Regression Analysis of Octal Rings as Mechanical Force Transducers

Transcription

1 Regression Analysis of Octal Rings as Mechanical Force Transdcers KHALED A. ABUHASEL* & ESSAM SOLIMAN** *Department of Mechanical Engineering College of Engineering, University of Bisha, Bisha, Kingdom of Sadi Arabia **Department of Mechanical Engineering College of Engineering, Prince Sattam bin Abdlaziz University Al-kharj, Kingdom of Sadi Arabia & ** On leave, from Department of Prodction Engineering, Faclty of Engineering, Alexandria University. Abstract: - This paper presents analytical approach for octal rings as mechanical force transdcers. The work first analyzes the characteristics of octal rings as mechanical force transdcers, sing a finite element model of the ring to determine its state of strain pon the application of load. It also correlates correlate ring design parameters and performance measres sing an L9 orthogonal array of finite element simlations. Design parameters inclde height, thickness, width, and edge crvatre. Performance measres inclde sensitivity and stiffness. Model simlation reslts showed considerable variation in strain along ring face with considerable difference in imm vales between tensile and compressive strains. Also, revealed a region of a relatively large tensile strain within the ring not addressed in the literatre. The relation between strain gage length and average strain revealed an optimal gage length that improves ring performance. Moreover, simlation reslts showed that increasing ring height and decreasing its thickness increases its sensitivity and decreases its stiffness. Finally, reslts of the regression analysis indicated that there is enogh statistical evidence to say that the parameters, height and thickness, inflences the stiffness response and the parameters, height, thickness, and width, inflences the sensitivity response. Key-Words: - Octal rings, strain gage, average strain, sensitivity, stiffness, force transdcer, regression analysis. Introdction Mechanical force measrement has a wide range of applications. They inclde weighing systems, material testing, and performance evalation of eqipment. In addition, mechanical force measrement is essential for performance improvement and optimization of machining processes. Tool breakage detection and chatter control depend on the measrement of machining forces, and on line analysis of force signals. In addition, prediction of chip loading and accracy of machined srface rely on force measrement. A considerable amont of research work focsed on analyzing performance characteristics of octal rings. The prpose was to se them as force sensors for constrcting force dynamometers. M. Korencke and M.L. Hll [] developed empirical formlae to describe strain, stress and deflection in octagonal rings. They sed ANSYS finite element model and a nonlinear regression model to develop the eqations. There was reasonable agreement between experimental data and model eqations. The developed eqations provided close reslts to experimental data compared to eqations available from thin ring theory. However, validity of eqations was limited to range of ring thickness and width. Jeong-D Kim and Dang-Sik Kim [2] developed a combined type tool dynamometer for an ltraprecise lathe. They sed strain gages to measre static force and a piezo-electric film accelerator to measre dynamic force. They pointed ot that signal conditioning and processing are essential for improving accracy of force measrement. Ulvi Seker et al [3] sed a bending beam type dynamometer the main to measre machining force for the shaping process. Even thogh the athors designed the dynamometer, they did not give enogh details of its constrction. They gave the general characteristics of the load cell sed. They focsed of the measred force data rather than on the design of dynamometer. They sed ctting force data to correlate ctting parameters inclding depth of ct and federate to process performance measres E-ISSN: Volme 5, 26

2 inclding srface roghness of work part and tool life. Ihsan Korkotand Sedat Karabay [4, 5] sed octal strain rings to design milling and drilling dynamometers. They sed approximate eqations to estimate strain and stiffness in octal rings. They claimed that the dynamometers cold measre ctting force with ±5 N sensitivity and.5% or less cross sensitively. They presented no information regarding strain gage type or dimensions. In addition, they did not show clearly the procedre for recording and processing signals from dynamometer. SleymanYaldiz, and FarkUnsacar [6,7] designed a three-components force dynamometers for the measrement of ctting force in trning. They, also, sed octal rings as sensing element and sed approximate eqations from thin ring theory to design the rings. The range of the measred force was 35N. Sensitivity was ±5 N and cross sensitivity was.7-.92%. Length of strain gage