Tool holder apparatus, a tool, and a method of working an object with a tool

Abstract

This invention relates to a tool holder apparatus, a method of working an object and a tool, particularly for single point diamond turning (SPOT). The tool holder apparatus typically comprises: a tool holder which comprises: a base; a tool support extending from the base; a seat for a tool provided on the tool support, wherein the tool is locatable in the seat, in use; a sensor arrangement configured to generate electrical measurement signals indicative of, or associated with, at least an applied force to the tool, in use; and a piezoelectric actuator arrangement comprising at least one piezoelectric actuator operatively connected to the tool support, wherein the at least one piezoelectric actuator is configured to displace the tool support, or at least a part thereof, in use, in response to receiving suitable electrical control signal / s thereby to maintain a desired applied force to the tool, in use.

Description

[0001] TOOL HOLDER APPARATUS, A TOOL, AND A METHOD OF WORKING AN OBJECT WITH A TOOL

[0002] FIELD OF INVENTION

[0003] THIS INVENTION relates in general to metrology, a tool holder apparatus, a tool, and a method of working an object with a tool. In particular, though not necessarily exclusively, the invention relates to a cutting tool holder apparatus, a cutting tool, and a method of cutting or working on an object with a cutting tool in ultra-precision single-point diamond turning (SPDT).

[0004] BACKGROUND OF THE INVENTION

[0005] Ultra-precision single-point diamond turning (SPDT) technology is typically used to manufacture optical surfaces with optical surface finish with an average surface roughness down to one nanometre. The SPDT products have a wide range of applications in different fields of industry, aerospace, military, biomedical, electronics, and entertainment. There are different factors that influence the outcome of the SPDT process in terms of the quality of surface finish. Different factors can negatively affect the surface generation mechanisms and increase the surface roughness.

[0006] It is well stablished that cutting force is a critical factor for the cutting mechanisms and machining conditions. Increasing the cutting force can induce tool wear and friction, decrease the diamond tool life, and negatively affect the cutting stability and machining conditions. The cutting force can also induce cutting temperature and the positioning errors of the machine tool and decrease the surface accuracy of the machined product. Cutting force can be monitored as a signal for monitoring tool wear and surface defects. The mentioned effects are induced in machining hard-to-cut materials, including titanium alloys and stainless steel, which have poor machinability with SPDT technology. It is important to measure the cutting force during the cutting process and determine the optimum cutting parameters and machining conditions.

[0007] In ultra-precision SPDT applications, measuring the cutting force is important in determining the stable built-up-edge and minimum chip thickness during the SPDT process. In the diamond cutting process, tool edge radius can be increased to compensate for the uncut chip thickness and the effect of material elastic recovery. Increasing the tool edge radius can increase the minimum chip thickness. Measurement of the minimum chip thickness is complicated. Cutting force is used as a factor that has a correlation with the tool edge radius for modelling and estimating the minimum chip thickness. Cutting force can be used as a factor to monitor tool wear, tool life, and tool breakage.

[0008] To achieve the best possible machining conditions and maximum quality of surface finish with minimum surface roughness, it is important to precisely measure the cutting force in diamond cutting of different engineering materials. In this regard, it is desirable to have smart cutting tools for in-process measurement of cutting force in SPDT process that provides real-time measurement of cutting force with high sampling rate and quick response of the measurement system. These tools should have high precision, reliability, resolution, and repeatability.

[0009] Different techniques have been used in development of metrology systems for in-process measurement of cutting forces in high-precision machining applications, including piezoelectric, capacitive, optoelectronic, and strain gauge. There are many developments on the application of force sensors in different machining applications including milling and lathe machining processes. However, a limited number of attention has been given to specific high-precision force measurement systems with high performance for ultra-precision SPDT applications. In ultra-high-precision SPDT process, the application of so-called “smart” cutting tools has been emerging for improving the machining conditions and enabling in-process metrology of machining factors including cutting force and cutting temperature. Two types of force measurement techniques can be used for in-process metrology of cutting force in SPDT process. Acoustic waves could be used for measuring the change in the surface strain using contactless passive acoustic waves. Piezoelectric ceramic films are a category of solutions that have been widely used for different force measurement applications, including cutting force measurement in ultra-precision machining applications.

[0010] Some smart cutting tools make use of piezoelectric films for measuring the applied force in SPDT process as variation of the applied force changes the resistivity of the piezoelectric films, and the applied force can be measured by sensing the change in the resistance of the piezoelectric element. This technique enables measuring cutting force during the ultra-precision cutting process with high precision.

[0011] Other smart cutting tools use piezoceramic material, for real-time measurement of cutting forces along X, Y, and Z axes. In these tools, piezoelectric sensor arrays were implemented in the tool shank for measuring the applied force and, by using a decoupling algorithm, the changes in the signals generated by the piezoelectric sensor arrays were distinguished and the cutting forces were measured real-time.

[0012] In the ultra-high-precision SPDT processes, small cutting forces are executed during the diamond cutting process. Different methods have been used to enable a high-precision force measurement during the ultra-high-precision SPDT process. Although in the existing methods the amount of applied cutting force could be measured precisely, the positioning error of the cutting tool caused by tool holder surface deformation is not monitored and compensated.

[0013] It is an object of the present invention to address these issues and at least to provide a high-performance force measurement system with high frequency and quick response for in-process metrology of applied force with high precision, resolution, and repeatability, in real-time. SUMMARY OF THE INVENTION

[0014] According to a first aspect of the invention, there is provided a tool holder apparatus, wherein the tool holder apparatus comprises: a tool holder, wherein the tool holder comprises: a base; a tool support extending from the base; a seat for a tool provided on the tool support, wherein the tool is locatable in the seat, in use; a sensor arrangement configured to generate electrical measurement signals indicative of, or associated with, at least an applied force to the tool, in use; and a piezoelectric actuator arrangement comprising at least one piezoelectric actuator operatively connected to the tool support, wherein the at least one piezoelectric actuator is configured to displace the tool support, or at least a part thereof, in use, in response to receiving suitable electrical control signal / s thereby to maintain a desired applied force to the tool, in use.

[0015] The suitable electrical control signal / s received by the at least one piezoelectric actuator is / are associated with the electrical measurement signal / s generated by the sensor arrangement. The electrical measurement signals may correspond to or may be indicative of surface deflections or in other words, position errors, from a pre-calibrated initial or in other words, correct, position of the tool support. In this way, the electrical control signals correct the position errors, typically in real-time.

