A Simplified Method to Identify the Equivalent Joint Parameters of Holder-Tool Interface Xiaowei Tang1, Rong Yan1, Fangyu Peng2(), and Pengfei Wu1 1
National NC System Engineering Research Center, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, No.1037 LuoYu Rd., Wuhan, China
[email protected],
[email protected],
[email protected] 2 State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, No.1037 LuoYu Rd., Wuhan, China
[email protected]
Abstract. The clamping length of holder-tool often changes with the machining conditions and is the main factor affecting the stiffness and damping values of holder-tool interface. To avoid the need for repeating the measurements, the previous studies identify the joint stiffness-damping parameters based on genetic algorithm and calculate the joint parameters per unit area of holder-tool interface for response prediction. This paper proposes a simplified method to identify the joint parameters by simplifying the continuous contact interface to contact points in side of the clamping part. The equivalent joint stiffness-damping parameters are calculated by an inverse calculation method along the whole frequency band, which is more efficient than the genetic algorithm. The responses of holder-tool assembly with different clamping length are predicted based on the assumption of linear relationship between the stiffness-damping values and clamping length. At last, the experiment cases were carried out to verify the effective of the simplified method. Keywords: Holder-tool interface · Stiffness-damping · Identification · Simplified method
1
Introduction
Chatter is a severe obstacle to improve machining efficiency in high-speed machining. Selection of appropriate cutting parameters according to the stability lobe is the common method to avoid chatter and improve machining efficiency. The stability lobe calculation requires accurate measurements of frequency response function at the tool tip. Impact experiment at the tool tip is the direct and accurate method to obtain the frequency response function but with the expense of operation time on repeating the measurements. Many scholars had carried out much investigation on predicting the frequency response function by analysis method. T. L. Schmitz et al. [1,2] apply two substructures with spindle-holder and tool and proposed the two-component receptance © Springer International Publishing Switzerland 2015 H. Liu et al. (Eds.): ICIRA 2015, Part II, LNAI 9245, pp. 587–596, 2015. DOI: 10.1007/978-3-319-22876-1_51
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coupling substructure analysis (RCSA). Based on the two-component receptance coupling substructure analysis, T. L. Schmitz et al. [3] studied the three-component receptance coupling substructure analysis with spindle, holder and tool. M.R. Movahhedy, J.M. Gerami [4] demonstrated that two linear springs can accounts for the rotational responses and proposed a model avoiding rotational responses measurement while taking into account the bending modes. An optimization method based on genetic algorithm is employed to obtain joint parameters. For improving the prediction precision, T.L. Schmitz et al. [5] adopted continuous contact stiffness and damping to model the holder-tool interface. The stiffness and damping values are calculated by contact element of the finite element software ANSYS. K. Ahmadi, H. Ahmadian [6,7] used the concept of tool on resilient support and regarded that the tool is partly resting on a resilient support provided by the spindle-holder assembly. The distributed interface layer takes into account the change in normal contact pressure along the joint interface. M.F. Ghanati, R. Madoliat [8] used contact element of the finite element software ANSYS to model both the holder-tool interface and spindle-holder interface. From the above studies of receptance coupling substructure analysis, it is shown that accurate prediction of tool point dynamic requires accurate joint parameters of holder-tool interface. Continuous contact stiffness and damping model of holder-tool interface can achieve good accuracy, but the model is complex and takes a lot of calculation time when using genetic algorithm. In actual machining, the clamping length often varies with the altered processing conditions, this paper proposed a simplified joint parameters identifying method which use inverse calculation according impact experiment data and expend very little time compared to the genetic algorithm. The remainder of this paper was structured as follows. In section 2, the calculation formulations of equivalent joint parameters are given in detail. The identification of joint parameters according the proposed method and experiments data are shown in section 3 and the experimental verification are carried out to validate the efficiency of the proposed method. Finally, the conclusions are presented in the last section.
2
Formulations of Equivalent Joint Parameters
The continuous contact interface of holder-tool is simplified as the contact points in side of the clamping part as shown in Fig. 1. Points p and q are the ends of the cutter
edge part. When an exciting force Fp (ω) is applied on the point p where is the location for impact experiment, the corresponding vibration will appear at points 1, 2, p and q, the corresponding internal forces will be also produced at points 1 and 2 between tool and holder.
