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Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface
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CIRPJ-354; No. of Pages 9 CIRP Journal of Manufacturing Science and Technology xxx (2016) xxx–xxx
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Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface ¨ zs¸ahin a,*, Y. Altintas a, B. Denkena b W. Matthias a, O. O a b
Manufacturing Automation Laboratory, Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC, Canada V6T 1Z41 Institute of Production Engineering and Machine Tools (IFW), Leibniz Universita¨t Hannover, An der Universita¨t 2, Garbsen 30823, Germany
A R T I C L E I N F O
A B S T R A C T
Article history: Available online xxx
To identify stable cutting conditions with a high depth of cut, stability lobe diagrams are used. In order to predict these diagrams, frequency response functions (FRF) at the tool tip are required for every tool, holder and machine combination. To reduce the number of experimental tests, receptance coupling substructure analysis (RSCA) is proposed in the literature. In order to take full advantage of this method, contact parameters between holder and tool must be known. To identify these parameters this paper presents a new method based on free-free measurements. The obtained contact parameters led to good results for various tool lengths. Based on this, an extensive investigation is performed for the ER32 holder interface. Afterwards, the RCSA method is tested. Therefore, different spindle–holder–tool assemblies are modeled for two machine tools. Prediction and measurement of obtained tool-tip FRF shows a good match, especially for the frequency position. ß 2016 CIRP.
Keywords: Chatter stability Machine tool dynamics Contact dynamics Parameter identification
Introduction The instability of the cutting process as the cause of chattering is detected at the same time from Tlusty and Polacek [1] and Tobias and Fishwick [2]. Even today chatter is one of the main influences which set a limit to machining processes like turning, drilling, boring and milling. It has several effects, which have a negative influence on the cutting process. For example a poor surface quality, unacceptable inaccuracy and increased stress for the tool and machine [3]. For this reason the topic of chatter vibrations is still current. A variety of papers are giving a good summary about the research advancements in this field [3–5]. However, to get an efficiently operation process it is necessary to use process parameters, which were detected close to the border of chatter conditions. Altintas and Budak [6] proposed a control system approach to make an analytical determination of stability limits. This stability lobe diagram (SLD) presents the stable and unstable cutting conditions for a specific cutting process. In order to obtain stability diagrams frequency response functions (FRF) at tool tip are required. Tool point FRF is usually determined experimentally. But it is usual to use a lot of different tools and holders on a
* Corresponding author. Tel.: +1 90 312 586 8315; fax: +1 90 312 586 8091. ¨ zs¸ahin). E-mail address: [email protected] (O. O 1 www.mal.mech.ubc.ca.
machine. Thus, tool point FRF measurement is required for each combination of tool and holder. But this approach is very timeconsuming and increases the downtime of the machine and therefore the production costs. For this reason [7–9], proposed the receptance coupling substructure analysis method (RSCA) to eliminate the experimental dependency. One of the main obstacles for using the RCSA method is the joint interfaces between spindle, holder and tool. While spindle–holder contact dynamics will be approximated, in many cases, during identification of spindle receptance [10,11], the holder–tool interface causes more problems. Rezaei et al. [12] adopt Namazi et al. [10] approach and used inverse Receptance Coupling, first provided in [13], to approximate contact conditions between holder and tool. Instead of separating only the spindle they isolated the holder and inner tool path. Therefore, they approximate both joint dynamics in one receptance matrix. But this approach limits the possibilities, which will be offered by RCSA. To avoid this problem the dynamical behavior of the joint has to be modeled and the interface parameters between holder and tool must been known. Therefore, many researches are available which are dealing with various modeling approaches [14–18]. Schmitz and Donaldson [7] used for the first investigations a lump stiffness model. They coupled the outer tool part through linear and rotational springs and dampers to the spindle–holder assembly. The connection parameters are identified using a single tool-tip measurement and fit this FRF by the experimental data.
http://dx.doi.org/10.1016/j.cirpj.2016.02.005 1755-5817/ß 2016 CIRP.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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But the measurement of rotational response at joints is complicated. For this reason, Movahhedy and Germai [14] proposed a contact model with two parallel linear springs. To obtain the contact parameters they used a genetic algorithm. Later Schmitz and Powell [15] extended the three component model for a shrink fit holder and included multiple connections between tool and holder along the interface contact. The stiffness values are determined directly from the slope of the load-displacement curves for different positions inside the holder. They assumed that energy dissipation in the shrink fit connection occurred due to relative micro-slip between tool and holder. Thus, they calculated the damping by using the Coulomb damping approach. To extract the interface parameters of the joint interface between modular tools Park and Chae [16] used the inverse RCSA method. Like Schmitz and Donaldson [7] they used a lump stiffness model to describe the joint dynamics. The cross-coupled properties of the joint between translational and rotational degrees of freedom are assumed to be negligible because they have not a significant effect on the response of the assembled system. They obtain the contact parameters of the fastener joint by minimizing the deviation between the FRFs of the rigid system and the measured system. Ahmadi et al. [17,18] replaced the lump-stiffness model with a new approach. They modeled the joint interface between tool and holder using an elastic interface layer. Thereby, the interface stiffness can be defined as a variable function along the tool inserted shank length. Introduction of this layer enables to consider the varying contact pressure along this interface. The interface parameters are identified again by minimizing the deviation between the predicted FRF at the free end of the holder from the corresponding measured one. An approach, which is not based on a minimization between the deviation of the predicted and measured FRF, is presented by Ozsahin et al. [19]. They used an inverse RCSA method to calculate the complex stiffness matrix. For this purpose they need the receptance matrix of spindle, holder and tool and furthermore it is necessary to perform a tool-tip measurement. This stiffness matrix describes contact parameters for each frequency. The idea is to pick values close to the frequency of the first eigenvalue because there they expected the biggest impact of contact parameters. But, this approach is time consuming, due to the large area which has to be checked to identify the joint parameters. Moreover, this practice is very sensitive to noise and errors because during the method matrices with very small elements and low ranks are inverted. Thus, this approach is better suited for initial assessment. However, this method is used in many researches to obtain the contact parameters for further investigations [20–22]. Regardless of which model is used to couple parts it is indispensable to know stiffness and damping parameters between single interfaces. In literature, there does not exist an analytical model for the determination of interface parameters. Therefore, contact parameters at holder–tool and spindle–holder interfaces
h11;ff h11;Mf h21;ff ½H21 ¼ h 21;Mf h22;ff ½H22 ¼ h22;Mf ½H11 ¼
This paper presents an identification method for the contact parameters at holder–tool interface. In identification method proposed, holder–tool assembly dynamics is measured at free–free end conditions and contact parameters are identified using a fitting algorithm. The contact parameters obtained by this method are applicable for similar clamping setups. To verify the accuracy of the results different setups with blank tools of various lengths are modeled using identified contact parameters and measured by experimental modal analysis (EMA). Further, a differentiation between the previous experimental methods and the method developed in this study is made. Based on the new method, the influence of different clamping conditions on joint parameters of collet holders and thereby on dynamical behavior is presented. Afterwards, the generality of the identified parameters is demonstrated. Therefore, two machine tools are modeled and in each case a collet holder is clamped into the machine tool. For different blank tools the predicted dynamical transfer functions at the tool tip are compared with tool-tip measurements. Mathematical modeling Theory of receptance coupling In this section, a brief review of the RCSA method is presented based on the previous literature [23,24]. The basic receptance coupling equation for the rigid coupling of two structures in a free– free condition is presented in Eq. (1): # " ðHA;11 HA;12 ðH2 Þ1 HA;21 Þ ðHA;21 HA;12 ðH2 Þ1 HA;22 Þ F 1 X1 ¼ X2 ðHA;21 HA;22 ðH2 Þ1 HA;21 Þ ðHA;22 HA;22 ðH2 Þ1 HA;22 Þ F 2 (1) The displacement vector X is for translational and angular displacement components. Force vector F includes the force and moment applied at position 1 and 2. HA,ij are the generalized receptance matrices between the positions i and j. However not every connection can be assumed as inflexible like depicted in Fig. 1. To consider the stiffness and damping between such connections H2 can be modified with the complex stiffness matrix K: H2 ¼ HA;22 þ HB;22 þ K 1
Complex stiffness matrix contains interface parameters between two substructures and can be expressed by the translational stiffness kyf and damping cyf and the rotational stiffness kuM and cuM damping [16]. kyf þ ivcyf 0 (3) K¼ 0 kuM þ ivcuM Including contact dynamics, elastic coupling of two substructures can be expressed as follows:
hA11;ff h11;fM ¼ h11;MM hA11;Mf hA21;ff h21;fM ¼ h21;MM h A21;Mf hA22;ff h22;fM ¼ h22;MM hA22;Mf
are identified using experimental methods. These determined contact parameters will be valid only for the investigated setup. Thus, the advantage of the idea of receptance coupling does not longer exist.
