44 CHAPTER 3 IMPROVEMENT OF DYNAMIC CHARACTERISTICS OF CUTTING TOOL SYSTEM USING VISCOELASTIC DAMPER This chapter introduces a novel design for turning tool holder assembly with enhanced damping capability. The principle followed in the design phase is to enhance the damping capability through implementation of viscoelastic material interfaces. The evaluation criteria are the dynamic characteristics, frequency and damping ratio of the machining system. The main objective of the present chapter is to predict the damping ratio of the cutting tool system by using the following methods: Build a FEA model of the turning tool assembly and perform harmonic analysis by ANSYS software. Experimental methods using hammer test. 3.1 CHATTER When a machine becomes unstable and chatter occurs, its structure vibrates and there is dynamic variation of cutting force. If the tool contacts a hard spot or some irregularity on the work surface, it will bounce relative to the workpiece. In other words, the machine tool structure will vibrate. Due to the resulting variations in the depth of cut, the cutting force will oscillate about its steady or mean value. This cutting force oscillation will vibrate the machine tool structure and its dynamic characteristics in terms of the cutting
45 conditions. It is evident that self-excited machine tool vibration depends upon two things, The dynamic characteristics of the machine tool structure and The dynamic characteristics of the cutting forces. 3.2 SELECTION OF CHATTER CONTROL STRATEGY There are two main categories of vibration control systems active and passive. Active control systems have proved to be efficient in laboratory environment but the end users due to the complexity of the hardware have not welcomed its industrial application. The passive control technique does not need complicated hardware and the end-user does not need to introduce new handling routines. Implementations of passive damping in tooling equipment are already available in the market. 3.2.1 Passive Control The principle of passive vibration control is to convert the mechanical energy into some other forms, for instance heat. A common way to achieve passive damping is by using viscoelastic (VE) composite materials to dissipate the energy that causes vibration. The use of VE composite materials for damping purposes is quite common, this technique has been used in other fields of application, such as automotive and aeronautics. VE composite materials are used for damping enhancement generically in three different ways Free-layer dampers (FLD) Constrained-layer dampers (CLD) Tuned viscoelastic dampers (TVD).
46 The Last mentioned damper has been successfully adapted for designing tooling systems (Rashid 2005). The basic principle of TVD technique is to add a mass residing on a spring and a viscous damper at the point of maximum displacement. This additional single degree of freedom (SDOF) system must have the natural frequency close to the boring bar in order to transfer the vibrational energy to the TVD. If the damper is properly designed, it will dissipate the mechanical energy (Rüdinger 2006). Rivin et al (1992) propose a solution where the weight is integrated in the tool, hanging on rubber rings. The absorber is tuned by changing the stiffness of the additional system. Another example of application of TVD principle is proposed by Lee et al (2001), the TVD is tuned by changing the inertia mass. Rashid et al (2008) have used TVD technique even for milling operations. TVD technique is already successfully used in several successful commercial products. Rashid (2005) presents a solution as well with integrated damping interface applied to work holding systems for milling operations. When implementing such a solution it is of vital importance for the design to properly locate the pre-stressed VE composite layers in the structure to optimally exploit the property of VE material to give largest deformation in shear (Butler 2007). The mechanical damper elements are likely to be replaced by viscoelastic materials because of their simplicity and economy. Since the dynamic properties of viscoelastic material, such as elastic modulus and loss factor are in general dependent on the applied preload (or pre strain) and frequency, care is required in the design stage of dynamic damper to obtain the optimum turning and damping simultaneously. However, the difficulty can be overcome by using precise measurement setups and data processing and analyzing systems.
47 An optimal dynamic damper is attached to the tool structure. Its performance is verified by the decreased spectrum of the vibration signal at the chatter frequency. Which shows that, the improved cut surface profile, and the decreased magnitude of the transfer functions around the chatter frequency. Viscoelastic systems can generally be grouped into free layer and constrained layer technologies. 3.2.2 Passive Damping Technology using Viscoelastics (free layer) The free layer technique simply adds a viscoelastic material to the existing structure. The combined structure has a geometric damping characteristic in bending proportional to the product of the loss factor and modulus of the material. 3.2.3 Passive Damping Technology using Constrained Layer Damping (CLD) In constrained layer technique, the viscoelastic material is sandwiched between the structure and a high stiffness constraining layer. The effect of constraining layer is to change the principal deformation in the viscoelastic material from extension to shear. This permits tuning of the damping at a frequency specified by the geometry and material properties. A disadvantage of constraining layer techniques is that the geometry effectively filters out the low frequency damping since the bending energy is exclusively in the structural material and constraining layer. Thus at low frequencies the energy is not put into the damping material where it can be absorbed. These frequency effects, in addition to the frequency dependence of the viscoelastic materials, complicate designing a structural damper.