[0016] The suitable control signal / s received by the at least one piezoelectric actuator is / are proportionally and / or integrally related to the electrical measurement signal / s generated by the sensor arrangement. In one example embodiment, the voltage to the piezoelectric actuator may be increased or decreased to correct the position of the tool support from the initial position in a proportion manner based on feedback from the sensor arrangement. The tool holder apparatus comprises a processor, wherein the processor is configured to: receive electrical measurement signal / s generated by the sensor arrangement; compare the received electrical measurement signal / s with a precalibrated threshold, or range; generate suitable electrical control signal / s to control the piezoelectric actuator arrangement in a manner which is at least proportional to a deviation of received electrical measurement signal / s from the pre-calibrated threshold, or range; and transmit the suitable electrical control signal / s to the piezoelectric actuator arrangement.

[0017] It will be appreciated that the processor may be configured to implement a feedback control loop to continually monitor the position of the tool support and / or tool, in use, based on the received electrical measurement signals, and generate the electrical control signal / s to control the piezoelectric actuator arrangement to reposition the tool support and / or tool, in use to the initial position thereby correcting position errors thereof. This may be implemented in the manner described herein by monitoring the electrical measurement signals and comparing the same to electrical measurement signals which correspond to the initial position. In this regard, the processor may be configured to generate suitable electrical control signals to control the piezoelectric actuator arrangement to displace the tool support, or at least a part thereof, in a manner to maintain the electrical measurement signal / s, and thus the applied force to the tool, within the pre-calibrated threshold, or range. It will be understood by those skilled in the art that the pre-calibrated threshold, or range, may correspond to the initial or correct position of the tool support or tool.

[0018] The tool holder apparatus may comprise a suitable transmitter or transceiver device to transmit the electrical measurement signal / s from the tool holder apparatus to a remote receiver or transceiver. The tool holder apparatus may be configured to receive electrical control signals to control the piezoelectric actuator arrangement via the remote transceiver. In some example embodiments, the processor is remote from the tool holder apparatus.

[0019] The piezoelectric actuator may be a pre-loaded piezoceramic actuator. For example, the actuator may be a multi-layer piezoelectric actuator. The piezoelectric actuator may be a piezoceramic chip, typically a multi-layer piezoelectric chip. The piezoelectric actuator may be a preloaded piezoelectric stack actuator, for example, which could execute a maximum displacement of 173 pm at 175 VDC, with an average displacement of 988 nm / V. However, it will be appreciated that other chips may be used instead, or in addition. Moreover, the piezoelectric actuators described herein may be matched or mis-matched. Using the piezoelectric actuators in a preloaded configuration may compensate for the inertial forces that exist during the performance of the apparatus. In the designed configuration, a high bandwidth mechanical fixture guided nanopositioning mechanism using preloaded piezoelectric stack actuator. The piezoelectric actuators may be compact and stiff.

[0020] The sensor arrangement may comprise a strain gauge array operatively connected to the tool support, wherein the strain gauge array may be configured to generate electrical measurement signal / s indicative of surface strain experienced by the tool support, which is indicative of at least the applied force to the tool and / or position errors of the tool support from an initial position, in use.

[0021] The sensor arrangement may comprises the piezoelectric actuator arrangement, wherein the piezoelectric actuator arrangement is configured to generate electrical measurement signal / s indicative of, or associated with, at least an applied force to the tool, in use. It will be appreciated that when the strain gauge array is used, the change in the surface strain of the tool support to which the strain gauge array is connected to determines the amount of applied force. However, when piezoelectric actuator arrangement is used, the change in the physical properties of the piezoelectric material under the applied cutting force changes the electrical properties of the material which determines the amount of applied force. In both solutions, the cutting force is measured or determined.

[0022] The electrical measurement signal / s generated by the piezoelectric actuator arrangement may be indicative of, or associated with, an applied force which is lower than an applied force measured, or measurable, by the strain gauge array. The tool support may comprises a plurality of arms extending along respective axes, wherein the sensor arrangement comprises a strain gauge array operatively connected to each arm, and wherein the piezoelectric actuator arrangement comprises a plurality of piezoelectric actuators operatively connected to each arm, wherein the piezoelectric actuators are configured to displace each respective arm, or a part thereof, along their respective axes, in use, in response to receiving suitable electrical control signal / s

[0023] In one example, embodiment, the tool support may comprise: a first arm extending from the base along a first axis; a second arm extending from the base along a second axis, transverse to the first axis; and a third arm extending from the base along a third axis, transverse to the first and second axes, wherein the seat is provided at an intersection of the first, second and third arms.

[0024] The first, second, and third arms may extend cantilever fashion from the base.

[0025] With the abovementioned configuration, the sensor arrangement may comprise: a first strain gauge array operatively connected to the first arm, wherein the first strain gauge array is configured to generate electrical measurement signal / s indicative of surface strain experienced by the first arm, in use, which is indicative of the applied force to the tool along the first axis; a second strain gauge array operatively connected to the second arm, wherein the second strain gauge array is configured to generate electrical measurement signal / s indicative of surface strain experienced by the second arm, in use, which is indicative of the applied force to the tool along the second axis; and a third strain gauge array operatively connected to the third arm, wherein the third strain gauge array is configured to generate electrical measurement signal / s indicative of surface strain experienced by the third arm, in use, which is indicative of the applied force to the tool along the third axis.

[0026] The strain gauge arrays may be bonded to the respective arms to measure strain along each axis, i.e., each strain gauge array may be configured to measure strain in one axis.

[0027] Considering the configuration described above, the piezoelectric actuator arrangement may comprise: a first piezoelectric actuator operatively connected to the first arm, wherein the first piezoelectric actuator is configured to displace the first arm, or a part thereof, along the first axis, in use, in response to receiving suitable electrical control signal / s; a second piezoelectric actuator operatively connected to the second arm, wherein the second piezoelectric actuator is configured to displace the second arm, or a part thereof, along the second axis, in use, in response to receiving suitable electrical control signal / s; and a third piezoelectric actuator operatively connected to the third arm, wherein the third piezoelectric actuator is configured to displace the third arm, or a part thereof, along the third axis, in use, in response to receiving suitable electrical control signal / s.

[0028] The piezoelectric actuators may enable nanopositioning of the tool for compensating displacements and positioning errors of the tool with nanometer accuracy. It will be noted that the tool may be a cutting tool. In particular, the tool may be a diamond cutting tool, or diamond tool, for use in ultra-precision single-point diamond turning (SPDT).