(2)
hA12;ff hA11;fM hA11;MM hA12;Mf hA12;ff hA21;fM hA21;MM h A12;Mf hA22;ff hA22;fM hA22;MM hA22;Mf
hA12;fM hA21;ff ½H 1 hA12;MM 2 hA21;Mf hA12;fM hA21;ff ½H2 1 hA12;MM h A21;Mf hA22;fM hA22;ff ½H2 1 hA22;MM hA22;Mf
hA21;fM hA21;MM hA21;fM hA21;MM hA22;fM hA22;MM
(4)
In Eq. (4), subscript ff represents linear displacement–force, fM represents linear displacement–moment, Mf represents angular displacement–force and MM represents angular displacement– moment.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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Fig. 1. Rigid coupling of two substructure.
Identification of contact dynamics at the holder–tool interface
i1 Hht;11 ¼ Ht;11 Ht;12 Ht;22 þ Hh;22 þ ½K 1 Ht;21
Fig. 3. Schematic representation of fitting measurement and model.
Geometry y Information Material Propertiess Analysis Parameterrs
Algorithm Ht,11
Ht,12
ky
k
Ht,21
Ht,22
cy
c
substructure A
Hh,11
Hh,122
Hh,21 Hh,222
Joint Dynamics
substructure B
Hht,11
Hht,122
Hht,21 Hht,222
(5)
Output
Beam Theory
Input
RCSA
First the different sections of holder and tool are calculated analytically by Timoshenko beam theory [25]. Based on the RSCA method these sections are coupled rigidly and receptance matrix for tool–holder (Hh) and tool (Ht) for the free-free case are obtained. Finally holder receptances are coupled with the tool receptances elastically as shown in Fig. 2. Afterwards, end point FRF of the tool holder–tool assembly is measured at free–free end conditions. In order to satisfy free–free end conditions, holder–tool assembly is suspended by elastic ropes. Also holder–tool assembly is excited by an impact hammer and the response of the system is measured by laser vibrometer. It is possible to model this linear displacement–force tool-tip measurement by a single equation. Using the elastic coupling procedure given in Eq. (4) receptance matrix at the tool tip can be expressed as follows:
substructure C
where Hht;11 ¼
hht;11;ff hht;11;Mf
hht;11;fM hht;11;MM
EMA
(6)
As shown in Eq. (5), hht,11,ff can be expressed analytically using unknown contact parameters at holder–tool interface. The measured and calculated hht,11,ff are compared inside a fitting algorithm. This algorithm optimizes the absolute percentage difference between both FRFs, as shown in Fig. 3. Therefore, the four unknown contact parameters are used to minimize the deviation of both FRFs in a fixed range around the amplitudes. Different to previous approaches each determined frequency over a wide frequency spectrum is regarded instead of only the first dominant amplitude. For this purpose a nonlinear optimization function is used. The stiffness and damping values, which result in smallest differences, are the identified contact parameters. An overview of the approach is shown in Fig. 4. Experimental verification for identification of contact dynamics
hht,11,ff
fitting Algorithm m
Fig. 4. Overview of the joint identification approach.
Then identified parameters are used to predict end point FRFs of various holder and tool combinations. Tool dimensions used in identification are given in Table 1. Tool diameter is represented by Øtool, oltool represents tool length outside the holder, iltool represents tool length inside the holder and lholder represents total length of the holder. The identified translational and rotational stiffness and damping are given in Fig. 6. Note that in five different cases given in Table 1, tool lengths inside the holder are kept constant. Therefore, the only parameter affecting the contact area at holder– tool interface is tool diameter. Thus, the identification results given in Fig. 6 reflect the effect of tool diameter on contact parameters.
To verify the method, first contact parameters for five different carbide beams are identified using proposed method. The used free-free measurement arrangement is depicted in Fig. 5.
Fig. 2. Tool and tool–holder coupled by stiffness matrix.
Fig. 5. Free–free measurement arrangement for joint identification.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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Table 1 Assembly parameters for various carbide tool diameters. Øtool [mm] oltool [mm] iltool [mm] lholder [mm]
7.94 62.30 40.00 129.9
9.53 62.60 40.00 128.4
Table 2 Measurements and simulation with different tool lengths.
11.11 62.80 40.00 126.6
12.70 62.30 40.00 129.0
16.00 75.40 40.00 130.3
Øtool
oltool
v1
v2
v3
v1
v2
v3
[mm]
[mm]
[Hz]
[Hz]
[Hz]
[Hz]
[Hz]
[Hz]
7.94
24.9 113.5 23.8 114.2 30.3 114.9 37.0 113.2
7857 627 8838 780 6942 941 5761 1151
11,200 3204 12,020 3738 11,695 4233 11,460 4937
– 8470 – 9505 – 10,110 – 10,550
7820 623 8931 769 6940 930 5809 1129
11,280 3237 11,930 3749 11,940 4224 11,400 4919
– 8518 – 9499 – 10,120 – 10,550
9.53
The identified translational stiffness (Fig. 6a) of the Ø7.94 mm tool is 3.44e8 N/m and increase until a tool diameter of Ø16 mm to 1.43e9 N/m. During same range the rotational stiffness (Fig. 6b) increases from 2.54e4 Nm/rad to 2.45e5 Nm/rad. The almost constant translational stiffness of the first three diameters can be explained by various clamping conditions. Each collet can fix tools in a specific range of diameters. Dependent on the tool diameter the range changes how far the collet fits into the holder. For ER32 holder a difference of more or less 5 mm is possible. Thereby, clamping conditions inside the interface change. For example the effected clamping surface and the pressure distribution are varying. However, identification of damping parameters inside the contact interface is more difficult. Damping is low and height of amplitude varies between every measurement. This could be due to the free-free measurement arrangement. Both damping values increase with an increasing diameter. Bigger outliers can only be noticed for rotational damping of the Ø9.58 mm tool (Fig. 6d). But due to the fact that magnitude is varying and damping is low enough that it does not affect the modeling of spindle–holder–tool assembly, we neglect the damping in further research. In order to check the accuracy of the identified contact parameters, different tools with different outer lengths are clamped to the holder while inner length kept the same like during the identification. Then, end point FRFs are calculated for new holder–tool combinations at free–free end conditions using previously identified contact parameters. Afterwards, the measurements are compared with predicted FRFs, summarized in
8
x 10
3.0
Rotational Stiffness
Translational Stiffness
15
N/m
5
0
a)
8
10
12
mm
Ns/m 150 100 50 0 6
1.5 1.0 0.5 8
10
12 mm 16
Tool Diameter
0.14
Rotational Damping
Translational Damping
250
c)
2.0
b)
Tool Diameter
5
Nm/rad
0
16
x 10
8
10
12
14 mm 18
Tool Diameter
Nms/rad 0.10 0.08
11.11 12.70
Measurement
Predicted
Table 2. For each diameter a shorter and longer tool is examined. The identified contact parameters are showing good results. With one exception each deviation is below 2%, which is an indication that models and parameters are correct. Differentiation to classical optimization based on tool point FRF measurement In this study, contact parameters are identified using measured end point FRFs of holder–tool assembly at free-free end conditions. Different than the proposed method, in literature, contact parameters are often identified using tool point FRFs measured on machining centers. This approach might lead to different sets of solutions depending on the local minimum of the optimization method. In order to compare these two different approaches, first holder–tool assembly is clamped to machining center and tool point FRF is measured. In addition spindle dynamics is identified experimentally using the identification procedure proposed by Namazi et al. [10]. Then analytically calculated holder–tool receptance matrices are coupled with the experimentally obtained spindle receptances and tool point FRF is obtained. Note that, comparison of different optimization techniques is accomplished by using different contact parameters in the elastic coupling of holder and tool dynamics as given in Table 3. Among given contact parameters sets given in Table 3, the curve fitted set is obtained by using free–free FRF measurement and the proposed identification approach. On contrary, these three remaining parameter sets are obtained by using a measurement performed on machining center. Therefore, the stiffness and damping values are changed manually until a good match between measurement and model is obtained. Calculated tool point FRFs using different contact parameters are given in Fig. 7 with the measured tool point FRF. As shown in Fig. 7, frequencies show a good match for each FRF and even magnitude differences are acceptable for each set. Thus, it can be assumed that the four parameter sets provide good results for the spindle–holder–tool assembly. But problems become apparent, if these parameters are used to predict dynamical behavior of the holder–tool free–free assembly. For that purpose, dynamics of the same holder–tool assembly given in Fig. 7 is obtained analytically and experimentally for freefree end conditions. Similarly during the analytical model holder
0.06 0.04
Table 3 Different parameter sets for holder–tool interface.
0.02
kyf
k um
cyf
cum
[N/m]
[Nm/rad]
[Ns/m]
[Nms/rad]
3.52E + 08 4.00E + 07 5.00E + 12 6.50E + 06
3.96E + 04 4.60E + 04 3.89E + 04 6.00E + 12
– – – 10
0.0097 – 0.018 3000
d)
0 6
8
10 12 14 mm 18
Tool Diameter
Fig. 6. Translational and rotational stiffness and damping for different tool diameters.