48 Rivin (1983) suggested that the regenerative chatter vibration could effectively be suppressed by enlarging the damping capacity of the system. The properties and prospective applications of ultra thin rubber layered laminates for travel bearings are experimentally determined and presented with some possible application and it is concluded that the ultra thin rubber layered laminates can be used in the suppression of chatter vibration especially for existing machine tools. Rivin (1989) proposed reduced stiffness tool concept and its importance of the improvement of machining conditions. The principle followed in this research is to enhance the damping ability of critical structural components of the machine tool. In this chapter, the focus is mainly on the insert seating in the tool holder. The shim protects both the insert and tool holder from damage due to high cutting forces. The shim material is replaced with different damping materials and dynamic characteristic are predicted by using FEM and hammer test. Passive damping treatments for tool holder assembly structures are analyzed using finite element techniques. Method for finite element analysis of damped structures can generally be placed in response prediction methods. The modal frequency response analysis method is efficient, but uses modes based on constant stiffness, even though the damping may be a function of frequency. This method is reasonably accurate as long as the calculated response frequency range is not over a decade. The direct frequency response method used frequency dependent complex material properties, which makes this method accurate but expensive in computation.
49 3.3 HARMONIC ANALYSIS OF DAMPED TOOL USING FEM A 3D model of cutting tool is developed using Pro-E, which consists of VE coated carbide insert, shim seat, and the tool holder. Part model of the tool holder and insert are as shown in Figure 3.1 and 3.2. Small details of the clamping parts are neglected in the model due to certain limitations of the analysis package. Details of tool holder and insert used in analysis are given in Appendix 2. The basic dimensions of the model are: Turning insert : 12.7 x 12.7 x 4.7 mm 3 Shim seat : 11.7 x 11.7 x 3 mm 3 Tool holder : 125 x 20 x 20 mm 3 Figure 3.1 Model of tool holder Figure 3.2 Model of cutting tool insert
50 The part model of the tool holder, insert and shim are assembled together using assembly module of Pro-E. The assembly model of the tool holder shown in Figure 3.3 is exported to ANSYS to perform the harmonic analysis. Figure 3.3 Assembly model of tool holder The response of the tool holder assembly is predicted by using the finite element methods. Harmonic analysis are performed for the following three models, 1. Tool holder assembly with carbide shim (Figure 3.4) 2. Tool holder with constrained layer damping (CLD) shim (Figure 3.5 and Figure 3.6)and 3. Tool holder with carbide shim with viscoelastic material, Poly Tetra Flora Ethylene (Figure 3.7)
51 Figure 3.4 Tool holder with carbide shim Figure 3.5 Tool holder with CLD shim
52 Figure 3.6 Constrained layer damper Most CLD applications use a three-layer sandwich system that is formed by laminating the base layer to a damping layer and then adding a third constraining layer (Figure 3.6). Typically, the constraining layer is of the same material as the base layer, but exceptions are common. (Brain Joyal and Jennifer Renninger) Insert Shim PTFE Coating Tool Holder Figure 3.7 Tool holder PTFE coated carbide shim
53 3.3.1 Selection of Element The 8-node brick element solid 45 is used to represent the tool holder, carbide insert and shim. The solid 185 is used to represent the PTFE layer. The interior boundaries of the insert are in contact with the shim seat and the holder and the surfaces are assumed to be smooth and held together. The bottom surface of the tool holder, which is held in the tool post and top surface, which is clamped by screws are identified and the all degrees of freedoms are arrested. The material property for holder, insert and shim are defined using linear isotropic models. An isotropic linear viscoelastic model is used to represent the damping layer. The viscoelastic properties are defined through the use of Tables A1.3 and A1.4. The materials of tool holder and their properties used in the model are presented in the Table 3.1. Table 3.1 Cutting tool materials and properties Sl. No Part name Material Young s Modulas (E) N/mm 2 Poisson ratio () Density ) kg/m 3 1 Holder Tool steel 207e3 0.3 7.844e-6 2 Insert Carbide insert 534e3 0.22 11.9e-6 3 Shim Carbide 534e3 0.22 11.9e-6 Natural rubber 5 0.4999 1.0e-9 Poly Tetra Flora Ethylene (Teflon) 0.5e3 0.028 2.2e-6 After defining the material property the part of the model is meshed. The holder is meshed with coarse mesh and the shim, insert and viscoelastic layer (0.002 mm) are fine meshed as shown in Figure 3.8. The harmonic analysis module is then used to find the responses of the tool holder, when it is subjected to a force or displacement controlled harmonic excitations.
