motor drives the screw rod to rotate synchronously with its own rotation, which makes the screw slide move on screw rod, thus driving the DC motor The drill needle is produced by Rinntech company (Germany).Figure 2 depicts the drill geometry.The drill tip is flat and 3 mm wide, with a 1.5 mm shaft diameter.The drill resistance is concentrate at the tip.
The drill resistance increases as the density of the wood drilled by the needle increases; at the same time, the rotation speed of the DC motor decreases and the controller increases the average voltage at both ends of the DC motor to increase the output torque.Drill resistance decreases with wood density, so the rotation speed of the DC motor increases and the controller decreases the average voltage at both ends of the DC motor to decrease the output torque.Therefore, drill resistance is positively correlated with the voltage of the DC motor and negatively correlated with its speed.
It is not easy to measure drill needle resistance in real time, so the voltage and speed of the DC motor can be used to determine its relative value.We find that the voltage of the DC motor corrected by the speed correction factor k best expresses the drill resistance [31].The correction factor k and the corrected voltage U 1 are calculated as follows: where k is the correction factor; n 0 is the set rotation speed of the DC motor, r/min; n is the actual rotation speed of the DC motor, r/min; U is the actual voltage of the DC Motor, V; U 1 is the corrected voltage of the DC Motor,V.We set the rotation speed of drill needle to 3500 r/min in our experiment.The period for DC motor voltage and rotation speed sampling was 1 ms.The feed speed of the drill needle is controlled by the step motor.We set different step motor speeds according to different drill feed speeds.The distance between adjacent sample points changed throughout the test as the drill feed speed changed, because the sampling period was fixed.The distance between the adjacent sample points was calculated according to the feed speeds.

Test Methods
The feed speed of drill needle was set to 5 cm/min, 10 cm/min, 15 cm/min, 20 cm/min, 30 cm/min, 40 cm/min, 60 cm/min, Fig. 3 Experimental method: drill enters wood block 80 cm/min, and 120 cm/min, in turn.We changed the drill feed speed after measuring the resistance data of 60 blocks at the same speed.The drill needle penetrated the wood block along the radial direction and parallel to one side of the block.To avoid the crossing or overlapping of the drilling needle paths on the same block, the distance between the adjacent starting drill points was about 7 mm and needles moved in the same direction.A diagram of our experimental method is shown in Fig. 3.
We measured the length of the side parallel to the drill direction with a vernier caliper and took the side length as the drilled path length of each block.We assumed that the average wood density and average moisture content of each drill path of the same wood block were constant, that is, when the drill feed speed is uniform, the average resistance of each drilled path is equal.The resistance data of each wood at each drill feed speed constitutes a group of resistance data.

Average Resistance of Each Wood Block at Each Feed Speed
After the micro drill resistance instrument started, the drill needle moved forward 1 cm in its shell (i.e., without loading) before exiting the shell and entering the wood (i.e., with loading).The micro drill resistance instrument stopped after the drill needle emerged from the block.The drill needle was thus in a no-load state at the beginning and end of the resistance curve and was under loading only the middle part of the curve (Fig. 4).
We first calculated the distance between the sampling points of drill resistance at each feed speed in the given sample period.Then, we removed the resistance data of the drill needle in parts of the curve without loading.According to the drilled path length in each wood block, we summed the resistance values and number of resistance sampling points throughout the drilling process.Finally, we averaged the resistance of each wood block at each feed speed to determine the relationship between drill resistance and feed speed.A scatter plot between the average resistance and drill feed speed is shown in Fig. 5.
As shown in Fig. 4, drill resistance increases with feed speed; however, the increase in resistance slows down beyond a certain speed.The relationship between drill resistance and feed speed may not be a simple linear relationship, but rather a logarithmic function relationship.

Feed Speed Variations
We describe variations in drill feed speed here according to increase as well as change time.The increase x 1 in feed speed between each set feed speed is: where x 1 is the increase between each feed speed; s i is the ith set drill feed speed.The change time x 2 of feed speed between each set feed speed is: where x 2 is the speed change time; s i is the ith set drill feed speed.

Changes in Resistance Between Different Feed Speeds for Each Block
We calculated the change value of resistance y between each feed speed for each block as follows: where y is the change value of resistance between each feed speed of each block; r i is the average resistance of the ith set drill feed speed of each block.

Model Construction
We used 40 groups from the original 60 groups of resistance data to establish models between the changes in resistance and the changes in feed rate.We built five linear models with R language [32,33].The dependent variable of these models is the change value of drill resistance y and the independent variables are as listed in Table 1.Model 5 contains the independent variables with higher R 2 were selected in Model 1 and Model 2 or the independent variables with higher R 2 in Model 3 and Model 4.

Test Model
The remaining 20 groups of resistance data that were not used to build model were used to test Models 1-5.The R 2 of each model was calculated [34,35], then the model with the highest R 2 was selected to express the conversion algorithm of drill resistance measured by the micro drill resistance instrument at different feed speeds.

Changes in Resistance with Increase in Feed Speed
We took the change value of the resistance y as the dependent variable with increase in feed speed x 1 or its natural logarithm ln(x 1 ) as the independent variables to establish two respective linear models.As we hypothesized, when the increase in feed   speed x 1 is 0, the change value of resistance y is 0. Thus, the intercept of Model 1 is 0. Our correlation analysis between the change value of resistance and feed speed increase is shown in Table 2.A scatter plot of the resistance change value and feed speed increase is shown in Fig. 6.