A Simplified Method to Identify the Equivalent Joint Parameters
Holder structure B
1 UB(x)
2
589
Fp(¦ Ø )
2 1 UA(x) Tool
structure A point p
point q
Fig. 1. Equivalent joint parameters of continuous holder-tool interface
The structure A and structure B in Fig. 1 are analyzed respectively. The internal force produced on the structure A at point 1 and 2 are F1_ A and F2_ A , and the internal force applied on structure B are F1_ B and F2_ B , consequently, there are the flowing compatibility condition:
F1_ A + F1_ B = 0
(1)
F2 _ A + F2 _ B = 0 The equilibrium conditions at structure A provide the following equation: HAp1F1_ A + HAp2F2 _ A + HApp Fp = X p HAq1F1_ A + HAq2 F2 _ A + HAqp Fp = Xq
(2)
where X p and X q are the displacement produced on the combination of structure A and structure B at points p and q, HAij are FRFs between points i and j on the structure A. X p and X q can be denoted by the FRFs H pp and H qp on the structure A-B assem-
bly and the force Fp . X p = H pp Fp
(3)
X q = Hqp Fp The Eqs. (2) and (3) can be rearranged as follows: −1
F1_ A HAp1 HAp2 H pp − HApp F = Fp HA HA H − HA q 2 qp qp 2_ A q1
(4)
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When the internal forces are obtained, the displacements on the structure A at point 1 and 2 can be calculated by the flowing equation:
X1_ A HA11 HA12 F1_ A HA1p X = F + Fp HA 2_ A HA21 HA22 2_ A 2p
(5)
Similarly, the displacements on the structure B at point 1 and 2 are X1_ B HB33 HB34 F1_ B X = 2_ B HB43 HB44 F2_ B
(6)
where HBij are FRFs between points i and j on the structure B. According the internal forces and the displacements on structure A and structure B at point 1 and 2, the joint parameters can be expressed as: 0 1 ( X1_ A − X1_ B ) KC1 F1_ B KC = 0 F 2 _ B 1 ( X 2 _ A − X 2 _ B ) 2
(7)
where the internal forces and the displacements are depended on the frequency of excitation, consequently, the joint parameters identified are not constant but distribute along the whole frequency band. The structure A and structure B are modeled by utilizing the finite element software ANSYS as shown in Fig. 2 (a). Harmonic analyses are performed to calculate the FRFs HAij and HBij . The FRFs H pp and H qp of structure A-B assembly are tested by impact experiment as shown in Fig. 2 (b).
a
b
Fig. 2. Finite element model and impact experiment
A Simplified Method to Identify the Equivalent Joint Parameters
3
Experiment and Analysis
3.1
Identification of Joint Parameters
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The holder of ISCAR HSK A100 ER32 and tool of SANDVIK Φ20 carbide end mill are used here to identify the joint parameters. The clamping torque and clamping length are 100 Nm and 20 mm, respectively. The material properties are defined in Table.1. According to Ref. [5,9]. Table 1. Holder and tool material properties. Density(Kg/m3)
Elastic modulus (GPa)
Holder
7850
210
0.3
0.003
Tool
14400
560
0.22
0.003
Poisson ratio damping ratio
The FRFs H pp and H qp obtained by impact experiment are shown in Fig. 3. -6
1
x 10
Hpp Hqp
Amplitude (m)
0.5 0 -0.5 -1 -1.5 1000
1500
2000 2500 3000 Frequency (Hz)
3500
4000
Real -7
5
x 10
Hpp Hqp
Amplitude (m)
0 -5 -10 X: 1848 Y: -1.742e-006
-15 -20 1000
1500
2000 2500 3000 Frequency (Hz)
3500
Imaginary Fig. 3. FRFs H pp and H qp
4000
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The equivalent joint stiffness-damping parameters calculated according Eq. (7) are shown in Fig. 4. 7
x 10 1.04 9
3
x 10
1.0395 K1 K2
1.039
2 Amplitude (N/m)
K1 K2
1850.646
1
1850.6465
1850.647
0 -1 -2 -3
0
1000
2000 Frequency (Hz)
3000
4000
C1 C2
0.632 5
2
x 10
0.631 C1 C2
0.63 Amplitude (N.s/m)
1
0.629 1859.2134
0
1859.2134
1859.2134
-1 -2 -3 0
1000
2000 Frequency (Hz)
3000
4000
Fig. 4. Joint stiffness-damping parameters
From Fig. 4, it is found that the stiffness and damping values vary with the frequency and show the asymmetrical characteristics about horizontal axis. The reason explained this phenomenon is that actual continuous contact interface between holder and tool is simplified only by the contact points in side of the clamping part. It is regarded that the equivalent joint stiffness-damping parameters at contact points in side of the clamping part are the same values. The same stiffness value of K1 and K2 appears in the amplitude 1.0395e7 N/m and frequency 1850 Hz. The same damping value of C1 and C2 appears in the amplitude 0.63 N×s/m and frequency 1859 Hz. The frequency 1850 Hz and 1859 Hz are very close to the modal frequency 1848 Hz of experiment data in Fig. 3, which accord with the selection principle of the stiffness-damping parameters in Ref. [10].
