5. Mechanical Design and Modelling
5.5 MRM Motion Modules (Modular Axes)
5.5.4 Linear Axes
Actuation of Linear Axes
Linear axes in conventional machine tools are driven by power screw mechanisms coupled to servo motors [57]. The Acme lead screw or re-circulating ball screws are ideal for machine tool slide applications. These screws provide good positioning accuracy, low friction and require less drive power than other screw profiles. During the development of a library of modules an ISO Metric screw profile was selected for linear modules. Although this thread profile is less optimal than Acme or re-circulating ball screws, the cost was significantly lower. Figure 5.8 illustrates the thread profile of a conventional ISO Metric screw.
Figure 5.8: ISO Metric Screw Profile [59]
The total torque required to drive a power screw in a direction opposing an applied load W (“raising the load”) is calculated by equation 5.10; where dm is the mean diameter of the screw.
For a single start ISO Metric thread, the lead L is equal to the pitch P; and the angle αn is equal to 30o. The coefficient of friction between the screw and the corresponding nut is f. The torque required to overcome collar/bearing friction is calculated by the second expression in equation 5.10, where dc is the collar diameterand fc is the coefficient of friction of the collar. The total torque required to drive a power screw in the same direction as the applied load (“lowering the load”) is calculated by equation 5.11. The linear speed V, power 𝑊 and efficiency of a power screw are calculated by equations 5.12, 5.13 and 5.14 respectively. N is the rotational speed of the screw in rev/min.
𝑇 =𝑊𝑑𝑚 2
𝑓𝜋𝑑𝑚 + 𝐿 cos 𝛼𝑛
𝜋𝑑𝑚cos 𝛼𝑛− 𝑓𝐿+𝑊𝑓𝑐𝑑𝑐
2 (5.10)
𝑇 =𝑊𝑑𝑚 2
𝑓𝜋𝑑𝑚 − 𝐿 cos 𝛼𝑛
𝜋𝑑𝑚cos 𝛼𝑛+ 𝑓𝐿+𝑊𝑓𝑐𝑑𝑐
2 (5.11) 𝑉 = 𝑁𝐿 (5.12) 𝑊 =𝜋𝑁
30𝑇 5.13 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑊𝐿
2𝜋𝑇 (5.14)
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5.5 MRM Motion Modules
Base Module (X - Axis)
The MRM base module is a central module to all MRM configurations. This module forms the foundational structure of the machine, upon which other modules are added. The body of the module is cast iron, which provided the strength and mass necessary to support the rest of the machine structure while providing vibration damping.
Figure 5.9: MRM Base Module (X-axis)
The drive mechanism consisted of a steel „dove tail‟ slide mechanism driven by an ISO Metric M20x2.5 power screw. Steel was selected as the slide material, as it would provide the necessary strength and durability against wear. The power screw is of high tensile steel and it turns in a nut that was manufactured out of brass. The screw is supported by a deep groove ball bearing on one end and is coupled to the motor on the opposite end. Figure 5.10 illustrates the drive mechanism of the module and Table 5.4 summarizes the module‟s specifications. The module code for all MRM modules is as follows “MRM-Type-Range-Moving Interface-Static Interface”.
Calculations for the loading specifications may be found in Appendix C.3 and C.4. The maximum normal (vertical) load on the slide has been specified as not applicable as the prior failure of other MRM modules in all configurations is expected prior to the failure of the slide under a normal load. Engineering drawings for the base module are located in Appendix G; these drawings are a sample of the drawings that were generated during this research, the CAD drawings of other modules are located on the supplementary DVD.
Figure 5.10: Drive Mechanism of the Base Module Dove Tail Slide +
Interface Power Screw
Bearing Housing Interface
Power Screw Bearing
Housing
Dove Tail Slide
Motor Coupling
Nut Housing
Motor Mounting Bracket
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5.5 MRM Motion Modules
The MRM base module is designated as the X-axis in both drilling and turning configurations.
The HTMs for this module in the drilling and turning configurations are given by equations 5.15 and 5.16 respectively; the limits are with reference to local frame „i+1‟. Refer to Appendix B.1 for calculations and illustrative diagrams.