[0029] The first axis may be an X-axis, wherein the first actuator may be configured to move the first arm, or part thereof, and thus the tool in a direction opposite to a back force on the tool, in use. The second axis may be a Y-axis, wherein the second actuator may be configured to move the second arm, or part thereof, and thus the tool in a direction opposite to an applied force, typically an applied cutting force, in use.

[0030] The third axis may be a Z-axis, wherein the third actuator may be configured to move the third arm, or part thereof, and thus the tool in a direction opposite to a feed force, in use.

[0031] According to another aspect of the invention, there is provided a method of working an object with a tool, wherein the method comprises: measuring applied forces to the tool, during use of the tool working on the object, with a sensor arrangement; comparing the measured applied forces with a pre-calibrated threshold or range; and displacing with tool with a piezoelectric actuator arrangement to maintain the pre-calibrated applied force threshold or range, in response to said comparing.

[0032] The method may comprise: measuring applied forces to the tool along three transverse axes relative to the tool; comparing the measured applied forces with a pre-calibrated threshold or range for each of the axes; and displacing the tool with the piezoelectric actuator arrangement comprising one or more piezoelectric actuators along each of the axes to maintain the pre-calibrated threshold or range for each of the axes, in response to said comparing.

[0033] The method may comprise measuring the applied forces to the tool with one or more strain gauge arrays. The method may comprise measuring the applied forces to the tool with the piezoelectric actuator arrangement. The applied forces measured by the piezoelectric actuator arrangement may be smaller than the applied forces measurable by the one or more strain gauge arrays.

[0034] The method comprises transmitting electrical measurement signals indicative of, or associated with, the measured applied forces to a remote endpoint device. The method may comprise receiving electric control signals from a remote endpoint device to control the piezoelectric actuator arrangement.

[0035] According to another aspect of the invention, there is provided a tool comprising: a tool holder apparatus as described herein; and a cutting tool operatively attached to the tool holder apparatus.

[0036] According to yet another example embodiment, of the invention, there is provided a tool holder apparatus comprising: a tool holder comprising: a base; a first arm attached to the base and extending along a first axis; and a seat operatively located on the first arm, wherein the seat is provided for a tool; a sensor arrangement configured to generate electrical measurement signals indicative of applied forces to the tool, in use; and a first piezoelectric actuator operatively connected to the first arm, wherein the first piezoelectric actuator is configured to displace the first arm, or a part thereof, along the first axis, in use, in response to receiving electrical control signals, wherein the electrical control signals are associated with the electrical measurement signals generated by the sensor arrangement.

[0037] BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 shows a high level schematic block diagram of a tool holder apparatus or system in accordance with an example embodiment of the invention;

[0039] Figure 2 shows a schematic view of a portion of the electronics of the tool holder apparatus of Figure 1 , particularly the electrical configuration and arrangement of the strain gauges;

[0040] Figure 3(a) to (c) shows a various perspective views of the tool holder in accordance with an example embodiment of the invention;

[0041] Figure 4 shows a schematic diagram illustrating another portion of the electronics of the tool holder apparatus of Figure 1 , particularly the electrical configuration and arrangement of the piezoelectric actuators operatively connected to, or interfaced with, the tool holder in accordance with an example embodiment of the invention;

[0042] Figure 5(a) to (c) shows a various perspective views of the tool holder in accordance with an example embodiment of the invention;

[0043] Figure 6 shows a schematic circuit diagram of the electronics of the tool holder apparatus of Figure 1 in accordance with an example embodiment of the invention;

[0044] Figure 7 shows another schematic diagram illustrating working principles of the tool holder apparatus of Figure 1 in accordance with an example embodiment of the invention;

[0045] Figure 8 shows a block diagram of a closed-loop control system in accordance with an example embodiment of the invention; and Figure 9(a) & (b) show more perspective views of the tool holder in accordance with an example embodiment of the invention.

[0046] DETAILED DESCRIPTION OF THE DRAWINGS

[0047] The following description of the invention is provided as an enabling teaching of the invention. Those skilled in the relevant art will recognise that many changes can be made to the embodiments described, while still attaining the beneficial results of the present invention. It will also be apparent that some of the desired benefits of the present invention can be attained by selecting some of the features of the present invention without utilising other features.

[0048] Accordingly, those skilled in the art will recognise that modifications and adaptations to the present invention are possible, and may even be desirable in certain circumstances, and are a part of the present invention. Thus, the following description is provided as illustrative of the principles of the present invention and not a limitation thereof.

[0049] It will be appreciated that the phrase “for example,” “such as”, and variants thereof describe non-limiting embodiments of the presently disclosed subject matter. Reference in the specification to “one example embodiment”, “another example embodiment”, “some example embodiment”, or variants thereof means that a particular feature, structure or characteristic described in connection with the embodiment(s) is included in at least one embodiment of the presently disclosed subject matter. Thus, the use of the phrase “one example embodiment”, “another example embodiment”, “some example embodiment”, or variants thereof does not necessarily refer to the same embodiment(s).

[0050] Unless otherwise stated, some features of the subject matter described herein, which are, described in the context of separate embodiments for purposes of clarity, may also be provided in combination in a single embodiment. Similarly, various features of the subject matter disclosed herein which are described in the context of a single embodiment may also be provided separately or in any suitable sub-combination. The headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description or the claims. For brevity, the word “may” is used in a permissive sense (i.e., meaning “having the potential to”), rather than the mandatory sense (i.e., meaning “must”).

[0051] The words “include,” “including,” and “includes” and the words “comprises”, “comprising”, and “comprises” mean including and comprising, but not limited thereto, respectively. Additionally, as used herein, the term “coupled” may refer to two or more components connected together, whether that connection is permanent (e.g., welded, cast, moulded, carved) or temporary (e.g., bolted, screwed, adhered via an adhesive), direct or indirect (i.e., through an intermediary), mechanical, chemical, optical, or electrical as is the case in a communicatively coupled components which may be in communication with each other wirelessly or in a hardwired fashion.

[0052] Referring to Figure 1 of the drawings, a tool holder apparatus or system in accordance with an example embodiment of the invention is generally referred to by reference numeral 100. The apparatus 100 is typically a smart cutting tool which comprises a physical tool holder 102, as illustrated in Figure 3, 4, 5 and 9, and electronics 104, as can be better seen in at least Figures 2, 4 and 6, which is operatively connected to the tool holder 102.