54 Figure 3.8 Meshed model of tool holder 3.3.2 Frequency Response Function and Damping Ratio A harmonic force is applied to top surface of the holder and nearby the insert as shown in Figure 3.8. The frequency, response is calculated over the frequency range covering the first mode of the tool. The frequency response curve similar to Figure 3.9 has been used to calculate the model damping of the tool in its first mode. Damping ratio is predicted by using the half power bandwidth method. The bandwidth is the frequency difference between upper and lower frequencies for which the power has dropped to the half of its maximum value (-3db) (Cheeke 2002).
55 Figure 3.9 Frequency response curve From the frequency response curve the following dynamic parameters are calculated, a) Natural Frequency The natural frequency of r th mode is identified from the peak value of FRF. Natural frequency = f r b) Damping Ratio and Loss Factor As n is known directly from the peak location of the transfer function, the damping constant and loss factor can be computed by determining the corresponding peak magnitude. Half power point at f 1 and f 2 are located from each side of the peak amplitude that is 0.707 times the amplitude. Loss factor and damping ratio can be calculated as below. Loss factor = 2 = f f1 2 f r (3.1)
56 Damping Ratio = f f 2 1 2 f r (3.2) c) Quality factor For small values of material damping (Stokoe et al 1999), the quality factor can be defined as the resonance frequency divided by the bandwidth: Quality factor =1/2 where Damping ratio ƒ r - peak response ƒ - half power band width ƒ 2 ƒ 1 3.3.3 Discussion of Results Frequency response curves for the three different shim model are presented here and from the curve the damping ratio for the tool holder assembly are calculated using the peak response and half band width. Frequency response curve for the carbide shim, PTFE coated carbide shim and CLD shim tool holder are presented in the Figure 3.9, Figures 3.10 and 3.11. As the fundamental natural frequency for tool tip point is 190 Hz (Claudiu Bisu et al 2009), the response curve is obtained in the frequency range of 100 Hz to 300 Hz.
57 Figure 3.10 Frequency response of tool with carbide shim using FEM Figure 3.11 Frequency response of tool with PTFE coated carbide shim using FEM
58 Figure 3.12 Frequency response of tool with CLD shim using FEM From the Figure 3.10, it is shown as the amplitude peak is 0.0106528 mm and the corresponding frequency is 210 Hz. Using the half bandwidth method, the damping ratio for carbide shim tool holder is calculated as follows, Peak response ƒ r = 210 Hz (at y is 0.106528e-1mm) Half power band width (ƒ 2 - ƒ 1) = 213-206 Hz Damping Ratio = 213-206/2(210) = 0.016667 The damping ratios for the tool holder assembly system with various shims are predicted using FEA which are tabulated in the Table 3.2.
59 Table 3.2 Damping ratios of cutting tool system by finite element method Types of damper Natural Freq(f r ) (Hz) Half Power Point Frequency (Hz) Loss factor 10-3 Damping ratio *10-3 Q factor f 1 f 2 CLD shim 210 207 213 0.0286 0.0143 34.96 Carbide shim 210 206 213 0.0334 0.0167 29.94 PTFE coated shim 180 165 196 0.1722 0.0861 5.81 Figure 3.13 Natural frequency and quality factor of cutting tool The term, quality factor that determines the sharpness of resonance frequencies originates from the field of electrical tuning where the sharpness of the resonant peak is desirable. The value increases along with the increasing value of natural frequencies in which the damping ratio becomes smaller as shown in Figures 3.13, and 3.14.