𝑖+1𝑖𝑀𝐵𝑎𝑠𝑒 −𝐷𝑟𝑖𝑙𝑙𝑖𝑛𝑔 =
1 0 0 0 1 0 0
0 0
0 1
0
𝑥 2152.5
1
257.5 ≤ 𝑥 ≤ 757.5 (5.15)
𝑖+1𝑖𝑀𝐵𝑎𝑠𝑒 −𝑇𝑢𝑟𝑛𝑖𝑛𝑔 =
1 0 0 0 1 0 0
0 0 0
1 0
𝑥 2.519
1
192.5 ≤ 𝑥 ≤ 692.5.5 (5.16)
Table 5.4: Specifications of the Base Module
Module Data MRM Base Module
Module Code (B = Base) MRM-B01-500-T1-T4/5
Module Control Resolution (refer to section 8.8) 4.883x10-3 mm
Module Range 500 mm
Moving Interface Type one
Static Interface(s) Type four and five
Max Speed 145 mm/min
Max Actuation Load 930 N
Max Normal Load on Moving Interface N/A
Work Table Slide Module (Y-Axis)
The “work table slide” module supports the worktable in the drilling configuration. This module is also of a foundational nature upon which further enhancement modules may be added. The module was created with a steel framework to provide adequate strength in the module. This system was intended to provide sufficient support during drilling operations, for other machining operations such as milling, a heavier cast iron structure with a dove tail slide is recommended.
Figure 5.11: MRM Work Table Slide Module (Y-axis)
Slide + Interface
Power Screw Support/Guide Rod
Steel Frame
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5.5 MRM Motion Modules
The drive mechanism of this module consisted of a steel slide driven by an ISO Metric M24x3 power screw. The screw was of high tensile steel and possesses a large diameter for added rigidity. The power screw is supported by two deep groove ball bearings at either end, and runs in a brass nut that is housed in the slide. Two 20 mm silver steel (BS-1407) rods from the support and guide mechanism for the slide as illustrated in Figure 5.12. Table 5.5 summarizes the module‟s specifications. Calculations for the loading specifications may be found in Appendix C.3 and C.4.
Figure 5.12: Drive mechanism of the Work Table Slide Module Table 5.5: Specifications of the Work Table Slide Module
Module Data Work Table Slide Module
Module Code (WTS = Work Table Slide) MRM – WTS01-300-T3-T5
Module Control Resolution 5.869x10-3 mm
Module Range 300 mm
Moving Interface Type 3
Static Interface(s) Type 5
Max Speed 174 mm/min
Max Actuation Load 930 N
Max Normal Load on Moving Interface 460 N
The work table slide module is designated as the Y-axis in the drilling configuration. The HTM for this module is given by equation 5.17; the limits are with reference to local frame „i+1‟. Refer to Appendix B.2 for calculations and illustrative diagrams.
𝑖+1𝑖𝑀𝑊𝑇 𝑆𝑙𝑖𝑑𝑒 =
1 0 0 0 1 0 0
0 0
0 1
0
155 𝑦
−111 1
−150 ≤ 𝑦 ≤ 150 (5.17)
Column Module (Z- Axis)
The column module supports the cutting head in the drilling configuration. The module was created mainly out of aluminium (295-T4) for weight saving, with four silver steel rods forming the support and guide mechanism for the slide (see Figure 5.13b).
Support/Guide Rod
Bearing Housing
Bearing Housing
Motor Coupling
Power Screw
Nut Housing + Slide
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5.5 MRM Motion Modules
Silver steel is a 1% carbon tool steel [60] that was specifically selected for its high strength to create a stable, light weight support structure for the drill cutting head. The modules weight was limited for easy, manual assembly. The drive mechanism of the module consisted of a centrally located ISO Metric M24x3 power screw. The screw is of high tensile steel and runs in a brass nut as illustrated in Figure 5.13.c. The screw is supported by thrust bearings at the top and bottom ends of the column. Table 5.6 summarizes the module‟s specifications.
a. b. c.
Figure 5.13 MRM Column Module (Z-axis)
a. Column Module – Front view
b. Column Module – Displaying support structure c. Column Module – Displaying drive mechanism
Table 5.6: Specifications of the Column Module
Module Data Column Module
Module Code (C=Column) MRM-C01-562-T2A/2B-T1
Module Control Resolution 5.869x10-3 mm
Module Range 600 mm
Moving Interfaces Type Two A and B
Static Interface Type One
Max Speed 174 mm/min
Max Actuation Load 2952 N
Max Normal Load on Moving Interface 300 N
The column module is designated as the Z-axis in the drilling configuration. The HTM for this module is given by equation 5.18; the limits are with reference to local frame „i+1‟. Refer to Appendix B.3 for calculations and illustrative diagrams. Calculations for the loading specifications may be found in Appendix C.3 and C.4.