[0053] The electronics 104 typically implements an electronic control system as described herein. To this end, the electronics 104 comprises a sensor arrangement 106 and a piezoelectric actuator arrangement communicatively coupled to a processor 110. It will be understood that the processor 110 may be in the form of one or more processors which may typically be one or a combination of microcontrollers, processors, graphics processors, or field programmable gate arrays (FPGAs) operable to achieve the desired operation / s as described herein. The processor arrangement 110 may be operable under instructions stored in an internal memory of the arrangement and / or external memory device (not shown) to perform the operations described or contemplated herein.

[0054] The tool holder 102 is typically a mechanical structure which comprises a rigid tool holder body is stable during the machining process. In this regard, the tool holder 102 comprises a rigid base 112 and three cantilever arms or beams: a first arm 114; a second arm 116; and a third arm 118 which are transverse to each other and intersect at a tool holder mount or support 120 for location of a diamond cutting tool, in use.

[0055] The tool holder 102 is sensitive to small forces applied to the cutting tool during the cutting process. The tool holder 102 also provides 3 degree-of-freedom in mechanism for nanopositioning of the cutting tool while minimizing the possibility of surface strain under applied forces in SPDT For this purpose, the tool holder 102 is typically constructed from tool steel material. In ultra-high-precision SPDT process, the cutting speed used is usually in a range of 300-3000 rpm. In this condition, the natural frequency of the machine tool is around 50 Hz. Therefore, the natural frequency of the designed tool holder is higher than 200KHz.

[0056] The sensor arrangement 106, as illustrated in Figure 2 and Figures 3(a) to (c), typically comprise three strain gauge arrays S1 , S2, S3, each comprising four strain gauges R operatively bonded to the arms 114 to 118 of the tool holder 102, particularly three surfaces which correspond to three axes (X, Y and Z) as described herein. In particular, the three groups of strain gauges S1 to S3 are bonded on the tool holder surface in areas of highest strain on the surface of tool holder 102 while maximizing the sensitivity of the force measurement along the X-, Y-, and Z-axis as can be seen in part in Figure 3.

[0057] It will be appreciated by those skilled in the art that the magnitude of the mechanical deformation of the tool holder 102 is very small and therefore, the corresponding strain could be expressed as a micro-strain. The strain and microstrain of the piezoelectric element could be expressed by the following equations:

[0058] , wherein, £ / is the strain, ei is micro-strain, ALZL is the change in surface strain in the desired dimension. In this condition, the change in the resistance of the strain gauge (gauge factor) could be calculated using the following equation:

[0059] , wherein, Ri is the resistance of the strain gauge, AF? is the change in the resistance of strain gauge, G is the gauge factor and is the specific strain of the strain gauge component. Therefore, the change in the resistance of the strain gauge could be expressed by the following equation:

[0060] A / ? = R. GF. EI

[0061] The first strain gauge array S1 comprises four active strain gauges Ri, R2, R3, R4 which are arranged on the surface of the tool holder along an X-axis (surface A) to detect back force and tool holder surface strain along X-axis. The first strain gain array S1 is typically attached to the first arm or beam 114 of the tool holder 102.

[0062] The second strain gauge array S2 comprises four active strain gauges Rs, Re, R7, Rs which are arranged on the surface of the tool holder along / -axis (surface B) to detect cutting force and tool holder surface strain along / -axis. The second strain gauge array S2 is typically attached to the second arm 116 of the tool holder 102.

[0063] Moreover, the third strain gauge array S3 comprises four active strain gauges R9, Rw, R11, R12 which are arranged on the surface of the tool holder along Z-axis (surface C) to detect feed force and tool holder surface strain along Z-axis. The third stain gauge array is typically attached to the third arm 118 of the tool holder 102.

[0064] The strain gauges R are bonded on the surfaces of the first in Wheatstone bridge configurations. In other words, the strain gauge arrays S1 to S3 may be Wheatstone bridge configurations of the respective strain gauges R. It will be appreciated that the strain gauge arrays S1 to S3 will be described herein also as the Wheatstone bridges S1 to S3.

[0065] It will be appreciated that an applied force in the respective direction causes deflection on the surface of the respective arm 114 to 118 and changes the resistance and output voltage of the strain gauge array S1 to S3 in the respective direction. When an external force is applied to the tool holder 102, the tool holder 102 generates a resisting force against the externally applied force (stress) at the same location. In this condition, the tension of the tool holder could be calculated by the following equation: MC a = — i

[0066] , wherein, a is tension of the surface, M is the bending moment, C is the displacement, and I is the moment of inertia. The amount of moment of inertia is in relation with the specifications of the cantilever arms and could be expressed by the following equation: where, I is the moment of inertia, b is the width of the arm, h is the thickness of the arm. It will be appreciated that each arm 114 to 118 may be substantially similar elongate arms which have a square or rectangular cross-sectional profile. Each arm 114 to 118 may be anchored to the body 112 in a manner to permit minor displacement of each arm along at least X, Y and Z axes.

[0067] The Natural frequency of the tool holder could be calculated by the following equation:

[0068] , wherein, fnis the frequency of the tool holder, E is the modulus of elasticity of the material, I is the moment of inertia, p is the density of the plate, B is breadth, D is width, and L is length. Strain measurement during the diamond cutting process requires high-precision systems as the change in the mechanical formation of the tool holder is very small resulting in small change in the resistance of the strain gauge.

[0069] As illustrated in Figure 2, each Wheatstone bridge S1 to S3 consists of four arms with resistive elements or strain gauges R that could convert the acquired signal to a bipolar voltage output that could be amplified and measured. For example, the output voltage of Wheatstone bridges S1 may be similar to the outputs of the Wheatstone bridges S2 and S3 thus a discussion of S1 follows but may be applicable to S2 and S3. As such the output voltage of the Wheatstone bridge S1 may be measured using the following equation: , wherein, Vois the measured output voltage, Veis the excitation voltage, and R1-R4 are the resistor elements. In the Wheatstone configuration that RI=R2 and R3=R4, when an active strain gauge is used in the configuration of Wheatstone bridge S1 (F?4±AR), the change in the output of the Wheatstone bridge S1 is in correlation with the change in the resistance of the strain gauge (AR). The Wheatstone bridge S1 allows measuring small changes in the resistance of the strain gauge by using the following equation:

[0070] AR = Rs* GF * si

[0071] , wherein, Rs is the resistance of the strain gauge element in no load condition, GF is the gauge factor of the strain gauge, and si is the strain factor of the strain gauge. In this condition, by measuring the output voltage of the Wheatstone bridge S1 , the change in the strain may be calculated. The output voltage of the designed bridge network S1 could be expressed by the following equation:

[0072] In this condition, the variation of the resistance of the active gauges could change the output voltage. By using the below equation, the strain could be measured, and the applied force could be determined:

[0073] Vo= Ve* —GF * £

[0074] In addition, the sensitivity of the bridge S1 may be can be expressed as:

[0075] In any event, it will be noted that the structure of strain gauge R is sensitive to dimensional changes when an external force is applied to surface in which strain gauge R is bonded on it. The output voltage of a Wheatstone bridge is directly proportional to bridge excitation and very sensitive to the small mechanical deformations that drive resistance imbalances in one or more legs of a bridge. It follows that the resistance of the strain gauges R will vary when the external forces are applied to the tool holder 102. Table 1 below presents the variations of resistance of strain gauges bonded on the tool holder. Fxindicates the back force applied along X-axis, Fyindicates the cutting force applied along / -axis, and Fzindicates the applied feed force along Z-axis, as illustrated in Figure 3(a).

[0076] Table 1 : The variation of resistance of the strain gauges Referring still to Figure 2, excitations of the Wheatstone bridges or strain gauge arrays S1 to S3 are connected to voltage excitation and the corresponding output voltage V / will appear on the measurement terminals of the bridges. In other words, the Wheatstone bridges S1 to S3 are communicatively coupled to the processor 110 via suitable amplification 124 and input / output 126 circuitry. A suitable power supply 128 typically drives the Wheatstone bridges S1 to S3.

[0077] The following equations express the output signals of the Wheatstone bridges S1 , S2, and S3, respectively:

[0078] , wherein, the Rj / Ri represents the resistance variation rate of the gauge Ri, AW is the change in the output voltage of the Wheatstone bridge or first strain gauge array S1 in the X-axis, A\yis the change in the output voltage of the Wheatstone bridge or second strain gauge array S2 in the / -axis, and AW is the change in the output voltage of the Wheatstone bridge or third strain gauge array S3 in the Z-axis, and Ri represents the number of the strain gauges R in each Wheatstone bridge configuration or strain gauge arrays S1 to S3.

[0079] During the diamond cutting process, applied forces, including cutting force (Fy), back force (Fx), and feed force (Fz) (see Figure 3(a)) act at the tool nose 122 and deform the tool holder 102 in nanometric scale. The twelve strain gauges R as described herein are configured in the three independent Wheatstone bridges S1 to S3 to measure the change in the surface strain corresponding to applied force in each axis. Three outputs are DC voltages that could be acquired, amplified, and used to calculate the applied force corresponding to the change in the output voltage of each Wheatstone bridge S1 to S3.

[0080] During the measurement, a specific amount of DC is applied to the input terminals of each Wheatstone bridge S1 to S3 from the power supply 128. The applied force changes the surface strain while the resistance of the strain gauges R is changed based on the stress / tension applied to the surface bonded on the tool holder 102.

[0081] It will be appreciated that the relationship between the changes in the output voltage and the applied force may be expressed by the following equation: AVx = Ksx. Fxvy = Ksy. FyA7z = KSZ. FZwherein, AW, Al / y, and AW are the respective voltage changes for each Wheatstone bridge S1 to S3 under the applied forces Fx, Fy, and Fzto the tool 122, respectively. Ksx, Ksy, and Kszare corresponding constant for indicating the relationship between the change in the output voltage and respective force applied. It follows that the decoupling measurement algorithm implemented within the control system is expressed as:

[0082] When an external force is applied to the tool holder 102, the change in the surface strain in three faces of the tool holder 102 is measured. The following equation could express the relationship between the applied force and the change in surface strain:

[0083] , wherein, Asx, Acy, and AEZ are respective change in the strain of the tool holder surface under the applied forces Fx, Fy, and Fzrespectively. Kcz, Kcz, and K£Zare corresponding constant for indicating the relationship between the surface strain change and respective forces applied. A x, A y, and A z are the respective change in the output voltage of the strain gauge bridge in X-, Y-, and Z-axis respectively. Veis the input voltage applied to strain gauge bridge and GF is the gauge factor of the strain gauge bridge. The decoupling measurement algorithm implemented within the control system is expressed as:

[0084] Therefore, when an external force is applied to the tool holder structure, the surface strain, which cause tool positioning error in the corresponding axis, could be determined. For correcting the occurred displacement, the preloaded PSAs are driven while pushing the tool holder by increasing the applied voltage at the terminals until the surface strain is compensated ( EI=0).

[0085] Referring now also to Figure 4 and Figures 5 (a) to (c), three piezoelectric stack arrays (PSAs) PSA I, PSA II, and PSA III are fixed to the tool holder 102 while mechanically interacting with each arm 114 to 118. In particular, each PSA I to PSA III may be interspaced between the base body 112 and each arm 114 to 118 along the respective X, Y, and Z axes or in other words X-, Y-, and Z-directions. Each PSA I to III may be operatively communicatively coupled to the microcontroller 110 via suitable driver 130 and input / output circuitry.

[0086] In the illustrated example embodiment, PSA I may be configured could push and move the tool holder in X-axis, PSA II may be configured to push and move the tool holder in Y-axis, and PSA III may be configured to push and move the tool holder in Z-axis. The PSAs are installed in g33 polarization direction so that the change in the length of each PSAs I to III could be effective and move the tool holder structure.

[0087] Also, when an external force is applied to the cutting tool, the tool holder body is deflected, and the applied force is transferred to the respective PSA I to III. It follows that PSA I aligned to the X-axis may be configured to measure the back force applied to the diamond tool during the diamond cutting process, the PSA II aligned with Y-axis may be configured to measure the cutting force that is applied to the diamond tool during the diamond cutting process, and PSA III aligned to the Z-axis may be configured to measure the feed force applied to the diamond tool during the diamond cutting process. In the diamond cutting process, the applied force is transferred to the PSA while influencing the electrical charge of the piezoelectric material. Two conductive plates are fixed to the sides of each PSA, as electrodes, for driving the component as well as measuring the change in the electrical charge of each component which is caused by the applied forces. It follows that a high- performance control system with high-precision amplifier and analog-to-digital converter is provided to enable measuring the small amounts of changes in the electrical charge generated by the PSAs and strain gauges. The PSA I to PSA III may be low-voltage PSAs which are used to measure the forces applied to the cutting tool during the diamond cutting process and to correct the positioning error caused by the applied forces at nanometric scale.