A Simplified Method to Identify the Equivalent Joint Parameters
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Experimental Verification
It is considered that the stiffness and damping values of the holder-tool interfaces are proportional to the clamping length of holder-tool on the condition that the same material properties and same clamping diameter. Two experimental cases with the change of clamping length are performed to verify this assumption. The stiffness and damping values calculated according to the ratio of clamping length are listed in Table. 2. Table 2. The stiffness and damping values of the two experimental cases. clamping length
tool diameter
(mm)
(mm)
Identified case
20
Case 1 Case 2
K (N/m)
C (N×s/m)
20
1.0395e7
0.63
30
20
1.0395e7×1.5
0.63×1.5
40
20
1.0395e7×2
0.63×2
Using the parameters in Table 2, the FRFs H pp of holder-tool assembly are regenerated. Fig. 5 depicts the predicted response versus the FRF obtained by conducting modal test on the assembly. Case 1 -7
3
x 10
Measured Predicted
Amplitude (m)
2 1 0 -1 -2 -3 -4
1000
1500
2000 2500 3000 Frequency (Hz)
3500
4000
Real Fig. 5. Predicted and measured frequency response for two cases
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1
x 10
Measured Predicted
Amplitude (m)
0 -1 -2 X: 2150 Y: -3.415e-007
-3 X: 2138 Y: -4.854e-007
-4 -5
1000
1500
2000 2500 3000 Frequency (Hz)
3500
4000
Imaginary
Case 2 -7
4
x 10
Measured Predicted
Amplitude (m)
2 0 -2 -4 -6 1000
1500
2000 2500 3000 Frequency (Hz)
3500
4000
Real -7
2
x 10
Measured Predicted
Amplitude (m)
0 X: 2496 Y: -2.797e-007
-2 -4 -6 -8 1000
X: 2328 Y: -7.132e-007
1500
2000 2500 3000 Frequency (Hz)
Imaginary Fig. 5. (Continued)
3500
4000
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It is seen that the predicted response follows the experimental response closely for the clamping length of 30 mm in the modal frequencies with 2138 Hz and 2150 Hz respectively. When the clamping length is increased to 40 mm, there is 7.2% error between the predicted and measured response with the modal frequencies of 2496 Hz and 2328 Hz, respectively. The experimental verification indicates that the prediction method for joint parameters is feasible. The reason for the error of clamping length 40 mm may be that the holder and tool are connected by collet which has two contact surfaces with one connected to the holder and the other connected to the tool. However, the proposed method simplified the two contact surfaces to one contact surfaces. Hence, the ratio between the stiffness-damping values and clamping length does not follow the linear relationship strictly when the clamping length varies greatly.
4
Conclusions
Holder-tool interface stiffness and damping is one of the main obstacles in accurately predicting the tool tip response of spindle-holder-tool combination. The clamping length is one of the main factors affecting the stiffness and damping values which are considered to be proportional to the clamping length in this paper. For the purpose of improving computational efficiency, the continuous contact interface along the holder-tool clamping length is equivalent to the contact points at side of the clamping part and an inverse calculation method according impact experiment data is used to calculate the joint parameters directly. Comparisons between predicted and measured response validate the efficiency of the proposed method. Later research will focus on the improving the accuracy of model for more precise identification of the joint stiffness-damping parameters. Acknowledgment. This work was partially supported by the National Natural Science Foundation of China under Grant No. 51275189, the Project of Key Technology Innovation Project of Hubei Province under Grant No. 2013AAA008 and the National Natural Science Foundation of China under Grant No. 51421062.
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5. Schmitz, T.L., Powell, K., Won, D., Duncan, G.S., Sawyer, W.G., Ziegert, J.C.: Shrink fit tool holder connection stiffness damping modeling for frequency response prediction in milling. Int. J. Mach. Tools Manuf. 47, 1368–1380 (2007) 6. Ahmadi, K., Ahmadian, H.: Modelling machine tool dynamics using a distributed parameter tool–holder joint interface. Int. J. Mach. Tools Manuf. 47, 1916–1928 (2007) 7. Ahmadian, H., Nourmohammadi, M.: Tool point dynamics prediction by a three-component model utilizing distributed joint interfaces. Int. J. Mach. Tools Manuf. 50, 998–1005 (2010) 8. Ghanati, M.F., Madoliat, R.: New Continuous Dynamic Coupling for Three Component Modeling of Tool–Holder-Spindle Structure of Machine Tools With Modified Effected Tool Damping. J. Manuf. Sci. Eng. Trans. ASME 134, 021015-1–021015-19 (2012) 9. Ertürk, A., Özgüven, H.N., Budak, E.: Analytical modeling of spindle-tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF. Int. J. Mach. Tools Manuf. 46, 1901–1912 (2006) 10. Özsahin, O., Ertürk, A., Özgüven, H.N., Budak, E.: A closed-form approach for identification of dynamical contact parameters in spindle-holder-tool assemblies. Int. J. Mach. Tools Manuf. 49, 25–35 (2009)