Curve fitted set Manual set 1 Manual set 2 Manual set 3
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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CIRPJ-354; No. of Pages 9 W. Matthias et al. / CIRP Journal of Manufacturing Science and Technology xxx (2016) xxx–xxx
x 10
5
-4
1.2 measurement curve fitted set manual set 1 manual set 2 manual set 3
Magnitude
m/N 0.8 0.6 0.4 0.2 0
0
2000
4000
6000
Hz
10000
Frequency
Fig. 10. Free–free measurement for holder–tool and predicted FRF with different parameter contact sets (short tool Ø9.53 mm).
not represent the real interface parameters. But only one set can be used to calculate the model for different tool lengths. Furthermore, it is possible that errors during spindle identification will be compensated by contact parameters, if the spindle–holder–tool assembly is used to identify these parameters. Investigation of the effect of clamping parameters to contact dynamics Clamping torque In the following step the effect of various clamping torque on contact parameters are studied. Thus, the five carbide beams from Table 1 are mounted inside the holder. For each diameter clamping torque is changed in four steps from 95 Nm to 155 Nm. Thereby, a torque of 135 Nm is recommended by the manufacturer and 155 Nm is the permitted maximum. For each case interface parameters are identified. All diameters show a similar behavior during the variation of clamping torque. The investigated first and second eigenvalue are increasing if a rising clamping torque is used. This is depicted in Fig. 11 for the Ø11.11 mm beam.
Translational Stiffness
and tool are coupled using different contact parameter sets given in Table 3. The measured and predicted FRFs for free–free end conditions are given in Fig. 8. For this case the outer tool length is 114 mm. As seen from Fig. 8, in free–free end conditions higher modes of the system becomes visible in the frequency range of interest and accuracy of different contact parameter sets becomes visible. Although all contact parameter sets provide accurate predictions for the first mode, only curve fitted set gives accurate predictions for the remaining modes. Since first mode is the dominant mode that determines the stability and inaccuracy in higher frequencies does not cause wrong stability predictions researchers often do not pay attention to the accuracy of the identified contact parameters. However, if we use contact parameters for various tool lengths, the difference and accuracy becomes clear. For that purpose, same contact parameter sets given in Table 3 are employed in the modeling of different holder–tool combinations. In these cases, tool length outside the holder is changed. But in order to keep contact area same in all cases, tool length inside the holder and tool diameter is kept as 40 mm and 9.53 mm respectively. Calculated tool point FRFs for tool stick out length of 63 mm and 24 mm are given with the measured FRFs in Figs. 9 and 10 respectively. As seen from Fig. 9, again only the identified parameters provide accurate predictions for all modes in the frequency range. Parameter set 3 does not lead to the right behavior even for the first mode. Although parameter set 1 gives accurate predictions for the first mode, errors in second mode is large enough to produce an error for the stability. Therefore, contact parameter sets 1 and 3 lose their applicability for decreased tool length. Finally as seen from Fig. 10, when the tool length outside the holder decreased to 24 mm, contact parameter set 2 loses it prediction accuracy and only identified contact parameters continue to provide accurate FRF predictions. Therefore, it should be noted that it is possible to model a specific system with different parameter sets, which are
Fig. 9. Free–free measurement for holder–tool and predicted FRF with different parameter contact sets (medium tool Ø9.53 mm).
a) Fig. 8. Free–free measurement for holder–tool and predicted FRF with different contact parameter sets (long tool Ø9.53 mm).
4.0
x 10
8
Rotational Stiffness
Fig. 7. Tool tip measurement and predicted FRF with different parameter sets.
N/m 3.0 2.5 2.0
100
120
Torque
Nm
160
b)
7.0
x 10
4
Nm/rad 6.0 5.5 5.0
100
120
Nm
160
Torque
Fig. 11. Translational and rotational stiffness for various clamping torque (Ø11.11 mm).
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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CIRPJ-354; No. of Pages 9
v1
v2
kyf
k um
[Nm]
[Hz]
[Hz]
[N/m]
[Nm/rad]
7.94
95 115 135 155
1692 1694 1694 1695
9104 9111 9116 9120
3.29E + 08 3.33E + 08 3.36E + 08 3.36E + 08
2.32E + 04 2.33E + 04 2.34E + 04 2.35E + 04
9.53
95 115 135 155
1997 1998 2004 2006
9754 9780 9814 9837
3.19E + 08 3.35E + 08 3.52E + 08 3.66E + 08
3.90E + 04 3.90E + 04 3.96E + 04 4.00E + 04
11.11
95 115 135 155
2295 2299 2306 2311
10,010 10,050 10,110 10,170
2.90E + 08 3.06E + 08 3.29E + 08 3.51E + 08
6.00E + 04 6.05E + 04 6.13E + 04 6.19E + 04
95 115 135 155
2693 2702 2706 2712
10,290 10,320 10,340 10,350
5.52E + 08 5.82E + 08 6.28E + 08 6.59E + 08
1.01E + 05 1.03E + 05 1.04E + 05 1.05E + 05
95 115 135 155
2601 2606 2612 2614
9461 9478 9475 9484
1.29E + 09 1.31E + 09 1.35E + 09 1.35E + 09
2.44E + 05 2.48E + 05 2.53E + 05 2.54E + 05
12.70
16.00
Over the complete torque range v1 has changed from 2295 Hz to 2311 Hz. Meanwhile, v2 increased from 10,010 Hz to 10,170 Hz, which means the difference for both eigenvalues is less than 1.6%. This deviation is similar for each tool diameter, presented in Table 4. Therefore, it can be noted that the influence of clamping torque is low for this holder and tool connection. Although the change of eigenvalues is low, the percentage difference for stiffness parameters is huge. For example, the translational stiffness of the Ø12.7 mm beam changed during the investigated range from 5.5e8 N/m to 6.6e8 N/m, which is a difference about 20%. This is based on the fact that the connection is very inflexible. The stiffness parameters are high and approximate asymptotically to behavior of rigid connection. Clamping length
Trans. Stiffness
8
Ø9.53
N/m 3
a)
c)
x 10
12
40
x 10
8
mm
20
Ø12.7
N/m 10
40
mm
20
Clamping Length
Trans. Stiffness
5
8
x 10
8
Ø11.11
N/m 6
b) Trans. Stiffness
Trans. Stiffness
To investigate the effect of clamping length (tool length inside the holder) variation, contact parameters for three different inner lengths are identified. Therefore, the clamping length is reduced from the full size of 40 mm to 20 mm. But different clamping lengths have a low effect on translational stiffness. For a tool diameter of Ø9.53 mm, Ø11.11 mm, Ø12.7 mm and Ø16 mm the stiffness is almost constant, depicted in Fig. 12.
30
40
x 10
8
mm
20
Ø16
x 10
4
Nm/rad 3
a) 12
40 x 10
4
mm
d)
20
20
Nm/rad 10
40
mm
Nm/rad 6 30
20
mm
20
mm
4
Ø16
40
20
mm
20
Clamping Length
d)
Fig. 13. Rotational stiffness for various clamping length (a) tool Ø9.53 mm tool, (b) Ø11.11 mm, (c) Ø12.7 mm and (d) Ø16 mm tool.
A similar behavior is noticeable for rotational stiffness. The Ø9.53 mm and Ø12.7 mm tool have a maximum for 30 mm. The stiffness of the Ø11.11 mm tool decrease for a decreasing clamping length, while the Ø16 mm tool shows an opposite behavior, shown in Fig. 13. The influence of various clamping length is not as big as maybe expected. A reason for this is that the clamping interface can be modeled as two springs in series, depicted in Fig. 14. The total stiffness can be calculated with following equation: K ges ¼
k1 k2 k1 þ k2
(15)
The outer surface is bigger and therefore should be the stiffness k1 in this area smaller. Consequently, a change of k2 has a lower influence on the total stiffness. This demonstrates again the modeling problems for a clamping interface of a collet chuck connection. Similar to the varying holder length, the pressure distribution may change during modifying the clamping length. Thereby, contact parameters can be unpredictably influenced. Material Besides carbide tools, tools made of HSS are often used for milling and drilling operations. Therefore, differences for identified contact parameters are investigated between both materials. The stiffness’s of four assemblies, close to those from Table 1, are determined. HSS tools show the same trend like carbide beams for an increasing diameter, shown in Fig. 15. Again the constant stiffness for the first three diameters can be explained by various clamping conditions. The difference between both materials varies between 10% for the Ø9.54 mm tool and 31% for Ø12.70 mm tool. The rotational stiffness shows even a bigger deviation. Except for the Ø12.7 mm tool, each difference is over 45%. It is already known the identification of translational and rotational stiffness is very sensitive. But these differences are too great to ignore. It can be expected that it is not possible to transfer identified contact parameters for one of both materials without any bigger error. Therefore, various materials should be investigated separately. collet k1
40
40 x 10
Nm/rad
20
Clamping Length
c)
Ø11.11
x 10
8
b)
Ø12.7
holder N/m
4
Ø9.53
Rot. Stiffness
Torque
[mm]
5
Rot. Stiffness
Øtool
Rot. Stiffness
Table 4 Eigenvalues and stiffness for various clamping torque.
Rot. Stiffness
W. Matthias et al. / CIRP Journal of Manufacturing Science and Technology xxx (2016) xxx–xxx
6
tool
k2
Clamping Length
Fig. 12. Translational stiffness for various clamping length (a) tool Ø9.53 mm tool, (b) Ø11.11 mm, (c) Ø12.7 mm and (d) Ø16 mm tool.