[0088] An important aspect in design of a high-precision force measurement system using PSA is the material characteristics of the piezoelectric chip. When a DC voltage resource is connected to the electrodes of a piezoelectric component, its dimensions change based on the amplitude of the applied voltage. The domain of the displacements is correlated with the amount of the applied voltage.

[0089] It will be appreciated by those skilled in the art that the mechanical quality factor Qmis a dimensionless quality factor for calculating the mechanical loses in dynamic performance of piezoelectric component. The Qmis the ratio of in-put energy per oscillation cycle over the total energy consumed in the cycle. This factor could be calculated as follows: where, Qmis the mechanical quality factor, fpis the parallel resonance frequency, fsis the series resonance frequency, C is capacitance, and Zsis the impedance at the resonance. The dielectric relative permittivity of a piezoelectric component £ris defined as the ratio between the absolute dielectric constant and the permittivity of free space o =8.85*1 O’12F / m. The capacitance of a piezoelectric component is measured at a frequency below the resonance frequency of the piezoceramic, usually at 1 KHz. The capacitance could be calculated using the following equation: where, C is the capacitance, Eris the relative dielectric permittivity, Eo is dielectric permittivity of free space, A is the area of the electrode, and D is the electrode spacing. The capacitance of a rectangular plate piezoceramic could be simplified to the following equation: where, f is the capacitance, E is the relative dielectric permittivity, L is length, 1 / V is width, and Tis thickness of the piezoceramic material.

[0090] When a range of different frequencies is applied to the piezoceramic component, the series resonance frequency ( ) could be obtained at the minimum impedance and the parallel resonance frequency (fp) could be obtained at the maximum impedance. The resonance frequency of a plate piezoceramic can be calculated using the following equation: f _NT

[0091] Jr ~Twhere, N is the frequency constant of the longitudinal / transverse oscillation of the piezoceramic plate, NT is the frequency constant for the thickness mode oscillation of the piezoceramic plate, L is length, and 1 / V is width, and Tis thickness.

[0092] Piezoelectric charge constant (d) denotes the rate of generated electrical charge and the applied force. The charge constant of piezoelectric component could be measured using the following equation:

[0093] Q = d.F where, Q is the generated electrical charge, is the charge constant, and is the applied force. Voltage and charge constants denote the ratio between the force applied and the amount of electric field generated. Voltage and charge constants are in correlation with the capacitance of the piezoceramic component. Therefore, by measuring the generated electrical charge, the amount of applied force could be determined. The charge constant of a piezoelectric component is expressed by the following equation: d — EQ. £ -. g where, d is the piezoelectric charge constant, Eris the relative dielectric permittivity, o is dielectric permittivity of free space, and g is the piezoceramic voltage constant.

[0094] The mentioned characteristics of the piezoelectric materials are used for determining the characteristics of the multi-layer piezo stack actuators. Each PSA I to III may be a piezoceramic chip consisting of stacked piezoelectric ceramic layers between the integrated electrodes. The ceramic layers are mechanically in series and the electrodes are electrically parallel. The capacitance of a rectangular plate piezo stack could be calculated using the following equation: where, Tis the capacitance of the piezoceramic component, s 33 is the relative dielectric permittivity in 33 polarization direction, L is length, 1 / V is width, and Tis the thickness of the piezoceramic component. In this condition, the executed length, transverse, and thickness displacements could be calculated using the following equations:

[0095] . ... d31.W.V

[0096] AW = — - T

[0097] ^T = d33.V where, A 1 / V is the width displacement, AL is length displacement, and AT is thickness displacement, dsi is the piezoceramic charge constant in 31 polarization direction, l / Vis width, V is electrical voltage applied, L is length, and Tis thickness of the piezoelectric component. d-13 is the piezoceramic charge constant in 13 polarization direction and c / 33 is the piezoceramic charge constant in 33 polarization direction. A specific amount of voltage may be applied to each PSA I to PSA III from the power supply 128 to make desired displacement and to achieve the position correction in each axis (X, Y, Z). The amount of required voltage may be determined or calculated using the following equations: where, g is the voltage constant, F is the generated / applied force, t is thickness, 1 / V is width, and L is length of the piezo stack. The applied force may be calculated by measuring the electrical voltage generated across the piezoceramic component by means of voltage constant using following equation: U = 933- h.-F

[0098] , wherein, g33is the voltage constant of the piezoceramic in 33 polarization direction, h is the height of piezoceramic element, is the applied force, and A is the area of piezoceramic component.

[0099] When an external force is applied to each PSA I to III, it changes the electrical charge and physical properties of the same. Applying a force generates a negative / positive electrical charge according to the position and direction of the force applied. This is used as feedback to determine the amount of applied force. The change in the electrical characteristics of the PSAs is measured by measuring the input / output voltage at the terminals of each piezoceramic component. In this regard, from the foregoing, the following equations expresses the relationship between the applied force and the change in the electrical charge of the PSAs I to III:

[0100] , wherein, AFXis the change in the electrical charge of PSA I, At / yis the change in the electrical charge of PSA II, and At / Zis the change in the electrical charge of PSA Pz. Kpx, Kpy, and Kpzare corresponding constants for indicating the relationship between the change in the electrical charge and respective force applied, h is the height of the piezoceramic chip, gss represents the 33 polarizations direction of the piezoelectric material, A is the area of each piezoceramic chip, and Fx, Fy, and Fzare applied forces in X-, Y-, and Z-directions. By measuring the change in the electrical charge of each PSA I to III, the control system could calculate the corresponding applied force. The decoupling measurement algorithm implemented within the control system could be expressed as:

[0101] Moreover, by measuring the change in the electrical potential of each PSA I to III, the change in the height of each PSA I to III may be calculated and the position error in the corresponding axis could be determined. The following equation may express the relationship between the change in the height of the PSAs I to III and the change in their electrical charge:

[0102] , wherein, h.pxis the change in the height of the PSA I, A / ipyis the change in the height of the PSA II, and hpzis the change in the height of the PSA III. Kpx, Kpy, and Kpzare corresponding constants for indicating the relationship between the change in the electrical charge and respective force applied, h is the height of the PSA, g33 represents the 33 polarizations direction of the PSA, A is the area of each PSA, and Fx, Fy, and Fzare applied forces in X-, Y-, and Z-directions. By measuring the change in the electrical potential of each PSA, the change in the height of the chip corresponding to position displacement in respective axis could be calculated. The decoupling measurement algorithm implemented within the control system is expressed as:

[0103] Referring to Figure 6 to 8 of the drawings, a circuit diagram in accordance with an example embodiment of the invention is shown.