Resistance Changes with Feed Speed Change Time
We next took the resistance change y as the dependent variable with feed speed change time x 2 or its natural logarithm ln(x 2 ) as independent variables to establish two respective linear models.As we hypothesized, when the change time of the feed speed x 2 is 1, the resistance change value y is 0. The intercept of Model 4 is 0. Our correlation analysis between the resistance change value and feed speed change time is shown in Table 3, and a corresponding scatter plot is shown in Fig. 7.

Changes in Resistance with Feed Speed Increase and Change Time
The R 2 of Model 1 is higher than that of Model 2, and the R 2 of Model 4 is higher than that of Model 3, so we selected the increase in feed speed x 1 and the natural logarithm of feed speed change time ln(x 2 ) as the independent variables for Model 5. We hypothesized that a feed speed increase x 1 of 0 and feed speed change time x 2 of 1 would yield a y value of 0, so the intercept of Model 5 is 0. Our correlation analysis between the resistance change value, feed speed increase x 1 , and natural logarithm of feed speed change time ln(x 2 ) is shown in Table 4.

Model Test Results
The remaining 20 groups of resistance data that were not used to build model were used to test the five models as shown in Table 5.
The R 2 of Model 5 is the highest, so we used this model to express the conversion algorithm of drill resistance as measured by the micro drill resistance instrument at different feed speeds.We predicted feed speeds with Model 5 based on the resistance values of 20 wood blocks at feed speed of 5 cm/min.The average accuracy of the predicted resistance value is 95.467%.Our comparative analysis of the estimated and measured resistance valules for 20 groups of test data is shown in Fig. 8.

Discussion
The rotation speed and feed speed of the drill are two important parameters significantly affecting the accuracy and efficiency of the micro drill resistance instrument.Sharapov et al. [41] found positive correlations between feed rate per major cutting edge and DR (FR) for the individually tested wood species can be described by allometric functions (R2 = 0.93-0.99).The rotation speed and feed speed of the drill are generally set according to the density of the wood substrate to be drilled, in order to balance measurement accuracy and efficiency.But it is very difficult to find the appropriate feed speed and rotation speed for the drill.For example, Downes et al. [19] used the IML Resistograph PD400 to assess the basic density of plantation eucalyptus and found this to be the case.Drill feed speed was set to 200 cm/min and drill rotation speed to 2500 rpm, but the settings damaged the equipment; drill feed speed was reset to 150 cm/min and drill rotation speed to 3500 rpm.When the feed speed or rotation speed of the drill needle are different, it is necessary to convert the drill resistance at different speeds into the drill resistance at the same speed.Downes et al. [19] found the relationship between the resistance measured under those two sampling conditions was linear and converted the resistance data measured under the second sampling condition into that measured under the first sampling condition.In the present study, the drill rotation speed was fixed but the drill feed speeds differed.We found that the drill resistance is positively related to its feed speed and developed a conversion algorithm for resistance with different feed speeds accordingly.We found that the conversion accuracy for drill resistance is up to 95%.
The research results have laid a solid foundation for converting the drill resistance at different feed speeds into the drill resistance at the same feed speed.
However, due to some issues with our self-made micro drill resistance instrument, such as the drill cannot drill into high wood density at a faster feed speed.So we tested only one tree species here.In future research, we will further improve the design scheme of the micro drill resistance instrument to achieve the goal that the drill can drill into hardwood at a higher speed, and we can test more tree species.
How to non-destructively measure tree-rings and wood density of standing tree is a challenge in worldwide forestry.At present, the main methods used for non-destructive measurement of standing wood include increment core method, X-ray method and micro drill resistance method.Although the increment core method has accurate measurement results, it still has a negative impact on the growth of living trees.The X-ray method equipment is expensive, bulky, and not suitable for field operations.The micro drill resistance instrument is small, lightweight, and easy to use, but its measurement accuracy is not high, so it has not yet been widely used.At present, micro drill resistance instruments are mainly produced by Rinntech and IML companies.Due to technical confidentiality, users are not clear about the principle of the equipment and cannot make improvements to equipment defects, which limits the development of micro drill resistance instrument technology.In 2017, under the guidance of academician Tang Shouzheng of the Chinese Academy of Sciences, we began to study the principle of the micro drill resistance instrument and its application in measuring tree-rings and wood density [36].We have achieved a series of research results, such as a method for identifying peak valley annual rings [36,37], a new mathematical model for the relationship between drill needle resistance [38] and so on [39][40][41].However, there are still some problems with the equipment, so the instruments need further improvement.We hope that more and more scholars will invest in the research and development of micro drill resistance instrument to accelerate the development of micro drill resistance instrument technology.

Conclusions
The resistance of a drill is positively related to its feed speed when its rotation speed remains constant.The drill resistance can be converted as necessary to align with different feed speeds.Drill resistance is positively correlated with changes in feed speed and the natural logarithm of feed speed change time.The accuracy of the proposed conversion algorithm proposed reaches 95%.When the micro drill resistance instrument is used to measure the resistance of Paulownia trees, the algorithm can be used to convert resistance between different drill feed speeds.It may have reference value for the use of the micro drill resistance instrument to measure other tree species.In addition, if the drill feed speed error of the instrument is high, the proposed algorithm provides a feasible method to improve its accuracy.

Fig. 2
Fig. 2 Geometry of the drill

Fig. 7
Fig. 7 Scatter plot: resistance change and feed speed change time

Fig. 8
Fig. 8 Comparison: estimated resistance and measured resistance, 20 groups of test data

Table 1
Independent variables of five linear models

Table 2
Correlation analysis between resistance change value and increase in feed speed

Table 3
Correlation analysis between resistance change value and increase in feed speed

Table 4
Correlation analysis between resistance change value and increase in feed speed

Table 5
Model test results