was 6 mm, abot 3% of the length of the octal ring face, which was 6.6 mm. Y. Chen et. al. [] sed extended octal rings and strain gages to design a dynamometer for a tractor drawbar. They sed finite element analysis to determine points of imm strain at the rings. They fixed strain gages at these points to get imm possible sensitively of the dynamometer. However, they did not consider strain distribtion arond points of imm strain. Sadat Karabay [9,, and ] sed strain gages with different forms of octal strain rings to design force dynamometers for the drilling and milling processes. They sed eqations from thin ring theory for the design of the rings. No attention was given to strain distribtion along the area where strain gages were fixed. They sed calibration to correlate signal from a strain gage bridge and ctting forces. Sleyman Yalidz et. al. [2] sed octal rings and strain gages to design a force dynamometer for the milling process. They determined the dynamic characteristics of the dynamometer sing the impact test. They showed that the natral freqencies of the dynamometers were low. The only extra featre in their design is sing large nmber of strain gages to increase dynamometer sensitively. This work considers octal rings as sensing element for measring mechanical force, together with strain gages. The aim of the work is to investigate strain distribtion along the different faces and regions of the ring, with the prpose of deciding on the best area on the ring to adhere strain gages to end p with imm possible sensitivity to mechanical force. In addition, this work, considers the correlation between design parameters of the ring and its performance measres. Mechanical forces are measred indirectly sing two main techniqes; in the first one, the force acts on a piezoelectric crystal that accmlates charge proportional to the magnitde of the force. A charge amplifier, then, converts charges to volt. In general, piezoelectric sensors are very sensitive to mechanical forces and have wide bandwidth, over 5 KHz. They are available in different configrations and sensitivities. In addition, charge amplifiers are available in wide range of configration and characteristics. However, they are expensive, delicate and reqire a considerable attention when sed within the harsh machining environment. They are ssceptible to noise from nearby electrical drives. Therefore, the present work will not consider piezoelectric sensors. In the second techniqe, the force acts on an elastic mechanical member. The strain and deflection of the member are proportional to force. A common mechanical member for force measrement is octal ring. A strain gage converts strain in the strain ring into eqivalent volt sing a bridge. Octal rings are easy to manfactre to the reqired size. Strain gages are relatively inexpensive and are available in a wide range of configrations and characteristics. In addition, bridges, in particlar Wheatstone bridge, are easy to operate and maintain. Therefore, octal rings with strain gages are the candidate for sensing mechanical forces in the present work. 2 Geometric Models In order to stdy the state of strain of octal rings, a 3D geometrical model of a ring was constrcted sing the Solid Edge Software package. Fig. shows the model. The basic design parameters are height, H, width, W, thickness, T, and edge radis R. Other parameters sch as face length, L s and inner hole diameter, D, are derived from the basic design parameters. Then, the finite element method was applied to the model sing the same software package. Tetrahedral finite elements were sed for the finite element model as shown in Fig.. The material of the ring was selected to be Alminm 6 with GPa modls of elasticity,.33 Poisson ratio, MPa yield stress and 6.94 MPa ltimate tensile strength. Fig, also, shows faces and regions of interest where imm strains E-ISSN: Volme 5, 26

3 or imm deformations are expected to take place. Fig. Geometric and finite element models and basic design parameters of the octal ring. A concentrated force, F z, is applied normal to the face C ot, in the negative z-direction. The concentrated force represents the worst loading condition of the ring considering deflection and ring stiffness. The magnitde of the force is selected to be F z = N. Sch selection ensres no plastic deformation takes place within the ring for the range of design parameters sed for the present work and given in the next section. The model considers a ring rigidly fixed at its bottom srface. This simlates a ring welded to its base. The method of fixation of the ring affects mainly state of strain and stress arond the fixation region. However, interest is in strains at faces and regions away from ring bottom. Therefore, this work does not give the method of fixation a considerable attention. In addition, the applied force tends to fix the bottom face of the ring to its base. Upon application of the load and simlating the model, stresses and strains of all srface finite elements of the ring were available. Strains at the elements within the aforementioned faces and regions of interest were recorded manally sing a strain pick featre of the software. In addition, the positions of the elements, with respect of the XYZ coordinate system of Fig., were recorded and stored in data strctres within the MATLAB software. All strains, deformations and stresses, were recorded in the ZX-plane. 