[0104] The circuit diagram presents the detailed implementation of electronics 104 and particularly the electronic control system of the smart cutting tool in accordance with an example embodiment of the invention which implements the closed-loop system illustrated in Figure 8. The control system should be able to distinguish the small changes in the output voltage of the strain gauge arrays S1 to S3 and the PSAs I to III so that the tool position as well as applied forces can be measured and set. In the circuit diagram illustrated in Figure 6, a microcontroller 1 is used. Three load cell amplifiers 2, 3, 4 with 24-bit analog to digital converter, are used in the design of the control system to amplify the acquired voltage signals of the Wheatstone bridges with high precision.

[0105] The amplifiers could communicate with the microcontroller 1 via two-wire interface (data and clock). The strain gauge Wheatstone bridges 5, 6, 7 are connected to the amplifiers and the output of amplifiers are connected to digital pins of the microcontroller 1 . By using the strain gauges bonded on three surfaces of the tool holder body, the deformation on the surface could be measured and the applied force corresponding the surface deflection could be indirectly calculated. The change in the measured voltage could be distinguished via microcontroller 1 and the corresponding strain of the surface could be calculated.

[0106] By determining the amount of strain / tension of the tool holder surface, the change in the initial position of the diamond tool could be determined and corrected with high precision.

[0107] Three PSAs 11 , 12, 13 are used in the system. When an external force is applied to the system at the tool nose, the tool holder bends, and the applied force is transferred to the piezo stack actuators placed at the other side of the tool holder body. The applied force presses the PSA at a nanometric scale which causes a change in the physical properties of the piezoceramic component and changes the resistance and capacitance of the component. The applied force cause generation of a small amount of electrical charge that could be positive or negative. This causes a change in the drive voltage of the piezoceramic element.

[0108] By measuring the change in the voltage at the driving / detecting electrodes, the generated electrical charge as well as the applied force could be calculated. By changing the amount of the applied voltage, it is possible to change the position of the cutting tool.

[0109] An AC voltage input is connected to two DC-DC transformers 18 for providing the required power for driving the control system and the piezoceramics. The outputs of the transformers are connected to voltage regulator in which a noiseless input voltage without voltage drop is secured. By using a voltage regulator 17, a regulated VDC is connected to the control system. In addition, three DC-DC step- down power modules 14, 15, 16 are implemented within the system to supply the required voltage for loading the PSAs. A dual H-bridge driver 8, 9, 10 is used to supply the required voltage for charging / driving each PSA.

[0110] Moreover, by using the strain gauges bonded on the surface of the tool holder the small surface deflections (position errors) could be monitored and corrected realtime. The outputs of strain gauges are used as position feedbacks to identify and correct the position errors occurred. The position feedbacks are used in the designed closed-loop control system, for measuring the surface deformities caused by the applied force and accurately setting the position of the diamond tool in the desired location. According to the direction of deformity occurred on the tool shank surface, which could be determined using the output signal of the strain gauges, the control system increase / decrease the amplitude of the voltage applied to the piezoceramic chips while using the position feedback to achieve the initial (correct) position of the surface and compensate the positioning displacement of the diamond tool. Moreover, the control system should be able to connect to a hybrid controller and transmit the acquired data when the device is used in a hybrid machining platform.

[0111] By using wireless communication protocols, the control system could connect to a Bluetooth or WIFI network and communicate with a hybrid controller. The control system could transmit data, including the measured cutting forces as well as the position of the diamond tool compared to its initial position, to a network, software applications, and intelligent systems of the hybrid machining platform. The control system could also receive commands from the user or hybrid controller for changing the position of the diamond tool with a precision down to 1 nanometer and set / correct the positioning errors of the diamond tool during the diamond cutting process.

[0112] In present disclosure, by combining a three-dimensional surface strain measurement system and a three-dimensional nanopositioning system, a hybrid cutting tool has been developed to be used in ultra-high-precision SPDT applications. The smart cutting tool measures the applied forces to the diamond tool in the diamond cutting process in three dimensions where cutting forces are at 0.1 N and tool displacements are at 1 nm scales. Two types of position feedbacks are used to determine the displacement of the diamond tool in X-, Y-, and Z-axis. Three strain gauge measurement systems are bonded on three surfaces of the tool holder to measure the surface deflections in three dimensions. Moreover, three PSAs are fixed to different surfaces of the moving part of the tool holder, and mechanically interacted with the tool holder for nanopositioning of the cutting tool. In the designed configuration, the cutting force (Fy), feed force (Fz), and back forces (Fx) are transferred to the piezoceramic chips while changing the electrical charge of the chips and compressing them in nanometric scales. The applied force to each PSA could be calculated using the change in the electrical charge of the chip. Subsequently, the cutting force, feed force, and back forces applied to the diamond tool could be determined using the change in the surface strain as well as the change in the length of the respective PSA.

[0113] Moreover, by implementing three PSAs, a high-precision 3 DOF XYZ nanopositioning system with nanometric resolution is advantageously enabled. The designed control system may compensate for the surface deflections and displacement of the diamond tool by applying small changes to the drive voltage of each PSA and change the length of each PSA by increasing / decreasing the applied drive voltage. By increasing / decreasing the amount of the drive voltage applied to the piezoceramic chip, the length of the PSA could be precisely controlled. Therefore, it is possible to compensate the displacement of the tool holder and the diamond tool by applying a precise voltage level that reset the position of the diamond tool to its initial position with nanometer positioning accuracy. The output of the strain gauge systems as well as the change in the drive voltage level of each PSA are the feedback used for compensating the position errors in three dimensions.

[0114] By using the transverse piezoelectric effect as well as the symmetric arrangement of the sensors integrated with the delicate design of the tool holder structure, the relationships between the applied forces and respective electric charges are established. Subsequently, the decoupling algorithms are derived.

Claims

CLAIMS1 . A tool holder apparatus, wherein the tool holder apparatus comprises: a tool holder, wherein the tool holder comprises: a base; a tool support extending from the base; a seat for a tool provided on the tool support, wherein the tool is locatable in the seat, in use; a sensor arrangement comprising a strain gauge array operatively connected to the tool support, wherein the strain gauge array is configured to generate electrical measurement signal / s indicative of, or associated with, surface strain experienced by the tool support, which is indicative of at least an applied force to the tool and / or position errors of the tool support from an initial position, in use; and a piezoelectric actuator arrangement comprising at least one piezoelectric actuator operatively connected to the tool support, wherein the at least one piezoelectric actuator is configured to displace the tool support, or at least a part thereof, in use, in response to receiving suitable electrical control signal / s thereby to maintain a desired applied force to the tool, in use.