60 Figure 3.14 Loss factor and damping ratio of cutting tool It has been shown that the FE simulation can accurately predict the damping ratio of the tool holder assembly with different shim materials. For complex structures where the use of simple equations is not appropriate, FEA simulation could give accurate results. PTFE shim tool holder is having high loss factor and higher damping ratio too. 3.4 EXPERIMENTAL MODAL ANALYSIS The experimental approach to modelling the dynamic behaviours of structures through impact hammer test (modal testing) consists of the following four steps: Setting up the modal test Taking the measurements Analysing the measured test data Documented results and compare with modelling data
61 3.4.1 Impact Hammer Test A hammer is a device that produces an excitation force pulse to the test structure. It consists of hammer tip, force transducer, balancing mass and handle as shown in Figure 3.15. When the tips strike on the cutting tool, the pulse distributes the energy to a wide range of spectrum. An accelerometer is used to measure the acceleration of cutting tool. The signal transformed by signal conditioner before an analyser processing it. There are two aspects in the acceleration measurements, i.e frequency and amplitude. The type of accelerometer used in this experiment is piezoelectric accelerometer. Hammer tip Force Transducer Acceleromete Figure 3.15 Impact hammer and accelerometer
62 3.4.2 Experimental Procedure Cutting tool is clamped at the four-way tool post to simulate realistic boundary condition. An accelerometer is attached at the bottom surface of the tool holder as shown in Figure 3.16. Repeatedly, the hammer is struck on the same position for 5 times to obtain average frequency response function. Figure 3.16 Experimental setups for hammer test 3.4.3 Results and Analysis Figure 3.17 shows the computed set of test data of FRF from hammer excitation, which is solved using FFT analyser. The response signal
63 obtained from accelerometer with respect to the function of time is shown in Figure 3.17. Figure 3.17 Layout of LMS test express FFT analyzer 3.4.3.1 Frequency Response Function (FRF) Plots The graph in Figures 3.18 to 3.20 shows the plot of spectrum power intensity of noise level in decibel unit over frequency for the cutting tool with various shims. The spectrum is continuous and the band frequency range of measurement is selected to be 500 Hz with the frequency ranging from 0 to 500 Hz.
64 Figure 3.18 Frequency response function of carbide shim using hammer test Figure 3.19 Frequency response function of PTFE coated carbide shim using hammer test
65 Figure 3.20 Frequency response function of CLD shim using hammer test The FRF plots clearly indicate that at certain frequencies of cutting tool, the excitation input force caused cutting tool structure having narrow peaks and high value of spectrum power intensity of noise level as shown in FRF. These peaks of the FRF plots are the natural frequencies of the cutting tool. It can be seen that the noise spectrum obtained from the experimental result shows peak intensity of cutting tool range between 10 to 20 db with natural frequency of 50 Hz. The modes of vibration and its natural frequencies are well separated which allows the mode to be extracted from the peak resonance frequencies. The cutting tool s modal damping therefore can be obtained by using peak picking method.
66 3.4.3.2 Assessment of FRF Data: Peak Picking Method Peak picking method is a single degree of freedom method in view of the fact that each experimentally determined resonance transfers function. The approach is to compare the resonance region with an analytical transfer function of a damped single degree of freedom system. Steps for peak picking method are summarized as below: a) Estimating Natural Frequency The natural frequency of r th mode is identified from the peak value of FRF as shown in Figure 3.21. Figure 3.21 Peak picking method and half band width b) Estimation of Damping Ratio As natural frequency, ƒ r is known directly from the peak location of the transfer function, the damping constant and loss factor can be computed using half bandwidth method.
67 FRF plots shows how modes can cause the cutting tool structure to vibrate. At small input force form, the hammer can cause a very large response of natural frequencies. This is clearly indicated from the narrow peak in FRF plots. Therefore, when the tool is excited at one of the peak frequencies, the response of cutting tool per unit force will be large. The PTFE coated carbide shim provides wider half band width in FRF plots when compared with carbide shim and CLD shim as shown in Figure 3.15. The damping ratios for various shims are calculated from the response curve which are listed in the Table 3.3. Table 3.3 Damping ratios of cutting tool system by hammer test Sl.No. Types of shim in the tool hoder Damping ratio of tool holder () 1 Carbide shim 0.0097 2 CLD shim 0.0143 3 PTFE coated shim 0.0546 As finite element model is approximated to the real structure, the damping ratio obtained from the hammer test is relatively low compared with the FEA results. From the Table 3.3 it is observed that the PTFE coated carbide shim tool holder has higher damping ratio compared with carbide shim and CLD shim tool holder.
68 and hammer test The following results are revealed from the finite element analysis As PTFE coated carbide shim has wider band width in frequency response function in both FEM and hammer test method, the damping ratio is higher when compared with conventional carbide shim and CLD shim tool holder. The CLD shim gives lower damping ratio in FEM analysis. The techniques of constraining layer is that the geometry effectively filters out the low frequency damping, since the bending energy is exclusively in the structural material and constraining layer. Thus at low frequencies, the energy is not dissipated by the damping material where it can be absorbed. These frequency effects, in addition to the frequency dependence of the viscoelastic materials, complicate designing a structural damper. More confidence can be placed from the results of finite element model if the measurements taken on the true structure of cutting tool are performed using impact hammer test to validate the computational modelling. Finite element method can predict the approximated damping ratio with minimum cost where as in hammer test equipment and FFT analyzer are expensive inspite of its accuracy.