3 Design of simlations Performance measres of an octal ring are mainly sensitivity and stiffness. Sensitivity, S z, is defined as: S z = ε F z () Where F z is the force acting on the ring and ε is the imm measrable strain in the ring. Similarly, stiffness, K z, of the ring is defined as: K z = F z α (2) Where, α is the imm measrable deflection at the C ot srface of the ring, basically, at the point of application of the load. The sffix z in eqations and 2 indicates that sensitivity and stiffness are determined in the z- direction. Sensitivity and stiffness of the ring in the x-direction can be dealt with in the same way as in z-direction and, therefore, are not considered in the present work. Finite element simlations were condcted to correlate the design parameters and the performance measres. Simlation design parameters followed an L 9 orthogonal array. Table shows the levels of design parameters for the simlations. The table also gives the vales of the derived parameters. Becase the size of the ring varies from one simlation to another, the nmber of finite elements, N f, and nmber of nodes, N n, for the finite element model vary as well. Finite element size, E s, is selected to give reasonably smooth strain distribtion. Table gives vales of finite element model parameters. Table Levels of design parameters 4 Reslts and Discssions Fig 2.a shows strain distribtion along the face Tm ot for SIM 2. The dashed line represents the ring profile while the solid line represents the strain distribtion. The strain, ε t, is in tension state and therefore, has positive vales in the figre. The figre also shows the z-positions of the element of the face at which ε t is recorded. It can be observed from the figre that the strain varies considerably along the face and the strain, ε t = 67.7 [μm m], is almost seven times larger than the minimm strain, [μm m]. Fig. 2.c is an enlarged view of Fig 2.a, arond the middle of Tm ot where the z-position is zero. It can be observed from the figre that ε t is shifted from the center of the face, Tm ot by.4 [mm]. The shift vale corresponds to 6% of the length of Tm ot, L s. In the literatre, [5, 6] ε t is sally considered at the middle of Tm ot. Fig 2.b shows strain distribtion over the region Cm in for the same simlation, SIM 2. Again, the dashed line E-ISSN: Volme 5, 26

4 represents the ring profile while the solid line represents strain distribtion. The strain, ε c, is in compression state, and is represented by negative vales. The figre also gives the z- position of the elements of the region Cm in at which ε c is recorded. From figre, it can be observed that ε c is.9 [µm/m] which is 63% larger than ε t. Fig. 2.d is also an enlarged view of Fig. 2.b arond the zero z-position. It shows that ε c is shifted by.77 [mm] from the zero z-position. The distribtions of ε t and ε c and the conseqent observations are the same for all simlations. Strain ε c is always larger, in absolte vale, than ε t. Also, both ε t and ε c are shifted from the zero z-position by different vales. Table 2 smmarizes the reslts of all simlations for ε t and ε c vales and the corresponding shift vales. The implication of the aforementioned observations is nonlinear relation between the load and otpt volt of any force sensor sing octal rings as transdcers. It is common to give force sensor imm nonlinearity as a sensor specification. Understanding the sorce of sch nonlinearity helps in redcing it and ths improving sensor performance. tensile state with positive vales. The imm vale of ε, ε =. [µm/m], is located at the zero x-position. Table 2 lists the vales of ε for all simlations. The shift vales of ε are always zero. In Table 2, it can be observed that the vales of ε considerably larger than those of ε and relatively larger than the vales of ε. t c As a reslt, it is better to employ ε and ε c for the arms of any bridge sed with the octal ring. This is becase their large vales, compared to the vales of ε t, will reslt in a higher sensitivity to the applied load. However, nonlinearity is navoidable at this stage. Fig. 3, also, shows the distribtion of the deflections, α, along the face C ot. The deflection is given for finite elements on C ot at different x-positions. From the figre, it can be seen that the imm deflection, α, is 9 [µm] and is located at the zero x- position. The corresponding stiffness, K z, is.363*6 N/m. The distribtions of α and ε are similar for all simlation and α is always at zero x-position. Table 2 lists all vales of α for all simlation. It also lists all calclated vales of K z and S z for all simlations sing eqations and 2. The S z vales listed in Table are calclated based on ε vales for F z = N. Fig. 2 Strain distribtion along Tm ot and Cm in for SIM 2. Table 2 Maximm strain and deflection vales and performance measres Fig. 3 Strain and deflection distribtions along T in and C ot respectively. Fig. 3 shows strain, ε, along T in and x- positions of the finite elements on T in at which ε vales are recorded, for SIM 2. The strain, ε, is in E-ISSN: Volme 5, 26