2. A tool holder apparatus as claimed in claim 1 , wherein the suitable electrical control signal / s received by the at least one piezoelectric actuator is / are associated with the electrical measurement signal / s generated by the sensor arrangement.

3. A tool holder as claimed in either claim 1 or 2, wherein the suitable control signal / s received by the at least one piezoelectric actuator is / are proportionally and / or integrally related to the electrical measurement signal / s generated by the sensor arrangement.

4. A tool holder apparatus as claimed in any one of the preceding claims, wherein the tool holder apparatus comprises a processor, wherein the processor is configured to: receive electrical measurement signal / s generated by the sensor arrangement; compare the received electrical measurement signal / s with a precalibrated threshold, or range; generate suitable electrical control signal / s to control the piezoelectric actuator arrangement in a manner which is at least proportional to a deviation of received electrical measurement signal / s from the pre-calibrated threshold, or range; and transmit the suitable electrical control signal / s to the piezoelectric actuator arrangement.

5. A tool holder apparatus as claimed in claim 4, wherein the processor is configured to generate suitable electrical control signals to control the piezoelectric actuator arrangement to displace the tool support, or at least a part thereof, in a manner to maintain the electrical measurement signal / s, and thus the applied force to the tool, within the pre-calibrated threshold, or range.

6. A tool holder apparatus as claimed in any one of the preceding claims, wherein the tool holder apparatus comprises a suitable transmitter or transceiver device to transmit the electrical measurement signal / s from the tool holder apparatus to a remote receiver or transceiver.

7. A tool holder apparatus as claimed in any one of the preceding claims, wherein the sensor arrangement comprises the piezoelectric actuator arrangement, wherein the piezoelectric actuator arrangement is configured to generate electrical measurement signal / s indicative of, or associated with, at least an applied force to the tool, in use.

8. A tool holder apparatus as claimed in claim 7, wherein the electrical measurement signal / s generated by the piezoelectric actuator arrangement is indicative of, or associated with, an applied force which is lower than an applied force measured, or measurable, by the strain gauge array.

9. A tool holder apparatus as claimed in any one of the preceding claims, wherein the tool support comprises a plurality of arms extending along respective axes, wherein the sensor arrangement comprises a strain gauge array operatively connected to each arm, and wherein the piezoelectric actuator arrangement comprises a plurality of piezoelectric actuators operatively connected to each arm, wherein the piezoelectric actuators are configured to displace each respective arm, or a part thereof, along their respective axes, in use, in response to receiving suitable electrical control signal / s10. A tool holder apparatus as claimed in any one of the preceding claims, wherein the tool support comprises: a first arm extending from the base along a first axis; a second arm extending from the base along a second axis, transverse to the first axis; and a third arm extending from the base along a third axis, transverse to the first and second axes, wherein the seat is provided at an intersection of the first, second and third arms.

11. A tool holder apparatus as claimed in claim 10, wherein the first, second, and third arms extend cantilever fashion from the base.

12. A tool holder apparatus as claimed in either claim 10 or 11 , wherein the sensor arrangement comprises:a first strain gauge array operatively connected to the first arm, wherein the first strain gauge array is configured to generate electrical measurement signal / s indicative of surface strain experienced by the first arm, in use, which is indicative of the applied force to the tool along the first axis; a second strain gauge array operatively connected to the second arm, wherein the second strain gauge array is configured to generate electrical measurement signal / s indicative of surface strain experienced by the second arm, in use, which is indicative of the applied force to the tool along the second axis; and a third strain gauge array operatively connected to the third arm, wherein the third strain gauge array is configured to generate electrical measurement signal / s indicative of surface strain experienced by the third arm, in use, which is indicative of the applied force to the tool along the third axis.

13. A tool holder apparatus as claimed in any one of claims 10 to 12, wherein the piezoelectric actuator arrangement comprises: a first piezoelectric actuator operatively connected to the first arm, wherein the first piezoelectric actuator is configured to displace the first arm, or a part thereof, along the first axis, in use, in response to receiving suitable electrical control signal / s; a second piezoelectric actuator operatively connected to the second arm, wherein the second piezoelectric actuator is configured to displace the second arm, or a part thereof, along the second axis, in use, in response to receiving suitable electrical control signal / s; and a third piezoelectric actuator operatively connected to the third arm, wherein the third piezoelectric actuator is configured to displace the third arm, or a part thereof, along the third axis, in use, in response to receiving suitable electrical control signal / s.

14. A tool holder apparatus as claimed in any one of the preceding claims, wherein the tool is a cutting tool.

15. A tool holder apparatus as claimed in any one of the preceding claims, wherein the tool is a diamond cutting tool.

16. A method of working an object with a tool, wherein the method comprises: measuring applied forces to the tool, during use of the tool working on the object, with a sensor arrangement comprising one or more strain gauge arrays; comparing the measured applied forces with a pre-calibrated threshold or range; and displacing with tool with a piezoelectric actuator arrangement to maintain the pre-calibrated applied force threshold or range, in response to said comparing.

17. A method of working an object with a tool as claimed in claim 16, wherein the method comprises: measuring applied forces to the tool along three transverse axes relative to the tool; comparing the measured applied forces with a pre-calibrated threshold or range for each of the axes; displacing the tool with the piezoelectric actuator arrangement comprising one or more piezoelectric actuators along each of the axes to maintain the pre-calibrated threshold or range for each of the axes, in response to said comparing.

18. A method of working an object with a tool as claimed in either claim 16 or claim 17, wherein the method comprises measuring the applied forces to the tool with the piezoelectric actuator arrangement.

19. A method of working an object with a tool as claimed in claim 18, wherein the applied forces measured by the piezoelectric actuator arrangement is smaller than the applied forces measurable by the one or more strain gauge arrays.

20. A method of working an object with a tool as claimed in any one of claims 16 to 18, wherein the method comprises transmitting electrical measurement signals indicative of, or associated with, the measured applied forces to a remote endpoint device.

21. A tool comprising: a tool holder apparatus as claimed in any one of claims 1 to 15; and a cutting tool operatively attached to the tool holder apparatus.

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