Fig. 14. ER 32 holder–tool interface model with springs in series.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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x 108
14 carbide HSS
N/m
Rotational Stiffness
Translational Stiffness
8
6 5 4 3
a)
2
8
10
mm
Tool Diameter
14
x 104
Table 5 Different tool assemblies for tool-tip measurement inside Mori Seiki machine.
carbide HSS
Nm/rad
Øtool
10
Medium tool
Long tool
Stiffness
iltool
oltool
iltool
oltool
kyf
k um
8
[mm]
[mm]
[mm]
[mm]
[mm]
[N/m]
[Nm/rad]
6
7.94 9.53 11.11 12.7 16.0
40 40 40 40 40
62.5 62.5 62.8 62.3 75.7
40 40 40 40 –
113.5 114.2 114.6 113.2 –
3.36e8 3.52e8 3.29e8 6.28e8 1.35e9
2.34e4 3.96e4 6.13e4 1.04e5 2.53e5
4 2
b)
7
0
8
10
mm
14
Tool Diameter
Fig. 15. Translational and rotational stiffness of carbide and HSS beams.
Prediction of tool point FRFs on machine tools The identified contact parameters are verified for two different machine assemblies. Therefore, various holder–tool setups are mounted into Mori Seiki machine. Later similar setups are clamped into the Quaser UX600. Tool-tip measurements are performed for each case and the results are compared with predicted FRFs, obtained by RSCA method. Case study 1 In this case study different holder–tool combinations are clamped to Mori Seiki NT3150 DCG machining center. For the analysis medium and long carbide tools are used with a full clamping length of 40 mm. The recommended clamping torque of 135 Nm is applied. Short tools are neglected because the main amplitude is located in a high frequency range. In this area noise of the identified spindle FRF distort the prediction made by RSCA. The modeling parameters of different cases are presented in Table 5. First spindle dynamic of the machining center is identified using the method proposed by Namazi et al. [10]. Analytically calculated holder–tool assembly is coupled with experimentally obtained spindle dynamics. Note that, holder and tool are coupled using contact parameters which are identified previously using
free–free measurements. Calculated tool point FRFs are given in Fig. 16 with the experimentally measured FRFs. As shown in Fig. 16, tool point FRF can be predicted accurately using RCSA method with previously identified contact parameters. Only the long Ø11.11 mm and Ø16 mm tool have with 3% a bigger frequency deviation. Even three of the tested setups show a difference lower than 1%. The excepted magnitude fits for the most cases. But if two modes are located close together, the RSCA model has problems to predict the correct amplitude for both mode. This can be noticed for the tool length of 63 mm in Fig. 16a. The tool-tip measurement of the long Ø7.94 mm tool has also a variation to the predicted magnitude. The measured amplitude is 50% higher than expected. A bigger difference is also noticeable for the medium Ø12.7 mm tool in Fig. 16d. The amplitudes of predicted and measured FRFs differ about 100%. Even if the already low damping parameters are neglected, it is not possible to improve the fitting. Consequently, it might be reasonably assumed that the deviation is based on modeling errors. The main problem is the identification of the spindle FRF. It is not possible to excite each frequency with an impact hammer test. During the investigation it could be noticed that for some frequency ranges the prediction error is bigger as for other frequencies. For example the position and amplitude of the eigenvalue fits well after changing the outer length of the medium Ø12.7 mm tool about 10 mm. Because with bigger tool length frequencies shift in a lower area without spindle identification limitations.
Fig. 16. Predicted and measured tool tip FRF for medium and long tools with different diameters on Mori Seiki NT3150 DCG.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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Fig. 17. Predicted and measured tool tip FRF for medium and long tools with different diameters on Quaser UX600.
Case study 2 In this case study different holder–tool combinations are clamped to Quaser UX600 machining center. Similar to case study 1, spindle dynamics is identified experimentally and analytically obtained holder–tool assembly is coupled with experimentally obtained spindle dynamics. For the holder–tool interface, again previously identified contact parameters are employed. The Mori Seiki and the Quaser machine have a different spindle interface. Therefore, a different ER32 holder is used, similar to the previous one. The collet interface is the same, thus it is assumed that contact parameters are identical. For the analysis same carbide tools are used like before, presented in Table 5. Calculated tool point FRFs are given in Fig. 17 with the experimentally measured FRFs. Results show that the prediction of the dynamical tool-tip behavior matches well with the measurements. For each case the frequency deviation is lower than 2%. The only exception is the medium Ø9.53 mm tool, which has a frequency error of 3%. However, the excepted magnitude fits for most cases. Only the medium Ø12.7 mm tool shows a bigger error. Similar to the case study 1, the RSCA model has problems to predict the correct magnitude for two close modes. Furthermore, a bigger difference is noticed for the medium Ø7.94 mm tool. This variation is again based on the spindle identification. As with the Mori Seiki machine, it is maybe not possible to excite every frequency with an impact hammer test. But in general the prediction based on Timoshenko beam models and identified interface parameters shows again acceptable results. Conclusion In order to predict chatter stability, tool point FRF should be measured. But, when the number of holder–tool combinations in machine shop is considered, it is difficult to perform experiment for each combination. Therefore, compared to experimental techniques, RCSA provides an efficient tool to predict tool point FRFs since it eliminates the experimental dependency. However, accuracy of the RCSA method depends on the contact parameters at the holder–tool interface. Thus, for better stability predictions, contact parameters should be included in modeling procedure.
In this paper, an identification method for contact parameters at holder–tool interface is presented. In the method proposed contact parameters are identified using analytically calculated and experimentally obtained end point FRFs of the holder–tool assembly at free-free end conditions. Using the method, contact parameters for various tool lengths were identified. The accuracy of the determined parameters was demonstrated by varying the outer tool length. Based on the identified contact parameters two different machining centers were modeled and compared with tool-tip measurements which are shown a good correlation. Further, it was demonstrated that it is possible to model a specific system with different contact parameter sets. But only one set which is obtained using the identification method proposed can be used to calculate the model for various tool lengths. In addition, effects of geometric parameters such as tool diameter, tool material, tool length inside holder and clamping torque on contact parameters are investigated. For instance, it was shown that stiffness increase for an increasing tool diameter, whereas various clamping torque has negligible effects on contact parameters. Furthermore, experimental results demonstrate that material properties also affect stiffness between holder and tool. The influence of changing clamping length is low for ER32 holder. This is because the collet has two contact surfaces and thereby it is possible to model the connection by two springs. This should be considered in further investigations. Based on the proposed approach in this paper, extensive contact parameters studies can be made for other connection concepts.
References [1] Tlusty, J., Polacek, M., 1957, Beispiele der Behandlung der Selbsterregten Schwingung der Werkzeugmaschinen, FoKoMa, Hanser Verlag, Mu¨nchen. [2] Tobias, S.A., Fishwick, W., 1958, Theory of Regenerative Machine Tool Chatter, The Engineer, London: 258. [3] Altintas, Y., Weck, M., 2004, Chatter Stability of Metal Cutting and Grinding, CIRP Annals – Manufacturing Technology, 53:619–642. [4] Quintana, G., Ciurana, J., 2011, Chatter in Machining Process: A Review, International Journal of Machine Tools & Manufacture, 51:363–376. [5] Siddhpura, M., 2012, A Review of Chatter Vibration Research in Turning, International Journal of Machine Tools & Manufacture, 61:27–47. [6] Altintas, Y., Budak, E., 1995, Analytical Prediction of Stability Lobes in Milling, Annals CIRP, 44/1: 357–362.
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CIRPJ-354; No. of Pages 9 W. Matthias et al. / CIRP Journal of Manufacturing Science and Technology xxx (2016) xxx–xxx [7] Schmitz, T.L., Donaldson, R., 2000, Predicting high speed machining dynamics by substructure analysis, CIRP Annals – Manufacturing Technology, 49:303–308. [8] Schmitz, T.L., Davies, M.A., Medicus, K., Snyder, J., 2001, Improving High -Speed Machining Material Removal Rates by Rapid Dynamic Analysis, CIRP Annals – Manufacturing Technology, 50:263–268. [9] Schmitz, T.L., Davies, M., Kennedy, M.D., 2002, Tool Point Frequency Response Prediction for High-Speed Machining by RCSA, Journal of Manufacturing Science and Engineering, 123:700–707. [10] Namazi, M., Altintas, Y., Abe, T., Rajapakse, N., 2007, Modeling and Identification of Tool Holder–Spindle Interface Dynamics, International Journal of Machine Tools and Manufacture, 7/9: 1333–1341. [11] Kumar, U.V., Riggs, A.W., Schmitz, T.L., 2010, Improved Spindle Dynamics Identification Techniques for Receptance Coupling Substructure Analysis (RCSA), ASPE Annual Meeting, 17–20. [12] Rezaei, M.M., Movahhedy, M.R., Moradi, H., Ahmadian, M.T., 2012, Extending the Inverse Receptance Coupling Method for Prediction of Tool–Holder Joint Dynamics in Milling, Journal of Manufacturing Processes, 14:199–207. [13] Schmitz, T., Duncan, G.S., 2005, Three-Component Receptance Coupling Substructure Analysis for Tool Point Dynamics Prediction, Journal of Manufacturing Science and Engineering, 127/4:781–790. [14] Movahhedy, M.R., Germai, J.M., 2005, Prediction of Spindle Dynamics in Milling by Sub-Structure Coupling, International Journal of Machine Tools and Manufacture, 46:243–251. [15] Schmitz, T.L., Powell, K., 2007, Shrink Fit Tool Holder Connection Stiffness/ Damping Modeling for Frequency Response Prediction in Milling, International Journal of Machine Tools and Manufacture, 47:1368–1380. [16] Park, S.S., Chae, J., 2008, Joint Identification of Modular Tools Using a Novel Receptance Coupling Method, International Journal of Advanced Manufacturing Technology, 35:1251–1262.