5 Fig. 4 Effect of different levels of design parameters on imm strains To analyze the effect of the different levels of the design parameters on ε t,c,, the graphical variation of means method has employed. The method implies calclating the average vales for ε t,c, for each level for each design parameter. Then, the average vales have compared by plotting them as shown in Fig.4. The figre shows that increasing H increases ε t,c, vales while increasing T and W decreases ε t,c, vales. In addition, the figre shows that R does not have a direct effect on ε t,c,. Moreover, the figre shows that ε c and ε get close to each other as T increases and as H decreases. These reslts are similar to the theoretical reslts available in the literatre. In fact, the theoretical vales of ε and ε t c were calclated for all simlation sing eqations 3 and 4 [6, 7]. Eqation 3 is for circlar rings, and strain has designated by the sperscript c while eqation 4 is for octal rings and strain has designated by the sperscript o. c ε c t = ε = ±.9 F z D (3) 2 E W T 2 ε t o = ε c o = ±.7 F z D 2 E W T 2 (4) Where E is modls of elastically [N/mm2] Fig. 5 compares the average vales of the c o theoretical strains, ε t,c and ε t,c, for each level of each design parameter as described earlier for Fig. 4. o o Fig 5 also shows the vales of ε t and ε t for the sake of comparison between simlated and theoretical strains. It is clear from the figre that the effects of the different levels of the different design c o parameters on ε t and ε t are the same as their effects on ε t in terms of trends. However, simlated ε t vales are slightly lower than o theoretical ε t vales and considerably lower c than ε t vales. Fig. 5, also, shows that the averaged vales of ε c are located between the c o averaged vales of ε and those of ε c vales. Fig.6 shows how the different levels of the design parameters affects sensitivity. From the figre, it is possible to notice that increasing H increases S z while increasing T and W decreases it. In addition, R does not have a direct effect on S z. Fig. 7 shows the effects of the different levels of the design parameters on simlated and theoretically calclated ring stiffness. Theoretical ring stiffness is given for circlar and octal rings sing eqations 5 and 6 respectively []. k c = 4.47 E W T3 R 3 [N/mm2] (5) k o = E W T3 R 3 [N/mm2] (6) Fig. 5 Simlated and theoretical effects of design parameters on imm strains at Tm ot From the figre 7, it can be seen that increasing height, H, redces stiffness while increasing ring thickness, T, increases stiffness considerably. The width of the ring, W, does not have clear effect of stiffness. These reslts are the same for simlated and theoretical reslts. Fig. 4.d shows that increasing the edge radis redces stiffness. Stiffness vale is the highest for sharp edges, R = [mm]. This is becase edges works as obstacles to srface strain propagation from one ring face to the other. As a reslt, the total deflection at srface C ot is redced. Fig. 6 Effect of design parameters on strain sensitivity S z. E-ISSN: Volme 5, 26

6 Fig. 9 shows the effects of F z on ε t,c, and ε for SIM 2. From the figre, it is evident that ε and ε are linearly proportional to load. The average strain ε is given for a strain gage length L g = 9 [mm]. It is lower than ε for all load vales. The figre also shows that increasing the load increases the difference between ε and ε. This implies that the load affects stress distribtion as well as the imm strain vale. Fig. 7 Simlated and theoretical effects of design parameters on imm strains at Cm in From Figs. 2 and 3, it is clear that ε t, ε c and ε take place at niqe finite elements. As a reslt, they are practically difficlt to measre sing strain gages. This is becase a strain gage has a finite length and therefore it measres the average strain within the region it adheres to. The average strain on Tm ot, ε t, is calclated from the eqation: L ε t = g ε(z) dz = N s ε(j) E L g N s s j= (7) Where, L g is the length of strain gage and z represents the z-position of the finite element within the gage length. The z-position is sed for strain gages at Tm ot and C in while the x-position is sed for strain gage at T in. The nmber