Kinematics of Selected parts of metal Cutting machine

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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

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Figure 3. Levers for setting the rates

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Figure 4. Belt pulleys on engine and transmission

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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

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

Table 1. Output rates (min^-1)

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Tables index

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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

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

Figure 7. Schema of meshing cogwheels

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Calculation of transfer ratio (u_R), angular velocities (ω), tangential (a_t) and normal components (a_n) 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

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Figure 9. Shaft A

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Figure 10. Shaft B

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Figure 11. Shaft C

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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

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

Figure 13. Schema of cogwheels connection

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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

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Figure 15. Shaft B₂₃

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Figure 16. Shaft D

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Figure 17. Shaft B₇₈

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Figure 18. Shaft C

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