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[17] Ahmadi, K., Ahmadian, H., 2007, Modelling Machine Tool Dynamics Using a Distributed Parameter Tool–Holder Joint Interface, International Journal of Machine Tools and Manufacture, 47:1916–1928. [18] Ahmadian, H., Nourmohammadi, M., 2010, Tool Point Dynamics Prediction by a Three-Component Model Utilizing Distributed Joint Interfaces, International Journal of Machine Tools and Manufacture, 50:998–1005. ¨ zs¸ahin, O., Ertu¨rk, A., O ¨ zgu¨ven, H.N., Budak, E., 2009, A Closed-Form Ap[19] O proach for Identification of Dynamical Contact Parameters in Spindle–Holder–Tool Assemblies, International Journal of Machine Tools and Manufacture, 49:25–35. [20] Albertelli, P., Goletti, M., Monno, M., 2013, A new Receptance Coupling Substructure Analysis Methodology to Improve Chatter Free Cutting Conditions Prediction, International Journal of Machine Tools & Manufacture, 72:16–24. ¨ zgu¨ven, N., 2015, Dynamic Characterization of Bolted Joints Using FRF [21] Tol, S., O Decoupling and Optimization, Mechanical Systems and Signal Processing, 54– 55:124–138. [22] Mehrpouya, M., Graham, E., Park, S.S., 2013, FRF Based Joint Dynamics Modeling and Identification, Mechanical Systems and Signal Processing, 39:265–279. [23] Schmitz, T.L., Smith, K., 2011, Mechanical Vibrations – Modeling and Measurement, Springer-Verlag, London. [24] Altintas, Y., 2012, Manufacturing Automation—Metal Cutting Mechanics, Machine Tool Vibration and CNC Design, Cambridge University, New York . ¨ zgu¨ven, H.N., Budak, E., 2006, Analytical Modeling of Spindle–Tool [25] Ertu¨rk, A., O Dynamics on Machine Tools Using Timoshenko Beam Model and Receptance Coupling for the Prediction of Tool Point FRF, International Journal of Machine Tools and Manufacture, 46:1901–1912.
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CIRPJ-354; No. of Pages 9 CIRP Journal of Manufacturing Science and Technology xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj
Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface ¨ zs¸ahin a,*, Y. Altintas a, B. Denkena b W. Matthias a, O. O a b
Manufacturing Automation Laboratory, Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC, Canada V6T 1Z41 Institute of Production Engineering and Machine Tools (IFW), Leibniz Universita¨t Hannover, An der Universita¨t 2, Garbsen 30823, Germany
A R T I C L E I N F O
A B S T R A C T
Article history: Available online xxx
To identify stable cutting conditions with a high depth of cut, stability lobe diagrams are used. In order to predict these diagrams, frequency response functions (FRF) at the tool tip are required for every tool, holder and machine combination. To reduce the number of experimental tests, receptance coupling substructure analysis (RSCA) is proposed in the literature. In order to take full advantage of this method, contact parameters between holder and tool must be known. To identify these parameters this paper presents a new method based on free-free measurements. The obtained contact parameters led to good results for various tool lengths. Based on this, an extensive investigation is performed for the ER32 holder interface. Afterwards, the RCSA method is tested. Therefore, different spindle–holder–tool assemblies are modeled for two machine tools. Prediction and measurement of obtained tool-tip FRF shows a good match, especially for the frequency position. ß 2016 CIRP.
Keywords: Chatter stability Machine tool dynamics Contact dynamics Parameter identification
Introduction The instability of the cutting process as the cause of chattering is detected at the same time from Tlusty and Polacek [1] and Tobias and Fishwick [2]. Even today chatter is one of the main influences which set a limit to machining processes like turning, drilling, boring and milling. It has several effects, which have a negative influence on the cutting process. For example a poor surface quality, unacceptable inaccuracy and increased stress for the tool and machine [3]. For this reason the topic of chatter vibrations is still current. A variety of papers are giving a good summary about the research advancements in this field [3–5]. However, to get an efficiently operation process it is necessary to use process parameters, which were detected close to the border of chatter conditions. Altintas and Budak [6] proposed a control system approach to make an analytical determination of stability limits. This stability lobe diagram (SLD) presents the stable and unstable cutting conditions for a specific cutting process. In order to obtain stability diagrams frequency response functions (FRF) at tool tip are required. Tool point FRF is usually determined experimentally. But it is usual to use a lot of different tools and holders on a
* Corresponding author. Tel.: +1 90 312 586 8315; fax: +1 90 312 586 8091. ¨ zs¸ahin). E-mail address: [email protected] (O. O 1 www.mal.mech.ubc.ca.
machine. Thus, tool point FRF measurement is required for each combination of tool and holder. But this approach is very timeconsuming and increases the downtime of the machine and therefore the production costs. For this reason [7–9], proposed the receptance coupling substructure analysis method (RSCA) to eliminate the experimental dependency. One of the main obstacles for using the RCSA method is the joint interfaces between spindle, holder and tool. While spindle–holder contact dynamics will be approximated, in many cases, during identification of spindle receptance [10,11], the holder–tool interface causes more problems. Rezaei et al. [12] adopt Namazi et al. [10] approach and used inverse Receptance Coupling, first provided in [13], to approximate contact conditions between holder and tool. Instead of separating only the spindle they isolated the holder and inner tool path. Therefore, they approximate both joint dynamics in one receptance matrix. But this approach limits the possibilities, which will be offered by RCSA. To avoid this problem the dynamical behavior of the joint has to be modeled and the interface parameters between holder and tool must been known. Therefore, many researches are available which are dealing with various modeling approaches [14–18]. Schmitz and Donaldson [7] used for the first investigations a lump stiffness model. They coupled the outer tool part through linear and rotational springs and dampers to the spindle–holder assembly. The connection parameters are identified using a single tool-tip measurement and fit this FRF by the experimental data.
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But the measurement of rotational response at joints is complicated. For this reason, Movahhedy and Germai [14] proposed a contact model with two parallel linear springs. To obtain the contact parameters they used a genetic algorithm. Later Schmitz and Powell [15] extended the three component model for a shrink fit holder and included multiple connections between tool and holder along the interface contact. The stiffness values are determined directly from the slope of the load-displacement curves for different positions inside the holder. They assumed that energy dissipation in the shrink fit connection occurred due to relative micro-slip between tool and holder. Thus, they calculated the damping by using the Coulomb damping approach. To extract the interface parameters of the joint interface between modular tools Park and Chae [16] used the inverse RCSA method. Like Schmitz and Donaldson [7] they used a lump stiffness model to describe the joint dynamics. The cross-coupled properties of the joint between translational and rotational degrees of freedom are assumed to be negligible because they have not a significant effect on the response of the assembled system. They obtain the contact parameters of the fastener joint by minimizing the deviation between the FRFs of the rigid system and the measured system. Ahmadi et al. [17,18] replaced the lump-stiffness model with a new approach. They modeled the joint interface between tool and holder using an elastic interface layer. Thereby, the interface stiffness can be defined as a variable function along the tool inserted shank length. Introduction of this layer enables to consider the varying contact pressure along this interface. The interface parameters are identified again by minimizing the deviation between the predicted FRF at the free end of the holder from the corresponding measured one. An approach, which is not based on a minimization between the deviation of the predicted and measured FRF, is presented by Ozsahin et al. [19]. They used an inverse RCSA method to calculate the complex stiffness matrix. For this purpose they need the receptance matrix of spindle, holder and tool and furthermore it is necessary to perform a tool-tip measurement. This stiffness matrix describes contact parameters for each frequency. The idea is to pick values close to the frequency of the first eigenvalue because there they expected the biggest impact of contact parameters. But, this approach is time consuming, due to the large area which has to be checked to identify the joint parameters. Moreover, this practice is very sensitive to noise and errors because during the method matrices with very small elements and low ranks are inverted. Thus, this approach is better suited for initial assessment. However, this method is used in many researches to obtain the contact parameters for further investigations [20–22]. Regardless of which model is used to couple parts it is indispensable to know stiffness and damping parameters between single interfaces. In literature, there does not exist an analytical model for the determination of interface parameters. Therefore, contact parameters at holder–tool and spindle–holder interfaces
h11;ff h11;Mf h21;ff ½H21 ¼ h 21;Mf h22;ff ½H22 ¼ h22;Mf ½H11 ¼
This paper presents an identification method for the contact parameters at holder–tool interface. In identification method proposed, holder–tool assembly dynamics is measured at free–free end conditions and contact parameters are identified using a fitting algorithm. The contact parameters obtained by this method are applicable for similar clamping setups. To verify the accuracy of the results different setups with blank tools of various lengths are modeled using identified contact parameters and measured by experimental modal analysis (EMA). Further, a differentiation between the previous experimental methods and the method developed in this study is made. Based on the new method, the influence of different clamping conditions on joint parameters of collet holders and thereby on dynamical behavior is presented. Afterwards, the generality of the identified parameters is demonstrated. Therefore, two machine tools are modeled and in each case a collet holder is clamped into the machine tool. For different blank tools the predicted dynamical transfer functions at the tool tip are compared with tool-tip measurements. Mathematical modeling Theory of receptance coupling In this section, a brief review of the RCSA method is presented based on the previous literature [23,24]. The basic receptance coupling equation for the rigid coupling of two structures in a free– free condition is presented in Eq. (1): # " ðHA;11 HA;12 ðH2 Þ1 HA;21 Þ ðHA;21 HA;12 ðH2 Þ1 HA;22 Þ F 1 X1 ¼ X2 ðHA;21 HA;22 ðH2 Þ1 HA;21 Þ ðHA;22 HA;22 ðH2 Þ1 HA;22 Þ F 2 (1) The displacement vector X is for translational and angular displacement components. Force vector F includes the force and moment applied at position 1 and 2. HA,ij are the generalized receptance matrices between the positions i and j. However not every connection can be assumed as inflexible like depicted in Fig. 1. To consider the stiffness and damping between such connections H2 can be modified with the complex stiffness matrix K: H2 ¼ HA;22 þ HB;22 þ K 1
Complex stiffness matrix contains interface parameters between two substructures and can be expressed by the translational stiffness kyf and damping cyf and the rotational stiffness kuM and cuM damping [16]. kyf þ ivcyf 0 (3) K¼ 0 kuM þ ivcuM Including contact dynamics, elastic coupling of two substructures can be expressed as follows:
hA11;ff h11;fM ¼ h11;MM hA11;Mf hA21;ff h21;fM ¼ h21;MM h A21;Mf hA22;ff h22;fM ¼ h22;MM hA22;Mf
are identified using experimental methods. These determined contact parameters will be valid only for the investigated setup. Thus, the advantage of the idea of receptance coupling does not longer exist.