of finite elements on Tm ot and within the length of the strain gage, L g, is N s. Eqation gives N s as: N s = L g () E s The strain gage adheres to the strain ring so that the middle of the strain gage is at the zero z- position for the Tm ot face and the C in region and at zero x-position for the T in face. It is evident from eqation 7 that the length of strain gage affects ε t, εc and ε. Fig. shows the effect of L g on ε t,c, for simlations, 2, 4 and 7. From figre, it is clear that increasing L g decreases ε t,c,. It is also clear that there is a length of strain gage at which ε c and ε are eqal, 7 mm for simlation 4 as an example. Sch length is the optimm design length of the strain gage for the octal ring of simlation 4. This is becase sch length will reslt in eqal tensile and compressive strains in the arms of the bridge connected to the ring. As a reslt, the nonlinearity of the force sensor is redced. Fig. Effect of gage length on average strain. Fig. 9 Effect of load FF zz on imm strain. 5 Statistical Point of View Dring statistical analysis of the interaction between the parameters (height, thickness, width, and edge crvatre) to the responses (Stiffness and Sensitivity), the R-Sq of stiffness and sensitivity respectively 4.% and 6.% which is close to, indicating a high positive correlation between the parameters (height, thickness, width, and edge E-ISSN: Volme 5, 26

7 crvatre) to the responses (Stiffness and Sensitivity). 5. Regression analysis of stiffness In this experimental stdy, an empirical model was developed throgh the regression analysis to stdy the parameters (height, thickness, width, and edge crvatre) to the response (Stiffness). The estimated regression coefficients in the stiffness regression eqation (9) shows that the following parameters; i.e., height, thickness have noteworthy inflence on the stiffness. The p vale for these parameters shows that the vales are approximately eqal or less than alpha level of.5. It can therefore be conclded that there is enogh statistical evidence to say that the parameters (height, thickness) inflences the response (Stiffness). On the other hand, the estimated regression coefficients of width and edge crvatre parameters have less inflence on the stiffness. The p vale for these parameters shows that the vales are higher than alpha level of.5. It can therefore be conclded that there is enogh statistical evidence to say that the parameters (width and edge crvatre) have less inflence the response (Stiffness).The regression eqation is K = H [mm] + T [mm] +.64 W [mm]-5.4r[mm] (9) Percent Freqency Normal Probability Plot of the s Histogram of the s Fitted Vale Fig.. The Assmptions of Analysis of Variance (Regression). It is also clear from Fig. that there is a significant difference between the parameters (height, thickness, width, and edge crvatre) to the response (Stiffness). The reslt clearly indicates height and thickness parameters have inflence on the stiffness. Moreover, the width and edge crvatre parameters have less inflence on the response (Stiffness). H [mm] Plots for K s Verss the Order of the Data T [mm] - -2 Interaction Plot (data means) for K s Verss the Fitted Vales Observation Order H [mm] T [mm] 4 6 W [mm] 5 W [mm] 6 S = R-Sq = 4.% R-Sq(adj) = 6.2% Analysis of Variance Sorce DF SS MS F P Regression Error Total Minitab software (Version 6, 2) was sed to perform the Regression Analysis of stiffness. The assmptions on which the analysis (Regression) was based pon were normality, independence, additivity, and eqality of variances. The assmptions on the Regression Analysis of Stiffness were based on were normality of residals and homogeneity of variance for residals. These reslts are indicated in Fig.. R [mm] Fig.. Interaction plot for the parameters (height, thickness, width, and edge crvatre) to the response (Stiffness). 5.2 Regression analysis of sensitivity In this experimental stdy, an empirical model was developed throgh the regression analysis to stdy the parameters (height, thickness, width, and edge crvatre) to the response (Sensitivity). The estimated regression coefficients in the sensitivity regression eqation () shows that the following parameters; i.e., height, thickness, width have noteworthy inflence on the sensitivity. The p vale for these parameters shows that the vales are approximately eqal or less than alpha level of.5. E-ISSN: Volme 5, 26

