﻿ Kinematics of Selected parts of metal Cutting machine

### Kinematics of Selected parts of metal Cutting machine

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## Kinematics of Selected parts of metal Cutting machine

1Faculty of Mechanical Engineering, Department of Applied Mechanics and Mechatronics, Technical University of Košice, Letná 9, Košice, Slovak Republic

### Abstract

This article deals with kinematics of mechanical part of lathe in cases of highest and lowest speeds during machining for selected parts of the machine. Calculations are made or cut in startup mode in steady state. Not stated all calculations because of their large-scale. Calculations are for real machine tool, which is used in workshop practice. Analogy, it can do the same when other machine in which the gear unit and the various modes of operation.

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• Filas, Jozef, and Vladimír Marton. "Kinematics of Selected parts of metal Cutting machine." American Journal of Mechanical Engineering 1.7 (2013): 241-245.
• Filas, J. , & Marton, V. (2013). Kinematics of Selected parts of metal Cutting machine. American Journal of Mechanical Engineering, 1(7), 241-245.
• Filas, Jozef, and Vladimír Marton. "Kinematics of Selected parts of metal Cutting machine." American Journal of Mechanical Engineering 1, no. 7 (2013): 241-245.

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### 1. Introduction

The use of metal cutting machines as well as lathes for machining components from various materials with different dimensions requires the drive of lathe to be able to change the cutting speed on the surface of the machined component.

It is therefore very important to know the kinematics of motion of the whole machine part of lathe, but also its individual members.

In this paper we focus on the calculation of selected kinematic parameters of the parts of lathe connected so that the spindle of lathe had the intended rates. We focused on two parameters: the minimum speed and the maximum speed. Analogy would be followed for any other speed.

Figure 1 shows an overall view of specific type of center lathe, which will undergo partial kinematic analysis.

Figure 1. Center lathe

The lathe is intended for various uses. Machining of outer surface of cylinders and cones, machining by copying, coils production, shaping by grooving tools and so on.

Figure 2, Figure 3, Figure 4 show other parts of the lathe.

Figure 2. Transmission of the lathe
Figure 3. Levers for setting the rates
Figure 4. Belt pulleys on engine and transmission

### 2. Transfer of Drive from Engine to Head of the Lathe

Transmission of lathe has multiple shafts. Overall simplified schema of the drive is illustrated on Figure 5.

Figure 5. Schema of lathe’s drive

Table 1 shows rates of lathe’s head depending on levers setting Figure 3.

### 3. Calculation of Kinematic Parameters

3.1. Calculation of Kinematic Parameters for the Fastest Gear

Input (motor) is 1750 rates per minute and by multistage transmission, illustrated on Figure 6, head of the lathe reaches 2000 rates per minute.

Figure 6. Positioning of shafts and wheels in transmission

Figure 7 shows a simplified schematic view of mutually meshing cogwheels positioned on multiple shafts.

Figure 7. Schema of meshing cogwheels

Calculation of transfer ratio (uR), angular velocities (ω), tangential (at) and normal components (an) accelerations on circumferences of individual cogwheels goes as following:

Transfer number:

 (1)

Wheel on shaft S:

 (2)

Wheels on shaft A:

 (3)

Wheels on shaft B:

 (4)

Wheel on shaft C:

 (5)

Figure 8, Figure 9, Figure 10, Figure 11 illustrate kinematic parameters of points on circumferences of meshing cogwheels on the transmission.

Figure 8. Shaft S
Figure 9. Shaft A
Figure 10. Shaft B
Figure 11. Shaft C
3.2. Calculation of Kinematic Parameters for the Slowest Gear

Rate of motor at the beginning of kinematic chain is 1750 rates per minute, which is transformed in transmission to 12 rates per minute on head of the lathe.

Figure 12 shows schema of positioning of shafts and cogwheels for the slowest gear.

Figure 12. Positioning of shafts and cogwheels in transmission

Figure 13 shows simplified schema of mutually meshing cogwheels, which are positioned on multiple shafts.

Figure 13. Schema of cogwheels connection

Transfer number:

Transfer from motor to shaft S:

Input rates to transmission:

Wheel on shaft S:

 (6)

Calculations of kinematic variables on shafts A, B, D, Care analogous calculations in Section 1.3.

Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 illustrate kinematic parameters of point on circumferences of mutually meshing cogwheels in the transmission.

Figure 14. Shaft S
Figure 15. Shaft B23
Figure 16. Shaft D
Figure 17. Shaft B78
Figure 18. Shaft C

### 4. Conclusion

Similarly, it would be possible to determine the selected kinematic variables for other modes work machine Results can be verified by other methods of kinematics.

### Acknowledgement

The works has been accomplished under the research project VEGA 1/1205/12 Numerical modelling of mechatronic systems.

### References

 [1] Jančina,J., Pekárek, F.,: MECHANIKAII-KINEMATIKA. Bratislava, 1987. In article [2] Medvec, A., Stradiot, J., Záhorec, O., Caban, S.,: MECHANIKAIII-DYNAMIKA, Bratislava 1996. In article [3] Šimčák,F.,Trebuňa,F.,:METÓDYEXPERIMENTÁLNEJANALÝZYNAPATOSTI, Košice, 2011. In article [4] Šolek, P.,: TECHNICKÁMECHANIKA. Bratislava, 2009. In article [5] Marton,V.,: Kinematickáanalýzapohonuobrábaciehostroja (Bakalárska práca), SjF TU Košice, 2013. In article