(2)
hA12;ff hA11;fM hA11;MM hA12;Mf hA12;ff hA21;fM hA21;MM h A12;Mf hA22;ff hA22;fM hA22;MM hA22;Mf
hA12;fM hA21;ff ½H 1 hA12;MM 2 hA21;Mf hA12;fM hA21;ff ½H2 1 hA12;MM h A21;Mf hA22;fM hA22;ff ½H2 1 hA22;MM hA22;Mf
hA21;fM hA21;MM hA21;fM hA21;MM hA22;fM hA22;MM
(4)
In Eq. (4), subscript ff represents linear displacement–force, fM represents linear displacement–moment, Mf represents angular displacement–force and MM represents angular displacement– moment.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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3
Fig. 1. Rigid coupling of two substructure.
Identification of contact dynamics at the holder–tool interface
i1 Hht;11 ¼ Ht;11 Ht;12 Ht;22 þ Hh;22 þ ½K 1 Ht;21
Fig. 3. Schematic representation of fitting measurement and model.
Geometry y Information Material Propertiess Analysis Parameterrs
Algorithm Ht,11
Ht,12
ky
k
Ht,21
Ht,22
cy
c
substructure A
Hh,11
Hh,122
Hh,21 Hh,222
Joint Dynamics
substructure B
Hht,11
Hht,122
Hht,21 Hht,222
(5)
Output
Beam Theory
Input
RCSA
First the different sections of holder and tool are calculated analytically by Timoshenko beam theory [25]. Based on the RSCA method these sections are coupled rigidly and receptance matrix for tool–holder (Hh) and tool (Ht) for the free-free case are obtained. Finally holder receptances are coupled with the tool receptances elastically as shown in Fig. 2. Afterwards, end point FRF of the tool holder–tool assembly is measured at free–free end conditions. In order to satisfy free–free end conditions, holder–tool assembly is suspended by elastic ropes. Also holder–tool assembly is excited by an impact hammer and the response of the system is measured by laser vibrometer. It is possible to model this linear displacement–force tool-tip measurement by a single equation. Using the elastic coupling procedure given in Eq. (4) receptance matrix at the tool tip can be expressed as follows:
substructure C
where Hht;11 ¼
hht;11;ff hht;11;Mf
hht;11;fM hht;11;MM
EMA
(6)
As shown in Eq. (5), hht,11,ff can be expressed analytically using unknown contact parameters at holder–tool interface. The measured and calculated hht,11,ff are compared inside a fitting algorithm. This algorithm optimizes the absolute percentage difference between both FRFs, as shown in Fig. 3. Therefore, the four unknown contact parameters are used to minimize the deviation of both FRFs in a fixed range around the amplitudes. Different to previous approaches each determined frequency over a wide frequency spectrum is regarded instead of only the first dominant amplitude. For this purpose a nonlinear optimization function is used. The stiffness and damping values, which result in smallest differences, are the identified contact parameters. An overview of the approach is shown in Fig. 4. Experimental verification for identification of contact dynamics
hht,11,ff
fitting Algorithm m
Fig. 4. Overview of the joint identification approach.
Then identified parameters are used to predict end point FRFs of various holder and tool combinations. Tool dimensions used in identification are given in Table 1. Tool diameter is represented by Øtool, oltool represents tool length outside the holder, iltool represents tool length inside the holder and lholder represents total length of the holder. The identified translational and rotational stiffness and damping are given in Fig. 6. Note that in five different cases given in Table 1, tool lengths inside the holder are kept constant. Therefore, the only parameter affecting the contact area at holder– tool interface is tool diameter. Thus, the identification results given in Fig. 6 reflect the effect of tool diameter on contact parameters.
To verify the method, first contact parameters for five different carbide beams are identified using proposed method. The used free-free measurement arrangement is depicted in Fig. 5.
Fig. 2. Tool and tool–holder coupled by stiffness matrix.
Fig. 5. Free–free measurement arrangement for joint identification.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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Table 1 Assembly parameters for various carbide tool diameters. Øtool [mm] oltool [mm] iltool [mm] lholder [mm]
7.94 62.30 40.00 129.9
9.53 62.60 40.00 128.4
Table 2 Measurements and simulation with different tool lengths.
11.11 62.80 40.00 126.6
12.70 62.30 40.00 129.0
16.00 75.40 40.00 130.3
Øtool
oltool
v1
v2
v3
v1
v2
v3
[mm]
[mm]
[Hz]
[Hz]
[Hz]
[Hz]
[Hz]
[Hz]
7.94
24.9 113.5 23.8 114.2 30.3 114.9 37.0 113.2
7857 627 8838 780 6942 941 5761 1151
11,200 3204 12,020 3738 11,695 4233 11,460 4937
– 8470 – 9505 – 10,110 – 10,550
7820 623 8931 769 6940 930 5809 1129
11,280 3237 11,930 3749 11,940 4224 11,400 4919
– 8518 – 9499 – 10,120 – 10,550
9.53
The identified translational stiffness (Fig. 6a) of the Ø7.94 mm tool is 3.44e8 N/m and increase until a tool diameter of Ø16 mm to 1.43e9 N/m. During same range the rotational stiffness (Fig. 6b) increases from 2.54e4 Nm/rad to 2.45e5 Nm/rad. The almost constant translational stiffness of the first three diameters can be explained by various clamping conditions. Each collet can fix tools in a specific range of diameters. Dependent on the tool diameter the range changes how far the collet fits into the holder. For ER32 holder a difference of more or less 5 mm is possible. Thereby, clamping conditions inside the interface change. For example the effected clamping surface and the pressure distribution are varying. However, identification of damping parameters inside the contact interface is more difficult. Damping is low and height of amplitude varies between every measurement. This could be due to the free-free measurement arrangement. Both damping values increase with an increasing diameter. Bigger outliers can only be noticed for rotational damping of the Ø9.58 mm tool (Fig. 6d). But due to the fact that magnitude is varying and damping is low enough that it does not affect the modeling of spindle–holder–tool assembly, we neglect the damping in further research. In order to check the accuracy of the identified contact parameters, different tools with different outer lengths are clamped to the holder while inner length kept the same like during the identification. Then, end point FRFs are calculated for new holder–tool combinations at free–free end conditions using previously identified contact parameters. Afterwards, the measurements are compared with predicted FRFs, summarized in
8
x 10
3.0
Rotational Stiffness
Translational Stiffness
15
N/m
5
0
a)
8
10
12
mm
Ns/m 150 100 50 0 6
1.5 1.0 0.5 8
10
12 mm 16
Tool Diameter
0.14
Rotational Damping
Translational Damping
250
c)
2.0
b)
Tool Diameter
5
Nm/rad
0
16
x 10
8
10
12
14 mm 18
Tool Diameter
Nms/rad 0.10 0.08
11.11 12.70
Measurement
Predicted
Table 2. For each diameter a shorter and longer tool is examined. The identified contact parameters are showing good results. With one exception each deviation is below 2%, which is an indication that models and parameters are correct. Differentiation to classical optimization based on tool point FRF measurement In this study, contact parameters are identified using measured end point FRFs of holder–tool assembly at free-free end conditions. Different than the proposed method, in literature, contact parameters are often identified using tool point FRFs measured on machining centers. This approach might lead to different sets of solutions depending on the local minimum of the optimization method. In order to compare these two different approaches, first holder–tool assembly is clamped to machining center and tool point FRF is measured. In addition spindle dynamics is identified experimentally using the identification procedure proposed by Namazi et al. [10]. Then analytically calculated holder–tool receptance matrices are coupled with the experimentally obtained spindle receptances and tool point FRF is obtained. Note that, comparison of different optimization techniques is accomplished by using different contact parameters in the elastic coupling of holder and tool dynamics as given in Table 3. Among given contact parameters sets given in Table 3, the curve fitted set is obtained by using free–free FRF measurement and the proposed identification approach. On contrary, these three remaining parameter sets are obtained by using a measurement performed on machining center. Therefore, the stiffness and damping values are changed manually until a good match between measurement and model is obtained. Calculated tool point FRFs using different contact parameters are given in Fig. 7 with the measured tool point FRF. As shown in Fig. 7, frequencies show a good match for each FRF and even magnitude differences are acceptable for each set. Thus, it can be assumed that the four parameter sets provide good results for the spindle–holder–tool assembly. But problems become apparent, if these parameters are used to predict dynamical behavior of the holder–tool free–free assembly. For that purpose, dynamics of the same holder–tool assembly given in Fig. 7 is obtained analytically and experimentally for freefree end conditions. Similarly during the analytical model holder
0.06 0.04
Table 3 Different parameter sets for holder–tool interface.