8 It can therefore be conclded that there is enogh statistical evidence to say that the parameters (height, thickness, width) inflences the response (Sensitivity). On the other hand, the estimated regression coefficient of edge crvatre parameter has less inflence on the sensitivity. The p vale for this parameter shows that the vale is higher than alpha level of.5. It can therefore be conclded that there is enogh statistical evidence to say that the parameter (edge crvatre) has less inflence the response (Sensitivity). The regression eqation is: S = H [mm] T [mm] -.32 W [mm] -.55 R [mm] () significant difference between the parameters (height, thickness, width, and edge crvatre) to the response (Sensitivity). The reslt clearly indicates the height, the thickness, and the width parameters have inflence on the sensitivity. Moreover, the edge crvatre parameter has less inflence on the response (Sensitivity). H [mm] Interaction Plot (data means) for S T [mm] H [mm] T [mm] 4 6 W [mm]. 3.. W [mm] 6 S = R-Sq = 6.% R-Sq(adj) = 72.% Analysis of Variance Sorce DF SS MS F P Regression Error Total 9.74 Minitab software (Version 6, 2) was sed to perform the Regression Analysis of sensitivity. The assmptions on which the analysis (Regression) was based pon were normality, independence, additivity, and eqality of variances. The assmptions on the Regression Analysis of Sensitivity were based on were normality of residals and homogeneity of variance for residals. These reslts are indicated in Fig. 2. Percent Freqency Normal Probability Plot of the s Histogram of the s Plots for S.5. 2 Fitted Vale Fig. 2. The Assmptions of Analysis of Variance (Regression) s Verss the Fitted Vales s Verss the Order of the Data Observation Order 3 9 R [mm] Fig. 3. Interaction plot for the parameters (height, thickness, width, and edge crvatre) to the response (Sensitivity). 6 Conclsions Based on research findings, we can conclde that the regressions models for calclation of the parameters (height, thickness, width, and edge crvatre) to the responses (Stiffness and Sensitivity) are developed. The R-Sq of stiffness and sensitivity respectively 4.% and 6.% which is close to, indicating a high positive correlation between the parameters (height, thickness, width, and edge crvatre) to the responses (Stiffness and Sensitivity). Among different interactions, interactions between thickness parameter and responses (Stiffness and Sensitivity) are most significant. Simlations showed that considerable variation in strain along ring face. The relation between strain gage length and strain showed that an optimal gage length improves ring performance. Simlation reslts showed that imm compressive strain is considerably larger than imm tensile strain. They also revealed a region of large tensile strain within the ring not exploited in the literatre. It is also clear from Fig. 3 that there is a E-ISSN: Volme 5, 26

9 Acknowledgments Financial and in-kind received spport from the Deanship of Scientific Research, Vice Rectorate for Post Gradate and Scientific Research, Prince Sattam bin Abdaziz University (PSAU) is grateflly acknowledged. Financial spport of this work throgh the Deanship of scientific research, Prince Sattam Abdl Aziz University, nder project # 2//24 is grateflly acknowledged. References: [] M. Korencke, M.L. Hll, 99. A method for designing mlti-load component dynamometers incorporating octagonal strain rings. Jornal of experimental mechanics. Jne, [2] Jeong D Kim, Dang-SikKim, 997. Development of a combined-type tool dynamometer with a piezo-film accelerometer for an ltra-precision lathe. Jornal of Materials Processing Technology. 7, [3] Ulvi Seker, Abdllah Krt, Ibrahim Ciftci, 22. Design and constrction of a dynamometer for measrement of ctting forces dring machining with linear motion. Jornal of Materials and Design. 23, [4] Ihsan Korkot, 23. A dynamometer design and its constrction for milling operation. Jornal of Materials and Design. 24, [5] Sedat Karabay, 27. Analysis of drill dynamometer with octagonal ring type transdcers for monitoring of ctting forces in drilling and allied process. Jornal of Materials and Design. 2, [6] SleymanYaldiz, FarkUnsacar, 26. Design, development and testing of a trning dynamometer for ctting force measrement. Jornal of Materials and Design. 27, [7] SleymanYaldiz, FarkUnsacar, 26. A dynamometer design for measrement the ctting forces on trning. Jornal of Measrement. 39, 9. [] Y. Chen, N.B. McLaghlin, S. Tessier, 27. Doble extended octagonal ring (DEOR) drawbar dynamometer. Jornal of Soil & Tillage Research. 93, [9] Sadat Karabay, 27. Analysis of drill dynamometer with octagonal ring type transdcers for monitoring of ctting forces in drilling and allied process. Jornal of Materials and Design. 2, [] Sadat Karabay Design, 27. Criteria for electro-mechanical transdcers and arrangement for measrement of strains de to metal ctting forces acting on dynamometers. Jornal of Materials and Design. 2, [] Sadat Karabay, 27. Performance testing of a constrcted drilling dynamometer by deriving empirical eqations for drill torqe and thrst on SAE 2 steel. Jornal of Materials and Design. 2, [2] SleymanYaldiz, FarkUnsacar, Haci Saglam, Hakan Isik, 27. Design, development and testing of a for-component milling dynamometer for the measrement of ctting force and torqe. Jornal of Mechanical System and Signal Processing. 2, E-ISSN: Volme 5, 26