Support/
Guide Rod
Power Screw
Brass Nut
Slide Slide +
Interface
Aluminium Frame
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5.5 MRM Motion Modules
𝑖+1𝑖𝑀𝐶𝑜𝑙𝑢𝑚𝑛 =
1 0 0 0 1 0 0
0 0 0
1 0
−54.5 0𝑧 1
85 ≤ 𝑧 ≤ 647 (5.18)
Cross Slide Module (Y-Axis and C-Axis)
a. b.
Figure 5.14: Cross Slide Module and Tool Post (Y and C axes)
a. MRM Cross Slide Module – Rear view
b. MRM Cross Slide Module – Illustrative side view
The cross slide module contains a tool post and is responsible for feeding the tool into a rotating work piece in the turning configuration. The module was a COTS unit of hardware that was retrofitted with a servo drive motor. The body of the module is steel and the servo drive system is supported by an aluminium bracket. The steel body is ideal for vibration damping and the support of high machining forces. The drive mechanism consisted of the tool post being driven by a 12x2 metric trapezoidal power screw.
Figure 5.15: MRM Automated Work Clamp
Tool Post
Tool Post Removed Slide Rotary Base Interface Plate
Motor Coupling
Work Clamp
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5.5 MRM Motion Modules
The cross slide module possessed two additional features. The first feature was the ability of the module to be transformed into an automated device for work clamping. This display of reconfigurability is achieved by the design of the tool post to be modular and removable from the base of the module. Figure 5.15 illustrates the reconfigured module with the tool post removed.
The second feature was the ability of the module to rotate about its axis. This effectively created a rotational axis (C-axis). The rotary indexing feature of this module is manually manipulated; the rotation is illustrated in Figure 5.16.b. Table 5.7 summarizes the module‟s specifications.
Calculations for the loading specifications may be found in Appendix C.3 and C.4.
a. b.
Figure 5.16: Cross Slide Module Displaying Additional Rotary Axis
a. Cross slide module at home position
b. Cross slide module orientated at 45o to the home position
Table 5.7: Specifications of the Cross Slide Module
Module Data Cross Slide Module
Module Code (CS= Cross Slide) MRM-CS01-115-T0-T1
Module Control Resolution 3.906 x10-3 mm
Module Range (Y axis) 115 mm
Module Range (C axis) 360o
Static Interface Type One
Max Speed 116 mm/min
Max Actuation Load 250 N
Max Load on Tool (vertical and horizontal) 2500 N
This module provides both the Y and C axes in the turning configuration. The HTM for this module is given by equation 5.19; the limits are with reference to local frame „i+1‟. Refer to Appendix B.4 for calculations and illustrative diagrams.
𝑖+1𝑖𝑀𝐶𝑟𝑜𝑠𝑠 𝑆𝑙𝑖𝑑𝑒 =
𝑐𝛼 −𝑠𝛼 0
𝑠𝛼 𝑐𝛼 0
0
0 0
0 1
0
0 𝑦 168
1
−90 ≤ 𝑦 ≤ 25; −360° ≤∝≤ 360° (5.19)
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5.5 MRM Motion Modules
Idealized Performance of Linear Axes
Performance characteristics of the servo drive system implemented in the MRM axes were presented in Section 5.5.3. By manipulating the performance characteristics of the drive motor a corresponding idealized performance characteristic may be developed for the performance of a module under the action of a resisting load. Rearranging equation 5.10 yields the force that a power screw mechanism is capable of acting against for a given input torque:
𝑊 = 𝑇 𝑑𝑚 2
𝑓𝜋𝑑𝑚 + 𝐿 cos 𝛼𝑛 𝜋𝑑𝑚cos 𝛼𝑛− 𝑓𝐿+𝑓𝑐𝑑𝑐
2
−1
(5.20) Equation 5.20 and the motor performance data have been used to generate Figures 5.17 and 5.18.
These figures represent the ideal performance of the linear motion modules with regard to actuation force and speed (Figure 5.17) and the electric current requirements of the modules under corresponding loads (Figure 5.18). These figures have been generated purely from the actuation characteristics of the associated motor and equation 5.20; the forces presented do not necessarily represent the maximum forces sustainable by the modules. Refer to Appendix C.1 for calculations.
Figure 5.17: Graph of Actuation Force vs Speed for Linear Axes
Figure 5.18: Graph of Actuation Force vs Current for Linear Axes 0
2000 4000 6000 8000 10000 12000 14000
0 50 100 150 200
Force (N)
Speed (mm/min)
Actuation Force vs Speed
Base Work Table Slide Column Cross Slide
0 2000 4000 6000 8000 10000 12000 14000
0 5 10 15 20
Force (N)
Current (amps)
Actuation Force vs Current
Base Work Table Slide Column Cross Slide
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5.5 MRM Motion Modules