0.02
kyf
k um
cyf
cum
[N/m]
[Nm/rad]
[Ns/m]
[Nms/rad]
3.52E + 08 4.00E + 07 5.00E + 12 6.50E + 06
3.96E + 04 4.60E + 04 3.89E + 04 6.00E + 12
– – – 10
0.0097 – 0.018 3000
d)
0 6
8
10 12 14 mm 18
Tool Diameter
Fig. 6. Translational and rotational stiffness and damping for different tool diameters.
Curve fitted set Manual set 1 Manual set 2 Manual set 3
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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x 10
5
-4
1.2 measurement curve fitted set manual set 1 manual set 2 manual set 3
Magnitude
m/N 0.8 0.6 0.4 0.2 0
0
2000
4000
6000
Hz
10000
Frequency
Fig. 10. Free–free measurement for holder–tool and predicted FRF with different parameter contact sets (short tool Ø9.53 mm).
not represent the real interface parameters. But only one set can be used to calculate the model for different tool lengths. Furthermore, it is possible that errors during spindle identification will be compensated by contact parameters, if the spindle–holder–tool assembly is used to identify these parameters. Investigation of the effect of clamping parameters to contact dynamics Clamping torque In the following step the effect of various clamping torque on contact parameters are studied. Thus, the five carbide beams from Table 1 are mounted inside the holder. For each diameter clamping torque is changed in four steps from 95 Nm to 155 Nm. Thereby, a torque of 135 Nm is recommended by the manufacturer and 155 Nm is the permitted maximum. For each case interface parameters are identified. All diameters show a similar behavior during the variation of clamping torque. The investigated first and second eigenvalue are increasing if a rising clamping torque is used. This is depicted in Fig. 11 for the Ø11.11 mm beam.
Translational Stiffness
and tool are coupled using different contact parameter sets given in Table 3. The measured and predicted FRFs for free–free end conditions are given in Fig. 8. For this case the outer tool length is 114 mm. As seen from Fig. 8, in free–free end conditions higher modes of the system becomes visible in the frequency range of interest and accuracy of different contact parameter sets becomes visible. Although all contact parameter sets provide accurate predictions for the first mode, only curve fitted set gives accurate predictions for the remaining modes. Since first mode is the dominant mode that determines the stability and inaccuracy in higher frequencies does not cause wrong stability predictions researchers often do not pay attention to the accuracy of the identified contact parameters. However, if we use contact parameters for various tool lengths, the difference and accuracy becomes clear. For that purpose, same contact parameter sets given in Table 3 are employed in the modeling of different holder–tool combinations. In these cases, tool length outside the holder is changed. But in order to keep contact area same in all cases, tool length inside the holder and tool diameter is kept as 40 mm and 9.53 mm respectively. Calculated tool point FRFs for tool stick out length of 63 mm and 24 mm are given with the measured FRFs in Figs. 9 and 10 respectively. As seen from Fig. 9, again only the identified parameters provide accurate predictions for all modes in the frequency range. Parameter set 3 does not lead to the right behavior even for the first mode. Although parameter set 1 gives accurate predictions for the first mode, errors in second mode is large enough to produce an error for the stability. Therefore, contact parameter sets 1 and 3 lose their applicability for decreased tool length. Finally as seen from Fig. 10, when the tool length outside the holder decreased to 24 mm, contact parameter set 2 loses it prediction accuracy and only identified contact parameters continue to provide accurate FRF predictions. Therefore, it should be noted that it is possible to model a specific system with different parameter sets, which are
Fig. 9. Free–free measurement for holder–tool and predicted FRF with different parameter contact sets (medium tool Ø9.53 mm).
a) Fig. 8. Free–free measurement for holder–tool and predicted FRF with different contact parameter sets (long tool Ø9.53 mm).
4.0
x 10
8
Rotational Stiffness
Fig. 7. Tool tip measurement and predicted FRF with different parameter sets.
N/m 3.0 2.5 2.0
100
120
Torque
Nm
160
b)
7.0
x 10
4
Nm/rad 6.0 5.5 5.0
100
120
Nm
160
Torque
Fig. 11. Translational and rotational stiffness for various clamping torque (Ø11.11 mm).
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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CIRPJ-354; No. of Pages 9
v1
v2
kyf
k um
[Nm]
[Hz]
[Hz]
[N/m]
[Nm/rad]
7.94
95 115 135 155
1692 1694 1694 1695
9104 9111 9116 9120
3.29E + 08 3.33E + 08 3.36E + 08 3.36E + 08
2.32E + 04 2.33E + 04 2.34E + 04 2.35E + 04
9.53
95 115 135 155
1997 1998 2004 2006
9754 9780 9814 9837
3.19E + 08 3.35E + 08 3.52E + 08 3.66E + 08
3.90E + 04 3.90E + 04 3.96E + 04 4.00E + 04
11.11
95 115 135 155
2295 2299 2306 2311
10,010 10,050 10,110 10,170
2.90E + 08 3.06E + 08 3.29E + 08 3.51E + 08
6.00E + 04 6.05E + 04 6.13E + 04 6.19E + 04
95 115 135 155
2693 2702 2706 2712
10,290 10,320 10,340 10,350
5.52E + 08 5.82E + 08 6.28E + 08 6.59E + 08
1.01E + 05 1.03E + 05 1.04E + 05 1.05E + 05
95 115 135 155
2601 2606 2612 2614
9461 9478 9475 9484
1.29E + 09 1.31E + 09 1.35E + 09 1.35E + 09
2.44E + 05 2.48E + 05 2.53E + 05 2.54E + 05
12.70
16.00
Over the complete torque range v1 has changed from 2295 Hz to 2311 Hz. Meanwhile, v2 increased from 10,010 Hz to 10,170 Hz, which means the difference for both eigenvalues is less than 1.6%. This deviation is similar for each tool diameter, presented in Table 4. Therefore, it can be noted that the influence of clamping torque is low for this holder and tool connection. Although the change of eigenvalues is low, the percentage difference for stiffness parameters is huge. For example, the translational stiffness of the Ø12.7 mm beam changed during the investigated range from 5.5e8 N/m to 6.6e8 N/m, which is a difference about 20%. This is based on the fact that the connection is very inflexible. The stiffness parameters are high and approximate asymptotically to behavior of rigid connection. Clamping length
Trans. Stiffness
8
Ø9.53
N/m 3
a)
c)
x 10
12
40
x 10
8
mm
20
Ø12.7
N/m 10
40
mm
20
Clamping Length
Trans. Stiffness
5
8
x 10
8
Ø11.11
N/m 6
b) Trans. Stiffness
Trans. Stiffness
To investigate the effect of clamping length (tool length inside the holder) variation, contact parameters for three different inner lengths are identified. Therefore, the clamping length is reduced from the full size of 40 mm to 20 mm. But different clamping lengths have a low effect on translational stiffness. For a tool diameter of Ø9.53 mm, Ø11.11 mm, Ø12.7 mm and Ø16 mm the stiffness is almost constant, depicted in Fig. 12.
30
40
x 10
8
mm
20
Ø16
x 10
4
Nm/rad 3
a) 12
40 x 10
4
mm
d)
20
20
Nm/rad 10
40
mm
Nm/rad 6 30
20
mm
20
mm
4
Ø16
40
20
mm
20
Clamping Length
d)
Fig. 13. Rotational stiffness for various clamping length (a) tool Ø9.53 mm tool, (b) Ø11.11 mm, (c) Ø12.7 mm and (d) Ø16 mm tool.
