Contents

1 Notation 5

2 Background and introduction 6

2.1 Background………………………………………………………………………… 6

2.2 Aim and scope…………………………………………………………………….. 7

2.3 Methodology………………………………………………………………………. 7

3 Theory 8

3.1 Chatter Vibrations……………………………………………………………….. 8

3.2 Chatter stability objective……………………………………………………… 9

4 Parting and Grooving Operation 10

4.1 General information……………………………………………………………. 10

4.2 Mathematical models of cutting force…………………………………… 10

4.3 Chip formations…………………………………………………………………. 10

5 Simulation approach 11

5.1 Modelling…………………………………………………………………………. 11

5.2 Simulation results………………………………………………………………. 11

6 Damper suggestions 11

7 Conclusions 11

8 Future work 11

Appendices

1 Notation

2 Background and introduction

2.1 Background

Metal cutting is an important process in the way of shaping steal and manufacturing industries. There is some different cutting methods for an example milling, drilling, boring, turning, parting and grooving this project is mainly about the grooving and parting equipment.1

Parting and grooving is an operation where the material to be cut is spinning around and the cutting blade is pushed to the surface. Parting is the operation preformed when the material is cut of and is usually preformed in the end of the metal cutting operation. Grooving is done to make grooves externally or internally on the material.2

This form of metal cutting has a long overhang and are sensitive to chatter vibrations. When this happens, the surface finish is getting bad and the tool is getting damaged. According to Tobias 3 there are three different vibrations in machine tooling

· free vibration

caused by shocks from eater other machines transmitted from the foundation or from imbalances in the machine.

· forced vibration

Is a periodical imbalance in the machine caused by varying forces caused by unbalance in rotary or gears for an example?

· self-induced vibration

is caused by the machine tooling itself or by other self-induced forces in the machine.

All types of vibrations are important for the surface finish but self-induced vibrations are the vibration of interest in this thesis. This effect in machine cutting is called chatter vibration and in machine tooling it is caused mainly by varying chip load do to vibrations. It is effecting the surface finish and the tool life time negatively.3

2.2 Aim and scope

The main purpose of this thesis is to create a simulation model that can be used to evaluate damping solutions in parting and grooving operations. Investigate if material form the tool body itself can be used as a passive damper and have a positive effect on the stability of the cutting tool. Regarding stability in the metal cutting operation, this model is intended to be a tool to evaluate damping solutions in parting and grooving.

In the Parting operation, the following questions are to be answered:

· What modes are of interest in the specific tool?

· What natural frequencies are of interest in the specific tool?

· What impact dose a specific damper solution have on the tool?

· How can the damper be simulated?

The model should be able to in a fast way evaluate the efficiency of a chatter damping solution before physical testing.

2.3 Methodology

The work in this master thesis has been divided into four sections in order to get an overline of the work, and also obtain the basic knowledge of the methods used. The project is divided into following four parts:

· Theoretical studies within the field of reduction of the chatter vibration during the parting and grooving operation and substructure for the simulation of the tested structure in time domain and frequency domain using FRF coupling.

· Perform simple substructure of MDOF system, including the stability lobes plot and stable and unstable vibration simulation, to evaluate the tested structures in MATLAB.

· Perform measurement on the desired structure with and without the designed damper, such as the holder of the cutting tool and use this data for substructure.

· Measurements on complete structure to verify that the developed method of damper effectively reduce the regenerative vibration.

MATLAB has been used in the calculations needed to substructure and also has been used to evaluate the results.

3 Theory

3.1 Chatter Vibrations

Chatter vibration is caused by a regenerative between the metal cutting tool and the workpiece and is a problem to reach maximum removal rate. Chatter vibrations result in large relative displacement between the tool and the workpiece during machining. This is resulting in bad surface finish and high tool where.4

The biggest cause of this effect is the dynamic chip thickness which creates a wavy surface area on the work peace as in Figure 3-1. When the tool and the workpiece is not in phase, chatter vibration makes the chip thickness to grow exponentially when oscillation is closing to the structures natural frequency. Causing the chatter vibration may be dynamic chip thickness or mode couplings.5, 6

Figure ?3?1 Regenerative chatter effect in turning.

The vibration in the chip thickness is caused by a phase shift in vibration marks left on the machined surface between two consecutive cuts. The phase shift depends on the dynamics of the tip of cutting tool assembly. Furthermore, the dynamic chip thickness leads to the cut forces to vary1 with time.

Chatter vibrations can be described as a model in the cutting process do regard orthogonal turning of a disk where the tool is fed in the radial direction of the disk. When the workpiece has turned on full rotation the wavy surface will result in a vibration in chip thickness (h(t)) as can be seen in Figure 3-1 and the chip thickness starts with deviating dynamically from its static value (h0). The phase shift (?) between the previous and currently cut surface is generated by this process. The inner wave (y(t)) and outer wave (y(t-T)) respectively represent the current and previously cut surface.

3.2 Chatter stability objective

The chatter stability of the tool vibration can be divided into three forms. The first case is a stable form where the vibration is damped out over time and the amplitude of the vibration diminishes. The second case shows an unstable form where the vibration amplitude grows large over time. The third case is when the vibration keeps critically stable with undamped and ingrown vibration amplitude. Mathematically, these three cases are dependent on the real part of the root of characteristic equation of transfer function and the stability boundary where the system stays in critically stable with respect to the depth of cut, alim, can, for details see 1 be shown by

(1)

where Kf is the cutting force coefficient, R(H(?)) the real part of relative FRF between tool and workpiece, and ? the chatter frequency. Here it can be seen that only negative values of the real part of FRF, R(H(?)), can produce the valid positive value of alim. The spindle speed (n) and the number of waves (k) is related to the frequency (?) by using the follow stability law proposed by Tobias 3:

(2)

where k is the integer number of waves.

The expression (1) indicates that the depth of cut (alim) is inversely proportional to the flexibility of the structure in the radial direction which means the cutting tool in this paper and to the cutting force coefficient (Kf) that is dependent to the work material, thereby the harder the work material is, the larger the cutting force coefficient has, thus reducing the depth of cut. In other words, reducing the depth of cut causes the negative effects on the productivity as well.

4 Parting and Grooving Operation

4.1 General information

In parting and grooving the work material is rotating and the cutting tool is feed radially on the material.

Parting is mainly the operation done to cut a material of straight true. This operation implies that if the spindle speed stays the same the cutting speed will gradually decrease to zero. Decreasing of the cutting tool is not good for the cutting edge and will damage the cutting edge. add reference from Sandvik

Add figure of cutting tool

Assume that

4.2 Mathematical models of cutting force

As is mentioned in Section 3.1, the dynamic chip thickness causes change of the

4.3 Chip formations

5 Simulation approach

5.1 Modelling

5.2 Simulation results

6 Damper suggestions

7 Conclusions

8 Future work