Receptance coupling based algorithm for the identification of contact parameters at holder–tool interface

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Abstract

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.

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], [4], [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 machine. Thus, tool point FRF measurement is required for each combination of tool and holder. But this approach is very time-consuming and increases the downtime of the machine and therefore the production costs. For this reason [7], [8], [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], [15], [16], [17], [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. 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], [21], [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 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.

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.

Section snippets

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):X1X2=(HA,11HA,12(H2)1HA,21)(HA,21HA,22(H2)1HA,21)(HA,21HA,12(H2)1HA,22)(HA,22HA,22(H2)1HA,22)F1F2

The displacement vector X is for translational and angular displacement components. Force vector F includes the force and moment applied at position 1 and

Experimental verification for identification of contact dynamics

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.

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

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

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

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.

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

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