A similar behavior is noticeable for rotational stiffness. The Ø9.53 mm and Ø12.7 mm tool have a maximum for 30 mm. The stiffness of the Ø11.11 mm tool decrease for a decreasing clamping length, while the Ø16 mm tool shows an opposite behavior, shown in Fig. 13. The influence of various clamping length is not as big as maybe expected. A reason for this is that the clamping interface can be modeled as two springs in series, depicted in Fig. 14. The total stiffness can be calculated with following equation: K ges ¼
k1 k2 k1 þ k2
(15)
The outer surface is bigger and therefore should be the stiffness k1 in this area smaller. Consequently, a change of k2 has a lower influence on the total stiffness. This demonstrates again the modeling problems for a clamping interface of a collet chuck connection. Similar to the varying holder length, the pressure distribution may change during modifying the clamping length. Thereby, contact parameters can be unpredictably influenced. Material Besides carbide tools, tools made of HSS are often used for milling and drilling operations. Therefore, differences for identified contact parameters are investigated between both materials. The stiffness’s of four assemblies, close to those from Table 1, are determined. HSS tools show the same trend like carbide beams for an increasing diameter, shown in Fig. 15. Again the constant stiffness for the first three diameters can be explained by various clamping conditions. The difference between both materials varies between 10% for the Ø9.54 mm tool and 31% for Ø12.70 mm tool. The rotational stiffness shows even a bigger deviation. Except for the Ø12.7 mm tool, each difference is over 45%. It is already known the identification of translational and rotational stiffness is very sensitive. But these differences are too great to ignore. It can be expected that it is not possible to transfer identified contact parameters for one of both materials without any bigger error. Therefore, various materials should be investigated separately. collet k1
40
40 x 10
Nm/rad
20
Clamping Length
c)
Ø11.11
x 10
8
b)
Ø12.7
holder N/m
4
Ø9.53
Rot. Stiffness
Torque
[mm]
5
Rot. Stiffness
Øtool
Rot. Stiffness
Table 4 Eigenvalues and stiffness for various clamping torque.
Rot. Stiffness
W. Matthias et al. / CIRP Journal of Manufacturing Science and Technology xxx (2016) xxx–xxx
6
tool
k2
Clamping Length
Fig. 12. Translational stiffness for various clamping length (a) tool Ø9.53 mm tool, (b) Ø11.11 mm, (c) Ø12.7 mm and (d) Ø16 mm tool.
Fig. 14. ER 32 holder–tool interface model with springs in series.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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x 108
14 carbide HSS
N/m
Rotational Stiffness
Translational Stiffness
8
6 5 4 3
a)
2
8
10
mm
Tool Diameter
14
x 104
Table 5 Different tool assemblies for tool-tip measurement inside Mori Seiki machine.
carbide HSS
Nm/rad
Øtool
10
Medium tool
Long tool
Stiffness
iltool
oltool
iltool
oltool
kyf
k um
8
[mm]
[mm]
[mm]
[mm]
[mm]
[N/m]
[Nm/rad]
6
7.94 9.53 11.11 12.7 16.0
40 40 40 40 40
62.5 62.5 62.8 62.3 75.7
40 40 40 40 –
113.5 114.2 114.6 113.2 –
3.36e8 3.52e8 3.29e8 6.28e8 1.35e9
2.34e4 3.96e4 6.13e4 1.04e5 2.53e5
4 2
b)
7
0
8
10
mm
14
Tool Diameter
Fig. 15. Translational and rotational stiffness of carbide and HSS beams.
Prediction of tool point FRFs on machine tools The identified contact parameters are verified for two different machine assemblies. Therefore, various holder–tool setups are mounted into Mori Seiki machine. Later similar setups are clamped into the Quaser UX600. Tool-tip measurements are performed for each case and the results are compared with predicted FRFs, obtained by RSCA method. Case study 1 In this case study different holder–tool combinations are clamped to Mori Seiki NT3150 DCG machining center. For the analysis medium and long carbide tools are used with a full clamping length of 40 mm. The recommended clamping torque of 135 Nm is applied. Short tools are neglected because the main amplitude is located in a high frequency range. In this area noise of the identified spindle FRF distort the prediction made by RSCA. The modeling parameters of different cases are presented in Table 5. First spindle dynamic of the machining center is identified using the method proposed by Namazi et al. [10]. Analytically calculated holder–tool assembly is coupled with experimentally obtained spindle dynamics. Note that, holder and tool are coupled using contact parameters which are identified previously using
free–free measurements. Calculated tool point FRFs are given in Fig. 16 with the experimentally measured FRFs. As shown in Fig. 16, tool point FRF can be predicted accurately using RCSA method with previously identified contact parameters. Only the long Ø11.11 mm and Ø16 mm tool have with 3% a bigger frequency deviation. Even three of the tested setups show a difference lower than 1%. The excepted magnitude fits for the most cases. But if two modes are located close together, the RSCA model has problems to predict the correct amplitude for both mode. This can be noticed for the tool length of 63 mm in Fig. 16a. The tool-tip measurement of the long Ø7.94 mm tool has also a variation to the predicted magnitude. The measured amplitude is 50% higher than expected. A bigger difference is also noticeable for the medium Ø12.7 mm tool in Fig. 16d. The amplitudes of predicted and measured FRFs differ about 100%. Even if the already low damping parameters are neglected, it is not possible to improve the fitting. Consequently, it might be reasonably assumed that the deviation is based on modeling errors. The main problem is the identification of the spindle FRF. It is not possible to excite each frequency with an impact hammer test. During the investigation it could be noticed that for some frequency ranges the prediction error is bigger as for other frequencies. For example the position and amplitude of the eigenvalue fits well after changing the outer length of the medium Ø12.7 mm tool about 10 mm. Because with bigger tool length frequencies shift in a lower area without spindle identification limitations.
Fig. 16. Predicted and measured tool tip FRF for medium and long tools with different diameters on Mori Seiki NT3150 DCG.
Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005
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CIRPJ-354; No. of Pages 9 W. Matthias et al. / CIRP Journal of Manufacturing Science and Technology xxx (2016) xxx–xxx
8
Fig. 17. Predicted and measured tool tip FRF for medium and long tools with different diameters on Quaser UX600.
Case study 2 In this case study different holder–tool combinations are clamped to Quaser UX600 machining center. Similar to case study 1, spindle dynamics is identified experimentally and analytically obtained holder–tool assembly is coupled with experimentally obtained spindle dynamics. For the holder–tool interface, again previously identified contact parameters are employed. The Mori Seiki and the Quaser machine have a different spindle interface. Therefore, a different ER32 holder is used, similar to the previous one. The collet interface is the same, thus it is assumed that contact parameters are identical. For the analysis same carbide tools are used like before, presented in Table 5. Calculated tool point FRFs are given in Fig. 17 with the experimentally measured FRFs. Results show that the prediction of the dynamical tool-tip behavior matches well with the measurements. For each case the frequency deviation is lower than 2%. The only exception is the medium Ø9.53 mm tool, which has a frequency error of 3%. However, the excepted magnitude fits for most cases. Only the medium Ø12.7 mm tool shows a bigger error. Similar to the case study 1, the RSCA model has problems to predict the correct magnitude for two close modes. Furthermore, a bigger difference is noticed for the medium Ø7.94 mm tool. This variation is again based on the spindle identification. As with the Mori Seiki machine, it is maybe not possible to excite every frequency with an impact hammer test. But in general the prediction based on Timoshenko beam models and identified interface parameters shows again acceptable results. Conclusion In order to predict chatter stability, tool point FRF should be measured. But, when the number of holder–tool combinations in machine shop is considered, it is difficult to perform experiment for each combination. Therefore, compared to experimental techniques, RCSA provides an efficient tool to predict tool point FRFs since it eliminates the experimental dependency. However, accuracy of the RCSA method depends on the contact parameters at the holder–tool interface. Thus, for better stability predictions, contact parameters should be included in modeling procedure.
In this paper, an identification method for contact parameters at holder–tool interface is presented. In the method proposed contact parameters are identified using analytically calculated and experimentally obtained end point FRFs of the holder–tool assembly at free-free end conditions. Using the method, contact parameters for various tool lengths were identified. The accuracy of the determined parameters was demonstrated by varying the outer tool length. Based on the identified contact parameters two different machining centers were modeled and compared with tool-tip measurements which are shown a good correlation. Further, it was demonstrated that it is possible to model a specific system with different contact parameter sets. But only one set which is obtained using the identification method proposed can be used to calculate the model for various tool lengths. In addition, effects of geometric parameters such as tool diameter, tool material, tool length inside holder and clamping torque on contact parameters are investigated. For instance, it was shown that stiffness increase for an increasing tool diameter, whereas various clamping torque has negligible effects on contact parameters. Furthermore, experimental results demonstrate that material properties also affect stiffness between holder and tool. The influence of changing clamping length is low for ER32 holder. This is because the collet has two contact surfaces and thereby it is possible to model the connection by two springs. This should be considered in further investigations. Based on the proposed approach in this paper, extensive contact parameters studies can be made for other connection concepts.
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Please cite this article in press as: Matthias, W., et al., Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface. CIRP Journal of Manufacturing Science and Technology (2016), http://dx.doi.org/10.1016/j.cirpj.2016.02.005